The Department of Mathematical Sciences offers certain intermediate and advanced courses periodically: every semester, every fall or spring, once every other year, or once every four years.
Complete Course Rotation
Download the entire course rotation in xls format.
Should you need a copy of a syllabus, please contact our office staff at mathstaff@uwm.edu.
Important Changes as of AY 201819 Math 537 will be offered in Spring 2019 instead of Fall 2018.
Important Changes as of AY 201617
 MathStat 361 and 362 will be offered every semester
 Math 453 may not be offered.
 MathStat 566 is offered in alternate years, along with 562; 568 and 565 alternate with those (updated 9/10/15)
 Act Sci courses are included: 591593, 691, 692, 795, and 599 capstone.
 Math 768771 and Math 751752 to be offered annually.
 Comp math courses will be introduced: 415, 417, 615, 617 (the first two replacing 414 and 416).
 Topics courses 801, 809, 813, 8014, 815, 821, 841, 851, 873 will be offered depending on demand, and are not listed.
 Offering of courses in any semester is subject to sufficient enrollment and adequate staff and budget.
100 and 200 Level courses
Atmospheric Science AtmSci 100 – every Fall and Spring
 AtmSci 106 – every Summer and WinteriM
 AtmSci 109 – online every Fall and Spring
 AtmSci 240 – every Fall and Spring (updated 9/10/15)
Mathematics
 Math 092/094/098 & 102/103/105/108 – offered most every Fall, Spring, Summer, WinteriM
 Math 116, 117 – every Fall, Spring, Summer, UWinteriM
 Math 175, 176 – every Fall and Spring
 Math 205 – every Fall and Spring
 Math 211 – every Fall, Spring, Summer
 Math 221/222 sequence – every academic year (fallspring)
 Math 231, 232, 233, 234 – every Fall, Spring, Summer
 Math 275, 276, 277, 278 – each at least once during the academic year, possibly more often
Mathematical Statistics
 MthStat 215 – every Fall, Spring, Summer, and usually UWinteriM
FAQ on Math 92, 102, 103, 111 (scheduling, prerequisite, etc.)
Question: Do I need to take a math class at UWM?
Answer:
 All UWM students must satisfy the twolevel Quantitative Literacy requirement in order to graduate: Quantitative Literacy Parts A (QLA) and B (QLB). Many departments offer QLB courses (ask your advisor which is right for you), but QLA is only satisfied by a Math curricular area course or equivalent placement exam score.
 If you earned a Math Placement Test Code of 30 or higher, you satisfied your QLA requirement via this test!
 Earning a grade of C or higher in Math 102 or 103 (or 105, 108, 175) will also satisfy QLA – and these courses also satisfy the L&S math requirement for the BA degree.
Question: Who can take Math 092/102 or Math 103 to satisfy their degree requirements?
Answer:

 Primarily students in the Arts, Humanities, and Social Welfare can take 102 or 103, as they do not need to take any further math or science courses.
 Most students in the School of Education who do not place directly into Math 175 are advised to take 103 or 092+102 first.
 Anyone in a STEM, Business, or Health Sci program, or anyone interested in the BS in L&S, will need different math courses for their program, and should consult their advisor to find the right courses (Math 094, 098, 105, 115, 116, 117, 211, 231, etc.).
 All students should double check their program requirements and/or consult their academic advisor when choosing which math courses to take each semester.
 Majors whose math requirement is satisfied by Math 103 or 92+102
 Africology
 Anthropology
 Art
 Art Education
 Art History
 Classics
 Communication
 Comparative Literature
 Criminal Justice
 Dance
 English
 Film
 Film Studies
 French
 German
 Global Studies (tracks other than Global Management)
 History
 Inter Arts
 International Studies
 Italian
 Jewish Studies
 Journalism, Advertising, and Media Studies
 Latin American, Caribbean, and Latino Studies
 Linguistics
 Music
 Music Education
 Philosophy
 Political Science
 Psychology (BA)
 Religious Studies
 Russian
 Social Work
 Sociology
 Spanish
 Theatre
 Women’s Studies
Question: Do I qualify for Math 103?
Answer:
 The prerequisite of Math 103 is either an ACTmath subscore of 18 or higher, or Math Placement Level 10—attained by earning a level 10 on the Math Placement Test, a grade of C or better in Math 90, or a grade of D or better in Math 94.
Question: When can I take Math 103?
Answer:
 Students are expected to complete QLA within their first 60 credits, so that they can complete their QLB course without delays to their graduation.
 Starting AY 1718, Math 103 will primarily shift to Spring semesters.
 Math 103 will be offered in summer and UWinterm (if sufficient enrollment).
 There will be a limited number of sections of 103 offered each Fall (either online, in evenings and/or in early mornings), for students who couldn’t complete 103 earlier in their program due to special circumstances
Question: Should/Could I take Math/Philos 111 to satisfy my QLA?
Answer:
 Math or Philos 111 is a good QLA choice for students who intend to take Philos 211 as their QLB course. (Note: Philos 211 is a logic course and is NOT the same as Math 211 Survey of Calculus).
 Math 111 is “jointly offered” with Philos 111. No matter which one you register for, it’s the same class and you’ll get QLA credit (as long as you get a C or better.
 Math/Philos 111 has the same prereq as Math 103.
Question: I don’t meet the prerequisite of Math 103. What math course should I take?
Answer:
 You should take Math 92 and Math 102, as effective Fall 2018 Math 092 has no prerequisite.
Question: When can I take Math 092 and 102?
Answer:
 Students must complete remedial course work (Math 9x) in their first 30 credits, basically the first year.
 Math 092&102 will primarily shift to Spring and be offered in paired corequisite sections. For example, Math 092 Section 57 MW 1112:15, and Math 102 Section 57 TR 1112:15, will meet in the same room with the same instructor, and the courses will be paired in PAWS so that students must enroll in both. Students will work in 092 on Mon (or Wed) on the background needed for the 102 material for Tues (or Thurs).
 For students with extraordinary schedule restrictions: there will be a very limited number of freestanding 092’s each term, with enrollment by permission only. Contact Kelly Kohlmetz kellyk2@uwm.edu for permission to enroll.
 For students taking a paired 092+102, their 092 grade will not be lower than the grade they earn in 102.
 Starting Spring 2018, there will be a very limited number of freestanding sections of 102 offered each fall and spring. For example, for students who take the linked 092/102 and who pass 092 but not 102, or students who were given permission to take a freestanding 092.
 Starting Summer 2018, each of 092 and 102 will be offered in summers, not paired, likely both online, with 092 in first 6 week session and 102 in second 6 week session.
 Starting in Fall 2018, online versions of each of 092 and 102 will be offered, not paired, with enrollment by permission only (for permission contact Kelly Kohlmetz kellyk2@uwm.edu)
Question: Why must I take 6 credits of math in the same semester, if I’m not in a hurry to finish math since I have no more math requirements?
Answer:
 The short answer: We care about your success, and you’re more likely to pass both courses if you’re taking math every day–focusing more on math and having fewer other courses to keep track of.
 The traditional model of taking Math 092 in fall and 102 in spring is a “leaky pipeline.” Only about half of students who enroll in Math 092 in fall finish 102 in spring. This failure negatively affects student success and retention.
 The corequisite model has been showed to significantly increase student success. For example, the entire Tennessee Board of Regents Universities and Community Colleges increased the percent of students who passed a creditbearing math course in their first year from 59% to 75% by implementing corequisite remediation!
Question: Why must I take 6 “credits” of math courses in one semester, if I struggle with math?
Answer:
 As stated above: We care about your success, and you’re more likely to pass both courses if you’re taking math every day–focusing more on math and having fewer other courses to worry about.
 Meeting four days per week allows the instructor to get to know your individual areas of strength and weakness – and to have the time and flexibility to address them in ways to help you succeed.
 PLEASE NOTE: You will be taking sixcredits of math! Be sure that you are allowing yourself enough time in your schedule for homework every night, weekly tutoring and weekly meetings with your instructor. This will be the equivalent of TWO courses worth of homework and studying, which means about 12 hours of time is needed outside of class. We advise you not to load your schedule with more than two other courses.
Course Listings
Undergraduate (U and U/G): ATM SCIATM SCI
 ATM SCI 100  Survey of Meteorology (3 units; U)
 Concepts and principles of meteorology; cyclones, fronts, thunderstorms, tornadoes, air pollution, and climate. Interpretation of weather maps, charts, and forecasts. 2 hrs lec, 2 hrs labdis. Counts as repeat of 3 cr Atm Sci 100 taken for 4 cr. Prereq: none.
 ATM SCI 106  Principles and Forecasting of the Weather (3 units; U)
 What makes the weather, general circulation of the atmosphere, analysis of meteorological data and their use in predicting the weather. Prereq: none.
 ATM SCI 108  Rain and Snow (3 units; U)
 Study of precipitation properties and processes in the atmosphere. Structure of precipitating systems ranging from small to large scale. Prereq: none.
 ATM SCI 109  Thunderstorms, Tornadoes and Hurricanes (3 units; U)
 The study of basic processes that lead to dry and moist convection. Characteristic atmospheric structure and cloud microphysical processes that produce thunderstorms, tornadoes and hurricanes. Prereq: none.
 ATM SCI 110  The Origin, Composition, and Structure of the Planetary Atmospheres (3 units; U)
 Origin of the solar system, its planets, and planetary atmospheres. Prereq: none.
 ATM SCI 194  FirstYear Seminar: (3 units; U)
 Specific topics are announced in the Schedule of Classes each time the class is offered. Open only to freshmen. Students may earn cr in just one L&S FirstYear Sem (course numbers 192, 193, 194). Prereq: none.
 ATM SCI 199  Independent Study (13 units; U)
 For further information, consult dept chair. May be retaken to 6 cr max. Prereq: 2.5 gpa; writ cons instr, dept chair, & asst dean for SAS.
 ATM SCI 240  Introduction to Meteorology (3 units; U)
 Quantitative approach to understanding fundamental concepts in meteorology. Radiation, heat balance of the atmosphere, thermodynamics, horizontal motion, general circulation, atmospheric observations, clouds, weather map analysis. Not open for cr to students with Atm Sci 201. Prereq: Physics 209(P) & 214(P); Math 232(C).
 ATM SCI 289  Internship in Atmospheric Sciences, Lower Division (16 units; U)
 Application of basic knowledge of Atmospheric Sciences in business, organizational, educational, political or other appropriate setting. One cr earned for academic work based on 40 hrs in internship. May be retaken to 6 cr max. Prereq: soph st.; 2.50 gpa; cons supervising faculty member.
 ATM SCI 297  Study Abroad: (112 units; U)
 Designed to enroll students in UWM sponsored program before course work level, content, and credits are determined and/or in specially prepared course work. May be retaken w/chg in topic. Prereq: acceptance for Study Abroad Prog.
 ATM SCI 299  Ad Hoc: (16 units; U)
 Course created expressly for offering in a specified enrollment period. Requires only dept & assoc dean approval. In exceptional circumstances, can be offered in one add'l sem. May be retaken w/chg in topic. Prereq: none; add'l prereqs may be assigned to specific topic.
 ATM SCI 330  AirPollution Meteorology (3 units; U/G)
 Pollutant sources and sinks, fundamental pollutant chemistry, monitoring techniques, averaging boundary layers and turbulence, diffusion theories, diffusion models, regional and globalscale pollution problems. Prereq: Atm Sci 240(P); Chem 102(P); stats course recom.
 ATM SCI 350  Atmospheric Thermodynamics (3 units; U/G)
 Radiant energy, sensible heat, and atmospheric thermodynamics; the gas laws; hydrostatic and psychrometric equations; dry and moist convection; clouds and their physical and energy relations. Optional field exercise. Prereq: jr st; Physics 210(P); Math 232(P); Atm Sci 240(P).
 ATM SCI 351  Dynamic Meteorology I (3 units; U/G)
 The role of dynamics in atmospheric physics; equations of motion; symmetric circulation models; gravity waves; Rossby waves, quasigeostrophy; introduction to instability of atmospheric flows. Prereq: jr st; Atm Sci 240(P); Math 233(P).
 ATM SCI 352  Dynamic Meteorology II (3 units; U/G)
 Circulation, vorticity, potential vorticity; shallow water equations: Poincare, Kelvin, and Rossby waves, energy and enstrophy; quasigeostrophy for a stratified atmosphere; barotropic and baroclinic instability. Prereq: jr st; Atm Sci 351(P); Math 234(P).
 ATM SCI 360  Synoptic Meteorology I (4 units; U/G)
 Fundamental principles; synopticscale structure and dynamics; equivalent barotropic model; vertical motions; introduction to and application of quasigeostrophic theory. Prereq: jr st; Math 232(P); Physics 210(P); Atm Sci 240(P).
 ATM SCI 361  Synoptic Meteorology II (4 units; U/G)
 Extension of quasigeostrophic theory to Qvectors; isentropic potential vorticity applied to midlatitude weather systems; fronts and jets. Prereq: jr st; Atm Sci 360(P).
 ATM SCI 381  Honors Seminar: (3 units; U)
 Selected topics. May be retaken w/chg in topic to 9 cr max. Prereq: soph st; Honors 200(P); cons Honors College dir.
 ATM SCI 405  Atmospheric Science for inService Teachers: (13 units; U/G)
 Basic, advanced or new topics in atmospheric sciences for inservice teachers. May be retaken w/chg in topic to 9 cr max. Prereq: inservice teacher; add'l prereqs depending on topic.
 ATM SCI 460  Mesoscale Circulations (3 units; U/G)
 Theory, analysis and forecasting of mesoscale flows, including convective systems, polar lows, terrain and surfaceforced flows, jet streams and hurricanes. Prereq: jr st; Atm Sci 360(R) or cons instr.
 ATM SCI 460G  Mesoscale Circulations (3 units; U/G)
 Theory, analysis and forecasting of mesoscale flows, including convective systems, polar lows, terrain and surfaceforced flows, jet streams and hurricanes. Prereq: jr st; Atm Sci 360(R) or cons instr.
 ATM SCI 464  Physical Meteorology: Cloud Physics (3 units; U/G)
 Formation of cloud droplets, droplet growth by condensation, formation of ice crystals, precipitation processes, weather radars, cloud models. Prereq: jr st; Physics 210(P); Math 232(P); Atm Sci 350(P).
 ATM SCI 470  Tropical Meteorology (3 units; U/G)
 Dynamics and energetics of tropical circulations. Origins and evolution of equatorial disturbances and easterly waves. Structure and dynamics of tropical cyclones. Hurricane modeling and prediction. Prereq: Atm Sci 351(P) or 360(P).
 ATM SCI 480  The General Circulation and Climate Dynamics (3 units; U/G)
 Historical overview, the zonally symmetric circulation, momentum, heat and water budgets, stationary waves, the El Nino Southern oscillation, global warming, interpentadal variability in the North Atlantic. Prereq: jr st; Atm Sci 351(P).
