# College of Letters and Science

## MATH Mathematical Sciences

This course information produced at 01:00 on 08/29/2014.
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90 Basic Mathematics. 0 cr. U. Arithmetic operations involving whole numbers, integers, positive and negative rational numbers; decimals, percents; ratio, proportion; radicals; descriptive statistics; units of measure; geometry; introduction to algebra.|Fee for 3 cr assessed; credits count toward credit load for Financial Aid and enrollment verification only. Not open to students eligible for math courses that carry graduation credit. Prereq: none.
92 (effective 09/02/2014) Mathematical Literacy for College Students I. 0 cr. U. Introduction to numeracy, proportional reasoning, algebraic reasoning, and functions. Emphasis on developing conceptual and procedural tools that support the use of key mathematical concepts in context.|Fee for 3 cr assessed; counts as 3 cr toward cr load for Fin Aid & enrollment verification. Prereq: Placement level E or D.
94 Preparation for College Mathematics. 0 cr. U. Combination of the content of Math 90 and Math 95. Use of computer adaptive testing software to provide individualized instruction in a laboratory setting.|Fee for 6 cr assessed; credits count toward credit load for Financial Aid and enrollment verification only. Math 94 counts as repeat of Math 90 & 95. Prereq: none.
95 Essentials of Algebra. 0 cr. U. Number systems; linear equations, inequalities; exponent notation, radicals; polynomials, operations, factoring, rational expressions; coordinate geometry; linear systems; quadratic equations.|Fee for 3 cr assessed; credits count toward credit load for Financial Aid and enrollment verification only. Prereq: math placement level D.
98 (effective 09/02/2014) Algebraic Literacy I. 0 cr. U. Arithmetic number systems; linear equations, inequalities; exponent notation, radicals; polynomials, operations, factoring; modeling; coordinate geometry; linear systems; quadratic equations.|Fee for 3 cr assessed; counts as 3 cr toward credit load for Fin Aid & enrollment verification only. Prereq: math placement level D.
102 (effective 09/02/2014) Mathematical Literacy for College Students II. 3 cr. U. Continuation of Math 92, with an integrated approach to numeracy, proportional reasoning, algebraic reasoning, and functions.|Prereq: C or better in Math 92.
103 (106) Contemporary Applications of Mathematics. 3 cr. U. Logical inference, probability and statistical inference, geometric growth, with selected topics such as linear programming, patterns, binary codes.|Prereq: math placement level C.
105 Intermediate Algebra. 3 cr. U. Algebraic techniques with polynomials, rational expressions, equations and inequalities, exponential and logarithmic functions, rational exponents, conic sections, systems of linear equations.|Prereq: math placement level C.
105 (effective 09/02/2014) Intermediate Algebra. 3 cr. U. Algebraic techniques with polynomials, rational expressions, equations and inequalities, exponential and logarithmic functions, rational exponents, systems of linear equations.|Not open for cr to students who have cr in Math 108(ER). Prereq: math placement level C.
108 (effective 09/02/2014) Algebraic Literacy II. 3 cr. U. Continuation of Math 98 in polynomials, equations, and inequalities; exponential, logarithmic, and periodic functions; rational expressions and exponents; and systems of linear equations.|Not open for credit for students who have cr in Math 105(ER). Prereq: C or better Math 98.
116 College Algebra. 3 cr. U. Function concepts. Polynomial, rational, exponential, and logarithmic functions. Systems of equations and inequalities. Matrices and determinants. Sequences and series. Analytic geometry and conic sections. Induction.|2 cr may be used to repeat 2 cr of Math 115. Prereq: math placement level B.
117 (effective 09/02/2014) Trigonometry. 2 cr. U. Trigonometric functions; graphs, identities, equations, inequalities; inverse trigonometric functions; solutions of triangles with applications; complex numbers; polar coordinates.|Repeats 2 cr of Math 115. Prereq: math placement level B.
117 Trigonometry. 2 cr. U. Trigonometric functions; graphs, identities, equations, inequalities; inverse trigonometric functions; solutions of triangles with applications; complex numbers; polar coordinates.|Repeats 2 cr of Math 115. Prereq: math placement level B.
175 Mathematical Explorations for Elementary Teachers I. 3 cr. U. Theory of arithmetic of whole numbers, fractions, and decimals. Introduction to algebra, estimation and problem-solving strategies.|Prereq: Math placement level A, AB, B, or C & regis in elementary, early childhood, or exceptional educ curric.
176 Mathematical Explorations for Elementary Teachers II. 3 cr. U. A continuation of Math 175 in geometry, statistics, and probability.|Prereq: grade of C or better in Math 175(P).
194 First-Year Seminar: (Subtitled). 3 cr. U. Specific topics are announced in the Schedule of Classes each time the class is offered.|Open only to freshmen. Students may earn cr in just one L&S First-Year Sem (course numbers 192, 193, 194). Prereq: none.
