• 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: 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.

• 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

• 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 two-level Quantitative Literacy requirement in order to graduate: Quantitative Literacy Parts A (QLA) and B (QLB). Many departments offer QLB courses (ask your advisor which is right for you), but QLA is only satisfied by a Math curricular area course or equivalent placement exam score.
• If you earned a Math Placement Test Code of 30 or higher, you satisfied your QLA requirement via this test!
• Earning a grade of C or higher in Math 102 or 103 (or 105, 108, 175) will also satisfy QLA – and these courses also satisfy the L&S math requirement for the BA degree.

Question: Who can take Math 092/102 or Math 103 to satisfy their degree requirements?
Answer:

• • Primarily students in the Arts, Humanities, and Social Welfare can take 102 or 103, as they do not need to take any further math or science courses.
  • Most students in the School of Education who do not place directly into Math 175 are advised to take 103 or 092+102 first.
  • Anyone in a STEM, Business, or Health Sci program, or anyone interested in the BS in L&S, will need different math courses for their program, and should consult their advisor to find the right courses (Math 094, 098, 105, 115, 116, 117, 211, 231, etc.).
  • All students should double check their program requirements and/or consult their academic advisor when choosing which math courses to take each semester.
  Majors whose math requirement is satisfied by Math 103 or 92+102
  • Africology
  • Anthropology
  • Art
  • Art Education
  • Art History
  • Classics
  • Communication
  • Comparative Literature
  • Criminal Justice
  • Dance
  • English
  • Film
  • Film Studies
  • French
  • German
  • Global Studies (tracks other than Global Management)
  • History
  • Inter Arts
  • International Studies
  • Italian
  • Jewish Studies
  • Journalism, Advertising, and Media Studies
  • Latin American, Caribbean, and Latino Studies
  • Linguistics
  • Music
  • Music Education
  • Philosophy
  • Political Science
  • Psychology (BA)
  • Religious Studies
  • Russian
  • Social Work
  • Sociology
  • Spanish
  • Theatre
  • Women’s Studies

Question: Do I qualify for Math 103?
Answer:

• The prerequisite of Math 103 is either an ACT-math 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 17-18, 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 co-requisite sections. For example, Math 092 Section 57 MW 11-12:15, and Math 102 Section 57 TR 11-12:15, 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 co-requisite 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 credit-bearing math course in their first year from 59% to 75% by implementing co-requisite 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 six-credits 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.

Math

MATH 75 Math Success Strategies

0 cr. Undergraduate.
Highly interactive format providing mathematics instruction and instilling study skills and strategies for succeeding in mathematics courses.

MATH 90 Basic Mathematics

0 cr. Undergraduate.
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.

MATH 92 Mathematical Literacy for College Students I

0 cr. Undergraduate.
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.

MATH 94 Foundations of Elementary Mathematics

0 cr. Undergraduate.
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.

MATH 95 Essentials of Algebra

0 cr. Undergraduate.
Number systems; linear equations, inequalities; exponent notation, radicals; polynomials, operations, factoring, rational expressions; coordinate geometry; linear systems; quadratic equations.

MATH 98 Algebraic Literacy I

0 cr. Undergraduate.
Arithmetic number systems; linear equations, inequalities; exponent notation, radicals; polynomials, operations, factoring; modeling; coordinate geometry; linear systems; quadratic equations.

MATH 102 Mathematical Literacy for College Students II

3 cr. Undergraduate.
Continuation of MATH 92, with an integrated approach to numeracy, proportional reasoning, algebraic reasoning, and functions.

MATH 103 Contemporary Applications of Mathematics

3 cr. Undergraduate.
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.

MATH 105 Introduction to College Algebra

3 cr. Undergraduate.
Algebraic techniques with polynomials, rational expressions, equations and inequalities, exponential and logarithmic functions, rational exponents, systems of linear equations.

MATH 108 Algebraic Literacy II

3 cr. Undergraduate.
Continuation of MATH 98 in polynomials, equations, and inequalities; exponential, logarithmic, and periodic functions; rational expressions and exponents; and systems of linear equations.

MATH 111 Introduction to Logic - Critical Reasoning

3 cr. Undergraduate.
Students learn a broad variety of fundamental logical methods - techniques used to identify, analyze, model, evaluate, and criticize different types of real-world reasoning.

MATH 115 Precalculus

4 cr. Undergraduate.
Essential topics from college algebra and trigonometry for students intending to enroll in calculus.

MATH 116 College Algebra

3 cr. Undergraduate.
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.

MATH 117 Trigonometry

2 cr. Undergraduate.
Trigonometric functions; graphs, identities, equations, inequalities; inverse trigonometric functions; solutions of triangles with applications; complex numbers; polar coordinates.

MATH 175 Mathematical Explorations for Elementary Teachers I

3 cr. Undergraduate.
Theory of arithmetic of whole numbers, fractions, and decimals. Introduction to algebra, estimation and problem-solving strategies.

MATH 176 Mathematical Explorations for Elementary Teachers II

3 cr. Undergraduate.
A continuation of MATH 175 in geometry, statistics, and probability.

MATH 194 First-Year Seminar:

3 cr. Undergraduate.
Specific topics are announced in the Schedule of Classes each time the class is offered.

MATH 199 Independent Study

1-3 cr. Undergraduate.
Regularly offered courses may not be taken as Independent Study.

MATH 205 Introductory Finite Mathematics

3 cr. Undergraduate.
Elementary deterministic and probabilistic discrete mathematics and applications to a wide variety of disciplines. Topics may include linear programming, Markov chains, optimization, stochastic processes.

MATH 208 Quantitative Models for Business

4 cr. Undergraduate.
Applications of algebra, functions, and optimization methods in business and economics settings.

MATH 211 Survey in Calculus and Analytic Geometry I

4 cr. Undergraduate.
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.

MATH 212 Survey in Calculus and Analytic Geometry II

4 cr. Undergraduate.
Continuation of first semester survey of calculus with applications to business administration, economics, and non-physical sciences. Topics include integration, multivariable calculus, Taylor polynomials and applications.

MATH 213 Calculus with Life Sciences Applications

4 cr. Undergraduate.
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.

MATH 221 Honors Calculus I

5 cr. Undergraduate.
Calculus of functions of one and several variables; sequences, series, differentiation, integration; introduction to differential equations; vectors and vector functions; applications.

MATH 222 Honors Calculus II

5 cr. Undergraduate.
Continuation of Math 221.

MATH 231 Calculus and Analytic Geometry I

4 cr. Undergraduate.
Limits, derivatives, and graphs of algebraic, trigonometric, exponential, and logarithmic functions; antiderivatives, the definite integral, and the fundamental theorem of calculus, with applications.

MATH 232 Calculus and Analytic Geometry II

4 cr. Undergraduate.
Continuation of Math 231. Applications of integration, techniques of integration; infinite sequences and series; parametric equations, conic sections, and polar coordinates.

MATH 233 Calculus and Analytic Geometry III

4 cr. Undergraduate.
Continuation of MATH 232. Three-dimensional analytic geometry and vectors; partial derivatives; multiple integrals; vector calculus, with applications.

