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.
 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)
 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
 MthStat 215 – every Fall, Spring, Summer, and usually UWinteriM
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.
 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
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.
What makes the weather, general circulation of the atmosphere, analysis of meteorological data and their use in predicting the weather.
Study of precipitation properties and processes in the atmosphere. Structure of precipitating systems ranging from small to large scale.
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.
Origin of the solar system, its planets, and planetary atmospheres.
Specific topics are announced in the Schedule of Classes each time the class is offered.
For further information, consult dept chair.
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.
Application of basic knowledge of Atmospheric Sciences in business, organizational, educational, political or other appropriate setting.
Designed to enroll students in UWM sponsored program before course work level, content, and credits are determined and/or in specially prepared course work.
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.
Pollutant sources and sinks, fundamental pollutant chemistry, monitoring techniques, averaging boundary layers and turbulence, diffusion theories, diffusion models, regional and globalscale pollution problems.
Pollutant sources and sinks, fundamental pollutant chemistry, monitoring techniques, averaging boundary layers and turbulence, diffusion theories, diffusion models, regional and globalscale pollution problems.
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.
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.
The role of dynamics in atmospheric physics; equations of motion; symmetric circulation models; gravity waves; Rossby waves, quasigeostrophy; introduction to instability of atmospheric flows.
The role of dynamics in atmospheric physics; equations of motion; symmetric circulation models; gravity waves; Rossby waves, quasigeostrophy; introduction to instability of atmospheric flows.
Circulation, vorticity, potential vorticity; shallow water equations: Poincare, Kelvin, and Rossby waves, energy and enstrophy; quasigeostrophy for a stratified atmosphere; barotropic and baroclinic instability.
Circulation, vorticity, potential vorticity; shallow water equations: Poincare, Kelvin, and Rossby waves, energy and enstrophy; quasigeostrophy for a stratified atmosphere; barotropic and baroclinic instability.
Fundamental principles; synopticscale structure and dynamics; equivalent barotropic model; vertical motions; introduction to and application of quasigeostrophic theory.
Fundamental principles; synopticscale structure and dynamics; equivalent barotropic model; vertical motions; introduction to and application of quasigeostrophic theory.
Extension of quasigeostrophic theory to Qvectors; isentropic potential vorticity applied to midlatitude weather systems; fronts and jets.
Extension of quasigeostrophic theory to Qvectors; isentropic potential vorticity applied to midlatitude weather systems; fronts and jets.
Selected topics.
Basic, advanced or new topics in atmospheric sciences for inservice teachers.
Basic, advanced or new topics in atmospheric sciences for inservice teachers.
Theory, analysis and forecasting of mesoscale flows, including convective systems, polar lows, terrain and surfaceforced flows, jet streams and hurricanes.
Theory, analysis and forecasting of mesoscale flows, including convective systems, polar lows, terrain and surfaceforced flows, jet streams and hurricanes.
Formation of cloud droplets, droplet growth by condensation, formation of ice crystals, precipitation processes, weather radars, cloud models.
Formation of cloud droplets, droplet growth by condensation, formation of ice crystals, precipitation processes, weather radars, cloud models.
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.
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.
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.
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.
Designed to enroll students in UWM sponsored program before course work level, content, and credits are determined and/or in specially prepared course work.
Designed to enroll students in UWM sponsored program before course work level, content, and credits are determined and/or in specially prepared course work.
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.
Mathematical and statistical tools applicable to the investigation of atmospheric problems; the nature and treatment of atmospheric data.
Mathematical and statistical tools applicable to the investigation of atmospheric problems; the nature and treatment of atmospheric data.
Surface energy budget; radiation balance and heat transfer; boundarylayer profiles of wind, temperature and moisture; turbulence and boundarylayer fluxes; evapotranspiration; special topics.
Surface energy budget; radiation balance and heat transfer; boundarylayer profiles of wind, temperature and moisture; turbulence and boundarylayer fluxes; evapotranspiration; special topics.
Basic laws of radiation, absorption and scattering, weather radar, retrieval of soundings, remote sensing and climate, weather satellites.
Basic laws of radiation, absorption and scattering, weather radar, retrieval of soundings, remote sensing and climate, weather satellites.
Properties of atmospheric sound, gravity, Rossby waves. Baroclinic instability, cyclogenesis, frontogenesis, and the general circulation. Introduction to numerical prediction.
Properties of atmospheric sound, gravity, Rossby waves. Baroclinic instability, cyclogenesis, frontogenesis, and the general circulation. Introduction to numerical prediction.
Student writes a paper under supervision of an advisor on an approved topic not covered in the student's regular course work.
overs techniques used to analyze data and test scientific hypotheses for both diagnostic/understanding and prognostic/prediction applications, particularly in the atmospheric and related sciences.
overs techniques used to analyze data and test scientific hypotheses for both diagnostic/understanding and prognostic/prediction applications, particularly in the atmospheric and related sciences.
Intensive topical studies of currently active problem areas.
Intensive topical studies of currently active problem areas.
Application of advanced principles of atmospheric sciences in a business, organizational, educational, political or other appropriate setting.