199 Independent Study. 1-3 cr. U. Regularly offered courses may not be taken as Independent Study.|Retakable w/chg in topic to 9 cr max. Prereq: 2.5 gpa in all previous math courses; writ cons instr, dept chair & asst dean for SAS.
205 Introductory Finite Mathematics. 3 cr. U. Elements of mathematical logic, structures in sets; partitions and counting; probability theory, stochastic processes.|Prereq: math placement level B.
211 Survey in Calculus and Analytic Geometry. 4 cr. U. A one-semester survey with applications to business administration, economics, and non-physical sciences. Topics include coordinate systems, equations of curves, limits, differentiation, integration, applications.|May not be used as a prereq for Math 226, 227, 229, or 232. No cr for students with cr in Math 221, 226, 227, 228, or 231. Prereq: math placement level B.
221 Honors Calculus I. 5H cr. U. Calculus of functions of one and several variables; sequences, series, differentiation, integration; introduction to differential equations; vectors and vector functions; applications.|Max of 6 cr in combination of Math 221 & 222 may count toward Honors College reqs. Prereq: math placement level A+; cons instr or Honors College dir.
222 Honors Calculus II. 5H cr. U. Continuation of Math 221.|Max of 6 cr in combination of Math 221 & 222 may count toward Honors College reqs. Prereq: C or better in Math 221(P) or B or better in Math 232(P); cons instr.
231 Calculus and Analytic Geometry. 4 cr. U. Limits, derivatives, and graphs of algebraic, trigonometric, exponential, and logarithmic functions; antiderivatives, the definite integral, and the fundamental theorem of calculus, with applications.|Repeats Math 226, 227, & 228. Prereq: math placement level A.
232 Calculus and Analytic Geometry. 4 cr. U. Continuation of Math 231. Applications of integration, techniques of integration; infinite sequences and series; parametric equations, conic sections, and polar coordinates.|Prereq: grade of C or better in Math 226(P), 227(P), 228(P), 229(P), or 231(P).
233 Calculus and Analytic Geometry. 4 cr. U. Continuation of Math 232. Three-dimensional analytic geometry and vectors; partial derivatives; multiple integrals; vector calculus, with applications.|Counts as repeat of Math 229. Prereq: grade of C or better in Math 232(P).
234 Linear Algebra and Differential Equations. 4 cr. U. Elementary differential equations. Vectors; matrices; linear transformations; quadratic forms; eigenvalues; applications.|Prereq: grade of C or better in Math 232(P).
275 Problem Solving/Critical Thinking for Elementary Education Majors. 3 cr. U. Course provides a strong foundation in the exploration, teaching and communication (oral and written) of mathematical concepts via problem-solving experiences and discussion.|Prereq: Math 175(P) or cons instr.
276 Algebraic Structures for Elementary Education Majors. 3 cr. U. Topics for K-8 teachers. Basic patterns and rules that govern number systems, geometric transformations, and manipulation of algebraic expressions.|Counts as repeat of Math 299 w/same topic. Prereq: Math 175(P) or cons instr.
277 Geometry for Elementary Education Majors. 3 cr. U. Topics for K-8 teachers. Geometry as measuring tool-congruence, similarity, area, volume, and coordinates; geometry as axiomatic system-definitions, conjectures, proofs, counterexamples; rigid motions, symmetry.|Prereq: Math 176(P) or cons instr.
278 Discrete Probability and Statistics for Elementary Education Majors. 3 cr. U. Random experiments; histograms; sample spaces; equally likely outcomes for random experiments; permutations; combinations; binomial, geometric, hypergeometric distributions; expectation; conditional probabilities; max likelihood estimation & inference.|Math 278 and MthStat 278 are jointly offered; they count as repeats of one another. Prereq: Math 176(P) or cons instr.
297 Study Abroad: (Subtitled). 1-12 cr. U. Designed to enroll students in UWM sponsored programs before course work level, content and credits are determined and/or in specially prepared program course work.|Retakable w/chg in topic. Prereq: acceptance for Study Abroad Prog.
299 Ad Hoc: (Subtitled). 1-6 cr. U. Course created expressly for offering in a specified enrollment period. Requires only dept & assoc dean approval. In exceptional circumstances, can be offered in one add'l sem.|Retakable w/chg in topic. Prereq: none; add'l prereqs may be assigned to specific topic.
311 Theory of Interest. 4 cr. U/G. Interest theory: annuities, ammortization schedules, portfolio immunization. Financial derivatives: bonds, forwards, options. Topics are consistent with syllabus of SOA Financial Mathematics Exam.|Does not carry grad cr in Math Dept. Prereq: jr st & Math 232(P); or grad st.