 ATM SCI 497  Study Abroad: (112 units; U/G)
 Designed to enroll students in UWM sponsored program before course work level, content, and credits are determined and/or in specially prepared course work. May be retaken w/chg in topic. Prereq: jr st; acceptance for Study Abroad Prog.
 ATM SCI 499  Ad Hoc: (16 units; U)
 Course created expressly for offering in a specified enrollment period. Requires only dept & assoc dean approval. In exceptional circumstances, can be offered in one add'l sem. May be retaken w/chg in topic. Prereq: jr st; add'l prereqs may be assigned to specific topic.
 ATM SCI 500  Statistical Methods in Atmospheric Sciences (3 units; U/G)
 Mathematical and statistical tools applicable to the investigation of atmospheric problems; the nature and treatment of atmospheric data. Prereq: jr st; Atm Sci 240(P) or 350(P), & Math 232(P) or cons instr.
 ATM SCI 505  Micrometeorology (3 units; U/G)
 Surface energy budget; radiation balance and heat transfer; boundarylayer profiles of wind, temperature and moisture; turbulence and boundarylayer fluxes; evapotranspiration; special topics. Prereq: jr st; Atm Sci 351(P) & 330(P).
 ATM SCI 505G  Micrometeorology (3 units; U/G)
 Surface energy budget; radiation balance and heat transfer; boundarylayer profiles of wind, temperature and moisture; turbulence and boundarylayer fluxes; evapotranspiration; special topics. Prereq: jr st; Atm Sci 351(P) & 330(P).
 ATM SCI 511  Seminar in Atmospheric Radiation and Remote Sensing (3 units; U/G)
 Basic laws of radiation, absorption and scattering, weather radar, retrieval of soundings, remote sensing and climate, weather satellites. Prereq: jr st; Math 232(P); Atm Sci 350(P) & Physics 210(P).
 ATM SCI 520  Advanced Dynamic Meteorology (3 units; U/G)
 Properties of atmospheric sound, gravity, Rossby waves. Baroclinic instability, cyclogenesis, frontogenesis, and the general circulation. Introduction to numerical prediction. Prereq: jr st; Math 234(P), Atm Sci 350(P) & 351(P) or equiv.
 ATM SCI 599  Capstone Experience (1 units; U)
 Student writes a paper under supervision of an advisor on an approved topic not covered in the student's regular course work. May be retaken w/chg in topic to 2 cr max. Prereq: sr st; cons instr.
 ATM SCI 690  Seminar in Atmospheric Sciences: (13 units; U/G)
 Intensive topical studies of currently active problem areas. May be retaken w/chg in topic to 9 cr max. Satisfies L&S Seminar req. Prereq: jr st; cons instr.
 ATM SCI 690G  Seminar in Atmospheric Sciences: (13 units; U/G)
 Intensive topical studies of currently active problem areas. May be retaken w/chg in topic to 9 cr max. Satisfies L&S Seminar req. Prereq: jr st; cons instr.
 ATM SCI 695  Internship in Atmospheric Sciences, Upper Division (16 units; U)
 Application of advanced principles of atmospheric sciences in a business, organizational, educational, political or other appropriate setting. One cr earned for 40 hrs work. May be retaken to 6 cr max. Prereq: jr st; 300level or above course in atm sci; 3.0 gpa in the major; cons supervising faculty.
 ATM SCI 699  Advanced Independent Reading (13 units; U)
 Independent meteorological study. May be retaken w/chg in topic to 3 cr max. Prereq: jr st, 2.5 gpa, & writ cons instr, dept chair, & asst dean for SAS.
Undergraduate (U and U/G): MATH
Math
 MATH 75  Math Success Strategies (0 units; U)
 Strategies for improving attitudes about and performance in mathematics, including study skills for mathematics and mathematical mindsets. Fee for 1 cr assessed; credit counts toward credit load for Fin Aid and enrollment verification only. Satisfactory/Unsatisfactory only. Prereq: none.
 MATH 90  Basic Mathematics (0 units; U)
 Arithmetic operations involving whole numbers, integers, positive and negative rational numbers; decimals, percents; ratio, proportion; radicals; descriptive statistics; units of measure; geometry; introduction to algebra. Fee for 3 cr assessed; credits count toward credit load for Financial Aid and enrollment verification only. Not open to students eligible for math courses that carry graduation credit. Prereq: none.
 MATH 92  Mathematical Literacy for College Students I (0 units; U)
 Introduction to numeracy, proportional reasoning, algebraic reasoning, and functions. Emphasis on developing conceptual and procedural tools that support the use of key mathematical concepts in context. Fee for 3 cr assessed; counts as 3 cr toward cr load for Financial Aid & enrollment verification. Not recommended for students planning to take Calculus or Chem 100. Prereq: none.
 MATH 94  Foundations of Elementary Mathematics (0 units; U)
 Arithmetic, geometry, and beginning algebra; develops mathematical reasoning, problem solving, and facility with basic mathematical objects and their relationships. Individualized instruction via adaptive learning software. Fee for 6 cr assessed; credits count toward credit load for Financial Aid and enrollment verification only. Math 94 counts as repeat of Math 90 & 95. Prereq: none.
 MATH 95  Essentials of Algebra (0 units; U)
 Number systems; linear equations, inequalities; exponent notation, radicals; polynomials, operations, factoring, rational expressions; coordinate geometry; linear systems; quadratic equations. Fee for 3 cr assessed; credits count toward credit load for Financial Aid and enrollment verification only. Prereq: math placement level 10, which is earned by any of the following: (a) Level 10 on Math Placement Test; (b) grade of C or better in Math 090; or (c) grade of D in Math 094.
 MATH 98  Algebraic Literacy I (0 units; U)
 Arithmetic number systems; linear equations, inequalities; exponent notation, radicals; polynomials, operations, factoring; modeling; coordinate geometry; linear systems; quadratic equations. Fee for 3 cr assessed; counts as 3 cr toward credit load for Fin Aid & enrollment verification only. Prereq: math placement level 10, which is earned by any of the following: (a) Level 10 on Math Placement Test; (b) grade of C or better in Math 090; or (c) grade of D in Math 094.
 MATH 102  Mathematical Literacy for College Students II (3 units; U)
 Continuation of Math 92, with an integrated approach to numeracy, proportional reasoning, algebraic reasoning, and functions. Prereq: Grade of C or better in Math 92(P) or (C).
 MATH 102X  Mathematical Literacy for College Students II (3 units; U)
 Continuation of Math 92, with an integrated approach to numeracy, proportional reasoning, algebraic reasoning, and functions. Prereq: Grade of C or better in Math 92(P) or (C).
 MATH 103  Contemporary Applications of Mathematics (3 units; U)
 Logical inference, probability and statistical inference, geometric growth, with selected topics such as linear programming, patterns, binary codes. Not recom for students planning to take Calculus or Chem 100. Prereq: ACT math subscore of 18 or higher or Math Placement Level 10, which is earned by any of the following: (a) Level 10 on Math Placement Test; (b) Grade of C or better in Math 090; or (c) Grade of D in Math 094.
 MATH 105  Introduction to College Algebra (3 units; U)
 Algebraic techniques with polynomials, rational expressions, equations and inequalities, exponential and logarithmic functions, rational exponents, systems of linear equations. Counts as repeat of MATH 108. Prereq: Math Placement Level 20, which is earned by any of the following: (a) Level 20 or 26 on Math Placement Test; (b) Grade of C or better in Math 094, 095, or 098; or (c) ACT math subscore of 24 or higher.
 MATH 108  Algebraic Literacy II (3 units; U)
 Continuation of MATH 98 in polynomials, equations, and inequalities; exponential, logarithmic, and periodic functions; rational expressions and exponents; and systems of linear equations. Counts as repeat of MATH 105. Prereq: C or better MATH 98.
 MATH 111  Introduction to Logic  Critical Reasoning (3 units; U)
 Students learn a broad variety of fundamental logical methods  techniques used to identify, analyze, model, evaluate, and criticize different types of realworld reasoning. Jointly offered w/ Philos 111; they count as repeats of one another. Prereq: ACT math subscore of 18 or higher, or Math Placement Level 10, which is earned by any of the following: (a) Level 10 on Math Placement Test; (b) grade of C or better in Math 090; or (c) grade of D in Math 094.
 MATH 115  Precalculus (4 units; U)
 Essential topics from college algebra and trigonometry for students intending to enroll in calculus. Repeats 2 cr of MATH 116 & 2 cr of MATH 117. Prereq: Math Placement Level 30, which is earned by any of the following: (a) Level 30, 35, or 36 on Math Placement Test; (b) grade of C or better in MATH 105, MATH 108, or MATH 116; (c) score of 5 or higher on the IB Mathematical Studies  SL; (d) score of 3 or higher on the AP statistics exam; or (e) score of 63 or higher on the CLEP College Algebra Exam.
 MATH 116  College Algebra (3 units; U)
 Function concepts. Polynomial, rational, exponential, and logarithmic functions. Systems of equations and inequalities. Matrices and determinants. Sequences and series. Analytic geometry and conic sections. Induction. 2 cr may be used to repeat 2 cr of MATH 115. Prereq: Math Placement Level 20, which is earned by any of the following: (a) Level 20 or 26 on Math Placement Test; (b) Grade of C or better in MATH 94, MATH 95, or MATH 98; (c) ACT math subscore of 24 or higher.
 MATH 117  Trigonometry (2 units; U)
 Trigonometric functions; graphs, identities, equations, inequalities; inverse trigonometric functions; solutions of triangles with applications; complex numbers; polar coordinates. Repeats 2 cr of MATH 115. Prereq: Math Placement Level 30, which is earned by any of the following: (a) Level 30, 35, or 36 on Math Placement Test; (b) grade of C or better in MATH 105, MATH 108, or MATH 116; (c) score of 5 or higher on the IB Mathematical Studies  SL; (d) score of 3 or higher on the AP statistics exam; or (e) score of 63 or higher on the CLEP College Algebra Exam.
 MATH 175  Mathematical Explorations for Elementary Teachers I (3 units; U)
 Theory of arithmetic of whole numbers, fractions, and decimals. Introduction to algebra, estimation and problemsolving strategies. Prereq: Registration in elementary, early childhood, or exceptional educ curriculum; either a grade of C or better in MATH 102 or MATH 103, or Math Placement Level at least 20, which is earned by any of the following: (a) Level 20 or 26 on Math Placement Test; (b) Grade of C or better in MATH 94, MATH 95, or MATH 98; (c) ACT math subscore of 24 or higher.
 MATH 176  Mathematical Explorations for Elementary Teachers II (3 units; U)
 A continuation of MATH 175 in geometry, statistics, and probability. Prereq: grade of C or better in MATH 175(P).
 MATH 194  FirstYear Seminar: (3 units; U)
 Specific topics are announced in the Schedule of Classes each time the class is offered. Open only to freshmen. Students may earn cr in just one L&S FirstYear Sem (course numbers 192, 193, 194). Prereq: none.
 MATH 199  Independent Study (13 units; U)
 Regularly offered courses may not be taken as Independent Study. May be retaken w/chg in topic to 9 cr max. Prereq: 2.5 gpa in all previous math courses; writ cons instr, dept chair & asst dean for SAS.
 MATH 205  Introductory Finite Mathematics (3 units; U)
 Elements of mathematical logic, structures in sets; partitions and counting; probability theory, stochastic processes. Prereq: math placement level 30, which is earned by any of the following: (a) Level 30, 35, or 36 on Math Placement Test; (b) grade of C or better in Math 105, 108, or 116; (c) score of 5 or higher on the IB Mathematical Studies  SL; (d) score of 3 or higher on the AP statistics exam; or (e) score of 63 or higher on the CLEP College Algebra Exam.
 MATH 211  Survey in Calculus and Analytic Geometry (4 units; U)
 A onesemester survey with applications to business administration, economics, and nonphysical sciences. Topics include coordinate systems, equations of curves, limits, differentiation, integration, applications. May not be used as a prereq for Math 232. No cr for students with cr in Math 213, 221, or 231. Prereq: Math Placement Level 30, which is earned by any of the following: (a) Level 30, 35 or 36 on Math Placement Test; (b) grade of C or better in Math 105, 108, or 116; (c) score of 5 or higher on the IB Mathematical Studies  SL; (d) score of 3 or higher on the AP statistics exam; or (e) score of 63 or higher on the CLEP College Algebra Exam.
 MATH 213  Calculus with Life Sciences Applications (4 units; U)
 Limits, derivatives, graphing. Antiderivatives, the definite integral, and the fundamental theorem of calculus. Additional techniques and applications pertinent to the life sciences throughout the course. No cr for students with cr in Math 221 or 231. Prereq: Math Placement Level 40, which is earned by any of the following: (a) Level 40 on Math Placement Test; (b) grade of C or better in Math 115; (c) grade of C or better in both Math 116 and Math 117; (d) grade of C or better in both Math 211 and Math 117; (e) grade of C or better in Math 116 and Level 36 on Math Placement Test; (f) grade of C or better in Math 211 and Level 36 on Math Placement Test; (g) grade of C or better in Math 117 and Level 35 on Math Placement Test; or (h) score of 61 or higher on the CLEP Precalculus Exam.
 MATH 221  Honors Calculus I (5 units; U)
 Calculus of functions of one and several variables; sequences, series, differentiation, integration; introduction to differential equations; vectors and vector functions; applications. Max 6 cr in combination of Math 221 & 222 may count toward Honors College requirements. Prereq: cons instr or Honors College Director; Math Placement Level 45, earned by any of: (a) Level 45 Math Placement Test; (b) Level 40 Math Placement Test & ACT math subscore 30 or higher; (c) score of 4 or 5 on AP AB calculus exam; (d) score of 3 or higher on AP BC calculus exam; (e) score of 5 or higher on IB Mathematics HL; (f) grade of A or better in Math 116 & 117; (g) grade of A or better in Math 115.
 MATH 222  Honors Calculus II (5 units; U)
 Continuation of Math 221. Max of 6 cr in combination of Math 221 & 222 may count toward Honors College reqs. Prereq: C or better in Math 221(P) or B or better in Math 232(P); cons instr.
 MATH 231  Calculus and Analytic Geometry I (4 units; U)
 Limits, derivatives, and graphs of algebraic, trigonometric, exponential, and logarithmic functions; antiderivatives, the definite integral, and the fundamental theorem of calculus, with applications. No cr for students with cr in Math 213. Prereq: Math Placement Level 40, which is earned by any of the following: (a) Level 40 on Math Placement Test; (b) grade of C or better in Math 115; (c) grade of C or better in both Math 116 and Math 117; (d) grade of C or better in both Math 211 and Math 117; (e) grade of C or better in Math 116 and Level 36 on Math Placement Test; (f) grade of C or better in Math 211 and Level 36 on Math Placement Test; (g) grade of C or better in Math 117 and Level 35 on Math Placement Test; or (h) score of 61 or higher on the CLEP Precalculus Exam.