Independent meteorological study.
Math
Highly interactive format providing mathematics instruction and instilling study skills and strategies for succeeding in mathematics courses.
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.
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.
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.
Number systems; linear equations, inequalities; exponent notation, radicals; polynomials, operations, factoring, rational expressions; coordinate geometry; linear systems; quadratic equations.
Arithmetic number systems; linear equations, inequalities; exponent notation, radicals; polynomials, operations, factoring; modeling; coordinate geometry; linear systems; quadratic equations.
Continuation of Math 92, with an integrated approach to numeracy, proportional reasoning, algebraic reasoning, and functions.
Selected topics in applied mathematics and statistics, such as, but not limited to, voting theory, fair division, apportionment, graph theory, financial mathematics, and statistical inference.
Algebraic techniques with polynomials, rational expressions, equations and inequalities, exponential and logarithmic functions, rational exponents, systems of linear equations.
Continuation of MATH 98 in polynomials, equations, and inequalities; exponential, logarithmic, and periodic functions; rational expressions and exponents; and systems of linear equations.
Students learn a broad variety of fundamental logical methods  techniques used to identify, analyze, model, evaluate, and criticize different types of realworld reasoning.
Essential topics from college algebra and trigonometry for students intending to enroll in calculus.
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.
Trigonometric functions; graphs, identities, equations, inequalities; inverse trigonometric functions; solutions of triangles with applications; complex numbers; polar coordinates.
Theory of arithmetic of whole numbers, fractions, and decimals. Introduction to algebra, estimation and problemsolving strategies.
A continuation of MATH 175 in geometry, statistics, and probability.
Specific topics are announced in the Schedule of Classes each time the class is offered.
Regularly offered courses may not be taken as Independent Study.
Elementary deterministic and probabilistic discrete mathematics and applications to a wide variety of disciplines. Topics may include linear programming, Markov chains, optimization, stochastic processes.
Applications of algebra, functions, and optimization methods in business and economics settings.
A onesemester survey with applications to business administration, economics, and nonphysical sciences. Topics include coordinate systems, equations of curves, limits, differentiation, integration, applications.
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.
Calculus of functions of one and several variables; sequences, series, differentiation, integration; introduction to differential equations; vectors and vector functions; applications.
Continuation of Math 221.
Limits, derivatives, and graphs of algebraic, trigonometric, exponential, and logarithmic functions; antiderivatives, the definite integral, and the fundamental theorem of calculus, with applications.
Continuation of Math 231. Applications of integration, techniques of integration; infinite sequences and series; parametric equations, conic sections, and polar coordinates.
Continuation of MATH 232. Threedimensional analytic geometry and vectors; partial derivatives; multiple integrals; vector calculus, with applications.
Elementary differential equations. Vectors; matrices; linear transformations; quadratic forms; eigenvalues; applications.
Vector spaces, systems of linear equations, matrices, determinants, linear transformations, eigenvalues, eigenvectors; selected topics in applications. Emphasizes basic concepts and concrete examples.
Course provides a strong foundation in the exploration, teaching and communication (oral and written) of mathematical concepts via problemsolving experiences and discussion.
Topics for K8 teachers. Basic patterns and rules that govern number systems, geometric transformations, and manipulation of algebraic expressions.
Topics for K8 teachers. Geometry as measuring toolcongruence, similarity, area, volume, and coordinates; geometry as axiomatic systemdefinitions, conjectures, proofs, counterexamples; rigid motions, symmetry.
Random experiments; histograms; sample spaces; equally likely outcomes for random experiments; permutations; combinations; binomial, geometric, hypergeometric distributions; expectation; conditional probabilities; max likelihood estimation & inference.
Specific topics and any additional prerequisites announced in Schedule of Classes each time course is offered.
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.
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.
Construction and analysis of discrete and continuous mathematical models in applied, natural, and social sciences. Elements of programming, simulations, case studies from scientific literature.
Construction and analysis of discrete and continuous mathematical models in applied, natural, and social sciences. Elements of programming, simulations, case studies from scientific literature.
Primal and dual formulations of linear programming problems; simplex and related methods of solution; algorithms for transportation; optimization.
Primal and dual formulations of linear programming problems; simplex and related methods of solution; algorithms for transportation; optimization.
Introduction to operations research. Network analysis; integer programming; game theory; nonlinear programming; dynamic programming.
Introduction to operations research. Network analysis; integer programming; game theory; nonlinear programming; dynamic programming.
Number theory topics related to cryptography; discrete structures including graphs, partial orders, Latin squares and block designs; advanced counting techniques.
Elementary types and systems of differential equations, series solutions, numerical methods, Laplace transforms, selected applications.
Elementary types and systems of differential equations, series solutions, numerical methods, Laplace transforms, selected applications.
Topics selected from vector algebra; scalar and vector fields; line, surface, and volume integrals; theorems of Green, Gauss, and Stokes; vector differential calculus.
Topics selected from vector algebra; scalar and vector fields; line, surface, and volume integrals; theorems of Green, Gauss, and Stokes; vector differential calculus.