MATH 234 Linear Algebra and Differential Equations

4 cr. Undergraduate.
Elementary differential equations. Vectors; matrices; linear transformations; quadratic forms; eigenvalues; applications.

MATH 240 Matrices and Applications

3 cr. Undergraduate.
Vector spaces, systems of linear equations, matrices, determinants, linear transformations, eigenvalues, eigenvectors; selected topics in applications. Emphasizes basic concepts and concrete examples.

MATH 275 Problem Solving/Critical Thinking for Elementary Education Majors

3 cr. Undergraduate.
Course provides a strong foundation in the exploration, teaching and communication (oral and written) of mathematical concepts via problem-solving experiences and discussion.

MATH 276 Algebraic Structures for Elementary Education Majors

3 cr. Undergraduate.
Topics for K-8 teachers. Basic patterns and rules that govern number systems, geometric transformations, and manipulation of algebraic expressions.

MATH 277 Geometry for Elementary Education Majors

3 cr. Undergraduate.
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.

MATH 278 Discrete Probability and Statistics for Elementary Education Majors

3 cr. Undergraduate.
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 290 Topics in Mathematics:

3 cr. Undergraduate.
Specific topics and any additional prerequisites announced in Schedule of Classes each time course is offered.

MATH 297 Study Abroad:

1-12 cr. Undergraduate.
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.

MATH 299 Ad Hoc:

1-6 cr. Undergraduate.
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.

MATH 305 Introduction to Mathematical and Computational Modeling

3 cr. Undergraduate/Graduate.
Construction and analysis of discrete and continuous mathematical models in applied, natural, and social sciences. Elements of programming, simulations, case studies from scientific literature.

MATH 305G Introduction to Mathematical and Computational Modeling

3 cr. Undergraduate/Graduate.
Construction and analysis of discrete and continuous mathematical models in applied, natural, and social sciences. Elements of programming, simulations, case studies from scientific literature.

MATH 313 Linear Programming and Optimization

3 cr. Undergraduate/Graduate.
Primal and dual formulations of linear programming problems; simplex and related methods of solution; algorithms for transportation; optimization.

MATH 313G Linear Programming and Optimization

3 cr. Undergraduate/Graduate.
Primal and dual formulations of linear programming problems; simplex and related methods of solution; algorithms for transportation; optimization.

MATH 315 Mathematical Programming and Optimization

3 cr. Undergraduate/Graduate.
Introduction to operations research. Network analysis; integer programming; game theory; nonlinear programming; dynamic programming.

MATH 315G Mathematical Programming and Optimization

3 cr. Undergraduate/Graduate.
Introduction to operations research. Network analysis; integer programming; game theory; nonlinear programming; dynamic programming.

MATH 318 Topics in Discrete Mathematics

3 cr. Undergraduate.
Number theory topics related to cryptography; discrete structures including graphs, partial orders, Latin squares and block designs; advanced counting techniques.

MATH 320 Introduction to Differential Equations

3 cr. Undergraduate/Graduate.
Elementary types and systems of differential equations, series solutions, numerical methods, Laplace transforms, selected applications.

MATH 320G Introduction to Differential Equations

3 cr. Undergraduate/Graduate.
Elementary types and systems of differential equations, series solutions, numerical methods, Laplace transforms, selected applications.

MATH 321 Vector Analysis

3 cr. Undergraduate/Graduate.
Topics selected from vector algebra; scalar and vector fields; line, surface, and volume integrals; theorems of Green, Gauss, and Stokes; vector differential calculus.

MATH 321G Vector Analysis

3 cr. Undergraduate/Graduate.
Topics selected from vector algebra; scalar and vector fields; line, surface, and volume integrals; theorems of Green, Gauss, and Stokes; vector differential calculus.

MATH 322 Introduction to Partial Differential Equations

3 cr. Undergraduate/Graduate.
Partial differential equations of mathematical physics, boundary value problems in heat flow, vibrations, potentials, etc. Solved by Fourier series; Bessel functions and Legendre polynomials.

MATH 322G Introduction to Partial Differential Equations

3 cr. Undergraduate/Graduate.
Partial differential equations of mathematical physics, boundary value problems in heat flow, vibrations, potentials, etc. Solved by Fourier series; Bessel functions and Legendre polynomials.

MATH 341 Seminar: Introduction to the Language and Practice of Mathematics

3 cr. Undergraduate.
Facility with mathematical language and method of conjecture, proof and counter example, with emphasis on proofs. Topics: logic, sets, functions and others.

MATH 345 Mathematics from a Historical Perspective:

3 cr. Undergraduate.
Topics from the development of mathematics, such as famous problems, mathematicians, calculating devices; chronological outlines. Significant reading and writing assignments.

MATH 371 Introduction to Stochastic Models in Finance

3 cr. Undergraduate/Graduate.
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.

MATH 371G Introduction to Stochastic Models in Finance

3 cr. Undergraduate/Graduate.
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.

MATH 381 Honors Seminar:

3 cr. Undergraduate.
Significant topics to illustrate to non-mathematicians the characteristic features of mathematical thought. Only H.S. algebra and geometry assumed.

MATH 405 Mathematical Models and Applications

3 cr. Undergraduate/Graduate.
Modeling techniques for analysis and decision-making in social and life sciences and industry. Deterministic and stochastic modeling. Topics may vary with instructors.

MATH 405G Mathematical Models and Applications

3 cr. Undergraduate/Graduate.
Modeling techniques for analysis and decision-making in social and life sciences and industry. Deterministic and stochastic modeling. Topics may vary with instructors.

MATH 413 Introduction to Numerical Analysis

3 cr. Undergraduate/Graduate.
Root finding and solution of nonlinear systems; direct solution of linear systems; interpolation & approximation of functions; least squares; fast Fourier transform; quadrature.

MATH 413G Introduction to Numerical Analysis

3 cr. Undergraduate/Graduate.
Root finding and solution of nonlinear systems; direct solution of linear systems; interpolation & approximation of functions; least squares; fast Fourier transform; quadrature.

MATH 415 Introduction to Scientific Computing

3 cr. Undergraduate/Graduate.
Nonlinear systems; iterative solution of linear systems; initial value problems in ordinary differential equations; boundary value problems in ordinary and partial differential equations.

MATH 415G Introduction to Scientific Computing

3 cr. Undergraduate/Graduate.
Nonlinear systems; iterative solution of linear systems; initial value problems in ordinary differential equations; boundary value problems in ordinary and partial differential equations.

MATH 417 Computational Linear Algebra

3 cr. Undergraduate/Graduate.
Direct solution of linear systems; iterative solution of linear systems; least squares; eigenvalue problems.

MATH 417G Computational Linear Algebra

3 cr. Undergraduate/Graduate.
Direct solution of linear systems; iterative solution of linear systems; least squares; eigenvalue problems.

MATH 423 Complex Analysis

3 cr. Undergraduate/Graduate.
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.

MATH 423G Complex Analysis

3 cr. Undergraduate/Graduate.
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.

MATH 431 Modern Algebra with Applications

3 cr. Undergraduate/Graduate.
Groups, rings, fields, Boolean algebras with emphasis on their applications to computer science and other areas.

MATH 431G Modern Algebra with Applications

3 cr. Undergraduate/Graduate.
Groups, rings, fields, Boolean algebras with emphasis on their applications to computer science and other areas.