 MATH 232  Calculus and Analytic Geometry II (4 units; U)
 Continuation of Math 231. Applications of integration, techniques of integration; infinite sequences and series; parametric equations, conic sections, and polar coordinates. Prereq: grade of C or better in Math 231(P) or grade of B or better in Math 213(P).
 MATH 233  Calculus and Analytic Geometry III (4 units; U)
 Continuation of MATH 232. Threedimensional analytic geometry and vectors; partial derivatives; multiple integrals; vector calculus, with applications. Counts as repeat of MATH 229. Prereq: grade of C or better in MATH 232(P).
 MATH 234  Linear Algebra and Differential Equations (4 units; U)
 Elementary differential equations. Vectors; matrices; linear transformations; quadratic forms; eigenvalues; applications. Prereq: grade of C or better in Math 232(P).
 MATH 240  Matrices and Applications (3 units; U)
 Vectors, vector spaces, systems of linear equations, matrices, determinants, linear transformations, diagonalization, eigenvalues, eigenvectors; selected topics from quadratic forms, difference equations, numerical methods, and applications. Prereq: Grade at least C in a MATH or MTHSTAT course numbered 200 or higher OR Math Placement Level 40, earned by any of: Level 40 Math Placement Test; grade at least C in MATH 115; grade at least C in MATH 116 and MATH 117; grade at least C in MATH 211 and MATH 117; grade at least C in MATH 116 & Level 36 or 26 Math Placement Test; grade at least C in MATH 211 & Level 36 or 26 Math Placement Test; grade at least C in MATH 117 & Level 35 Math Placement Test; at least 61 on CLEP Precalculus exam.
 MATH 275  Problem Solving/Critical Thinking for Elementary Education Majors (3 units; U)
 Course provides a strong foundation in the exploration, teaching and communication (oral and written) of mathematical concepts via problemsolving experiences and discussion. Prereq: grade of C or better in Math 175(P) or cons instr.
 MATH 276  Algebraic Structures for Elementary Education Majors (3 units; U)
 Topics for K8 teachers. Basic patterns and rules that govern number systems, geometric transformations, and manipulation of algebraic expressions. Counts as repeat of Math 299 w/same topic. Prereq: grade of C or better in Math 175(P) or cons instr.
 MATH 277  Geometry for Elementary Education Majors (3 units; U)
 Topics for K8 teachers. Geometry as measuring toolcongruence, similarity, area, volume, and coordinates; geometry as axiomatic systemdefinitions, conjectures, proofs, counterexamples; rigid motions, symmetry. Prereq: grade of C or better in Math 176(P) or cons instr.
 MATH 278  Discrete Probability and Statistics for Elementary Education Majors (3 units; U)
 Random experiments; histograms; sample spaces; equally likely outcomes for random experiments; permutations; combinations; binomial, geometric, hypergeometric distributions; expectation; conditional probabilities; max likelihood estimation & inference. Math 278 and MthStat 278 are jointly offered; they count as repeats of one another. Prereq: grade of C or better in Math 176(P) or cons instr.
 MATH 290  Topics in Mathematics: (3 units; U)
 Specific topics and any additional prerequisites announced in Schedule of Classes each time course is offered. May be retaken w/chg in topic to 9 cr max. Prereq: satisfaction of Quantitative Literacy Part A GER.
 MATH 297  Study Abroad: (112 units; U)
 Designed to enroll students in UWM sponsored programs before course work level, content and credits are determined and/or in specially prepared program course work. May be retaken w/chg in topic. Prereq: acceptance for Study Abroad Prog.
 MATH 299  Ad Hoc: (16 units; U)
 Course created expressly for offering in a specified enrollment period. Requires only dept & assoc dean approval. In exceptional circumstances, can be offered in one add'l sem. May be retaken w/chg in topic. Prereq: none; add'l prereqs may be assigned to specific topic.
 MATH 305  Introduction to Mathematical and Computational Modeling (3 units; U/G)
 Construction and analysis of discrete and continuous mathematical models in applied, natural, and social sciences. Elements of programming, simulations, case studies from scientific literature. Counts as repeat of Math 690(675) w/topic Adv Math Models with Apps. Prereq: jr st; grade of C or better in Math 211(P) & one addl 200level or higher Math or MthStat course, or grade of B or better in Math 213(P), or grade of C or better in Math 231(P), or cons instr.
 MATH 305G  Introduction to Mathematical and Computational Modeling (3 units; U/G)
 Construction and analysis of discrete and continuous mathematical models in applied, natural, and social sciences. Elements of programming, simulations, case studies from scientific literature. Counts as repeat of Math 690(675) w/topic Adv Math Models with Apps. Prereq: jr st; grade of C or better in Math 211(P) & one addl 200level or higher Math or MthStat course, or grade of B or better in Math 213(P), or grade of C or better in Math 231(P), or cons instr.
 MATH 311  Theory of Interest (4 units; U)
 Interest theory: annuities, amortization schedules, portfolio immunization. Financial derivatives: bonds, forwards, options. Topics consistent w/syllabus of SOA Financial Mathematics Exam. Prereq: grade of C or better in Math 232(P).
 MATH 313  Linear Programming and Optimization (3 units; U/G)
 Primal and dual formulations of linear programming problems; simplex and related methods of solution; algorithms for transportation; optimization. Prereq: jr st; grade of C or better in Math/ElecEng 234(P) or Math 240(P); or grad st.
 MATH 313G  Linear Programming and Optimization (3 units; U/G)
 Primal and dual formulations of linear programming problems; simplex and related methods of solution; algorithms for transportation; optimization. Prereq: jr st; grade of C or better in Math/ElecEng 234(P) or Math 240(P); or grad st.
 MATH 315  Mathematical Programming and Optimization (3 units; U/G)
 Introduction to operations research. Network analysis; integer programming; game theory; nonlinear programming; dynamic programming. Prereq: jr st, grade of C or better in either Math 234(P) or 240(P), & grade of C or better in either Math 211(P) or 233(P); or cons instr; or grad st.
 MATH 315G  Mathematical Programming and Optimization (3 units; U/G)
 Introduction to operations research. Network analysis; integer programming; game theory; nonlinear programming; dynamic programming. Prereq: jr st, grade of C or better in either Math 234(P) or 240(P), & grade of C or better in either Math 211(P) or 233(P); or cons instr; or grad st.
 MATH 318  Topics in Discrete Mathematics (3 units; U)
 Number theory topics related to cryptography; discrete structures including graphs, partial orders, Latin squares and block designs; advanced counting techniques. Jointly offered with & count as repeat of CompSci 318. Prereq: a grade of C or better in CompSci 317(P) or Math 341(P).
 MATH 320  Introduction to Differential Equations (3 units; U/G)
 Elementary types and systems of differential equations, series solutions, numerical methods, Laplace transforms, selected applications. No grad cr in Math Sci. Prereq: jr st, grade of C or better in both Math 232(P) & 240(P), or grade of C or better in Math/ElecEng 234(P); or grad st.
 MATH 320G  Introduction to Differential Equations (3 units; U/G)
 Elementary types and systems of differential equations, series solutions, numerical methods, Laplace transforms, selected applications. No grad cr in Math Sci. Prereq: jr st, grade of C or better in both Math 232(P) & 240(P), or grade of C or better in Math/ElecEng 234(P); or grad st.
 MATH 321  Vector Analysis (3 units; U/G)
 Topics selected from vector algebra; scalar and vector fields; line, surface, and volume integrals; theorems of Green, Gauss, and Stokes; vector differential calculus. Prereq: jr st, grade of C or better in Math 233(P); or grad st.
 MATH 322  Introduction to Partial Differential Equations (3 units; U/G)
 Partial differential equations of mathematical physics, boundary value problems in heat flow, vibrations, potentials, etc. Solved by Fourier series; Bessel functions and Legendre polynomials. Prereq: jr st, Math 320(P), & grade of C or better in Math 233(P); or grad st.
 MATH 341  Seminar: Introduction to the Language and Practice of Mathematics (3 units; U)
 Facility with mathematical language and method of conjecture, proof and counter example, with emphasis on proofs. Topics: logic, sets, functions and others. Prereq: Math Placement Level 40, which is earned by any of the following: (a) Level 40 on Math Placement Test; (b) grade of C or better in MATH 115; (c) grade of C or better in both MATH 116 and MATH 117; (d) grade of C or better in both MATH 211 and MATH 117; (e) grade of C or better in MATH 116 and Level 36 or 26 on Math Placement Test; (f) grade of C or better in MATH 211 and Level 36 or 26 on Math Placement Test; (g) grade of C or better in MATH 117 and Level 35 on Math Placement Test; or (h) score of 61 or higher on the CLEP Precalculus Exam.
 MATH 345  Mathematics from a Historical Perspective: (3 units; U)
 Topics from the development of mathematics, such as famous problems, mathematicians, calculating devices; chronological outlines. Significant reading and writing assignments. May be retaken w/chg in topic to 9 cr max. Add'l prereqs announced in SOC each offering. Prereq: Grade of C or better in Math 232(P); satisfaction of OWCA.
 MATH 371  Introduction to Stochastic Models in Finance (3 units; U/G)
 Elementary modeling of financial instruments for students in mathematics, economics, business, etc. Statistical and stochastic tools leading to the BlackScholes model. Real data parameter fitting. Prereq: jr st & one of the following pairs; Econ 413(431)(P) & 506(P), Bus Adm 210(P) & 350(P), Bus Adm 701(P) & 702(P), or Math 234(P) & MthStat 361(P), or cons instr; or grad st.
 MATH 381  Honors Seminar: (3 units; U)
 Significant topics to illustrate to nonmathematicians the characteristic features of mathematical thought. Only H.S. algebra and geometry assumed. May be retaken w/chg in topic to 9 cr max. Not open for cr toward a major in Math. Prereq: soph st; Honors 200(P); cons Honors College dir.
 MATH 405  Mathematical Models and Applications (3 units; U/G)
 Modeling techniques for analysis and decisionmaking in social and life sciences and industry. Deterministic and stochastic modeling. Topics may vary with instructors. Prereq: jr st; one of: grade of C or better in Math 211(P), grade of B or better in Math 213(P), or grade of C or better in Math 231(P); & grade of C or better in either Math/ElecEng 234(P) or Math 240(P); or grad st.
 MATH 405G  Mathematical Models and Applications (3 units; U/G)
 Modeling techniques for analysis and decisionmaking in social and life sciences and industry. Deterministic and stochastic modeling. Topics may vary with instructors. Prereq: jr st; one of: grade of C or better in Math 211(P), grade of B or better in Math 213(P), or grade of C or better in Math 231(P); & grade of C or better in either Math/ElecEng 234(P) or Math 240(P); or grad st.
 MATH 413  Introduction to Numerical Analysis (3 units; U/G)
 Root finding and solution of nonlinear systems; direct solution of linear systems; interpolation & approximation of functions; least squares; fast Fourier transform; quadrature. Prereq: jr st, grade of C or better in Math 233(C), & grade of C or better in Math/ElecEng 234(C); or grad st.
 MATH 413G  Introduction to Numerical Analysis (3 units; U/G)
 Root finding and solution of nonlinear systems; direct solution of linear systems; interpolation & approximation of functions; least squares; fast Fourier transform; quadrature. Prereq: jr st, grade of C or better in Math 233(C), & grade of C or better in Math/ElecEng 234(C); or grad st.
 MATH 415  Introduction to Scientific Computing (3 units; U/G)
 Nonlinear systems; iterative solution of linear systems; initial value problems in ordinary differential equations; boundary value problems in ordinary and partial differential equations. Prereq: jr st, grade of C or better in Math 233(C), & grade of C or better in Math/ElecEng 234(C); or grad st.
 MATH 415G  Introduction to Scientific Computing (3 units; U/G)
 Nonlinear systems; iterative solution of linear systems; initial value problems in ordinary differential equations; boundary value problems in ordinary and partial differential equations. Prereq: jr st, grade of C or better in Math 233(C), & grade of C or better in Math/ElecEng 234(C); or grad st.
 MATH 417  Computational Linear Algebra (3 units; U/G)
 Direct solution of linear systems; iterative solution of linear systems; least squares; eigenvalue problems. Prereq: jr st & grade of C or better in Math/ElecEng 234(P) or Math 240(P); or grad st.
 MATH 417G  Computational Linear Algebra (3 units; U/G)
 Direct solution of linear systems; iterative solution of linear systems; least squares; eigenvalue problems. Prereq: jr st & grade of C or better in Math/ElecEng 234(P) or Math 240(P); or grad st.
 MATH 423  Complex Analysis (3 units; U/G)
 Complex numbers; definition and properties of analytic functions of a complex variable; conformal mapping; calculus of residues; applications to mathematics and physics. See also Math 713. Prereq: jr st; grade of C or better in Math 233(P); or grad st.
 MATH 431  Modern Algebra with Applications (3 units; U/G)
 Groups, rings, fields, Boolean algebras with emphasis on their applications to computer science and other areas. Does not carry grad cr in math sci. Prereq: jr st & grade of C or better in Math 232(P); or grad st.
 MATH 431G  Modern Algebra with Applications (3 units; U/G)
 Groups, rings, fields, Boolean algebras with emphasis on their applications to computer science and other areas. Does not carry grad cr in math sci. Prereq: jr st & grade of C or better in Math 232(P); or grad st.
 MATH 451  Axiomatic Geometry (3 units; U/G)
 An axiomatic approach to Euclidean and nonEuclidean geometry (historic role of the parallel postulate and models). Dept cons req'd for grad cr in math sci. Prereq: jr st, grade of C or better in both Math 341(P) & Math 232(C); or grad st.
 MATH 451G  Axiomatic Geometry (3 units; U/G)
 An axiomatic approach to Euclidean and nonEuclidean geometry (historic role of the parallel postulate and models). Dept cons req'd for grad cr in math sci. Prereq: jr st, grade of C or better in both Math 341(P) & Math 232(C); or grad st.
 MATH 453  Transformations in Geometry (3 units; U/G)
 Selected topics from vector geometry and geometric transformations such as the study of invariants and conics. Recom for secondary school teachers. Dept cons req'd for grad cr in math sci. Prereq: jr st, grade of C or better in both Math 341(P) & Math 232(C); or grad st.
 MATH 489  Internship in Mathematics, Upper Division (16 units; U)
 Application of advanced principles of mathematics in a business, organizational, educational, governmental, or other appropriate setting. One cr earned for academic work based on 40 hours in internship. May be retaken to 6 cr max. Prereq: jr st; 6 cr 300level or above in math or math stats; 2.5 gpa in the major; cons supervising faculty member.