313 Linear Programming and Optimization. 3 cr. U/G. Primal and dual formulations of linear programming problems; simplex and related methods of solution; algorithms for transportation; optimization.|Prereq: jr st; Math/ElecEng 234(P); or grad st.
314 Mathematical Programming and Optimization. 3 cr. U/G. Introduction to operations research. Network analysis; integer programming; game theory; nonlinear programming; dynamic programming.|Prereq: jr st; Math 313(P) or cons instr; or grad st.
320 Introduction to Differential Equations. 3 cr. U/G. Elementary types and systems of differential equations, series solutions, numerical methods, Laplace transforms, selected applications.|No grad cr in Math Sci. Prereq: jr st, Math 233(P) & Math 234(P) or ElecEng 234(P); or grad st.
321 Vector Analysis. 3 cr. U/G. Topics selected from vector algebra; scalar and vector fields; line, surface, and volume integrals; theorems of Green, Gauss, and Stokes; vector differential calculus.|Prereq: jr st, Math 233(P) & Math 234(P) or ElecEng 234(P); or grad st.
322 Introduction to Partial Differential Equations. 3 cr. U/G. Partial differential equations of mathematical physics, boundary value problems in heat flow, vibrations, potentials, etc. Solved by Fourier series; Bessel functions and Legendre polynomials.|Prereq: jr st, Math 320(P); or grad st.
341 Seminar: Introduction to the Language and Practice of Mathematics. 3 cr. U. Goal: facility with mathematical language and method of conjecture, proof and counter example, with emphasis on proofs. Topics: logic, sets, functions and others.|Prereq: math placement level A.
371 Introduction to Stochastic Models in Finance. 3 cr. U/G. Elementary modeling of financial instruments for students in mathematics, economics, business, etc. Statistical and stochastic tools leading to the Black-Scholes model. Real data parameter fitting.|Prereq: jr st & one of the following pairs; Econ 413(431)(P) & 506(P), Bus Adm 210(P) & 350(P), Bus Adm 701(P) & 702(P), or Math 234(P) & MthStat 361(P), or cons instr; or grad st.
381 Honors Seminar: (Subtitled). 3H cr. U. Significant topics to illustrate to non-mathematicians the characteristic features of mathematical thought. Only H.S. algebra and geometry assumed.|Retakable w/chg in topic to 9 cr max. Not open for cr toward a major in Math. Prereq: soph st; Honors 200(P); cons Honors College dir.
405 Mathematical Models and Applications. 3 cr. U/G. Construction and mathematical models with applications to the social and life sciences. Models may involve Markov chains, linear programming, game theory, graph theory and growth processes.|Prereq: jr st & either Math 234(P) or Math 205(P) & 211(P); or grad st.
413 Introduction to Numerical Analysis. 3 cr. U/G. Finite difference calculus; summation calculus; roots of polynomials; polynomial approximations; numerical solution of differential and integral equations; numerical quadrature; selected topics in computer programming.|Prereq: jr st, Math 233(C), & Math 234(C) or ElecEng 234(C); or grad st.
413 (effective 09/02/2014) Introduction to Numerical Analysis. 3 cr. U/G. Root finding and solution of nonlinear systems; direct solution of linear systems; interpolation & approximation of functions; least squares; fast Fourier transform; quadrature.|Prereq: jr st, Math 233(C), & Math 234(C) or ElecEng 234(C); or grad st.
414 Numerical Analysis. 3 cr. U/G. Systems of linear and nonlinear equations; eigenvalue and eigenvector problems; solution of ordinary and partial differential equations; initial and boundary value problems.|Prereq: jr st & Math 413(P) or ElecEng 413(P); or grad st.
415 (414) (effective 09/02/2014) Introduction to Scientific Computing. 3 cr. U/G. Nonlinear systems; iterative solution of linear systems; initial value problems in ordinary differential equations; boundary value problems in ordinary and partial differential equations.|Prereq: jr st, Math 233(P), 234(P) or ElecEng 234(P); or grad st.
416 Computational Linear Algebra. 3 cr. U/G. Linear transformations and matrices; direct solution of linear systems; errors, ill-conditioning, perturbed matrices; iterative refinements; least squares; Eigenvalues, Eigenvectors, inverse power and QR methods.|Prereq: jr st & Math/ElecEng 234(P); or grad st.
417 (416) (effective 09/02/2014) Computational Linear Algebra. 3 cr. U/G. Direct solution of linear systems; iterative solution of linear systems; least squares; eigenvalue problems.|Prereq: jr st & Math/ElecEng 234(P); or grad st.
431 Modern Algebra with Applications. 3 cr. U/G. Groups, rings, fields, Boolean algebras with emphasis on their applications to computer science and other areas.|Does not carry grad cr in math sci. Prereq: jr st & Math 232(P); or grad st.