MATH 451 Axiomatic Geometry

3 cr. Undergraduate/Graduate.
An axiomatic approach to Euclidean and non-Euclidean geometry (historic role of the parallel postulate and models).

MATH 451G Axiomatic Geometry

3 cr. Undergraduate/Graduate.
An axiomatic approach to Euclidean and non-Euclidean geometry (historic role of the parallel postulate and models).

MATH 453 Transformations in Geometry

3 cr. Undergraduate/Graduate.
Selected topics from vector geometry and geometric transformations such as the study of invariants and conics.

MATH 453G Transformations in Geometry

3 cr. Undergraduate/Graduate.
Selected topics from vector geometry and geometric transformations such as the study of invariants and conics.

MATH 489 Internship in Mathematics, Upper Division

1-6 cr. Undergraduate.
Application of advanced principles of mathematics in a business, organizational, educational, governmental, or other appropriate setting.

MATH 490 Topics in Mathematics:

3 cr. Undergraduate/Graduate.
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.

MATH 490G Topics in Mathematics:

3 cr. Undergraduate/Graduate.
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.

MATH 497 Study Abroad:

1-12 cr. Undergraduate/Graduate.
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.

MATH 497G Study Abroad:

1-12 cr. Undergraduate/Graduate.
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.

MATH 499 Ad Hoc:

1-6 cr. Undergraduate.
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.

MATH 511 Symbolic Logic

3 cr. Undergraduate/Graduate.
First-order predicate calculus; formal properties of theoretical systems; chief results of modern mathematical logic; advanced topics such as completeness and computability.

MATH 511G Symbolic Logic

3 cr. Undergraduate/Graduate.
First-order predicate calculus; formal properties of theoretical systems; chief results of modern mathematical logic; advanced topics such as completeness and computability.

MATH 521 Advanced Calculus I

3 cr. Undergraduate/Graduate.
Fundamental notions of sets and functions; limits, continuity; Riemann integral, improper integral; infinite series; uniform convergence; power series; improper integrals with a parameter.

MATH 521G Advanced Calculus I

3 cr. Undergraduate/Graduate.
Fundamental notions of sets and functions; limits, continuity; Riemann integral, improper integral; infinite series; uniform convergence; power series; improper integrals with a parameter.

MATH 522 Advanced Calculus II

3 cr. Undergraduate/Graduate.
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.

MATH 522G Advanced Calculus II

3 cr. Undergraduate/Graduate.
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.

MATH 531 Modern Algebra

3 cr. Undergraduate/Graduate.
Integers; groups; rings; fields; emphasis on proofs.

MATH 531G Modern Algebra

3 cr. Undergraduate/Graduate.
Integers; groups; rings; fields; emphasis on proofs.

MATH 535 Linear Algebra

3 cr. Undergraduate/Graduate.
Vector spaces; systems of linear equations; linear transformations and matrices; bilinear, quadratic, and Hermitian forms; eigentheory; canonical forms; selected topics. Emphasizes theory and proof.

MATH 535G Linear Algebra

3 cr. Undergraduate/Graduate.
Vector spaces; systems of linear equations; linear transformations and matrices; bilinear, quadratic, and Hermitian forms; eigentheory; canonical forms; selected topics. Emphasizes theory and proof.

MATH 537 Number Theory

3 cr. Undergraduate/Graduate.
Number theoretic functions; distribution of primes; Diophantine approximation; partitions; additive number theory; quadratic reciprocity.

MATH 537G Number Theory

3 cr. Undergraduate/Graduate.
Number theoretic functions; distribution of primes; Diophantine approximation; partitions; additive number theory; quadratic reciprocity.

MATH 551 Elementary Topology

3 cr. Undergraduate/Graduate.
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.

MATH 551G Elementary Topology

3 cr. Undergraduate/Graduate.
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.

MATH 553 Differential Geometry

3 cr. Undergraduate/Graduate.
The theory of curves and surfaces by differential methods.

MATH 553G Differential Geometry

3 cr. Undergraduate/Graduate.
The theory of curves and surfaces by differential methods.

MATH 571 Introduction to Probability Models

3 cr. Undergraduate/Graduate.
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.

MATH 571G Introduction to Probability Models

3 cr. Undergraduate/Graduate.
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.

MATH 575 High School Mathematics from an Advanced Viewpoint

3 cr. Undergraduate/Graduate.
Number systems; algebra of polynomials; theory of equations; functions; modeling; geometric measurement; geometric transformations; connections between advanced mathematics and high school topics.

MATH 575G High School Mathematics from an Advanced Viewpoint

3 cr. Undergraduate/Graduate.
Number systems; algebra of polynomials; theory of equations; functions; modeling; geometric measurement; geometric transformations; connections between advanced mathematics and high school topics.

MATH 581 Introduction to the Theory of Chaotic Dynamical Systems

3 cr. Undergraduate/Graduate.
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.

MATH 581G Introduction to the Theory of Chaotic Dynamical Systems

3 cr. Undergraduate/Graduate.
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.

MATH 591 Undergraduate Seminar:

1 cr. Undergraduate.
Specific topics and any additional prerequisites announced in Schedule of Classes each time course is offered.

MATH 599 Capstone Experience

1 cr. Undergraduate.
Student writes a paper under supervision of an advisor on an approved topic not covered in the student's regular course work.

MATH 601 Advanced Engineering Mathematics I

3 cr. Undergraduate/Graduate.
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.

MATH 601G Advanced Engineering Mathematics I

3 cr. Undergraduate/Graduate.
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.

MATH 602 Advanced Engineering Mathematics II

3 cr. Undergraduate/Graduate.
Continuation of Math 601. Partial differential equations, Fourier and Laplace transforms, convolutions, special functions, mathematical modeling.

MATH 602G Advanced Engineering Mathematics II

3 cr. Undergraduate/Graduate.
Continuation of Math 601. Partial differential equations, Fourier and Laplace transforms, convolutions, special functions, mathematical modeling.

MATH 615 Numerical Solution of Partial Differential Equations

3 cr. Undergraduate/Graduate.
Finite difference solution of elliptic boundary value problems and of evolution problems; solution of hyperbolic conservation laws; finite volume methods; finite element methods.

MATH 615G Numerical Solution of Partial Differential Equations

3 cr. Undergraduate/Graduate.
Finite difference solution of elliptic boundary value problems and of evolution problems; solution of hyperbolic conservation laws; finite volume methods; finite element methods.

MATH 617 Optimization

3 cr. Undergraduate/Graduate.
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.

MATH 617G Optimization

3 cr. Undergraduate/Graduate.
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.

MATH 621 Introduction to Analysis I

3 cr. Undergraduate/Graduate.
Topology of Euclidean space; continuity; differentiation of real and vector-valued functions; Riemann-Stieltjes integration.

MATH 621G Introduction to Analysis I

3 cr. Undergraduate/Graduate.
Topology of Euclidean space; continuity; differentiation of real and vector-valued functions; Riemann-Stieltjes integration.

MATH 622 Introduction to Analysis II

3 cr. Undergraduate/Graduate.
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.

MATH 622G Introduction to Analysis II

3 cr. Undergraduate/Graduate.
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.