 MATH 490  Topics in Mathematics: (3 units; U/G)
 Specific topics and any additional prerequisites announced in Schedule of Classes each time course is offered. May be retaken w/chg in topic to 9 cr max. Prereq: jr st; grade of C or better in a Math or MthStat course at the 200 level or above; or grad st.
 MATH 490G  Topics in Mathematics: (3 units; U/G)
 Specific topics and any additional prerequisites announced in Schedule of Classes each time course is offered. May be retaken w/chg in topic to 9 cr max. Prereq: jr st; grade of C or better in a Math or MthStat course at the 200 level or above; or grad st.
 MATH 497  Study Abroad: (112 units; U/G)
 Designed to enroll students in UWM sponsored programs before course work level, content and credits are determined and/or in specially prepared program course work. May be retaken w/chg in topic. Prereq: jr st; acceptance for Study Abroad Prog.
 MATH 499  Ad Hoc: (16 units; U)
 Course created expressly for offering in a specified enrollment period. Requires only dept & assoc dean approval. In exceptional circumstances, can be offered in one add'l sem. May be retaken w/chg in topic. Prereq: jr st; add'l prereqs may be assigned to specific topic.
 MATH 511  Symbolic Logic (3 units; U/G)
 Firstorder predicate calculus; formal properties of theoretical systems; chief results of modern mathematical logic; advanced topics such as completeness and computability. CompSci 511, Math 511 & Philos 511 are jointly offered; they count as repeats of one another. Prereq: jr st & either Philos 212(P) or 6 cr in math at the 300level or above.
 MATH 511G  Symbolic Logic (3 units; U/G)
 Firstorder predicate calculus; formal properties of theoretical systems; chief results of modern mathematical logic; advanced topics such as completeness and computability. CompSci 511, Math 511 & Philos 511 are jointly offered; they count as repeats of one another. Prereq: jr st & either Philos 212(P) or 6 cr in math at the 300level or above.
 MATH 521  Advanced Calculus I (3 units; U/G)
 Fundamental notions of sets and functions; limits, continuity; Riemann integral, improper integral; infinite series; uniform convergence; power series; improper integrals with a parameter. Prereq: jr st; grades of C or better in Math 232(P) & 341(P); or grad st.
 MATH 521G  Advanced Calculus I (3 units; U/G)
 Fundamental notions of sets and functions; limits, continuity; Riemann integral, improper integral; infinite series; uniform convergence; power series; improper integrals with a parameter. Prereq: jr st; grades of C or better in Math 232(P) & 341(P); or grad st.
 MATH 522  Advanced Calculus II (3 units; U/G)
 Linear functions; differentiation of functions of several variables (implicit functions, Jacobians); change of variable in multiple integrals; integrals over curves, surfaces; Green, Gauss, Stokes theorems. Prereq: jr st, Math 521(P), grade of C or better in Math 233(P), & grade of C or better in either Math 234(P) or 240(P); or grad st.
 MATH 522G  Advanced Calculus II (3 units; U/G)
 Linear functions; differentiation of functions of several variables (implicit functions, Jacobians); change of variable in multiple integrals; integrals over curves, surfaces; Green, Gauss, Stokes theorems. Prereq: jr st, Math 521(P), grade of C or better in Math 233(P), & grade of C or better in either Math 234(P) or 240(P); or grad st.
 MATH 531  Modern Algebra (3 units; U/G)
 Integers; groups; rings; fields; emphasis on proofs. Prereq: jr st; grade of C or better in Math 341(P).
 MATH 531G  Modern Algebra (3 units; U/G)
 Integers; groups; rings; fields; emphasis on proofs. Prereq: jr st; grade of C or better in Math 341(P).
 MATH 535  Linear Algebra (3 units; U/G)
 Vector spaces; linear transformations and matrices; characteristic values and vectors; canonical forms; bilinear, quadratic, and Hermitian forms; selected applications. Prereq: jr st, grade of C or better in either Math 234(P) or 240(P), & grade of C or better in Math 341(P); or grad st.
 MATH 535G  Linear Algebra (3 units; U/G)
 Vector spaces; linear transformations and matrices; characteristic values and vectors; canonical forms; bilinear, quadratic, and Hermitian forms; selected applications. Prereq: jr st, grade of C or better in either Math 234(P) or 240(P), & grade of C or better in Math 341(P); or grad st.
 MATH 537  Number Theory (3 units; U/G)
 Number theoretic functions; distribution of primes; Diophantine approximation; partitions; additive number theory; quadratic reciprocity. Prereq: jr st, grade of C or better in both Math 232(P) & 341(P); or grad st.
 MATH 537G  Number Theory (3 units; U/G)
 Number theoretic functions; distribution of primes; Diophantine approximation; partitions; additive number theory; quadratic reciprocity. Prereq: jr st, grade of C or better in both Math 232(P) & 341(P); or grad st.
 MATH 551  Elementary Topology (3 units; U/G)
 General theory of point sets in Euclidean spaces, with emphasis on topology of twodimensional and threedimensional spaces; elementary notions of metric spaces; applications. Prereq: jr st; grades of C or better in Math 233(P) & 341(P); or grad st.
 MATH 551G  Elementary Topology (3 units; U/G)
 General theory of point sets in Euclidean spaces, with emphasis on topology of twodimensional and threedimensional spaces; elementary notions of metric spaces; applications. Prereq: jr st; grades of C or better in Math 233(P) & 341(P); or grad st.
 MATH 553  Differential Geometry (3 units; U/G)
 The theory of curves and surfaces by differential methods. Prereq: jr st, grade of C or better in all of Math 233(P), 234(P) & 341(P); or grad st.
 MATH 571  Introduction to Probability Models (3 units; U/G)
 Probability review, Markov chains in discrete and continuous time. Random walks, branching processes, birth and death processes. Queuing theory. Applications to physical sciences, engineering, mathematics. Prereq: jr st; grade of C or better in Math 233(P); grade of C or better in Math/ElecEng 234(P) or in both Math 240(P) & 320(P); & one calculusbased course in statistics or probability at the 300 level or above; or grad st.
 MATH 571G  Introduction to Probability Models (3 units; U/G)
 Probability review, Markov chains in discrete and continuous time. Random walks, branching processes, birth and death processes. Queuing theory. Applications to physical sciences, engineering, mathematics. Prereq: jr st; grade of C or better in Math 233(P); grade of C or better in Math/ElecEng 234(P) or in both Math 240(P) & 320(P); & one calculusbased course in statistics or probability at the 300 level or above; or grad st.
 MATH 575  High School Mathematics from an Advanced Viewpoint (3 units; U/G)
 Number systems; algebra of polynomials; theory of equations; functions; modeling; geometric measurement; geometric transformations; connections between advanced mathematics and high school topics. Counts as repeat of Math 690(675) w/similar topic. Prereq: jr st, either Math 451(P) or 453(P), & either Math 431(P) or 531(P); or cons instr; or grad st.
 MATH 575G  High School Mathematics from an Advanced Viewpoint (3 units; U/G)
 Number systems; algebra of polynomials; theory of equations; functions; modeling; geometric measurement; geometric transformations; connections between advanced mathematics and high school topics. Counts as repeat of Math 690(675) w/similar topic. Prereq: jr st, either Math 451(P) or 453(P), & either Math 431(P) or 531(P); or cons instr; or grad st.
 MATH 581  Introduction to the Theory of Chaotic Dynamical Systems (3 units; U/G)
 Iterated mappings, one parameter families, attracting and repelling periodic orbits, topological transitivity, Sarkovski's theorem, chaos, bifurcation theory, period doubling route to chaos, horseshoe maps, attractors. Prereq: jr st & Math 521(P), 529(P) or 621(P), or cons instr; or grad st.
 MATH 591  Undergraduate Seminar: (1 units; U)
 Specific topics and any additional prerequisites announced in Schedule of Classes each time course is offered. May be retaken w/chg in topic to 4 cr max. Prereq: jr st; cons instr.
 MATH 599  Capstone Experience (1 units; U)
 Student writes a paper under supervision of an advisor on an approved topic not covered in the student's regular course work. May be retaken w/chg in topic to 2 cr max. Prereq: sr st; cons instr.
 MATH 601  Advanced Engineering Mathematics I (3 units; U/G)
 Sequences and series, elementary complex analysis; Fourier series; linear and nonlinear ordinary differential equations; matrix theory, elementary functional analysis; elementary solution of partial differential equations. Prereq: jr st; grade of C or better in both of Math 233(P) and Math/ElecEng 234(P); 3 cr Math at 300level or above; or cons instr; or grad st.
 MATH 601G  Advanced Engineering Mathematics I (3 units; U/G)
 Sequences and series, elementary complex analysis; Fourier series; linear and nonlinear ordinary differential equations; matrix theory, elementary functional analysis; elementary solution of partial differential equations. Prereq: jr st; grade of C or better in both of Math 233(P) and Math/ElecEng 234(P); 3 cr Math at 300level or above; or cons instr; or grad st.
 MATH 602  Advanced Engineering Mathematics II (3 units; U/G)
 Continuation of Math 601. Partial differential equations, Fourier and Laplace transforms, convolutions, special functions, mathematical modeling. Prereq: jr st; Math 601(P).
 MATH 602G  Advanced Engineering Mathematics II (3 units; U/G)
 Continuation of Math 601. Partial differential equations, Fourier and Laplace transforms, convolutions, special functions, mathematical modeling. Prereq: jr st; Math 601(P).
 MATH 615  Numerical Solution of Partial Differential Equations (3 units; U/G)
 Finite difference solution of elliptic boundary value problems and of evolution problems; solution of hyperbolic conservation laws; finite volume methods; finite element methods. Prereq: jr st; Math 413(P), 415(414)(P), or 417(416)(P); Math 322(P) or 602(P); or cons instr.
 MATH 615G  Numerical Solution of Partial Differential Equations (3 units; U/G)
 Finite difference solution of elliptic boundary value problems and of evolution problems; solution of hyperbolic conservation laws; finite volume methods; finite element methods. Prereq: jr st; Math 413(P), 415(414)(P), or 417(416)(P); Math 322(P) or 602(P); or cons instr.
 MATH 617  Optimization (3 units; U/G)
 Unconstrained and constrained optimization: linear, nonlinear, and dynamic programming; barrier, penalty, and Lagrangian methods; KarushKuhnTucker theory, quadratic, and sequential quadratic programming; evolutionary algorithms. Prereq: jr st; Math 321(P) or 602(P); or grad st or cons instr.
 MATH 621  Introduction to Analysis I (3 units; U/G)
 Topology of Euclidean space; continuity; differentiation of real and vectorvalued functions; RiemannStieltjes integration. Prereq: jr st: grades of C or better in Math 233(P), 341(P), & either 234(P) or 240(P); cons dept advisor; or grad st.
 MATH 621G  Introduction to Analysis I (3 units; U/G)
 Topology of Euclidean space; continuity; differentiation of real and vectorvalued functions; RiemannStieltjes integration. Prereq: jr st: grades of C or better in Math 233(P), 341(P), & either 234(P) or 240(P); cons dept advisor; or grad st.
 MATH 622  Introduction to Analysis II (3 units; U/G)
 Continues Math 621. Sequences and series of functions; uniform convergence; power series; functions of several variables; inverse and implicit function theorems; differential forms; Stokes' theorem. Prereq: jr st; Math 621(P) or cons instr; or grad st.
 MATH 622G  Introduction to Analysis II (3 units; U/G)
 Continues Math 621. Sequences and series of functions; uniform convergence; power series; functions of several variables; inverse and implicit function theorems; differential forms; Stokes' theorem. Prereq: jr st; Math 621(P) or cons instr; or grad st.
 MATH 631  Modern Algebra I (3 units; U/G)
 Group theory, including normal subgroups, quotients, permutation groups, Sylow's theorems, Abelian groups; field theory; linear algebra over general fields. Prereq: jr st; grade of C or better in Math 341(P) & either Math 234(P) or 240(P); cons dept advisor; or grad st.
 MATH 631G  Modern Algebra I (3 units; U/G)
 Group theory, including normal subgroups, quotients, permutation groups, Sylow's theorems, Abelian groups; field theory; linear algebra over general fields. Prereq: jr st; grade of C or better in Math 341(P) & either Math 234(P) or 240(P); cons dept advisor; or grad st.
 MATH 632  Modern Algebra II (3 units; U/G)
 Continuation of Math 631. Ring theory, including ideals, quotient rings, Euclidean rings, polynomial rings, unique factorization; modules, including vector spaces, linear transformations, canonical forms; bilinear forms. Prereq: jr st; Math 631(P) or cons instr; or grad st.
 MATH 632G  Modern Algebra II (3 units; U/G)
 Continuation of Math 631. Ring theory, including ideals, quotient rings, Euclidean rings, polynomial rings, unique factorization; modules, including vector spaces, linear transformations, canonical forms; bilinear forms. Prereq: jr st; Math 631(P) or cons instr; or grad st.
 MATH 690  Topics in Mathematics: (3 units; U/G)
 Specific topics and any additional prerequisites announced in Schedule of Classes each time course is offered. May be retaken w/chg in topic to 9 cr max. Prereq: jr st, at least one U/G Math or MthStat course; cons instr; or grad st.
 MATH 699  Independent Reading (13 units; U)
 See Advanced Independent Study. For further information, consult dept chair. May be retaken w/chg in topic. Prereq: jr st; 2.5 gpa, & writ cons instr, dept chair, & asst dean for SAS.
Undergraduate (U and U/G): MTHSTAT
MTHSTAT
 MTHSTAT 194  FirstYear Seminar: (3 units; U)
 Specific topics are announced in the Schedule of Classes each time the class is offered. Open only to freshman. Students may earn cr in just one L&S FirstYear Sem (course numbers 192, 193, 194). Prereq: none.
 MTHSTAT 199  Independent Study (13 units; U)
 For further information, consult dept chair. May be retaken to 6 cr max. Prereq: 2.5 gpa; writ cons instr, dept chair & asst dean for SAS.
 MTHSTAT 215  Elementary Statistical Analysis (3 units; U)
 Elementary probability theory; descriptive statistics; sampling distributions; basic problems of statistical inference including estimation; tests of statistical hypothesis in both one and two sample cases. Prereq: satisfaction of Quantitative Literacy Part A GER.
 MTHSTAT 278  Discrete Probability and Statistics for Elementary Education Majors (3 units; U)
 Random experiments; histograms; sample spaces; equally likely outcomes for random experiments; permutations; combinations; binomial, geometric, hypergeometric distributions; expectation; conditional probabilities; max likelihood estimation & inference. Math 278 and MthStat 278 are jointly offered; they count as repeats of one another. Prereq: grade of C or better in Math 176(P) or cons instr.