Partial differential equations of mathematical physics, boundary value problems in heat flow, vibrations, potentials, etc. Solved by Fourier series; Bessel functions and Legendre polynomials.
Partial differential equations of mathematical physics, boundary value problems in heat flow, vibrations, potentials, etc. Solved by Fourier series; Bessel functions and Legendre polynomials.
Facility with mathematical language and method of conjecture, proof and counter example, with emphasis on proofs. Topics: logic, sets, functions and others.
Topics from the development of mathematics, such as famous problems, mathematicians, calculating devices; chronological outlines. Significant reading and writing assignments.
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.
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.
Significant topics to illustrate to nonmathematicians the characteristic features of mathematical thought. Only H.S. algebra and geometry assumed.
Modeling techniques for analysis and decisionmaking in social and life sciences and industry. Deterministic and stochastic modeling. Topics may vary with instructors.
Modeling techniques for analysis and decisionmaking in social and life sciences and industry. Deterministic and stochastic modeling. Topics may vary with instructors.
Root finding and solution of nonlinear systems; direct solution of linear systems; interpolation & approximation of functions; least squares; fast Fourier transform; quadrature.
Root finding and solution of nonlinear systems; direct solution of linear systems; interpolation & approximation of functions; least squares; fast Fourier transform; quadrature.
Nonlinear systems; iterative solution of linear systems; initial value problems in ordinary differential equations; boundary value problems in ordinary and partial differential equations.
Nonlinear systems; iterative solution of linear systems; initial value problems in ordinary differential equations; boundary value problems in ordinary and partial differential equations.
Direct solution of linear systems; iterative solution of linear systems; least squares; eigenvalue problems.
Direct solution of linear systems; iterative solution of linear systems; least squares; eigenvalue problems.
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.
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.
Groups, rings, fields, Boolean algebras with emphasis on their applications to computer science and other areas.
Groups, rings, fields, Boolean algebras with emphasis on their applications to computer science and other areas.
An axiomatic approach to Euclidean and nonEuclidean geometry (historic role of the parallel postulate and models).
An axiomatic approach to Euclidean and nonEuclidean geometry (historic role of the parallel postulate and models).
Selected topics from vector geometry and geometric transformations such as the study of invariants and conics.
Selected topics from vector geometry and geometric transformations such as the study of invariants and conics.
Application of advanced principles of mathematics in a business, organizational, educational, governmental, or other appropriate setting.
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.
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.
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.
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.
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.
Firstorder predicate calculus; formal properties of theoretical systems; chief results of modern mathematical logic; advanced topics such as completeness and computability.
Firstorder predicate calculus; formal properties of theoretical systems; chief results of modern mathematical logic; advanced topics such as completeness and computability.
Fundamental notions of sets and functions; limits, continuity; Riemann integral, improper integral; infinite series; uniform convergence; power series; improper integrals with a parameter.
Fundamental notions of sets and functions; limits, continuity; Riemann integral, improper integral; infinite series; uniform convergence; power series; improper integrals with a parameter.
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.
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.
Integers; groups; rings; fields; emphasis on proofs.
Integers; groups; rings; fields; emphasis on proofs.
Vector spaces; systems of linear equations; linear transformations and matrices; bilinear, quadratic, and Hermitian forms; eigentheory; canonical forms; selected topics. Emphasizes theory and proof.
Vector spaces; systems of linear equations; linear transformations and matrices; bilinear, quadratic, and Hermitian forms; eigentheory; canonical forms; selected topics. Emphasizes theory and proof.
Number theoretic functions; distribution of primes; Diophantine approximation; partitions; additive number theory; quadratic reciprocity.
Number theoretic functions; distribution of primes; Diophantine approximation; partitions; additive number theory; quadratic reciprocity.
General theory of point sets in Euclidean spaces, with emphasis on topology of twodimensional and threedimensional spaces; elementary notions of metric spaces; applications.
General theory of point sets in Euclidean spaces, with emphasis on topology of twodimensional and threedimensional spaces; elementary notions of metric spaces; applications.
The theory of curves and surfaces by differential methods.
The theory of curves and surfaces by differential methods.
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.
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.
Number systems; algebra of polynomials; theory of equations; functions; modeling; geometric measurement; geometric transformations; connections between advanced mathematics and high school topics.
Number systems; algebra of polynomials; theory of equations; functions; modeling; geometric measurement; geometric transformations; connections between advanced mathematics and high school topics.
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.
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.
Specific topics and any additional prerequisites announced in Schedule of Classes each time course is offered.
Student writes a paper under supervision of an advisor on an approved topic not covered in the student's regular course work.
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.
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.
Continuation of Math 601. Partial differential equations, Fourier and Laplace transforms, convolutions, special functions, mathematical modeling.
Continuation of Math 601. Partial differential equations, Fourier and Laplace transforms, convolutions, special functions, mathematical modeling.
Finite difference solution of elliptic boundary value problems and of evolution problems; solution of hyperbolic conservation laws; finite volume methods; finite element methods.
Finite difference solution of elliptic boundary value problems and of evolution problems; solution of hyperbolic conservation laws; finite volume methods; finite element methods.