MATH 631 Modern Algebra I

3 cr. Undergraduate/Graduate.
Group theory, including normal subgroups, quotients, permutation groups, Sylow's theorems, Abelian groups; field theory; linear algebra over general fields.

MATH 631G Modern Algebra I

3 cr. Undergraduate/Graduate.
Group theory, including normal subgroups, quotients, permutation groups, Sylow's theorems, Abelian groups; field theory; linear algebra over general fields.

MATH 632 Modern Algebra II

3 cr. Undergraduate/Graduate.
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.

MATH 632G Modern Algebra II

3 cr. Undergraduate/Graduate.
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.

MATH 690 Topics in Mathematics:

3 cr. Undergraduate/Graduate.
Specific topics and any additional prerequisites announced in Schedule of Classes each time course is offered.

MATH 690G Topics in Mathematics:

3 cr. Undergraduate/Graduate.
Specific topics and any additional prerequisites announced in Schedule of Classes each time course is offered.

MATH 699 Independent Reading

1-3 cr. Undergraduate.
See Advanced Independent Study. For further information, consult dept chair.

MTHSTAT

MTHSTAT 194 First-Year Seminar:

3 cr. Undergraduate.
Specific topics are announced in the Schedule of Classes each time the class is offered.

MTHSTAT 199 Independent Study

1-3 cr. Undergraduate.
For further information, consult dept chair.

MTHSTAT 215 Elementary Statistical Analysis

3 cr. Undergraduate.
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.

MTHSTAT 216 Introduction to Statistical Computing and Data Science

3 cr. Undergraduate.
Introduction to hands-on data analysis, performed on large, complex and realistic data sets, using a scientific programming language like R.

MTHSTAT 278 Discrete Probability and Statistics for Elementary Education Majors

3 cr. Undergraduate.
Random experiments; histograms; sample spaces; equally likely outcomes for random experiments; permutations; combinations; binomial, geometric, hypergeometric distributions; expectation; conditional probabilities; max likelihood estimation & inference.

MTHSTAT 299 Ad Hoc:

1-6 cr. Undergraduate.
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.

MTHSTAT 361 Introduction to Mathematical Statistics I

3 cr. Undergraduate/Graduate.
Probability spaces; discrete and continuous, univariate and multivariate distributions; moments; independence, random sampling, sampling distributions; normal and related distributions; point and interval estimation.

MTHSTAT 361G Introduction to Mathematical Statistics I

3 cr. Undergraduate/Graduate.
Probability spaces; discrete and continuous, univariate and multivariate distributions; moments; independence, random sampling, sampling distributions; normal and related distributions; point and interval estimation.

MTHSTAT 362 Introduction to Mathematical Statistics II

3 cr. Undergraduate/Graduate.
Testing statistical hypothesis; linear hypothesis; regression; analysis of variance and experimental designs; distribution-free methods; sequential methods.

MTHSTAT 362G Introduction to Mathematical Statistics II

3 cr. Undergraduate/Graduate.
Testing statistical hypothesis; linear hypothesis; regression; analysis of variance and experimental designs; distribution-free methods; sequential methods.

MTHSTAT 461 Data Analysis and Graphing Using SAS-I

2 cr. Undergraduate.
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.

MTHSTAT 462 Data Analysis and Graphing Using SAS-II

2 cr. Undergraduate/Graduate.
Continuation of MthStat 461. Procedures GLM, LIFEREG, LIFETEST, LOGISTIC, PROBIT and advanced GRAPHING. Offered second half of sem.

MTHSTAT 462G Data Analysis and Graphing Using SAS-II

2 cr. Undergraduate/Graduate.
Continuation of MthStat 461. Procedures GLM, LIFEREG, LIFETEST, LOGISTIC, PROBIT and advanced GRAPHING. Offered second half of sem.

MTHSTAT 465 Introductory Mathematical Statistics for Social Sciences and Education

3 cr. Undergraduate/Graduate.
Probability distributions; parameter estimation and confidence intervals; hypothesis testing; applications.

MTHSTAT 465G Introductory Mathematical Statistics for Social Sciences and Education

3 cr. Undergraduate/Graduate.
Probability distributions; parameter estimation and confidence intervals; hypothesis testing; applications.

MTHSTAT 467 Introductory Statistics for Physical Sciences and Engineering Students

3 cr. Undergraduate/Graduate.
Concepts of probability and statistics; probability distributions of engineering applications; sampling distributions; hypothesis testing, parameter estimation; experimental design; regression analysis.

MTHSTAT 467G Introductory Statistics for Physical Sciences and Engineering Students

3 cr. Undergraduate/Graduate.
Concepts of probability and statistics; probability distributions of engineering applications; sampling distributions; hypothesis testing, parameter estimation; experimental design; regression analysis.

MTHSTAT 469 Biostatistics

3 cr. Undergraduate/Graduate.
Simple distributions, estimation and hypothesis testing, simple regression, analysis of variance, nonparametric methods in biology. Demography and vital statistics and bioassay and clinical trials.

MTHSTAT 469G Biostatistics

3 cr. Undergraduate/Graduate.
Simple distributions, estimation and hypothesis testing, simple regression, analysis of variance, nonparametric methods in biology. Demography and vital statistics and bioassay and clinical trials.

MTHSTAT 489 Internship in Mathematical Statistics, Upper Division

1-6 cr. Undergraduate.
Application of advanced principles of mathematical statistics in a business, organizational, educational, governmental, or other appropriate setting.

MTHSTAT 499 Ad Hoc:

1-6 cr. Undergraduate.
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.

MTHSTAT 562 Design of Experiments

3 cr. Undergraduate/Graduate.
Latin squares; incomplete block designs; factorial experiments; confounding; partial confounding; split-plot experiments; fractional replication.

MTHSTAT 562G Design of Experiments

3 cr. Undergraduate/Graduate.
Latin squares; incomplete block designs; factorial experiments; confounding; partial confounding; split-plot experiments; fractional replication.

MTHSTAT 563 Regression Analysis

3 cr. Undergraduate/Graduate.
Straight line, polynomial and multiple regression; multiple and partial correlation; testing hypotheses in regression; residual analysis.

MTHSTAT 563G Regression Analysis

3 cr. Undergraduate/Graduate.
Straight line, polynomial and multiple regression; multiple and partial correlation; testing hypotheses in regression; residual analysis.

MTHSTAT 564 Time Series Analysis

3 cr. Undergraduate/Graduate.
Autocorrelation; spectral density; linear models; forecasting; model identification and estimation.

MTHSTAT 564G Time Series Analysis

3 cr. Undergraduate/Graduate.
Autocorrelation; spectral density; linear models; forecasting; model identification and estimation.

MTHSTAT 565 Nonparametric Statistics

3 cr. Undergraduate/Graduate.
Sign, rank and permutation tests; tests of randomness and independence; methods for discrete data and zeroes and ties; power and efficiency of nonparametric tests.

MTHSTAT 565G Nonparametric Statistics

3 cr. Undergraduate/Graduate.
Sign, rank and permutation tests; tests of randomness and independence; methods for discrete data and zeroes and ties; power and efficiency of nonparametric tests.