 MTHSTAT 299  Ad Hoc: (16 units; U)
 Course created expressly for offering in a specified enrollment period. Requires only dept & assoc dean approval. In exceptional circumstances, can be offered in one add'l sem. May be retaken w/chg in topic. Prereq: none; add'l prereqs may be assigned to specific topic.
 MTHSTAT 361  Introduction to Mathematical Statistics I (3 units; U/G)
 Probability spaces; discrete and continuous, univariate and multivariate distributions; moments; independence, random sampling, sampling distributions; normal and related distributions; point and interval estimation. Not recom for grad students in math, or students not planning to take MthStat 362. Prereq: jr st; Math 233(P).
 MTHSTAT 361G  Introduction to Mathematical Statistics I (3 units; U/G)
 Probability spaces; discrete and continuous, univariate and multivariate distributions; moments; independence, random sampling, sampling distributions; normal and related distributions; point and interval estimation. Not recom for grad students in math, or students not planning to take MthStat 362. Prereq: jr st; Math 233(P).
 MTHSTAT 362  Introduction to Mathematical Statistics II (3 units; U/G)
 Testing statistical hypothesis; linear hypothesis; regression; analysis of variance and experimental designs; distributionfree methods; sequential methods. Not recom for grad students in math. Prereq: jr st; MthStat 361(P).
 MTHSTAT 362G  Introduction to Mathematical Statistics II (3 units; U/G)
 Testing statistical hypothesis; linear hypothesis; regression; analysis of variance and experimental designs; distributionfree methods; sequential methods. Not recom for grad students in math. Prereq: jr st; MthStat 361(P).
 MTHSTAT 461  Data Analysis and Graphing Using SASI (2 units; U)
 Introduction to SAS language programming. Procedures for handling raw data, SAS data, and parametric and nonparametric univariate data analysis; procedures for graphical display. Offered first half of sem. Does not count toward math sci major. Prereq: MthStat 215(P), 362(P), 465(P), 467(P), Bus Adm 210(P), or Econ 210(P).
 MTHSTAT 462  Data Analysis and Graphing Using SASII (2 units; U/G)
 Continuation of MthStat 461. Procedures GLM, LIFEREG, LIFETEST, LOGISTIC, PROBIT and advanced GRAPHING. Offered second half of sem. U cr does not count toward math sci major. Prereq: jr st; MthStat 461(P) or cons instr.
 MTHSTAT 465  Introductory Mathematical Statistics for Social Sciences and Education (3 units; U/G)
 Probability distributions; parameter estimation and confidence intervals; hypothesis testing; applications. Not open for cr to students w/cr in MthStat 467, 362, or for grad cr in math. Not open for cr toward major in math except in School of Education. Prereq: jr st; Math 211(P) or 232(P).
 MTHSTAT 467  Introductory Statistics for Physical Sciences and Engineering Students (3 units; U/G)
 Concepts of probability and statistics; probability distributions of engineering applications; sampling distributions; hypothesis testing, parameter estimation; experimental design; regression analysis. Not open for cr for Math majors or students with cr in MthStat 362 or 465. Prereq: jr st; Math 233(P).
 MTHSTAT 469  Biostatistics (3 units; U/G)
 Simple distributions, estimation and hypothesis testing, simple regression, analysis of variance, nonparametric methods in biology. Demography and vital statistics and bioassay and clinical trials. Not allowed as part of core curric for Math majors. Not open for cr to students with cr in MthStat 569 & not open for grad cr in Math. Prereq: jr st; an elementary stats course.
 MTHSTAT 489  Internship in Mathematical Statistics, Upper Division (16 units; U)
 Application of advanced principles of mathematical statistics in a business, organizational, educational, governmental, or other appropriate setting. One cr earned for academic work based on 40 hrs in internship. May be retaken to 6 cr max. Prereq: jr st; 6 cr 300level or above in Math or MthStat; 2.5 gpa in the major; cons supervising faculty member.
 MTHSTAT 499  Ad Hoc: (16 units; U)
 Course created expressly for offering in a specified enrollment period. Requires only dept & assoc dean approval. In exceptional circumstances, can be offered in one add'l sem. May be retaken w/chg in topic. Prereq: jr st; add'l prereqs may be assigned to specific topic.
 MTHSTAT 562  Design of Experiments (3 units; U/G)
 Latin squares; incomplete block designs; factorial experiments; confounding; partial confounding; splitplot experiments; fractional replication. Prereq: jr st; MthStat 362(P); Math 234(P) or 240(P).
 MTHSTAT 563  Regression Analysis (3 units; U/G)
 Straight line, polynomial and multiple regression; multiple and partial correlation; testing hypotheses in regression; residual analysis. Prereq: jr st; MthStat 467(P) or 362(P).
 MTHSTAT 563G  Regression Analysis (3 units; U/G)
 Straight line, polynomial and multiple regression; multiple and partial correlation; testing hypotheses in regression; residual analysis. Prereq: jr st; MthStat 467(P) or 362(P).
 MTHSTAT 564  Time Series Analysis (3 units; U/G)
 Autocorrelation; spectral density; linear models; forecasting; model identification and estimation. Prereq: jr st; MthStat 362(P).
 MTHSTAT 564G  Time Series Analysis (3 units; U/G)
 Autocorrelation; spectral density; linear models; forecasting; model identification and estimation. Prereq: jr st; MthStat 362(P).
 MTHSTAT 565  Nonparametric Statistics (3 units; U/G)
 Sign, rank and permutation tests; tests of randomness and independence; methods for discrete data and zeroes and ties; power and efficiency of nonparametric tests. Prereq: jr st; MthStat 362(P).
 MTHSTAT 566  Computational Statistics (3 units; U/G)
 Basics of programming and optimization techniques; resampling, bootstrap, and Monte Carlo methods; design and analysis of simulation studies. Prereq: jr st; MthStat 362(P) or cons instr.
 MTHSTAT 566G  Computational Statistics (3 units; U/G)
 Basics of programming and optimization techniques; resampling, bootstrap, and Monte Carlo methods; design and analysis of simulation studies. Prereq: jr st; MthStat 362(P) or cons instr.
 MTHSTAT 568  Multivariate Statistical Analysis (3 units; U/G)
 Multivariate normal distribution; Wishart distribution; Hotelling's T2; multivariate normal distribution; multivariate analysis of variance; classification problems. Prereq: jr st; MthStat 362(P); Math 234(P) or 240(P).
 MTHSTAT 568G  Multivariate Statistical Analysis (3 units; U/G)
 Multivariate normal distribution; Wishart distribution; Hotelling's T2; multivariate normal distribution; multivariate analysis of variance; classification problems. Prereq: jr st; MthStat 362(P); Math 234(P) or 240(P).
 MTHSTAT 591  Foundations of Professional Practice in Actuarial Science (1 units; U)
 Lecture and discussions on professional topics such as health, pension, life, casualty, regulation. May be retaken for cr once. Prereq: completion of actuarial sci prep curric or cons instr.
 MTHSTAT 592  Actuarial Science Laboratory I: Probability, Finance, and Economics (1 units; U)
 Fundamental probability tools for quantitatively assessing risk integrated with economic and financial concepts; application of tools to actuarial problems; introduction to insurance and risk management. Prereq: C or better in MthStat 361(P) or cons instr.
 MTHSTAT 593  Actuarial Science Laboratory II: Interest Theory, Finance, and Economics (1 units; U)
 Fundamental interest theory tools integrated with economic and financial concepts; financial mathematics; financial instruments; calculating present and accumulated values for various streams of cash flow. Prereq: C or better in Math 311(P) or cons instr.
 MTHSTAT 596  Actuarial Statistics I: Fitting of Loss Models (3 units; U/G)
 Statistical modeling of insurance data. Model specification, fitting and validation. Measures of confidence for modelbased decisions. Prereq: jr st; B or better in each Math 234(P) and MthStat 362(P); CompSci 151(P) or 201(P); or cons instr.
 MTHSTAT 597  Actuarial Statistics II: Credibility, Risk Measures and Related Topics (3 units; U/G)
 Statistical techniques for insurance data. Credibility and ratemaking. Risk measures. Dependent risks and copulas. Simulations. Prereq: jr st; B or better in each Math 234(P) and MthStat 362(P); CompSci 151(P) or 201(P); or cons instr.
 MTHSTAT 691  Actuarial Models I: Life Contingencies (3 units; U/G)
 Modeling and valuation of cash flows dependent on death, survival and other random events. Survival models for single and multiple risks. Life insurances and annuities. Prereq: jr st; B or better in each Math 571(P) and Math 311(P); or cons instr.
 MTHSTAT 691G  Actuarial Models I: Life Contingencies (3 units; U/G)
 Modeling and valuation of cash flows dependent on death, survival and other random events. Survival models for single and multiple risks. Life insurances and annuities. Prereq: jr st; B or better in each Math 571(P) and Math 311(P); or cons instr.
 MTHSTAT 692  Actuarial Models II: Financial Economics (3 units; U/G)
 Modeling and managing of financial risks. Interest rate models. Valuation of derivatives securities. Risk management. Prereq: jr st; B or better in each Math 571(P) and Math 311(P); or cons instr.
 MTHSTAT 692G  Actuarial Models II: Financial Economics (3 units; U/G)
 Modeling and managing of financial risks. Interest rate models. Valuation of derivatives securities. Risk management. Prereq: jr st; B or better in each Math 571(P) and Math 311(P); or cons instr.
Graduate: (U/G and G): ATM SCI, MATH, MTHSTAT
ATM SCI
 ATM SCI 330  AirPollution Meteorology (3 units; U/G)
 Pollutant sources and sinks, fundamental pollutant chemistry, monitoring techniques, averaging boundary layers and turbulence, diffusion theories, diffusion models, regional and globalscale pollution problems. Prereq: Atm Sci 240(P); Chem 102(P); stats course recom.
 ATM SCI 350  Atmospheric Thermodynamics (3 units; U/G)
 Radiant energy, sensible heat, and atmospheric thermodynamics; the gas laws; hydrostatic and psychrometric equations; dry and moist convection; clouds and their physical and energy relations. Optional field exercise. Prereq: jr st; Physics 210(P); Math 232(P); Atm Sci 240(P).
 ATM SCI 351  Dynamic Meteorology I (3 units; U/G)
 The role of dynamics in atmospheric physics; equations of motion; symmetric circulation models; gravity waves; Rossby waves, quasigeostrophy; introduction to instability of atmospheric flows. Prereq: jr st; Atm Sci 240(P); Math 233(P).
 ATM SCI 352  Dynamic Meteorology II (3 units; U/G)
 Circulation, vorticity, potential vorticity; shallow water equations: Poincare, Kelvin, and Rossby waves, energy and enstrophy; quasigeostrophy for a stratified atmosphere; barotropic and baroclinic instability. Prereq: jr st; Atm Sci 351(P); Math 234(P).
 ATM SCI 360  Synoptic Meteorology I (4 units; U/G)
 Fundamental principles; synopticscale structure and dynamics; equivalent barotropic model; vertical motions; introduction to and application of quasigeostrophic theory. Prereq: jr st; Math 232(P); Physics 210(P); Atm Sci 240(P).
 ATM SCI 361  Synoptic Meteorology II (4 units; U/G)
 Extension of quasigeostrophic theory to Qvectors; isentropic potential vorticity applied to midlatitude weather systems; fronts and jets. Prereq: jr st; Atm Sci 360(P).
 ATM SCI 405  Atmospheric Science for inService Teachers: (13 units; U/G)
 Basic, advanced or new topics in atmospheric sciences for inservice teachers. May be retaken w/chg in topic to 9 cr max. Prereq: inservice teacher; add'l prereqs depending on topic.
 ATM SCI 460  Mesoscale Circulations (3 units; U/G)
 Theory, analysis and forecasting of mesoscale flows, including convective systems, polar lows, terrain and surfaceforced flows, jet streams and hurricanes. Prereq: jr st; Atm Sci 360(R) or cons instr.
 ATM SCI 460G  Mesoscale Circulations (3 units; U/G)
 Theory, analysis and forecasting of mesoscale flows, including convective systems, polar lows, terrain and surfaceforced flows, jet streams and hurricanes. Prereq: jr st; Atm Sci 360(R) or cons instr.
 ATM SCI 464  Physical Meteorology: Cloud Physics (3 units; U/G)
 Formation of cloud droplets, droplet growth by condensation, formation of ice crystals, precipitation processes, weather radars, cloud models. Prereq: jr st; Physics 210(P); Math 232(P); Atm Sci 350(P).
 ATM SCI 470  Tropical Meteorology (3 units; U/G)
 Dynamics and energetics of tropical circulations. Origins and evolution of equatorial disturbances and easterly waves. Structure and dynamics of tropical cyclones. Hurricane modeling and prediction. Prereq: Atm Sci 351(P) or 360(P).
 ATM SCI 480  The General Circulation and Climate Dynamics (3 units; U/G)
 Historical overview, the zonally symmetric circulation, momentum, heat and water budgets, stationary waves, the El Nino Southern oscillation, global warming, interpentadal variability in the North Atlantic. Prereq: jr st; Atm Sci 351(P).
 ATM SCI 497  Study Abroad: (112 units; U/G)
 Designed to enroll students in UWM sponsored program before course work level, content, and credits are determined and/or in specially prepared course work. May be retaken w/chg in topic. Prereq: jr st; acceptance for Study Abroad Prog.
 ATM SCI 500  Statistical Methods in Atmospheric Sciences (3 units; U/G)
 Mathematical and statistical tools applicable to the investigation of atmospheric problems; the nature and treatment of atmospheric data. Prereq: jr st; Atm Sci 240(P) or 350(P), & Math 232(P) or cons instr.
 ATM SCI 505  Micrometeorology (3 units; U/G)
 Surface energy budget; radiation balance and heat transfer; boundarylayer profiles of wind, temperature and moisture; turbulence and boundarylayer fluxes; evapotranspiration; special topics. Prereq: jr st; Atm Sci 351(P) & 330(P).
 ATM SCI 505G  Micrometeorology (3 units; U/G)
 Surface energy budget; radiation balance and heat transfer; boundarylayer profiles of wind, temperature and moisture; turbulence and boundarylayer fluxes; evapotranspiration; special topics. Prereq: jr st; Atm Sci 351(P) & 330(P).
 ATM SCI 511  Seminar in Atmospheric Radiation and Remote Sensing (3 units; U/G)
 Basic laws of radiation, absorption and scattering, weather radar, retrieval of soundings, remote sensing and climate, weather satellites. Prereq: jr st; Math 232(P); Atm Sci 350(P) & Physics 210(P).