Unconstrained and constrained optimization: linear, nonlinear, and dynamic programming; barrier, penalty, and Lagrangian methods; KarushKuhnTucker theory, quadratic, and sequential quadratic programming; evolutionary algorithms.
Unconstrained and constrained optimization: linear, nonlinear, and dynamic programming; barrier, penalty, and Lagrangian methods; KarushKuhnTucker theory, quadratic, and sequential quadratic programming; evolutionary algorithms.
Topology of Euclidean space; continuity; differentiation of real and vectorvalued functions; RiemannStieltjes integration.
Topology of Euclidean space; continuity; differentiation of real and vectorvalued functions; RiemannStieltjes integration.
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.
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.
Group theory, including normal subgroups, quotients, permutation groups, Sylow's theorems, Abelian groups; field theory; linear algebra over general fields.
Group theory, including normal subgroups, quotients, permutation groups, Sylow's theorems, Abelian groups; field theory; linear algebra over general fields.
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.
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.
Specific topics and any additional prerequisites announced in Schedule of Classes each time course is offered.
Specific topics and any additional prerequisites announced in Schedule of Classes each time course is offered.
See Advanced Independent Study. For further information, consult dept chair.
MTHSTAT
Specific topics are announced in the Schedule of Classes each time the class is offered.
For further information, consult dept chair.
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.
Introduction to handson data analysis, performed on large, complex and realistic data sets, using a scientific programming language like R.
Random experiments; histograms; sample spaces; equally likely outcomes for random experiments; permutations; combinations; binomial, geometric, hypergeometric distributions; expectation; conditional probabilities; max likelihood estimation & inference.
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.
Probability spaces; discrete and continuous, univariate and multivariate distributions; moments; independence, random sampling, sampling distributions; normal and related distributions; point and interval estimation.
Probability spaces; discrete and continuous, univariate and multivariate distributions; moments; independence, random sampling, sampling distributions; normal and related distributions; point and interval estimation.
Testing statistical hypothesis; linear hypothesis; regression; analysis of variance and experimental designs; distributionfree methods; sequential methods.
Testing statistical hypothesis; linear hypothesis; regression; analysis of variance and experimental designs; distributionfree methods; sequential methods.
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.
Continuation of MthStat 461. Procedures GLM, LIFEREG, LIFETEST, LOGISTIC, PROBIT and advanced GRAPHING. Offered second half of sem.
Continuation of MthStat 461. Procedures GLM, LIFEREG, LIFETEST, LOGISTIC, PROBIT and advanced GRAPHING. Offered second half of sem.
Probability distributions; parameter estimation and confidence intervals; hypothesis testing; applications.
Probability distributions; parameter estimation and confidence intervals; hypothesis testing; applications.
Concepts of probability and statistics; probability distributions of engineering applications; sampling distributions; hypothesis testing, parameter estimation; experimental design; regression analysis.
Concepts of probability and statistics; probability distributions of engineering applications; sampling distributions; hypothesis testing, parameter estimation; experimental design; regression analysis.
Simple distributions, estimation and hypothesis testing, simple regression, analysis of variance, nonparametric methods in biology. Demography and vital statistics and bioassay and clinical trials.
Simple distributions, estimation and hypothesis testing, simple regression, analysis of variance, nonparametric methods in biology. Demography and vital statistics and bioassay and clinical trials.
Application of advanced principles of mathematical statistics in a business, organizational, educational, governmental, or other appropriate setting.
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.
Latin squares; incomplete block designs; factorial experiments; confounding; partial confounding; splitplot experiments; fractional replication.
Latin squares; incomplete block designs; factorial experiments; confounding; partial confounding; splitplot experiments; fractional replication.
Straight line, polynomial and multiple regression; multiple and partial correlation; testing hypotheses in regression; residual analysis.
Straight line, polynomial and multiple regression; multiple and partial correlation; testing hypotheses in regression; residual analysis.
Autocorrelation; spectral density; linear models; forecasting; model identification and estimation.
Autocorrelation; spectral density; linear models; forecasting; model identification and estimation.
Sign, rank and permutation tests; tests of randomness and independence; methods for discrete data and zeroes and ties; power and efficiency of nonparametric tests.
Sign, rank and permutation tests; tests of randomness and independence; methods for discrete data and zeroes and ties; power and efficiency of nonparametric tests.
Basics of programming and optimization techniques; resampling, bootstrap, and Monte Carlo methods; design and analysis of simulation studies.
Basics of programming and optimization techniques; resampling, bootstrap, and Monte Carlo methods; design and analysis of simulation studies.
Multivariate normal distribution; Wishart distribution; Hotelling's T2; multivariate normal distribution; multivariate analysis of variance; classification problems.
Multivariate normal distribution; Wishart distribution; Hotelling's T2; multivariate normal distribution; multivariate analysis of variance; classification problems.
Credibility theory, ratemaking, and reserving.
ATM SCI
Pollutant sources and sinks, fundamental pollutant chemistry, monitoring techniques, averaging boundary layers and turbulence, diffusion theories, diffusion models, regional and globalscale pollution problems.