MTHSTAT 566 Computational Statistics

3 cr. Undergraduate/Graduate.
Basics of programming and optimization techniques; resampling, bootstrap, and Monte Carlo methods; design and analysis of simulation studies.

MTHSTAT 566G Computational Statistics

3 cr. Undergraduate/Graduate.
Basics of programming and optimization techniques; resampling, bootstrap, and Monte Carlo methods; design and analysis of simulation studies.

MTHSTAT 568 Multivariate Statistical Analysis

3 cr. Undergraduate/Graduate.
Multivariate normal distribution; Wishart distribution; Hotelling's T2; multivariate normal distribution; multivariate analysis of variance; classification problems.

MTHSTAT 568G Multivariate Statistical Analysis

3 cr. Undergraduate/Graduate.
Multivariate normal distribution; Wishart distribution; Hotelling's T2; multivariate normal distribution; multivariate analysis of variance; classification problems.

MTHSTAT 597G Actuarial Statistics II

3 cr. Undergraduate.
Credibility theory, ratemaking, and reserving.

MATH

MATH 305 Introduction to Mathematical and Computational Modeling

3 cr. Undergraduate/Graduate.
Construction and analysis of discrete and continuous mathematical models in applied, natural, and social sciences. Elements of programming, simulations, case studies from scientific literature.

MATH 305G Introduction to Mathematical and Computational Modeling

3 cr. Undergraduate/Graduate.
Construction and analysis of discrete and continuous mathematical models in applied, natural, and social sciences. Elements of programming, simulations, case studies from scientific literature.

MATH 313 Linear Programming and Optimization

3 cr. Undergraduate/Graduate.
Primal and dual formulations of linear programming problems; simplex and related methods of solution; algorithms for transportation; optimization.

MATH 313G Linear Programming and Optimization

3 cr. Undergraduate/Graduate.
Primal and dual formulations of linear programming problems; simplex and related methods of solution; algorithms for transportation; optimization.

MATH 315 Mathematical Programming and Optimization

3 cr. Undergraduate/Graduate.
Introduction to operations research. Network analysis; integer programming; game theory; nonlinear programming; dynamic programming.

MATH 315G Mathematical Programming and Optimization

3 cr. Undergraduate/Graduate.
Introduction to operations research. Network analysis; integer programming; game theory; nonlinear programming; dynamic programming.

MATH 320 Introduction to Differential Equations

3 cr. Undergraduate/Graduate.
Elementary types and systems of differential equations, series solutions, numerical methods, Laplace transforms, selected applications.

MATH 320G Introduction to Differential Equations

3 cr. Undergraduate/Graduate.
Elementary types and systems of differential equations, series solutions, numerical methods, Laplace transforms, selected applications.

MATH 321 Vector Analysis

3 cr. Undergraduate/Graduate.
Topics selected from vector algebra; scalar and vector fields; line, surface, and volume integrals; theorems of Green, Gauss, and Stokes; vector differential calculus.

MATH 321G Vector Analysis

3 cr. Undergraduate/Graduate.
Topics selected from vector algebra; scalar and vector fields; line, surface, and volume integrals; theorems of Green, Gauss, and Stokes; vector differential calculus.

MATH 322 Introduction to Partial Differential Equations

3 cr. Undergraduate/Graduate.
Partial differential equations of mathematical physics, boundary value problems in heat flow, vibrations, potentials, etc. Solved by Fourier series; Bessel functions and Legendre polynomials.

MATH 322G Introduction to Partial Differential Equations

3 cr. Undergraduate/Graduate.
Partial differential equations of mathematical physics, boundary value problems in heat flow, vibrations, potentials, etc. Solved by Fourier series; Bessel functions and Legendre polynomials.

MATH 371 Introduction to Stochastic Models in Finance

3 cr. Undergraduate/Graduate.
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.

MATH 371G Introduction to Stochastic Models in Finance

3 cr. Undergraduate/Graduate.
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.

MATH 405 Mathematical Models and Applications

3 cr. Undergraduate/Graduate.
Modeling techniques for analysis and decision-making in social and life sciences and industry. Deterministic and stochastic modeling. Topics may vary with instructors.

MATH 405G Mathematical Models and Applications

3 cr. Undergraduate/Graduate.
Modeling techniques for analysis and decision-making in social and life sciences and industry. Deterministic and stochastic modeling. Topics may vary with instructors.

MATH 413 Introduction to Numerical Analysis

3 cr. Undergraduate/Graduate.
Root finding and solution of nonlinear systems; direct solution of linear systems; interpolation & approximation of functions; least squares; fast Fourier transform; quadrature.

MATH 413G Introduction to Numerical Analysis

3 cr. Undergraduate/Graduate.
Root finding and solution of nonlinear systems; direct solution of linear systems; interpolation & approximation of functions; least squares; fast Fourier transform; quadrature.

MATH 415 Introduction to Scientific Computing

3 cr. Undergraduate/Graduate.
Nonlinear systems; iterative solution of linear systems; initial value problems in ordinary differential equations; boundary value problems in ordinary and partial differential equations.

MATH 415G Introduction to Scientific Computing

3 cr. Undergraduate/Graduate.
Nonlinear systems; iterative solution of linear systems; initial value problems in ordinary differential equations; boundary value problems in ordinary and partial differential equations.

MATH 417 Computational Linear Algebra

3 cr. Undergraduate/Graduate.
Direct solution of linear systems; iterative solution of linear systems; least squares; eigenvalue problems.

MATH 417G Computational Linear Algebra

3 cr. Undergraduate/Graduate.
Direct solution of linear systems; iterative solution of linear systems; least squares; eigenvalue problems.

MATH 423 Complex Analysis

3 cr. Undergraduate/Graduate.
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.

MATH 423G Complex Analysis

3 cr. Undergraduate/Graduate.
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.

MATH 431 Modern Algebra with Applications

3 cr. Undergraduate/Graduate.
Groups, rings, fields, Boolean algebras with emphasis on their applications to computer science and other areas.

MATH 431G Modern Algebra with Applications

3 cr. Undergraduate/Graduate.
Groups, rings, fields, Boolean algebras with emphasis on their applications to computer science and other areas.

MATH 451 Axiomatic Geometry

3 cr. Undergraduate/Graduate.
An axiomatic approach to Euclidean and non-Euclidean geometry (historic role of the parallel postulate and models).

MATH 451G Axiomatic Geometry

3 cr. Undergraduate/Graduate.
An axiomatic approach to Euclidean and non-Euclidean geometry (historic role of the parallel postulate and models).

MATH 453 Transformations in Geometry

3 cr. Undergraduate/Graduate.
Selected topics from vector geometry and geometric transformations such as the study of invariants and conics.

MATH 453G Transformations in Geometry

3 cr. Undergraduate/Graduate.
Selected topics from vector geometry and geometric transformations such as the study of invariants and conics.

MATH 490 Topics in Mathematics:

3 cr. Undergraduate/Graduate.
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.

MATH 490G Topics in Mathematics:

3 cr. Undergraduate/Graduate.
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.

MATH 497 Study Abroad:

1-12 cr. Undergraduate/Graduate.
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.

MATH 497G Study Abroad:

1-12 cr. Undergraduate/Graduate.
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.