 ATM SCI 520  Advanced Dynamic Meteorology (3 units; U/G)
 Properties of atmospheric sound, gravity, Rossby waves. Baroclinic instability, cyclogenesis, frontogenesis, and the general circulation. Introduction to numerical prediction. Prereq: jr st; Math 234(P), Atm Sci 350(P) & 351(P) or equiv.
 ATM SCI 690  Seminar in Atmospheric Sciences: (13 units; U/G)
 Intensive topical studies of currently active problem areas. May be retaken w/chg in topic to 9 cr max. Satisfies L&S Seminar req. Prereq: jr st; cons instr.
 ATM SCI 690G  Seminar in Atmospheric Sciences: (13 units; U/G)
 Intensive topical studies of currently active problem areas. May be retaken w/chg in topic to 9 cr max. Satisfies L&S Seminar req. Prereq: jr st; cons instr.
 ATM SCI 705  Air Pollution Modeling (3 units; G)
 Computational techniques for determining surface fluxes of heat and momentum. Numerical methods for solving advection and diffusion problems; statistical diffusion modeling. Prereq: grad st; cons instr.
 ATM SCI 711  Cloud Dynamics (3 units; G)
 Atmospheric applications of turbulent flow theory. Nonprecipitating clouds: structure of individual cumulus clouds, stratocumulus and cumulus boundary layers. Precipitating clouds: thunderstorms, squall lines, hurricanes. Prereq: grad st; cons instr.
 ATM SCI 725  Remote Sensing of the Environment (3 units; G)
 Remote sensing technology, data processing, and analysis in meteorology, with application to oceanography and geology. Radar and acoustic sounding. Erts, sms/goes, thermal scanner, conventional weather satellites. Prereq: grad st in Physics, Math, Geog, Geo Sci, Engr, or Atm Sci.
 ATM SCI 750  Nonlinear Time Series Analysis (3 units; G)
 Phase space reconstruction; singular spectrum analysis; prediction; dimension estimation; application of nonlinear time series analysis techniques to selected data sets. Prereq: grad st; cons instr.
 ATM SCI 760  Advanced Cloud, Aerosol & Precipitation Principles, Processes & Interactions (4 units; G)
 (3 hr lc, 2 hr la). Theoretical & experimental look at cloud & precipitation formation, interaction & dissipation microphysics & chemistry aerosol physics & chemistry, & their application. Prereq: grad st; Atm Sci 464(C) or cons instr.
 ATM SCI 761  Advanced Synoptic/Mesoscale Meteorology (3 units; G)
 Advanced analysis techniques for snyoptic/mesoscale diagnoses, case studies of relevant circulation systems; role of planetary, synoptic, and mesoscale flows in system development. Prereq: grad st; cons instr.
 ATM SCI 888  Candidate for Degree (0 units; G)
 Available for graduate students who must meet minimum credit load requirement. Fee for 1 cr assessed. Prereq: grad st.
 ATM SCI 943  Seminar: Hydrology: (3 units; G)
 Retakable w/chg in topic to 9 cr max. Prereq: grad st.
 ATM SCI 950  Seminar on Topics in Atmospheric Sciences: (3 units; G)
 Selected topics in atmospheric dynamics, satellite meteorology, atmospheric & oceanic convection, air & water pollution, numerical prediction remote sensing, & others. Prereq: grad st in physical sciences or engineering. Retakable w/ chg in topic to 9 cr max.
 ATM SCI 990  Master's Thesis (18 units; G)
 Prereq: grad st; cons instr & completed thesis proposal.
 ATM SCI 997  Doctoral Externship (112 units; G)
 Prereq: grad st; admis to candidacy for the PhD.
 ATM SCI 998  Doctoral Dissertation (112 units; G)
 Prereq: grad st; admis to candidacy for PhD.
 ATM SCI 999  Advanced Independent Reading (14 units; G)
 Independent meteorological study. Retakable to 4 cr max. Prereq: grad st & cons instr.
MATH
 MATH 305  Introduction to Mathematical and Computational Modeling (3 units; U/G)
 Construction and analysis of discrete and continuous mathematical models in applied, natural, and social sciences. Elements of programming, simulations, case studies from scientific literature. Counts as repeat of Math 690(675) w/topic Adv Math Models with Apps. Prereq: jr st; grade of C or better in Math 211(P) & one addl 200level or higher Math or MthStat course, or grade of B or better in Math 213(P), or grade of C or better in Math 231(P), or cons instr.
 MATH 305G  Introduction to Mathematical and Computational Modeling (3 units; U/G)
 Construction and analysis of discrete and continuous mathematical models in applied, natural, and social sciences. Elements of programming, simulations, case studies from scientific literature. Counts as repeat of Math 690(675) w/topic Adv Math Models with Apps. Prereq: jr st; grade of C or better in Math 211(P) & one addl 200level or higher Math or MthStat course, or grade of B or better in Math 213(P), or grade of C or better in Math 231(P), or cons instr.
 MATH 313  Linear Programming and Optimization (3 units; U/G)
 Primal and dual formulations of linear programming problems; simplex and related methods of solution; algorithms for transportation; optimization. Prereq: jr st; grade of C or better in Math/ElecEng 234(P) or Math 240(P); or grad st.
 MATH 313G  Linear Programming and Optimization (3 units; U/G)
 Primal and dual formulations of linear programming problems; simplex and related methods of solution; algorithms for transportation; optimization. Prereq: jr st; grade of C or better in Math/ElecEng 234(P) or Math 240(P); or grad st.
 MATH 315  Mathematical Programming and Optimization (3 units; U/G)
 Introduction to operations research. Network analysis; integer programming; game theory; nonlinear programming; dynamic programming. Prereq: jr st, grade of C or better in either Math 234(P) or 240(P), & grade of C or better in either Math 211(P) or 233(P); or cons instr; or grad st.
 MATH 315G  Mathematical Programming and Optimization (3 units; U/G)
 Introduction to operations research. Network analysis; integer programming; game theory; nonlinear programming; dynamic programming. Prereq: jr st, grade of C or better in either Math 234(P) or 240(P), & grade of C or better in either Math 211(P) or 233(P); or cons instr; or grad st.
 MATH 320  Introduction to Differential Equations (3 units; U/G)
 Elementary types and systems of differential equations, series solutions, numerical methods, Laplace transforms, selected applications. No grad cr in Math Sci. Prereq: jr st, grade of C or better in both Math 232(P) & 240(P), or grade of C or better in Math/ElecEng 234(P); or grad st.
 MATH 320G  Introduction to Differential Equations (3 units; U/G)
 Elementary types and systems of differential equations, series solutions, numerical methods, Laplace transforms, selected applications. No grad cr in Math Sci. Prereq: jr st, grade of C or better in both Math 232(P) & 240(P), or grade of C or better in Math/ElecEng 234(P); or grad st.
 MATH 321  Vector Analysis (3 units; U/G)
 Topics selected from vector algebra; scalar and vector fields; line, surface, and volume integrals; theorems of Green, Gauss, and Stokes; vector differential calculus. Prereq: jr st, grade of C or better in Math 233(P); or grad st.
 MATH 322  Introduction to Partial Differential Equations (3 units; U/G)
 Partial differential equations of mathematical physics, boundary value problems in heat flow, vibrations, potentials, etc. Solved by Fourier series; Bessel functions and Legendre polynomials. Prereq: jr st, Math 320(P), & grade of C or better in Math 233(P); or grad st.
 MATH 371  Introduction to Stochastic Models in Finance (3 units; U/G)
 Elementary modeling of financial instruments for students in mathematics, economics, business, etc. Statistical and stochastic tools leading to the BlackScholes model. Real data parameter fitting. Prereq: jr st & one of the following pairs; Econ 413(431)(P) & 506(P), Bus Adm 210(P) & 350(P), Bus Adm 701(P) & 702(P), or Math 234(P) & MthStat 361(P), or cons instr; or grad st.
 MATH 405  Mathematical Models and Applications (3 units; U/G)
 Modeling techniques for analysis and decisionmaking in social and life sciences and industry. Deterministic and stochastic modeling. Topics may vary with instructors. Prereq: jr st; one of: grade of C or better in Math 211(P), grade of B or better in Math 213(P), or grade of C or better in Math 231(P); & grade of C or better in either Math/ElecEng 234(P) or Math 240(P); or grad st.
 MATH 405G  Mathematical Models and Applications (3 units; U/G)
 Modeling techniques for analysis and decisionmaking in social and life sciences and industry. Deterministic and stochastic modeling. Topics may vary with instructors. Prereq: jr st; one of: grade of C or better in Math 211(P), grade of B or better in Math 213(P), or grade of C or better in Math 231(P); & grade of C or better in either Math/ElecEng 234(P) or Math 240(P); or grad st.
 MATH 413  Introduction to Numerical Analysis (3 units; U/G)
 Root finding and solution of nonlinear systems; direct solution of linear systems; interpolation & approximation of functions; least squares; fast Fourier transform; quadrature. Prereq: jr st, grade of C or better in Math 233(C), & grade of C or better in Math/ElecEng 234(C); or grad st.
 MATH 413G  Introduction to Numerical Analysis (3 units; U/G)
 Root finding and solution of nonlinear systems; direct solution of linear systems; interpolation & approximation of functions; least squares; fast Fourier transform; quadrature. Prereq: jr st, grade of C or better in Math 233(C), & grade of C or better in Math/ElecEng 234(C); or grad st.
 MATH 415  Introduction to Scientific Computing (3 units; U/G)
 Nonlinear systems; iterative solution of linear systems; initial value problems in ordinary differential equations; boundary value problems in ordinary and partial differential equations. Prereq: jr st, grade of C or better in Math 233(C), & grade of C or better in Math/ElecEng 234(C); or grad st.
 MATH 415G  Introduction to Scientific Computing (3 units; U/G)
 Nonlinear systems; iterative solution of linear systems; initial value problems in ordinary differential equations; boundary value problems in ordinary and partial differential equations. Prereq: jr st, grade of C or better in Math 233(C), & grade of C or better in Math/ElecEng 234(C); or grad st.
 MATH 417  Computational Linear Algebra (3 units; U/G)
 Direct solution of linear systems; iterative solution of linear systems; least squares; eigenvalue problems. Prereq: jr st & grade of C or better in Math/ElecEng 234(P) or Math 240(P); or grad st.
 MATH 417G  Computational Linear Algebra (3 units; U/G)
 Direct solution of linear systems; iterative solution of linear systems; least squares; eigenvalue problems. Prereq: jr st & grade of C or better in Math/ElecEng 234(P) or Math 240(P); or grad st.
 MATH 423  Complex Analysis (3 units; U/G)
 Complex numbers; definition and properties of analytic functions of a complex variable; conformal mapping; calculus of residues; applications to mathematics and physics. See also Math 713. Prereq: jr st; grade of C or better in Math 233(P); or grad st.
 MATH 431  Modern Algebra with Applications (3 units; U/G)
 Groups, rings, fields, Boolean algebras with emphasis on their applications to computer science and other areas. Does not carry grad cr in math sci. Prereq: jr st & grade of C or better in Math 232(P); or grad st.
 MATH 431G  Modern Algebra with Applications (3 units; U/G)
 Groups, rings, fields, Boolean algebras with emphasis on their applications to computer science and other areas. Does not carry grad cr in math sci. Prereq: jr st & grade of C or better in Math 232(P); or grad st.
 MATH 451  Axiomatic Geometry (3 units; U/G)
 An axiomatic approach to Euclidean and nonEuclidean geometry (historic role of the parallel postulate and models). Dept cons req'd for grad cr in math sci. Prereq: jr st, grade of C or better in both Math 341(P) & Math 232(C); or grad st.
 MATH 451G  Axiomatic Geometry (3 units; U/G)
 An axiomatic approach to Euclidean and nonEuclidean geometry (historic role of the parallel postulate and models). Dept cons req'd for grad cr in math sci. Prereq: jr st, grade of C or better in both Math 341(P) & Math 232(C); or grad st.
 MATH 453  Transformations in Geometry (3 units; U/G)
 Selected topics from vector geometry and geometric transformations such as the study of invariants and conics. Recom for secondary school teachers. Dept cons req'd for grad cr in math sci. Prereq: jr st, grade of C or better in both Math 341(P) & Math 232(C); or grad st.
 MATH 490  Topics in Mathematics: (3 units; U/G)
 Specific topics and any additional prerequisites announced in Schedule of Classes each time course is offered. May be retaken w/chg in topic to 9 cr max. Prereq: jr st; grade of C or better in a Math or MthStat course at the 200 level or above; or grad st.
 MATH 490G  Topics in Mathematics: (3 units; U/G)
 Specific topics and any additional prerequisites announced in Schedule of Classes each time course is offered. May be retaken w/chg in topic to 9 cr max. Prereq: jr st; grade of C or better in a Math or MthStat course at the 200 level or above; or grad st.
 MATH 497  Study Abroad: (112 units; U/G)
 Designed to enroll students in UWM sponsored programs before course work level, content and credits are determined and/or in specially prepared program course work. May be retaken w/chg in topic. Prereq: jr st; acceptance for Study Abroad Prog.
 MATH 511  Symbolic Logic (3 units; U/G)
 Firstorder predicate calculus; formal properties of theoretical systems; chief results of modern mathematical logic; advanced topics such as completeness and computability. CompSci 511, Math 511 & Philos 511 are jointly offered; they count as repeats of one another. Prereq: jr st & either Philos 212(P) or 6 cr in math at the 300level or above.
 MATH 511G  Symbolic Logic (3 units; U/G)
 Firstorder predicate calculus; formal properties of theoretical systems; chief results of modern mathematical logic; advanced topics such as completeness and computability. CompSci 511, Math 511 & Philos 511 are jointly offered; they count as repeats of one another. Prereq: jr st & either Philos 212(P) or 6 cr in math at the 300level or above.
 MATH 521  Advanced Calculus I (3 units; U/G)
 Fundamental notions of sets and functions; limits, continuity; Riemann integral, improper integral; infinite series; uniform convergence; power series; improper integrals with a parameter. Prereq: jr st; grades of C or better in Math 232(P) & 341(P); or grad st.
 MATH 521G  Advanced Calculus I (3 units; U/G)
 Fundamental notions of sets and functions; limits, continuity; Riemann integral, improper integral; infinite series; uniform convergence; power series; improper integrals with a parameter. Prereq: jr st; grades of C or better in Math 232(P) & 341(P); or grad st.
 MATH 522  Advanced Calculus II (3 units; U/G)
 Linear functions; differentiation of functions of several variables (implicit functions, Jacobians); change of variable in multiple integrals; integrals over curves, surfaces; Green, Gauss, Stokes theorems. Prereq: jr st, Math 521(P), grade of C or better in Math 233(P), & grade of C or better in either Math 234(P) or 240(P); or grad st.