Pollutant sources and sinks, fundamental pollutant chemistry, monitoring techniques, averaging boundary layers and turbulence, diffusion theories, diffusion models, regional and globalscale pollution problems.
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.
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.
The role of dynamics in atmospheric physics; equations of motion; symmetric circulation models; gravity waves; Rossby waves, quasigeostrophy; introduction to instability of atmospheric flows.
The role of dynamics in atmospheric physics; equations of motion; symmetric circulation models; gravity waves; Rossby waves, quasigeostrophy; introduction to instability of atmospheric flows.
Circulation, vorticity, potential vorticity; shallow water equations: Poincare, Kelvin, and Rossby waves, energy and enstrophy; quasigeostrophy for a stratified atmosphere; barotropic and baroclinic instability.
Circulation, vorticity, potential vorticity; shallow water equations: Poincare, Kelvin, and Rossby waves, energy and enstrophy; quasigeostrophy for a stratified atmosphere; barotropic and baroclinic instability.
Fundamental principles; synopticscale structure and dynamics; equivalent barotropic model; vertical motions; introduction to and application of quasigeostrophic theory.
Fundamental principles; synopticscale structure and dynamics; equivalent barotropic model; vertical motions; introduction to and application of quasigeostrophic theory.
Extension of quasigeostrophic theory to Qvectors; isentropic potential vorticity applied to midlatitude weather systems; fronts and jets.
Extension of quasigeostrophic theory to Qvectors; isentropic potential vorticity applied to midlatitude weather systems; fronts and jets.
Basic, advanced or new topics in atmospheric sciences for inservice teachers.
Basic, advanced or new topics in atmospheric sciences for inservice teachers.
Theory, analysis and forecasting of mesoscale flows, including convective systems, polar lows, terrain and surfaceforced flows, jet streams and hurricanes.
Theory, analysis and forecasting of mesoscale flows, including convective systems, polar lows, terrain and surfaceforced flows, jet streams and hurricanes.
Formation of cloud droplets, droplet growth by condensation, formation of ice crystals, precipitation processes, weather radars, cloud models.
Formation of cloud droplets, droplet growth by condensation, formation of ice crystals, precipitation processes, weather radars, cloud models.
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.
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.
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.
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.
Designed to enroll students in UWM sponsored program before course work level, content, and credits are determined and/or in specially prepared course work.
Designed to enroll students in UWM sponsored program before course work level, content, and credits are determined and/or in specially prepared course work.
Mathematical and statistical tools applicable to the investigation of atmospheric problems; the nature and treatment of atmospheric data.
Mathematical and statistical tools applicable to the investigation of atmospheric problems; the nature and treatment of atmospheric data.
Surface energy budget; radiation balance and heat transfer; boundarylayer profiles of wind, temperature and moisture; turbulence and boundarylayer fluxes; evapotranspiration; special topics.
Surface energy budget; radiation balance and heat transfer; boundarylayer profiles of wind, temperature and moisture; turbulence and boundarylayer fluxes; evapotranspiration; special topics.
Basic laws of radiation, absorption and scattering, weather radar, retrieval of soundings, remote sensing and climate, weather satellites.
Basic laws of radiation, absorption and scattering, weather radar, retrieval of soundings, remote sensing and climate, weather satellites.
Properties of atmospheric sound, gravity, Rossby waves. Baroclinic instability, cyclogenesis, frontogenesis, and the general circulation. Introduction to numerical prediction.
Properties of atmospheric sound, gravity, Rossby waves. Baroclinic instability, cyclogenesis, frontogenesis, and the general circulation. Introduction to numerical prediction.
overs techniques used to analyze data and test scientific hypotheses for both diagnostic/understanding and prognostic/prediction applications, particularly in the atmospheric and related sciences.
overs techniques used to analyze data and test scientific hypotheses for both diagnostic/understanding and prognostic/prediction applications, particularly in the atmospheric and related sciences.
Intensive topical studies of currently active problem areas.
Intensive topical studies of currently active problem areas.
Fundamentals of signal detection in noisy multivariate spacetime data sets; empirical orthogonal functions, singular value decomposition, maximum covariance analysis and canonical correlation analysis; Fourier analysis; singular and multivariate spectrum analysis.
Computational techniques for determining surface fluxes of heat and momentum. Numerical methods for solving advection and diffusion problems; statistical diffusion modeling.
Atmospheric applications of turbulent flow theory. Nonprecipitating clouds: structure of individual cumulus clouds, stratocumulus and cumulus boundary layers. Precipitating clouds: thunderstorms, squall lines, hurricanes.
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.
Numerical methods for predicting atmospheric phenomena; numerical stability and dispersion; implicit and explicit damping methods; physical process parameterization; ensemble data assimilation techniques.
Phase space reconstruction; singular spectrum analysis; prediction; dimension estimation; application of nonlinear time series analysis techniques to selected data sets.
(3 hr lc, 2 hr la). Theoretical & experimental look at cloud & precipitation formation, interaction & dissipation microphysics & chemistry aerosol physics & chemistry, & their application.
