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 math-staff@uwm.edu.

**Important Changes as of 2016**

- 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: 591-593, 691, 692, 795, and 599 capstone.
- Math 768-771 and Math 751-752 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 (fall-spring)
- 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

## Course Listings

**Undergraduate (U and U/G): ATM SCI**

### ATM 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 lab-dis. 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**- First-Year 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 First-Year Sem (course numbers 192, 193, 194). Prereq: none.
**ATM SCI 199**- Independent Study (1-3 units; U)- For further information, consult dept chair. Retakable 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 (1-6 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. Retakable to 6 cr max. Prereq: jr st; 2.50 gpa; cons supervising faculty member.
**ATM SCI 297**- Study Abroad: (1-12 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. Retakable w/chg in topic. Prereq: acceptance for Study Abroad Prog.
**ATM SCI 299**- Ad Hoc: (1-6 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. Retakable w/chg in topic. Prereq: none; add'l prereqs may be assigned to specific topic.
**ATM SCI 330**- Air-Pollution 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 global-scale 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, quasi-geostrophy; 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; quasi-geostrophy 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; synoptic-scale structure and dynamics; equivalent barotropic model; vertical motions; introduction to and application of quasi-geostrophic 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 quasi-geostrophic theory to Q-vectors; isentropic potential vorticity applied to mid-latitude weather systems; fronts and jets. Prereq: jr st; Atm Sci 360(P).
**ATM SCI 381**- Honors Seminar: (3 units; U)- Selected topics. Retakable w/chg in topic to 9 cr max. Prereq: soph st; Honors 200(P); cons Honors College dir.
**ATM SCI 405**- Atmospheric Science for in-Service Teachers: (1-3 units; U/G)- Basic, advanced or new topics in atmospheric sciences for in-service teachers. Retakable w/chg in topic to 9 cr max. Prereq: in-service 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 surface-forced 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: (1-12 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. Retakable w/chg in topic. Prereq: jr st; acceptance for Study Abroad Prog.
**ATM SCI 499**- Ad Hoc: (1-6 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. Retakable 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; boundary-layer profiles of wind, temperature and moisture; turbulence and boundary-layer 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. Retakable w/chg in topic to 2 cr max. Prereq: sr st; cons instr.
**ATM SCI 690**- Seminar in Atmospheric Sciences: (1-3 units; U/G)- Intensive topical studies of currently active problem areas. Retakable 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 (1-6 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. Retakable to 6 cr max. Prereq: jr st; 300-level or above course in atm sci; 3.0 gpa in the major; cons supervising faculty.
**ATM SCI 699**- Advanced Independent Reading (1-3 units; U)- Independent meteorological study. Retakable 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 Fin Aid & enrollment verification. Prereq: Placement level E or D.
**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 D.
**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 D.
**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: C or better in Math 92.
**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. Prereq: math placement level C.
**MATH 105**- Intermediate Algebra (3 units; U)- Algebraic techniques with polynomials, rational expressions, equations and inequalities, exponential and logarithmic functions, rational exponents, systems of linear equations. Not open for cr to students who have cr in Math 108(ER). Prereq: math placement level C.
**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. Not open for credit for students who have cr in Math 105(ER). Prereq: C or better Math 98.
**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 AB.
**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 B.
**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 B.
**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 problem-solving strategies. Prereq: Math placement level A, AB, B, or C & regis in elementary, early childhood, or exceptional educ curric.
**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**- First-Year 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 First-Year Sem (course numbers 192, 193, 194). Prereq: none.
**MATH 199**- Independent Study (1-3 units; U)- Regularly offered courses may not be taken as Independent Study. Retakable 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 B.
**MATH 211**- Survey in Calculus and Analytic Geometry (4 units; U)- A one-semester survey with applications to business administration, economics, and non-physical 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 B.
**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 A.
**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 of 6 cr in combination of Math 221 & 222 may count toward Honors College reqs. Prereq: math placement level A+; cons instr or Honors College dir.
**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 213. Prereq: math placement level A.
**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. Three-dimensional 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. No cr for students with cr in Math 240. 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. No cr for students with cr in Math 234. Prereq: Math placement level A or grade of C or better in a Math or MthStat course numbered 200 or higher.
**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 problem-solving 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 K-8 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 K-8 teachers. Geometry as measuring tool-congruence, similarity, area, volume, and coordinates; geometry as axiomatic system-definitions, 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. Retakable w/chg in topic to 9 cr max. Prereq: satisfaction of Quantitative Literacy Part A GER.
**MATH 297**- Study Abroad: (1-12 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. Retakable w/chg in topic. Prereq: acceptance for Study Abroad Prog.
**MATH 299**- Ad Hoc: (1-6 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. Retakable 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 200-level 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 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 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 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)- Goal: 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 A.
**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. Retakable 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 OWC-A.
**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 Black-Scholes 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 non-mathematicians the characteristic features of mathematical thought. Only H.S. algebra and geometry assumed. Retakable 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 decision-making 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 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 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 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 451**- Axiomatic Geometry (3 units; U/G)- An axiomatic approach to Euclidean and non-Euclidean 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 (1-6 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. Retakable to 6 cr max. Prereq: jr st; 6 cr 300-level 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. Retakable 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: (1-12 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. Retakable w/chg in topic. Prereq: jr st; acceptance for Study Abroad Prog.
**MATH 499**- Ad Hoc: (1-6 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. Retakable w/chg in topic. Prereq: jr st; add'l prereqs may be assigned to specific topic.
**MATH 511**- Symbolic Logic (3 units; U/G)- First-order 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 300-level 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 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 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 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 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 551**- Elementary Topology (3 units; U/G)- General theory of point sets in Euclidean spaces, with emphasis on topology of two-dimensional and three-dimensional 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 calculus-based 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 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. Retakable 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. Retakable 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 300-level 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 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 617**- Optimization (3 units; U/G)- Unconstrained and constrained optimization: linear, nonlinear, and dynamic programming; barrier, penalty, and Lagrangian methods; Karush-Kuhn-Tucker 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 vector-valued functions; Riemann-Stieltjes 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 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 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 690**- Topics in Mathematics: (3 units; U/G)- Specific topics and any additional prerequisites announced in Schedule of Classes each time course is offered. Retakable 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 (1-3 units; U)- See Advanced Independent Study. For further information, consult dept chair. Retakable 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**- First-Year 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 First-Year Sem (course numbers 192, 193, 194). Prereq: none.
**MTHSTAT 199**- Independent Study (1-3 units; U)- For further information, consult dept chair. Retakable 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: (1-6 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. Retakable 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 362**- Introduction to Mathematical Statistics II (3 units; U/G)- Testing statistical hypothesis; linear hypothesis; regression; analysis of variance and experimental designs; distribution-free methods; sequential methods. Not recom for grad students in math. Prereq: jr st; MthStat 361(P).
**MTHSTAT 461**- Data Analysis and Graphing Using SAS-I (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 SAS-II (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 (1-6 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. Retakable to 6 cr max. Prereq: jr st; 6 cr 300-level or above in Math or MthStat; 2.5 gpa in the major; cons supervising faculty member.
**MTHSTAT 499**- Ad Hoc: (1-6 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. Retakable 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; split-plot 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 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 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 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 591**- Foundations of Professional Practice in Actuarial Science (1 units; U)- Lecture and discussions on professional topics such as health, pension, life, casualty, regulation. Retakable 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 Math 311(P) or 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 MthStat 361(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 model-based 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 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.