 MATH 522G  Advanced Calculus II (3 units; U/G)
 Linear functions; differentiation of functions of several variables (implicit functions, Jacobians); change of variable in multiple integrals; integrals over curves, surfaces; Green, Gauss, Stokes theorems. Prereq: jr st, Math 521(P), grade of C or better in Math 233(P), & grade of C or better in either Math 234(P) or 240(P); or grad st.
 MATH 531  Modern Algebra (3 units; U/G)
 Integers; groups; rings; fields; emphasis on proofs. Prereq: jr st; grade of C or better in Math 341(P).
 MATH 531G  Modern Algebra (3 units; U/G)
 Integers; groups; rings; fields; emphasis on proofs. Prereq: jr st; grade of C or better in Math 341(P).
 MATH 535  Linear Algebra (3 units; U/G)
 Vector spaces; linear transformations and matrices; characteristic values and vectors; canonical forms; bilinear, quadratic, and Hermitian forms; selected applications. Prereq: jr st, grade of C or better in either Math 234(P) or 240(P), & grade of C or better in Math 341(P); or grad st.
 MATH 535G  Linear Algebra (3 units; U/G)
 Vector spaces; linear transformations and matrices; characteristic values and vectors; canonical forms; bilinear, quadratic, and Hermitian forms; selected applications. Prereq: jr st, grade of C or better in either Math 234(P) or 240(P), & grade of C or better in Math 341(P); or grad st.
 MATH 537  Number Theory (3 units; U/G)
 Number theoretic functions; distribution of primes; Diophantine approximation; partitions; additive number theory; quadratic reciprocity. Prereq: jr st, grade of C or better in both Math 232(P) & 341(P); or grad st.
 MATH 537G  Number Theory (3 units; U/G)
 Number theoretic functions; distribution of primes; Diophantine approximation; partitions; additive number theory; quadratic reciprocity. Prereq: jr st, grade of C or better in both Math 232(P) & 341(P); or grad st.
 MATH 551  Elementary Topology (3 units; U/G)
 General theory of point sets in Euclidean spaces, with emphasis on topology of twodimensional and threedimensional spaces; elementary notions of metric spaces; applications. Prereq: jr st; grades of C or better in Math 233(P) & 341(P); or grad st.
 MATH 551G  Elementary Topology (3 units; U/G)
 General theory of point sets in Euclidean spaces, with emphasis on topology of twodimensional and threedimensional spaces; elementary notions of metric spaces; applications. Prereq: jr st; grades of C or better in Math 233(P) & 341(P); or grad st.
 MATH 553  Differential Geometry (3 units; U/G)
 The theory of curves and surfaces by differential methods. Prereq: jr st, grade of C or better in all of Math 233(P), 234(P) & 341(P); or grad st.
 MATH 571  Introduction to Probability Models (3 units; U/G)
 Probability review, Markov chains in discrete and continuous time. Random walks, branching processes, birth and death processes. Queuing theory. Applications to physical sciences, engineering, mathematics. Prereq: jr st; grade of C or better in Math 233(P); grade of C or better in Math/ElecEng 234(P) or in both Math 240(P) & 320(P); & one calculusbased course in statistics or probability at the 300 level or above; or grad st.
 MATH 571G  Introduction to Probability Models (3 units; U/G)
 Probability review, Markov chains in discrete and continuous time. Random walks, branching processes, birth and death processes. Queuing theory. Applications to physical sciences, engineering, mathematics. Prereq: jr st; grade of C or better in Math 233(P); grade of C or better in Math/ElecEng 234(P) or in both Math 240(P) & 320(P); & one calculusbased course in statistics or probability at the 300 level or above; or grad st.
 MATH 575  High School Mathematics from an Advanced Viewpoint (3 units; U/G)
 Number systems; algebra of polynomials; theory of equations; functions; modeling; geometric measurement; geometric transformations; connections between advanced mathematics and high school topics. Counts as repeat of Math 690(675) w/similar topic. Prereq: jr st, either Math 451(P) or 453(P), & either Math 431(P) or 531(P); or cons instr; or grad st.
 MATH 575G  High School Mathematics from an Advanced Viewpoint (3 units; U/G)
 Number systems; algebra of polynomials; theory of equations; functions; modeling; geometric measurement; geometric transformations; connections between advanced mathematics and high school topics. Counts as repeat of Math 690(675) w/similar topic. Prereq: jr st, either Math 451(P) or 453(P), & either Math 431(P) or 531(P); or cons instr; or grad st.
 MATH 581  Introduction to the Theory of Chaotic Dynamical Systems (3 units; U/G)
 Iterated mappings, one parameter families, attracting and repelling periodic orbits, topological transitivity, Sarkovski's theorem, chaos, bifurcation theory, period doubling route to chaos, horseshoe maps, attractors. Prereq: jr st & Math 521(P), 529(P) or 621(P), or cons instr; or grad st.
 MATH 601  Advanced Engineering Mathematics I (3 units; U/G)
 Sequences and series, elementary complex analysis; Fourier series; linear and nonlinear ordinary differential equations; matrix theory, elementary functional analysis; elementary solution of partial differential equations. Prereq: jr st; grade of C or better in both of Math 233(P) and Math/ElecEng 234(P); 3 cr Math at 300level or above; or cons instr; or grad st.
 MATH 601G  Advanced Engineering Mathematics I (3 units; U/G)
 Sequences and series, elementary complex analysis; Fourier series; linear and nonlinear ordinary differential equations; matrix theory, elementary functional analysis; elementary solution of partial differential equations. Prereq: jr st; grade of C or better in both of Math 233(P) and Math/ElecEng 234(P); 3 cr Math at 300level or above; or cons instr; or grad st.
 MATH 602  Advanced Engineering Mathematics II (3 units; U/G)
 Continuation of Math 601. Partial differential equations, Fourier and Laplace transforms, convolutions, special functions, mathematical modeling. Prereq: jr st; Math 601(P).
 MATH 602G  Advanced Engineering Mathematics II (3 units; U/G)
 Continuation of Math 601. Partial differential equations, Fourier and Laplace transforms, convolutions, special functions, mathematical modeling. Prereq: jr st; Math 601(P).
 MATH 615  Numerical Solution of Partial Differential Equations (3 units; U/G)
 Finite difference solution of elliptic boundary value problems and of evolution problems; solution of hyperbolic conservation laws; finite volume methods; finite element methods. Prereq: jr st; Math 413(P), 415(414)(P), or 417(416)(P); Math 322(P) or 602(P); or cons instr.
 MATH 615G  Numerical Solution of Partial Differential Equations (3 units; U/G)
 Finite difference solution of elliptic boundary value problems and of evolution problems; solution of hyperbolic conservation laws; finite volume methods; finite element methods. Prereq: jr st; Math 413(P), 415(414)(P), or 417(416)(P); Math 322(P) or 602(P); or cons instr.
 MATH 617  Optimization (3 units; U/G)
 Unconstrained and constrained optimization: linear, nonlinear, and dynamic programming; barrier, penalty, and Lagrangian methods; KarushKuhnTucker theory, quadratic, and sequential quadratic programming; evolutionary algorithms. Prereq: jr st; Math 321(P) or 602(P); or grad st or cons instr.
 MATH 621  Introduction to Analysis I (3 units; U/G)
 Topology of Euclidean space; continuity; differentiation of real and vectorvalued functions; RiemannStieltjes integration. Prereq: jr st: grades of C or better in Math 233(P), 341(P), & either 234(P) or 240(P); cons dept advisor; or grad st.
 MATH 621G  Introduction to Analysis I (3 units; U/G)
 Topology of Euclidean space; continuity; differentiation of real and vectorvalued functions; RiemannStieltjes integration. Prereq: jr st: grades of C or better in Math 233(P), 341(P), & either 234(P) or 240(P); cons dept advisor; or grad st.
 MATH 622  Introduction to Analysis II (3 units; U/G)
 Continues Math 621. Sequences and series of functions; uniform convergence; power series; functions of several variables; inverse and implicit function theorems; differential forms; Stokes' theorem. Prereq: jr st; Math 621(P) or cons instr; or grad st.
 MATH 622G  Introduction to Analysis II (3 units; U/G)
 Continues Math 621. Sequences and series of functions; uniform convergence; power series; functions of several variables; inverse and implicit function theorems; differential forms; Stokes' theorem. Prereq: jr st; Math 621(P) or cons instr; or grad st.
 MATH 631  Modern Algebra I (3 units; U/G)
 Group theory, including normal subgroups, quotients, permutation groups, Sylow's theorems, Abelian groups; field theory; linear algebra over general fields. Prereq: jr st; grade of C or better in Math 341(P) & either Math 234(P) or 240(P); cons dept advisor; or grad st.
 MATH 631G  Modern Algebra I (3 units; U/G)
 Group theory, including normal subgroups, quotients, permutation groups, Sylow's theorems, Abelian groups; field theory; linear algebra over general fields. Prereq: jr st; grade of C or better in Math 341(P) & either Math 234(P) or 240(P); cons dept advisor; or grad st.
 MATH 632  Modern Algebra II (3 units; U/G)
 Continuation of Math 631. Ring theory, including ideals, quotient rings, Euclidean rings, polynomial rings, unique factorization; modules, including vector spaces, linear transformations, canonical forms; bilinear forms. Prereq: jr st; Math 631(P) or cons instr; or grad st.
 MATH 632G  Modern Algebra II (3 units; U/G)
 Continuation of Math 631. Ring theory, including ideals, quotient rings, Euclidean rings, polynomial rings, unique factorization; modules, including vector spaces, linear transformations, canonical forms; bilinear forms. Prereq: jr st; Math 631(P) or cons instr; or grad st.
 MATH 690  Topics in Mathematics: (3 units; U/G)
 Specific topics and any additional prerequisites announced in Schedule of Classes each time course is offered. May be retaken w/chg in topic to 9 cr max. Prereq: jr st, at least one U/G Math or MthStat course; cons instr; or grad st.
 MATH 701  Industrial Mathematics I (3 units; G)
 Elementary functional analysis, wavelets, control theory. Use of mathematical software emphasized throughout. Prereq: grad st in nat sci discipline; Math 522(P) or 602(P) or 622(P).
 MATH 702  Industrial Mathematics II (3 units; G)
 Optimal control theory, digital signal processing, image processing, linear programming, nonlinear optimation, artificial neural networks. Use of mathematical software emphasized throughout. Prereq: grad st in nat sci discipline; Math 701(P).
 MATH 703  Boundary Value Problems (3 units; G)
 Analytic methods for PDE's in mathematical physics, emphasis on green's functions. Theory of distributions, fundamental solutions, generalized eigenfunction expansions, generalized fourier and laplace transforms. Prereq: grad st; Math 322(P) & 623(P).
 MATH 709  Differential Geometry (3 units; G)
 The theory of curves, surfaces, and manifolds in modern terminology. Global results on closed surfaces, geodesics, differential forms and tensor calculus.introduction to riemanniam geometry. Prereq: grad st; Math 522(P) or 622(P).
 MATH 711  Theory of Functions of a Real Variable I (3 units; G)
 Equivalence relations; cardinal and ordinal numbers; topology of real line; cantor and borel sets; lebesgue measure on real line; baire and measurable functions; lebesgue integral. Prereq: grad st; Math 522(P) & 551(P); or Math 622(P).
 MATH 712  Theory of Functions of a Real Variable II (3 units; G)
 Lebesgue integration; modes of convergence; lp spaces; vitali covering and lebesgue density theorems; dini derivates; differentiation; fundamental theorem of the lebesgue integral calculus; fubini's theorem. Prereq: grad st; Math 711(P).
 MATH 713  Theory of Functions of a Complex Variable I (3 units; G)
 Complex numbers; linear transformations; elementary functions; conformal mapping; complex integration; infinite sequences; dirichlet problem; multivalued functions. Prereq: grad st; Math 522(P) or 621(P).
 MATH 714  Theory of Functions of a Complex Variable II (3 units; G)
 Continuation of Math 713. Prereq: grad st; Math 713(P).
 MATH 715  Numerical Analysis (3 units; G)
 Interpolation and approximation; differentiation and quadrature; numerical solution of ordinary differential equations; solution of linear and nonlinear algebraic equations. Prereq: grad st; Math 413(P); Math 521(P) or 621(P).
 MATH 716  Ordinary Differential Equations (3 units; G)
 Existence and uniqueness theorems for systems of ode; qualitative properties of solutions, including stability and asymptotic behavior; general theory of linear systems; sturmliouville problems. Prereq: grad st; Math 522(P) or 622(P).
 MATH 719  Partial Differential Equations (3 units; G)
 First and second order equations; characteristics, cauchy problem; classical solutions of linear elliptic, parabolic and hyperbolic equations. Prereq: grad st; Math 522(P) or 622(P); math 320(P).
 MATH 721  Abstract Measure and Integration (3 units; G)
 General theory of measures and integration; differentiation of set functions; relation to stochastic variables; atomic measures; haar measure and integral applications to probability theory. Prereq: grad st; Math 712(P).
 MATH 726  Introduction to Functional Analysis (3 units; G)
 Basic notions of functional analysis in hilbert space will be introduced. The concepts will be illustrated by applications to elementary differential and integral equation problems. Prereq: grad st; Math 522(P) or 622(P).
 MATH 731  Abstract Algebra I (3 units; G)
 Basic course which is prerequisite for all other 700799 level courses in algebra; groups, rings, fields, galois theory, modules, and categories. Prereq: grad st; Math 632(P); cons instr.
 MATH 732  Abstract Algebra II (3 units; G)
 Continuation of Math 731. Prereq: grad st; Math 731(P).
 MATH 735  Theory of Groups (3 units; G)
 Topics selected from permutation groups; representations of groups and algebras; group algebras; group characters; extension problems; simple groups; solvable and nilpotent groups. Prereq: grad st; Math 732(P).
 MATH 736  Theory of Rings and Modules I (3 units; G)
 Noetherian and artinian rings and modules; primitive, prime and simple rings and ideals; radicals; localization; morita theory; construction and study of special classes of rings. Prereq: grad st; Math 732(P).
 MATH 737  Theory of Rings and Modules II (3 units; G)
 Continuation of Math 736. Prereq: grad st; Math 736(P) or cons instr.
 MATH 751  Introductory Topology I (3 units; G)
 Fundamental properties and examples of topological spaces and continuous functions, including compactness, connectedness, metrizability, completeness, product and quotient spaces, homeomorphisms, embedding, extension, and euclidean spaces. Prereq: grad st; Math 522(P) or 621(P).
 MATH 752  Introductory Topology II (3 units; G)
 Continuation of Math 751. Prereq: grad st; Math 751(P).
 MATH 753  Introduction to Algebraic Topology I (3 units; G)
 Homology theory; complexes and simplicial homology theory; general homology theories; cohomology rings; applications to manifolds, fixed point theorems, etc. Prereq: grad st; Math 632(P); Math 551(P) or 751(P) or cons instr.