Advanced analysis techniques for snyoptic/mesoscale diagnoses, case studies of relevant circulation systems; role of planetary, synoptic, and mesoscale flows in system development.
Available for graduate students who must meet minimum credit load requirement.
Selected topics in atmospheric dynamics, satellite meteorology, atmospheric & oceanic convection, air & water pollution, numerical prediction remote sensing, & others.
Externship for students enrolled in the Atmospheric Science PhD program.
Independent meteorological study.
MATH
Construction and analysis of discrete and continuous mathematical models in applied, natural, and social sciences. Elements of programming, simulations, case studies from scientific literature.
Construction and analysis of discrete and continuous mathematical models in applied, natural, and social sciences. Elements of programming, simulations, case studies from scientific literature.
Primal and dual formulations of linear programming problems; simplex and related methods of solution; algorithms for transportation; optimization.
Primal and dual formulations of linear programming problems; simplex and related methods of solution; algorithms for transportation; optimization.
Introduction to operations research. Network analysis; integer programming; game theory; nonlinear programming; dynamic programming.
Introduction to operations research. Network analysis; integer programming; game theory; nonlinear programming; dynamic programming.
Elementary types and systems of differential equations, series solutions, numerical methods, Laplace transforms, selected applications.
Elementary types and systems of differential equations, series solutions, numerical methods, Laplace transforms, selected applications.
Topics selected from vector algebra; scalar and vector fields; line, surface, and volume integrals; theorems of Green, Gauss, and Stokes; vector differential calculus.
Topics selected from vector algebra; scalar and vector fields; line, surface, and volume integrals; theorems of Green, Gauss, and Stokes; vector differential calculus.
Partial differential equations of mathematical physics, boundary value problems in heat flow, vibrations, potentials, etc. Solved by Fourier series; Bessel functions and Legendre polynomials.
Partial differential equations of mathematical physics, boundary value problems in heat flow, vibrations, potentials, etc. Solved by Fourier series; Bessel functions and Legendre polynomials.
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.
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.
Modeling techniques for analysis and decisionmaking in social and life sciences and industry. Deterministic and stochastic modeling. Topics may vary with instructors.
Modeling techniques for analysis and decisionmaking in social and life sciences and industry. Deterministic and stochastic modeling. Topics may vary with instructors.
Root finding and solution of nonlinear systems; direct solution of linear systems; interpolation & approximation of functions; least squares; fast Fourier transform; quadrature.
Root finding and solution of nonlinear systems; direct solution of linear systems; interpolation & approximation of functions; least squares; fast Fourier transform; quadrature.
Nonlinear systems; iterative solution of linear systems; initial value problems in ordinary differential equations; boundary value problems in ordinary and partial differential equations.
Nonlinear systems; iterative solution of linear systems; initial value problems in ordinary differential equations; boundary value problems in ordinary and partial differential equations.
Direct solution of linear systems; iterative solution of linear systems; least squares; eigenvalue problems.
Direct solution of linear systems; iterative solution of linear systems; least squares; eigenvalue problems.
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.
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.
Groups, rings, fields, Boolean algebras with emphasis on their applications to computer science and other areas.
Groups, rings, fields, Boolean algebras with emphasis on their applications to computer science and other areas.
An axiomatic approach to Euclidean and nonEuclidean geometry (historic role of the parallel postulate and models).
An axiomatic approach to Euclidean and nonEuclidean geometry (historic role of the parallel postulate and models).
Selected topics from vector geometry and geometric transformations such as the study of invariants and conics.
Selected topics from vector geometry and geometric transformations such as the study of invariants and conics.
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.
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.
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.
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.
Firstorder predicate calculus; formal properties of theoretical systems; chief results of modern mathematical logic; advanced topics such as completeness and computability.
Firstorder predicate calculus; formal properties of theoretical systems; chief results of modern mathematical logic; advanced topics such as completeness and computability.
Fundamental notions of sets and functions; limits, continuity; Riemann integral, improper integral; infinite series; uniform convergence; power series; improper integrals with a parameter.
Fundamental notions of sets and functions; limits, continuity; Riemann integral, improper integral; infinite series; uniform convergence; power series; improper integrals with a parameter.
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.
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.
Integers; groups; rings; fields; emphasis on proofs.
Integers; groups; rings; fields; emphasis on proofs.
Vector spaces; systems of linear equations; linear transformations and matrices; bilinear, quadratic, and Hermitian forms; eigentheory; canonical forms; selected topics. Emphasizes theory and proof.
Vector spaces; systems of linear equations; linear transformations and matrices; bilinear, quadratic, and Hermitian forms; eigentheory; canonical forms; selected topics. Emphasizes theory and proof.
Number theoretic functions; distribution of primes; Diophantine approximation; partitions; additive number theory; quadratic reciprocity.
Number theoretic functions; distribution of primes; Diophantine approximation; partitions; additive number theory; quadratic reciprocity.
General theory of point sets in Euclidean spaces, with emphasis on topology of twodimensional and threedimensional spaces; elementary notions of metric spaces; applications.