MATH 511 Symbolic Logic

3 cr. Undergraduate/Graduate.
First-order predicate calculus; formal properties of theoretical systems; chief results of modern mathematical logic; advanced topics such as completeness and computability.

MATH 511G Symbolic Logic

3 cr. Undergraduate/Graduate.
First-order predicate calculus; formal properties of theoretical systems; chief results of modern mathematical logic; advanced topics such as completeness and computability.

MATH 521 Advanced Calculus I

3 cr. Undergraduate/Graduate.
Fundamental notions of sets and functions; limits, continuity; Riemann integral, improper integral; infinite series; uniform convergence; power series; improper integrals with a parameter.

MATH 521G Advanced Calculus I

3 cr. Undergraduate/Graduate.
Fundamental notions of sets and functions; limits, continuity; Riemann integral, improper integral; infinite series; uniform convergence; power series; improper integrals with a parameter.

MATH 522 Advanced Calculus II

3 cr. Undergraduate/Graduate.
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.

MATH 522G Advanced Calculus II

3 cr. Undergraduate/Graduate.
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.

MATH 531 Modern Algebra

3 cr. Undergraduate/Graduate.
Integers; groups; rings; fields; emphasis on proofs.

MATH 531G Modern Algebra

3 cr. Undergraduate/Graduate.
Integers; groups; rings; fields; emphasis on proofs.

MATH 535 Linear Algebra

3 cr. Undergraduate/Graduate.
Vector spaces; systems of linear equations; linear transformations and matrices; bilinear, quadratic, and Hermitian forms; eigentheory; canonical forms; selected topics. Emphasizes theory and proof.

MATH 535G Linear Algebra

3 cr. Undergraduate/Graduate.
Vector spaces; systems of linear equations; linear transformations and matrices; bilinear, quadratic, and Hermitian forms; eigentheory; canonical forms; selected topics. Emphasizes theory and proof.

MATH 537 Number Theory

3 cr. Undergraduate/Graduate.
Number theoretic functions; distribution of primes; Diophantine approximation; partitions; additive number theory; quadratic reciprocity.

MATH 537G Number Theory

3 cr. Undergraduate/Graduate.
Number theoretic functions; distribution of primes; Diophantine approximation; partitions; additive number theory; quadratic reciprocity.

MATH 551 Elementary Topology

3 cr. Undergraduate/Graduate.
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.

MATH 551G Elementary Topology

3 cr. Undergraduate/Graduate.
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.

MATH 553 Differential Geometry

3 cr. Undergraduate/Graduate.
The theory of curves and surfaces by differential methods.

MATH 553G Differential Geometry

3 cr. Undergraduate/Graduate.
The theory of curves and surfaces by differential methods.

MATH 571 Introduction to Probability Models

3 cr. Undergraduate/Graduate.
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.

MATH 571G Introduction to Probability Models

3 cr. Undergraduate/Graduate.
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.

MATH 575 High School Mathematics from an Advanced Viewpoint

3 cr. Undergraduate/Graduate.
Number systems; algebra of polynomials; theory of equations; functions; modeling; geometric measurement; geometric transformations; connections between advanced mathematics and high school topics.

MATH 575G High School Mathematics from an Advanced Viewpoint

3 cr. Undergraduate/Graduate.
Number systems; algebra of polynomials; theory of equations; functions; modeling; geometric measurement; geometric transformations; connections between advanced mathematics and high school topics.

MATH 581 Introduction to the Theory of Chaotic Dynamical Systems

3 cr. Undergraduate/Graduate.
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.

MATH 581G Introduction to the Theory of Chaotic Dynamical Systems

3 cr. Undergraduate/Graduate.
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.

MATH 601 Advanced Engineering Mathematics I

3 cr. Undergraduate/Graduate.
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.

MATH 601G Advanced Engineering Mathematics I

3 cr. Undergraduate/Graduate.
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.

MATH 602 Advanced Engineering Mathematics II

3 cr. Undergraduate/Graduate.
Continuation of Math 601. Partial differential equations, Fourier and Laplace transforms, convolutions, special functions, mathematical modeling.

MATH 602G Advanced Engineering Mathematics II

3 cr. Undergraduate/Graduate.
Continuation of Math 601. Partial differential equations, Fourier and Laplace transforms, convolutions, special functions, mathematical modeling.

MATH 615 Numerical Solution of Partial Differential Equations

3 cr. Undergraduate/Graduate.
Finite difference solution of elliptic boundary value problems and of evolution problems; solution of hyperbolic conservation laws; finite volume methods; finite element methods.

MATH 615G Numerical Solution of Partial Differential Equations

3 cr. Undergraduate/Graduate.
Finite difference solution of elliptic boundary value problems and of evolution problems; solution of hyperbolic conservation laws; finite volume methods; finite element methods.

MATH 617 Optimization

3 cr. Undergraduate/Graduate.
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.

MATH 617G Optimization

3 cr. Undergraduate/Graduate.
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.

MATH 621 Introduction to Analysis I

3 cr. Undergraduate/Graduate.
Topology of Euclidean space; continuity; differentiation of real and vector-valued functions; Riemann-Stieltjes integration.

MATH 621G Introduction to Analysis I

3 cr. Undergraduate/Graduate.
Topology of Euclidean space; continuity; differentiation of real and vector-valued functions; Riemann-Stieltjes integration.

MATH 622 Introduction to Analysis II

3 cr. Undergraduate/Graduate.
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.

MATH 622G Introduction to Analysis II

3 cr. Undergraduate/Graduate.
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.

MATH 631 Modern Algebra I

3 cr. Undergraduate/Graduate.
Group theory, including normal subgroups, quotients, permutation groups, Sylow's theorems, Abelian groups; field theory; linear algebra over general fields.

MATH 631G Modern Algebra I

3 cr. Undergraduate/Graduate.
Group theory, including normal subgroups, quotients, permutation groups, Sylow's theorems, Abelian groups; field theory; linear algebra over general fields.

MATH 632 Modern Algebra II

3 cr. Undergraduate/Graduate.
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.

MATH 632G Modern Algebra II

3 cr. Undergraduate/Graduate.
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.

MATH 690 Topics in Mathematics:

3 cr. Undergraduate/Graduate.
Specific topics and any additional prerequisites announced in Schedule of Classes each time course is offered.

MATH 690G Topics in Mathematics:

3 cr. Undergraduate/Graduate.
Specific topics and any additional prerequisites announced in Schedule of Classes each time course is offered.

MATH 701 Industrial Mathematics I

3 cr. Graduate.
Elementary functional analysis, wavelets, control theory. Use of mathematical software emphasized throughout.

MATH 702 Industrial Mathematics II

3 cr. Graduate.
Optimal control theory, digital signal processing, image processing, linear programming, nonlinear optimation, artificial neural networks. Use of mathematical software emphasized throughout.

MATH 703 Boundary Value Problems

3 cr. Graduate.
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.

MATH 704 Potential Theory

3 cr. Graduate.
Newtonian potentials; harmonic functions in two or more dimensions; dirichlet and other boundary value problems; recent abstract formulations.

MATH 709 Differential Geometry

3 cr. Graduate.
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.

MATH 711 Theory of Functions of a Real Variable I

3 cr. Graduate.
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.