 MATH 754  Introduction to Algebraic Topology II (3 units; G)
 Continuation of Math 753. Prereq: grad st; Math 753(P).
 MATH 767  Statistical Methods for Engineers and Scientists (3 units; G)
 Elementary baysian decision theory; prior posterior and predictive distributions; posterior and preposterior analysis of two action decision problems; concept of likelihood functions for binomial, poisson, exponential and normal distributions; simple and multiple regression analysis; introduction to autoregressive models. Not open to students who have cr in ElecEng 767, which is identical to Math 767. Prereq: grad st; Math 362(P) or math 467(P).
 MATH 768  Applied Stochastic Processes (3 units; G)
 Concepts in queueing theory; exponential channels; applications of markov chains to queueing problems; queue disciplines with priorities. Not open to students who have cr in ElecEng 768, which is identical to Math 768. Prereq: grad st; Math 361(P) or math 467(P).
 MATH 771  Theory of Probability (3 units; G)
 Measuretheoretic foundations; limitlaw theorems; weak and strong laws of large numbers; central limit problem; conditional expectations, martingales; stochastic processes. Prereq: grad st; Math 471(C) or 712(C).
 MATH 781  Iterated Maps as Dynamical Systems (3 units; G)
 Periodic, recurrent and nonwandering points, kneading theory, unstable manifolds, unimodal mappings, turbulent and chaotic maps, symbolic dynamics, structural stability, topological conjugacy, topological dynamics. Prereq: grad st; Math 711(P) or cons instr.
 MATH 790  Master's Thesis (13 units; G)
 Cr count toward masters degree only if student completes thesis option. Prereq: grad st; cons instr.
 MATH 791  Master's Seminar (13 units; G)
 May not be taken for cr more than once. Prereq: grad st; cons instr.
 MATH 792  Industrial Internship (13 units; G)
 Students earn credits for serving in an industrial internship that involves work of an advanced mathematical nature. They must prepare a report based on the internship. Retakable w/chg in topic to 6 cr max. Prereq: grad st; cons instr.
 MATH 793  Scientific Computational Laboratory: (12 units; G)
 Retakable w/chg in topic to 6 cr max. Prereq: grad st; Math 715(C).
 MATH 799  Seminar in Mathematics: (13 units; G)
 Specific topics and any additional prerequisites announced in Timetable each time course is offered. Retakable w/chg in topic to 9 cr max. Prereq: grad st & cons instr.
 MATH 801  Topics in Applied Mathematics: (3 units; G)
 Specific topics and any additional prerequisites will be announced in the Timetable each time the course is offered. Retakable w/chg in topic to 9 cr max. Prereq: grad st; cons instr.
 MATH 807  Group Theory and Its Applications to Physics (3 units; G)
 Representations of discrete and continuous groups, including rotation groups, unitary groups and crystal point and space groups. Symmetries of elementary particles. Molecular obitals, energy bands. Counts as a repeat of Physics 807. Prereq: grad st; Physics 532(P).
 MATH 809  Topics in Differential Geometry: (13 units; G)
 Specific topics and any additional prerequisites will be announced in the Timetable each time the course is offered. Topics may be selected from Riemannian geometry, minimal surfaces and surfaces of prescribed mean curvature, geometric partial differential equations, or related areas of geometry. Retakable w/chg in topic to 9 cr max. Prereq: grad st; cons instr.
 MATH 813  Numerical Solution of Ordinary Differential Equations (3 units; G)
 Methods for initial value and boundary value problems; stiff equations, singular points and bifurcation. Prereq: grad st; Math 715(P).
 MATH 814  Numercal Solution of Partial Differential Equations (3 units; G)
 Finite difference and finite element methods for linear elliptic, parabolic and hyperbolic equations; nonlinear equations. Prereq: grad st; Math 715(P).
 MATH 815  Topics in Numerical Analysis: (3 units; G)
 Retakable w/chg in topic to 9 cr max. Prereq: grad st; Math 715(P).
 MATH 816  Advanced Ordinary Differential Equations (3 units; G)
 Existence and uniqueness theorems; singularity of solutions; oscillation and comparison theorems; poincarebendixon theory. Prereq: grad st; Math 716(P).
 MATH 817  Advanced Ordinary Differential Equations II (3 units; G)
 Continuation of Math 816; dynamical systems, bifurcation theory, topological methods. Prereq: grad st; Math 816(P).
 MATH 821  Advanced Topics in Real Analysis: (3 units; G)
 Specific topics and any additional prerequisites will be announced in the Timetable each time the course is offered. Retakable w/chg in topic to 9 cr max. Prereq: grad st; Math 712(P).
 MATH 825  Functional Analysis (3 units; G)
 Basic theorems of bspaces and fspaces including the closed graph; HahnBanach and BanachSteinhaus theorems; Banach algebras; generalized functions; spectral theory. Prereq: grad st; Math 712(P).
 MATH 841  Advanced Topics in Algebra: (3 units; G)
 Specific topics and any additional prerequisites will be announced in the Timetable each time the course is offered. Retakable w/chg in topic to 9 cr max. Prereq: grad st; Math 732(P); cons instr.
 MATH 843  Homological Algebra I (3 units; G)
 Modules; diagrams; categories; functors; complexes; cohomology; extensions; resolutions; injective and projective systems; graded modules; homological dimension; spectral sequences; derived functors. Prereq: grad st; Math 731(P).
 MATH 844  Homological Algebra II (3 units; G)
 Continuation of Math 843. Prereq: grad st; Math 843(P).
 MATH 851  Advanced Topics in Topology: (3 units; G)
 Specific topics and any additional prerequisites will be announced in the Timetable each time the course is offered. Retakable w/chg in topic to 9 cr max. Prereq: grad st; Math 752(P); cons instr.
 MATH 873  Advanced Topics in Probability: (3 units; G)
 Specific topics and any additional prerequisites will be announced in the Timetable each time the course is offered. Retakable w/chg in topic to 9 cr max. Prereq: grad st; cons instr.
 MATH 881  Topics in Nonlinear Dynamics: (3 units; G)
 Specific topics and any additional prerequisites will be announced in the Timetable each time the course is offered. Retakable w/chg in topic to 9 cr max. Prereq: grad st; Math 711(P); cons instr.
 MATH 888  Candidate for Degree (0 units; G)
 Available for graduate students who must meet minimum credit load requirement. Fee for 1 cr assessed. Prereq: grad st.
 MATH 990  Reading and Research (16 units; G)
 To be arranged with your instructor and department chair. Retakable. Prereq: grad st.
MTHSTAT
 MTHSTAT 361  Introduction to Mathematical Statistics I (3 units; U/G)
 Probability spaces; discrete and continuous, univariate and multivariate distributions; moments; independence, random sampling, sampling distributions; normal and related distributions; point and interval estimation. Not recom for grad students in math, or students not planning to take MthStat 362. Prereq: jr st; Math 233(P).
 MTHSTAT 361G  Introduction to Mathematical Statistics I (3 units; U/G)
 Probability spaces; discrete and continuous, univariate and multivariate distributions; moments; independence, random sampling, sampling distributions; normal and related distributions; point and interval estimation. Not recom for grad students in math, or students not planning to take MthStat 362. Prereq: jr st; Math 233(P).
 MTHSTAT 362  Introduction to Mathematical Statistics II (3 units; U/G)
 Testing statistical hypothesis; linear hypothesis; regression; analysis of variance and experimental designs; distributionfree methods; sequential methods. Not recom for grad students in math. Prereq: jr st; MthStat 361(P).
 MTHSTAT 362G  Introduction to Mathematical Statistics II (3 units; U/G)
 Testing statistical hypothesis; linear hypothesis; regression; analysis of variance and experimental designs; distributionfree methods; sequential methods. Not recom for grad students in math. Prereq: jr st; MthStat 361(P).
 MTHSTAT 462  Data Analysis and Graphing Using SASII (2 units; U/G)
 Continuation of MthStat 461. Procedures GLM, LIFEREG, LIFETEST, LOGISTIC, PROBIT and advanced GRAPHING. Offered second half of sem. U cr does not count toward math sci major. Prereq: jr st; MthStat 461(P) or cons instr.
 MTHSTAT 465  Introductory Mathematical Statistics for Social Sciences and Education (3 units; U/G)
 Probability distributions; parameter estimation and confidence intervals; hypothesis testing; applications. Not open for cr to students w/cr in MthStat 467, 362, or for grad cr in math. Not open for cr toward major in math except in School of Education. Prereq: jr st; Math 211(P) or 232(P).
 MTHSTAT 467  Introductory Statistics for Physical Sciences and Engineering Students (3 units; U/G)
 Concepts of probability and statistics; probability distributions of engineering applications; sampling distributions; hypothesis testing, parameter estimation; experimental design; regression analysis. Not open for cr for Math majors or students with cr in MthStat 362 or 465. Prereq: jr st; Math 233(P).
 MTHSTAT 469  Biostatistics (3 units; U/G)
 Simple distributions, estimation and hypothesis testing, simple regression, analysis of variance, nonparametric methods in biology. Demography and vital statistics and bioassay and clinical trials. Not allowed as part of core curric for Math majors. Not open for cr to students with cr in MthStat 569 & not open for grad cr in Math. Prereq: jr st; an elementary stats course.
 MTHSTAT 562  Design of Experiments (3 units; U/G)
 Latin squares; incomplete block designs; factorial experiments; confounding; partial confounding; splitplot experiments; fractional replication. Prereq: jr st; MthStat 362(P); Math 234(P) or 240(P).
 MTHSTAT 563  Regression Analysis (3 units; U/G)
 Straight line, polynomial and multiple regression; multiple and partial correlation; testing hypotheses in regression; residual analysis. Prereq: jr st; MthStat 467(P) or 362(P).
 MTHSTAT 563G  Regression Analysis (3 units; U/G)
 Straight line, polynomial and multiple regression; multiple and partial correlation; testing hypotheses in regression; residual analysis. Prereq: jr st; MthStat 467(P) or 362(P).
 MTHSTAT 564  Time Series Analysis (3 units; U/G)
 Autocorrelation; spectral density; linear models; forecasting; model identification and estimation. Prereq: jr st; MthStat 362(P).
 MTHSTAT 564G  Time Series Analysis (3 units; U/G)
 Autocorrelation; spectral density; linear models; forecasting; model identification and estimation. Prereq: jr st; MthStat 362(P).
 MTHSTAT 565  Nonparametric Statistics (3 units; U/G)
 Sign, rank and permutation tests; tests of randomness and independence; methods for discrete data and zeroes and ties; power and efficiency of nonparametric tests. Prereq: jr st; MthStat 362(P).
 MTHSTAT 566  Computational Statistics (3 units; U/G)
 Basics of programming and optimization techniques; resampling, bootstrap, and Monte Carlo methods; design and analysis of simulation studies. Prereq: jr st; MthStat 362(P) or cons instr.
 MTHSTAT 566G  Computational Statistics (3 units; U/G)
 Basics of programming and optimization techniques; resampling, bootstrap, and Monte Carlo methods; design and analysis of simulation studies. Prereq: jr st; MthStat 362(P) or cons instr.
 MTHSTAT 568  Multivariate Statistical Analysis (3 units; U/G)
 Multivariate normal distribution; Wishart distribution; Hotelling's T2; multivariate normal distribution; multivariate analysis of variance; classification problems. Prereq: jr st; MthStat 362(P); Math 234(P) or 240(P).
 MTHSTAT 568G  Multivariate Statistical Analysis (3 units; U/G)
 Multivariate normal distribution; Wishart distribution; Hotelling's T2; multivariate normal distribution; multivariate analysis of variance; classification problems. Prereq: jr st; MthStat 362(P); Math 234(P) or 240(P).
 MTHSTAT 596  Actuarial Statistics I: Fitting of Loss Models (3 units; U/G)
 Statistical modeling of insurance data. Model specification, fitting and validation. Measures of confidence for modelbased decisions. Prereq: jr st; B or better in each Math 234(P) and MthStat 362(P); CompSci 151(P) or 201(P); or cons instr.
 MTHSTAT 597  Actuarial Statistics II: Credibility, Risk Measures and Related Topics (3 units; U/G)
 Statistical techniques for insurance data. Credibility and ratemaking. Risk measures. Dependent risks and copulas. Simulations. Prereq: jr st; B or better in each Math 234(P) and MthStat 362(P); CompSci 151(P) or 201(P); or cons instr.
 MTHSTAT 691  Actuarial Models I: Life Contingencies (3 units; U/G)
 Modeling and valuation of cash flows dependent on death, survival and other random events. Survival models for single and multiple risks. Life insurances and annuities. Prereq: jr st; B or better in each Math 571(P) and Math 311(P); or cons instr.
 MTHSTAT 691G  Actuarial Models I: Life Contingencies (3 units; U/G)
 Modeling and valuation of cash flows dependent on death, survival and other random events. Survival models for single and multiple risks. Life insurances and annuities. Prereq: jr st; B or better in each Math 571(P) and Math 311(P); or cons instr.
 MTHSTAT 692  Actuarial Models II: Financial Economics (3 units; U/G)
 Modeling and managing of financial risks. Interest rate models. Valuation of derivatives securities. Risk management. Prereq: jr st; B or better in each Math 571(P) and Math 311(P); or cons instr.
 MTHSTAT 692G  Actuarial Models II: Financial Economics (3 units; U/G)
 Modeling and managing of financial risks. Interest rate models. Valuation of derivatives securities. Risk management. Prereq: jr st; B or better in each Math 571(P) and Math 311(P); or cons instr.
 MTHSTAT 761  Mathematical Statistics I (3 units; G)
 Probability and distribution theory; point and interval estimation; testing hypotheses; large sample inference; nonparametric inference; sequential analysis. Prereq: grad st; Math 522(C) or 622(C).
 MTHSTAT 762  Mathematical Statistics II (3 units; G)
 Continuation of MthStat 761. Prereq: grad st; MthStat 761(P).
 MTHSTAT 795  Actuarial Risk Theory (3 units; G)
 Risk models; premium principles; reinsurance contracts; ruin theory; ordering of risks; bonusmalus systems; IBNR techniques. Prereq: grad st; Math 571(P) & MthStat 596(P), or cons instr
 MTHSTAT 863  Hypothesis Testing (3 units; G)
 Exponential families; uniformly mostpowerful tests; least favorable priors; unbiased tests; invariant tests; applications to exponential families and the general linear hypothesis. Prereq: grad st; MthStat 762(P).
 MTHSTAT 869  Advanced Topics in Mathematical Statistics: (3 units; G)
 Specific topics and any additional prerequisites will be announced in the Timetable each time the course is offered. Retakable w/chg in topic to 9 cr max. Prereq: grad st; MthStat 762(P).