General theory of point sets in Euclidean spaces, with emphasis on topology of twodimensional and threedimensional spaces; elementary notions of metric spaces; applications.
The theory of curves and surfaces by differential methods.
The theory of curves and surfaces by differential methods.
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.
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.
Number systems; algebra of polynomials; theory of equations; functions; modeling; geometric measurement; geometric transformations; connections between advanced mathematics and high school topics.
Number systems; algebra of polynomials; theory of equations; functions; modeling; geometric measurement; geometric transformations; connections between advanced mathematics and high school topics.
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.
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.
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.
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.
Continuation of Math 601. Partial differential equations, Fourier and Laplace transforms, convolutions, special functions, mathematical modeling.
Continuation of Math 601. Partial differential equations, Fourier and Laplace transforms, convolutions, special functions, mathematical modeling.
Finite difference solution of elliptic boundary value problems and of evolution problems; solution of hyperbolic conservation laws; finite volume methods; finite element methods.
Finite difference solution of elliptic boundary value problems and of evolution problems; solution of hyperbolic conservation laws; finite volume methods; finite element methods.
Unconstrained and constrained optimization: linear, nonlinear, and dynamic programming; barrier, penalty, and Lagrangian methods; KarushKuhnTucker theory, quadratic, and sequential quadratic programming; evolutionary algorithms.
Unconstrained and constrained optimization: linear, nonlinear, and dynamic programming; barrier, penalty, and Lagrangian methods; KarushKuhnTucker theory, quadratic, and sequential quadratic programming; evolutionary algorithms.
Topology of Euclidean space; continuity; differentiation of real and vectorvalued functions; RiemannStieltjes integration.
Topology of Euclidean space; continuity; differentiation of real and vectorvalued functions; RiemannStieltjes integration.
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.
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.
Group theory, including normal subgroups, quotients, permutation groups, Sylow's theorems, Abelian groups; field theory; linear algebra over general fields.
Group theory, including normal subgroups, quotients, permutation groups, Sylow's theorems, Abelian groups; field theory; linear algebra over general fields.
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.
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.
Specific topics and any additional prerequisites announced in Schedule of Classes each time course is offered.
Specific topics and any additional prerequisites announced in Schedule of Classes each time course is offered.
Elementary functional analysis, wavelets, control theory. Use of mathematical software emphasized throughout.
Optimal control theory, digital signal processing, image processing, linear programming, nonlinear optimation, artificial neural networks. Use of mathematical software emphasized throughout.
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.
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.
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.
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.
Complex numbers; linear transformations; elementary functions; conformal mapping; complex integration; infinite sequences; dirichlet problem; multivalued functions.
Continuation of Math 713.
Interpolation and approximation; differentiation and quadrature; numerical solution of ordinary differential equations; solution of linear and nonlinear algebraic equations.
Existence and uniqueness theorems for systems of ode; qualitative properties of solutions, including stability and asymptotic behavior; general theory of linear systems; sturmliouville problems.
First and second order equations; characteristics, cauchy problem; classical solutions of linear elliptic, parabolic and hyperbolic equations.
General theory of measures and integration; differentiation of set functions; relation to stochastic variables; atomic measures; haar measure and integral applications to probability theory.
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.
Basic course which is prerequisite for all other 700799 level courses in algebra; groups, rings, fields, galois theory, modules, and categories.
Continuation of Math 731.
Topics selected from permutation groups; representations of groups and algebras; group algebras; group characters; extension problems; simple groups; solvable and nilpotent groups.
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.
Continuation of Math 736.
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.
Continuation of Math 751.
Homology theory; complexes and simplicial homology theory; general homology theories; cohomology rings; applications to manifolds, fixed point theorems, etc.
Continuation of Math 753.
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.
Concepts in queueing theory; exponential channels; applications of markov chains to queueing problems; queue disciplines with priorities.
Measuretheoretic foundations; limitlaw theorems; weak and strong laws of large numbers; central limit problem; conditional expectations, martingales; stochastic processes.
Periodic, recurrent and nonwandering points, kneading theory, unstable manifolds, unimodal mappings, turbulent and chaotic maps, symbolic dynamics, structural stability, topological conjugacy, topological dynamics.
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.
Specific topics and any additional prerequisites announced in Timetable each time course is offered.
Specific topics and any additional prerequisites will be announced in the Timetable each time the course is offered.
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.
Topics may be selected from Riemannian geometry, minimal surfaces and surfaces of prescribed mean curvature, geometric partial differential equations, or related areas of geometry. Specific topics and any additional prerequisites will be announced in the Timetable each time the course is offered
Methods for initial value and boundary value problems; stiff equations, singular points and bifurcation.
Finite difference and finite element methods for linear elliptic, parabolic and hyperbolic equations; nonlinear equations.
Specific topics and any additional prerequisites will be announced in the Timetable each time the course is offered.
Existence and uniqueness theorems; singularity of solutions; oscillation and comparison theorems; poincarebendixon theory.
Continuation of Math 816; dynamical systems, bifurcation theory, topological methods.
Specific topics and any additional prerequisites will be announced in the Timetable each time the course is offered.