**Graduate: (U/G and G): ATM SCI, MATH, MTHSTAT**

### ATM SCI

**ATM SCI 330**- Air-Pollution 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 global-scale 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, quasi-geostrophy; 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; quasi-geostrophy 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; synoptic-scale structure and dynamics; equivalent barotropic model; vertical motions; introduction to and application of quasi-geostrophic 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 quasi-geostrophic theory to Q-vectors; isentropic potential vorticity applied to mid-latitude weather systems; fronts and jets. Prereq: jr st; Atm Sci 360(P).
**ATM SCI 405**- Atmospheric Science for in-Service Teachers: (1-3 units; U/G)- Basic, advanced or new topics in atmospheric sciences for in-service teachers. Retakable w/chg in topic to 9 cr max. Prereq: in-service 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 surface-forced 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: (1-12 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. Retakable 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; boundary-layer profiles of wind, temperature and moisture; turbulence and boundary-layer 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: (1-3 units; U/G)- Intensive topical studies of currently active problem areas. Retakable 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 (1-3 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.
**ATM SCI 990**- Master's Thesis (1-8 units; G)- Prereq: grad st; cons instr & completed thesis proposal.
**ATM SCI 997**- Doctoral Externship (1-12 units; G)- Prereq: grad st; admis to candidacy for the PhD.
**ATM SCI 998**- Doctoral Dissertation (1-12 units; G)- Prereq: grad st; admis to candidacy for PhD.
**ATM SCI 999**- Advanced Independent Reading (1-4 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 200-level 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 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 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 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 Black-Scholes 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 decision-making 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 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 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 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 451**- Axiomatic Geometry (3 units; U/G)- An axiomatic approach to Euclidean and non-Euclidean 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. Retakable 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: (1-12 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. Retakable w/chg in topic. Prereq: jr st; acceptance for Study Abroad Prog.
**MATH 511**- Symbolic Logic (3 units; U/G)- First-order 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 300-level 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 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 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 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 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 551**- Elementary Topology (3 units; U/G)- General theory of point sets in Euclidean spaces, with emphasis on topology of two-dimensional and three-dimensional 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 calculus-based 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 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 300-level 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 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 617**- Optimization (3 units; U/G)- Unconstrained and constrained optimization: linear, nonlinear, and dynamic programming; barrier, penalty, and Lagrangian methods; Karush-Kuhn-Tucker 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 vector-valued functions; Riemann-Stieltjes 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 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 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 690**- Topics in Mathematics: (3 units; U/G)- Specific topics and any additional prerequisites announced in Schedule of Classes each time course is offered. Retakable 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; sturm-liouville 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 700-799 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 pre-posterior 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)- Measure-theoretic foundations; limit-law 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 non-wandering 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 (1-3 units; G)- Cr count toward masters degree only if student completes thesis option. Prereq: grad st; cons instr.
**MATH 791**- Master's Seminar (1-3 units; G)- May not be taken for cr more than once. Prereq: grad st; cons instr.
**MATH 792**- Industrial Internship (1-3 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: (1-2 units; G)- Retakable w/chg in topic to 6 cr max. Prereq: grad st; Math 715(C).
**MATH 799**- Seminar in Mathematics: (1-3 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: (1-3 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; poincare-bendixon 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 b-spaces and f-spaces including the closed graph; Hahn-Banach and Banach-Steinhaus 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 (1-6 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 362**- Introduction to Mathematical Statistics II (3 units; U/G)- Testing statistical hypothesis; linear hypothesis; regression; analysis of variance and experimental designs; distribution-free methods; sequential methods. Not recom for grad students in math. Prereq: jr st; MthStat 361(P).
**MTHSTAT 462**- Data Analysis and Graphing Using SAS-II (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; split-plot 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 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 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 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 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 model-based 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 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 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; bonus-malus 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 most--powerful 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).