MATH 712 Theory of Functions of a Real Variable II

3 cr. Graduate.
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.

MATH 713 Theory of Functions of a Complex Variable I

3 cr. Graduate.
Complex numbers; linear transformations; elementary functions; conformal mapping; complex integration; infinite sequences; dirichlet problem; multivalued functions.

MATH 714 Theory of Functions of a Complex Variable II

3 cr. Graduate.
Continuation of Math 713.

MATH 715 Numerical Analysis

3 cr. Graduate.
Interpolation and approximation; differentiation and quadrature; numerical solution of ordinary differential equations; solution of linear and nonlinear algebraic equations.

MATH 716 Ordinary Differential Equations

3 cr. Graduate.
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.

MATH 719 Partial Differential Equations

3 cr. Graduate.
First and second order equations; characteristics, cauchy problem; classical solutions of linear elliptic, parabolic and hyperbolic equations.

MATH 721 Abstract Measure and Integration

3 cr. Graduate.
General theory of measures and integration; differentiation of set functions; relation to stochastic variables; atomic measures; haar measure and integral applications to probability theory.

MATH 723 Entire Functions

3 cr. Graduate.
Representation theorems; zeros; order of growth; picard theorems; approximation by polynomials; generalization to meromorphic functions.

MATH 726 Introduction to Functional Analysis

3 cr. Graduate.
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.

MATH 731 Abstract Algebra I

3 cr. Graduate.
Basic course which is prerequisite for all other 700-799 level courses in algebra; groups, rings, fields, galois theory, modules, and categories.

MATH 732 Abstract Algebra II

3 cr. Graduate.
Continuation of Math 731.

MATH 735 Theory of Groups

3 cr. Graduate.
Topics selected from permutation groups; representations of groups and algebras; group algebras; group characters; extension problems; simple groups; solvable and nilpotent groups.

MATH 736 Theory of Rings and Modules I

3 cr. Graduate.
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.

MATH 737 Theory of Rings and Modules II

3 cr. Graduate.
Continuation of Math 736.

MATH 751 Introductory Topology I

3 cr. Graduate.
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.

MATH 752 Introductory Topology II

3 cr. Graduate.
Continuation of Math 751.

MATH 753 Introduction to Algebraic Topology I

3 cr. Graduate.
Homology theory; complexes and simplicial homology theory; general homology theories; cohomology rings; applications to manifolds, fixed point theorems, etc.

MATH 754 Introduction to Algebraic Topology II

3 cr. Graduate.
Continuation of Math 753.

MATH 767 Statistical Methods for Engineers and Scientists

3 cr. Graduate.
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.

MATH 768 Applied Stochastic Processes

3 cr. Graduate.
Concepts in queueing theory; exponential channels; applications of markov chains to queueing problems; queue disciplines with priorities.

MATH 771 Theory of Probability

3 cr. Graduate.
Measure-theoretic foundations; limit-law theorems; weak and strong laws of large numbers; central limit problem; conditional expectations, martingales; stochastic processes.

MATH 781 Iterated Maps as Dynamical Systems

3 cr. Graduate.
Periodic, recurrent and non-wandering points, kneading theory, unstable manifolds, unimodal mappings, turbulent and chaotic maps, symbolic dynamics, structural stability, topological conjugacy, topological dynamics.

MATH 790 Master's Thesis

1-3 cr. Graduate.

MATH 791 Master's Seminar

1-3 cr. Graduate.

MATH 792 Industrial Internship

1-3 cr. Graduate.
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.

MATH 793 Scientific Computational Laboratory:

1-2 cr. Graduate.

MATH 799 Seminar in Mathematics:

1-3 cr. Graduate.
Specific topics and any additional prerequisites announced in Timetable each time course is offered.

MATH 801 Topics in Applied Mathematics:

3 cr. Graduate.
Specific topics and any additional prerequisites will be announced in the Timetable each time the course is offered.

MATH 807 Group Theory and Its Applications to Physics

3 cr. Graduate.
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.

MATH 809 Topics in Differential Geometry:

1-3 cr. Graduate.
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

MATH 813 Numerical Solution of Ordinary Differential Equations

3 cr. Graduate.
Methods for initial value and boundary value problems; stiff equations, singular points and bifurcation.

MATH 814 Numercal Solution of Partial Differential Equations

3 cr. Graduate.
Finite difference and finite element methods for linear elliptic, parabolic and hyperbolic equations; nonlinear equations.

MATH 815 Topics in Numerical Analysis:

3 cr. Graduate.
Specific topics and any additional prerequisites will be announced in the Timetable each time the course is offered.

MATH 816 Advanced Ordinary Differential Equations

3 cr. Graduate.
Existence and uniqueness theorems; singularity of solutions; oscillation and comparison theorems; poincare-bendixon theory.

MATH 817 Advanced Ordinary Differential Equations II

3 cr. Graduate.
Continuation of Math 816; dynamical systems, bifurcation theory, topological methods.

MATH 819 Advanced Partial Differential Equations

3 cr. Graduate.
Theory of linear PDE's including; elliptic, parabolic and hyperbolic equations; weak solvability, regularity theorems. Fundamental solutions, asymptotic properties.

MATH 821 Advanced Topics in Real Analysis:

3 cr. Graduate.
Specific topics and any additional prerequisites will be announced in the Timetable each time the course is offered.

MATH 823 Advanced Topics in Complex Analysis:

3 cr. Graduate.
Specific topics and any additional prerequisites will be announced in the Timetable each time the course is offered.

MATH 825 Functional Analysis

3 cr. Graduate.
Basic theorems of b-spaces and f-spaces including the closed graph; Hahn-Banach and Banach-Steinhaus theorems; Banach algebras; generalized functions; spectral theory.

MATH 826 Functional Analysis

3 cr. Graduate.
Continuation of MATH 825.

MATH 827 Fourier Analysis

3 cr. Graduate.
Fourier coefficients; convergence of Fourier series and conjugate Fourier series; summability; functions of certain special classes; absolute convergence of trigonometric series; divergence; complex methods.

MATH 841 Advanced Topics in Algebra:

3 cr. Graduate.
Specific topics and any additional prerequisites will be announced in the Timetable each time the course is offered.

MATH 843 Homological Algebra I

3 cr. Graduate.
Modules; diagrams; categories; functors; complexes; cohomology; extensions; resolutions; injective and projective systems; graded modules; homological dimension; spectral sequences; derived functors.

MATH 844 Homological Algebra II

3 cr. Graduate.
Continuation of Math 843.

MATH 851 Advanced Topics in Topology:

3 cr. Graduate.
Specific topics and any additional prerequisites will be announced in the Timetable each time the course is offered.

MATH 857 Dimension Theory

3 cr. Graduate.
Topological definitions of dimension; dimension of Euclidean spaces, covering and imbedding theorems; mapping in spheres and applications; relations between homology and dimension.

MATH 873 Advanced Topics in Probability:

3 cr. Graduate.
Specific topics and any additional prerequisites will be announced in the Timetable each time the course is offered.

MATH 881 Topics in Nonlinear Dynamics:

3 cr. Graduate.
Specific topics and any additional prerequisites will be announced in the Timetable each time the course is offered.