Basic theorems of bspaces and fspaces including the closed graph; HahnBanach and BanachSteinhaus theorems; Banach algebras; generalized functions; spectral theory.
Specific topics and any additional prerequisites will be announced in the Timetable each time the course is offered.
Modules; diagrams; categories; functors; complexes; cohomology; extensions; resolutions; injective and projective systems; graded modules; homological dimension; spectral sequences; derived functors.
Continuation of Math 843.
Specific topics and any additional prerequisites will be announced in the Timetable each time the course is offered.
Specific topics and any additional prerequisites will be announced in the Timetable each time the course is offered.
Specific topics and any additional prerequisites will be announced in the Timetable each time the course is offered.
Available for graduate students who must meet minimum credit load requirement.
To be arranged with your instructor and department chair.
MTHSTAT
Probability spaces; discrete and continuous, univariate and multivariate distributions; moments; independence, random sampling, sampling distributions; normal and related distributions; point and interval estimation.
Probability spaces; discrete and continuous, univariate and multivariate distributions; moments; independence, random sampling, sampling distributions; normal and related distributions; point and interval estimation.
Testing statistical hypothesis; linear hypothesis; regression; analysis of variance and experimental designs; distributionfree methods; sequential methods.
Testing statistical hypothesis; linear hypothesis; regression; analysis of variance and experimental designs; distributionfree methods; sequential methods.
Continuation of MthStat 461. Procedures GLM, LIFEREG, LIFETEST, LOGISTIC, PROBIT and advanced GRAPHING. Offered second half of sem.
Continuation of MthStat 461. Procedures GLM, LIFEREG, LIFETEST, LOGISTIC, PROBIT and advanced GRAPHING. Offered second half of sem.
Probability distributions; parameter estimation and confidence intervals; hypothesis testing; applications.
Probability distributions; parameter estimation and confidence intervals; hypothesis testing; applications.
Concepts of probability and statistics; probability distributions of engineering applications; sampling distributions; hypothesis testing, parameter estimation; experimental design; regression analysis.
Concepts of probability and statistics; probability distributions of engineering applications; sampling distributions; hypothesis testing, parameter estimation; experimental design; regression analysis.
Simple distributions, estimation and hypothesis testing, simple regression, analysis of variance, nonparametric methods in biology. Demography and vital statistics and bioassay and clinical trials.
Simple distributions, estimation and hypothesis testing, simple regression, analysis of variance, nonparametric methods in biology. Demography and vital statistics and bioassay and clinical trials.
Latin squares; incomplete block designs; factorial experiments; confounding; partial confounding; splitplot experiments; fractional replication.
Latin squares; incomplete block designs; factorial experiments; confounding; partial confounding; splitplot experiments; fractional replication.
Straight line, polynomial and multiple regression; multiple and partial correlation; testing hypotheses in regression; residual analysis.
Straight line, polynomial and multiple regression; multiple and partial correlation; testing hypotheses in regression; residual analysis.
Autocorrelation; spectral density; linear models; forecasting; model identification and estimation.
Autocorrelation; spectral density; linear models; forecasting; model identification and estimation.
Sign, rank and permutation tests; tests of randomness and independence; methods for discrete data and zeroes and ties; power and efficiency of nonparametric tests.
Sign, rank and permutation tests; tests of randomness and independence; methods for discrete data and zeroes and ties; power and efficiency of nonparametric tests.
Basics of programming and optimization techniques; resampling, bootstrap, and Monte Carlo methods; design and analysis of simulation studies.
Basics of programming and optimization techniques; resampling, bootstrap, and Monte Carlo methods; design and analysis of simulation studies.
Multivariate normal distribution; Wishart distribution; Hotelling's T2; multivariate normal distribution; multivariate analysis of variance; classification problems.
Multivariate normal distribution; Wishart distribution; Hotelling's T2; multivariate normal distribution; multivariate analysis of variance; classification problems.
Probability and distribution theory; point and interval estimation; testing hypotheses; large sample inference; nonparametric inference; sequential analysis.
Continuation of MthStat 761.
Introduction to linear statistical models and methods. Core topics include: simple and multiple linear regression, model checking, variable transformations, outlier diagnostics, variable selection, and generalized linear models such as logistic regression.
Introduction to statistical models and methods for time series data analysis. Core topics include: exponential smoothing, ARIMA models, transfer functions and intervention models, statespace models, GARCH models.
Introduction to statistical computer programming. Main topics include: basics of programming in R or similar language; optimization and rootfinding algorithms; Monte Carlo numerical integration; random sample generation; bootstrap and permutation tests; comparative simulation studies.
Introduction to statistical models and methods for multivariate data analysis. Core topics include: multivariate random vectors and distributions, principal component analysis, canonical correlation analysis, factor analysis, classification and discrimination, clustering techniques, and multidimensional scaling.
Exponential families; uniformly mostpowerful tests; least favorable priors; unbiased tests; invariant tests; applications to exponential families and the general linear hypothesis.
Specific topics and any additional prerequisites will be announced in the Timetable each time the course is offered.