MATH 888 Candidate for Degree

0 cr. Graduate.
Available for graduate students who must meet minimum credit load requirement.

MATH 990 Reading and Research

1-6 cr. Graduate.
To be arranged with your instructor and department chair.

MTHSTAT

MTHSTAT 361 Introduction to Mathematical Statistics I

3 cr. Undergraduate/Graduate.
Probability spaces; discrete and continuous, univariate and multivariate distributions; moments; independence, random sampling, sampling distributions; normal and related distributions; point and interval estimation.

MTHSTAT 361G Introduction to Mathematical Statistics I

3 cr. Undergraduate/Graduate.
Probability spaces; discrete and continuous, univariate and multivariate distributions; moments; independence, random sampling, sampling distributions; normal and related distributions; point and interval estimation.

MTHSTAT 362 Introduction to Mathematical Statistics II

3 cr. Undergraduate/Graduate.
Testing statistical hypothesis; linear hypothesis; regression; analysis of variance and experimental designs; distribution-free methods; sequential methods.

MTHSTAT 362G Introduction to Mathematical Statistics II

3 cr. Undergraduate/Graduate.
Testing statistical hypothesis; linear hypothesis; regression; analysis of variance and experimental designs; distribution-free methods; sequential methods.

MTHSTAT 462 Data Analysis and Graphing Using SAS-II

2 cr. Undergraduate/Graduate.
Continuation of MthStat 461. Procedures GLM, LIFEREG, LIFETEST, LOGISTIC, PROBIT and advanced GRAPHING. Offered second half of sem.

MTHSTAT 462G Data Analysis and Graphing Using SAS-II

2 cr. Undergraduate/Graduate.
Continuation of MthStat 461. Procedures GLM, LIFEREG, LIFETEST, LOGISTIC, PROBIT and advanced GRAPHING. Offered second half of sem.

MTHSTAT 465 Introductory Mathematical Statistics for Social Sciences and Education

3 cr. Undergraduate/Graduate.
Probability distributions; parameter estimation and confidence intervals; hypothesis testing; applications.

MTHSTAT 465G Introductory Mathematical Statistics for Social Sciences and Education

3 cr. Undergraduate/Graduate.
Probability distributions; parameter estimation and confidence intervals; hypothesis testing; applications.

MTHSTAT 467 Introductory Statistics for Physical Sciences and Engineering Students

3 cr. Undergraduate/Graduate.
Concepts of probability and statistics; probability distributions of engineering applications; sampling distributions; hypothesis testing, parameter estimation; experimental design; regression analysis.

MTHSTAT 467G Introductory Statistics for Physical Sciences and Engineering Students

3 cr. Undergraduate/Graduate.
Concepts of probability and statistics; probability distributions of engineering applications; sampling distributions; hypothesis testing, parameter estimation; experimental design; regression analysis.

MTHSTAT 469 Biostatistics

3 cr. Undergraduate/Graduate.
Simple distributions, estimation and hypothesis testing, simple regression, analysis of variance, nonparametric methods in biology. Demography and vital statistics and bioassay and clinical trials.

MTHSTAT 469G Biostatistics

3 cr. Undergraduate/Graduate.
Simple distributions, estimation and hypothesis testing, simple regression, analysis of variance, nonparametric methods in biology. Demography and vital statistics and bioassay and clinical trials.

MTHSTAT 562 Design of Experiments

3 cr. Undergraduate/Graduate.
Latin squares; incomplete block designs; factorial experiments; confounding; partial confounding; split-plot experiments; fractional replication.

MTHSTAT 562G Design of Experiments

3 cr. Undergraduate/Graduate.
Latin squares; incomplete block designs; factorial experiments; confounding; partial confounding; split-plot experiments; fractional replication.

MTHSTAT 563 Regression Analysis

3 cr. Undergraduate/Graduate.
Straight line, polynomial and multiple regression; multiple and partial correlation; testing hypotheses in regression; residual analysis.

MTHSTAT 563G Regression Analysis

3 cr. Undergraduate/Graduate.
Straight line, polynomial and multiple regression; multiple and partial correlation; testing hypotheses in regression; residual analysis.

MTHSTAT 564 Time Series Analysis

3 cr. Undergraduate/Graduate.
Autocorrelation; spectral density; linear models; forecasting; model identification and estimation.

MTHSTAT 564G Time Series Analysis

3 cr. Undergraduate/Graduate.
Autocorrelation; spectral density; linear models; forecasting; model identification and estimation.

MTHSTAT 565 Nonparametric Statistics

3 cr. Undergraduate/Graduate.
Sign, rank and permutation tests; tests of randomness and independence; methods for discrete data and zeroes and ties; power and efficiency of nonparametric tests.

MTHSTAT 565G Nonparametric Statistics

3 cr. Undergraduate/Graduate.
Sign, rank and permutation tests; tests of randomness and independence; methods for discrete data and zeroes and ties; power and efficiency of nonparametric tests.

MTHSTAT 566 Computational Statistics

3 cr. Undergraduate/Graduate.
Basics of programming and optimization techniques; resampling, bootstrap, and Monte Carlo methods; design and analysis of simulation studies.

MTHSTAT 566G Computational Statistics

3 cr. Undergraduate/Graduate.
Basics of programming and optimization techniques; resampling, bootstrap, and Monte Carlo methods; design and analysis of simulation studies.

MTHSTAT 568 Multivariate Statistical Analysis

3 cr. Undergraduate/Graduate.
Multivariate normal distribution; Wishart distribution; Hotelling's T2; multivariate normal distribution; multivariate analysis of variance; classification problems.

MTHSTAT 568G Multivariate Statistical Analysis

3 cr. Undergraduate/Graduate.
Multivariate normal distribution; Wishart distribution; Hotelling's T2; multivariate normal distribution; multivariate analysis of variance; classification problems.

MTHSTAT 761 Mathematical Statistics I

3 cr. Graduate.
Probability and distribution theory; point and interval estimation; testing hypotheses; large sample inference; nonparametric inference; sequential analysis.

MTHSTAT 762 Mathematical Statistics II

3 cr. Graduate.
Continuation of MthStat 761.

MTHSTAT 763 Regression Analysis

3 cr. Graduate.
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.

MTHSTAT 764 Time Series Analysis

3 cr. Graduate.
Introduction to statistical models and methods for time series data analysis. Core topics include: exponential smoothing, ARIMA models, transfer functions and intervention models, state-space models, GARCH models.

MTHSTAT 766 Computational Statistics

3 cr. Graduate.
Introduction to statistical computer programming. Main topics include: basics of programming in R or similar language; optimization and root-finding algorithms; Monte Carlo numerical integration; random sample generation; bootstrap and permutation tests; comparative simulation studies.

MTHSTAT 768 Multivariate Statistical Analysis

3 cr. Graduate.
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.

MTHSTAT 863 Hypothesis Testing

3 cr. Graduate.
Exponential families; uniformly most--powerful tests; least favorable priors; unbiased tests; invariant tests; applications to exponential families and the general linear hypothesis.

MTHSTAT 869 Advanced Topics in Mathematical Statistics:

3 cr. Graduate.
Specific topics and any additional prerequisites will be announced in the Timetable each time the course is offered.