451 Axiomatic Geometry. 3 cr. U/G. An axiomatic approach to Euclidean and non-Euclidean geometry (historic role of the parallel postulate and models).|Dept permission necessary for grad cr in math sci. Prereq: jr st, Math 341(241)(P), & Math 232(C); or grad st.
453 Transformations in Geometry. 3 cr. U/G. Selected topics from vector geometry and geometric transformations such as the study of invariants and conics.|Recom for secondary school teachers. Departmental permission necessary for grad cr in math sci. Prereq: jr st, Math 341(241)(P), & Math 232(C); or grad st.
489 Internship in Mathematics, Upper Division. 1-6 cr. U. Application of advanced principles of mathematics in a business, organizational, educational, governmental, or other appropriate setting.|One cr earned for academic work based on 40 hours in internship. Retakable to 6 cr max. Prereq: jr st; 6 cr 300-level or above in math or math stats; 2.5 gpa in the major; cons supervising faculty member.
497 Study Abroad: (Subtitled). 1-12 cr. U/G. Designed to enroll students in UWM sponsored programs before course work level, content and credits are determined and/or in specially prepared program course work.|Retakable w/chg in topic. Prereq: jr st; acceptance for Study Abroad Prog.
499 Ad Hoc: (Subtitled). 1-6 cr. U. Course created expressly for offering in a specified enrollment period. Requires only dept & assoc dean approval. In exceptional circumstances, can be offered in one add'l sem.|Retakable w/chg in topic. Prereq: jr st; add'l prereqs may be assigned to specific topic.
511 Symbolic Logic. 3 cr. U/G. First-order predicate calculus; formal properties of theoretical systems; chief results of modern mathematical logic; advanced topics such as completeness and computability.|CompSci 511, Math 511 & Philos 511 are jointly offered; they count as repeats of one another. Prereq: jr st & either Philos 212(P) or 6 cr in math at the 300-level or above.
521 Advanced Calculus. 3 cr. U/G. Fundamental notions of sets and functions; limits, continuity; Riemann integral, improper integral; infinite series; uniform convergence; power series; improper integrals with a parameter.|Prereq: jr st, Math 232(P), & 341(241)(P); or grad st. Math 233(R) & 234(R).
522 Advanced Calculus. 3 cr. U/G. Linear functions; differentiation of functions of several variables (implicit functions, Jacobians); change of variable in multiple integrals; integrals over curves, surfaces; Green, Gauss, Stokes theorems.|Prereq: jr st, Math 233(P), 234(P) & 521(P); or grad st.
531 Modern Algebra. 3 cr. U/G. Integers; groups; rings; fields; emphasis on proofs.|Prereq: jr st; Math 234(P) & 341(P).
535 Linear Algebra. 3 cr. U/G. Vector spaces; linear transformations and matrices; characteristic values and vectors; canonical forms; bilinear, quadratic, and Hermitian forms; selected applications.|Prereq: jr st, Math 234(P) or 240(P), & Math 341(241)(P); or grad st.
537 Number Theory. 3 cr. U/G. Number theoretic functions; distribution of primes; Diophantine approximation; partitions; additive number theory; quadratic reciprocity.|Prereq: jr st, Math 232(P) & 341(241)(P); or grad st.
551 Elementary Topology. 3 cr. U/G. General theory of point sets in Euclidean spaces, with emphasis on topology of two-dimensional and three-dimensional spaces; elementary notions of metric spaces; applications.|Prereq: jr st & either Math 521(P) or 529(P); or grad st.
553 Differential Geometry. 3 cr. U/G. The theory of curves and surfaces by differential methods.|Prereq: jr st, Math 233(P), 234(P) & 341(241)(P); or grad st.
571 (472) Introduction to Probability Models. 3 cr. U/G. Probability review, Markov chains in discrete and continuous time. Random walks, branching processes, birth and death processes. Queuing theory. Applications to physical sciences, engineering, mathematics.|Prereq: jr st, Math 233(P), Math 234(P) or ElecEng 234(P), & one college-level course in statistics or probability; or grad st.
581 Introduction to the Theory of Chaotic Dynamical Systems. 3 cr. U/G. Iterated mappings, one parameter families, attracting and repelling periodic orbits, topological transitivity, Sarkovski's theorem, chaos, bifurcation theory, period doubling route to chaos, horseshoe maps, attractors.|Prereq: jr st & Math 521(P), 529(P) or 621(P), or cons instr; or grad st.
591 Undergraduate Seminar: (Subtitled). 1 cr. U. Specific topics and any additional prerequisites announced in Schedule of Classes each time course is offered.|Retakable w/chg in topic to 4 cr max. Prereq: jr st; cons instr.
599 Capstone Experience. 1 cr. U. Student writes a paper under supervision of an advisor on an approved topic not covered in the student's regular course work.|Prereq: sr st; writ cons instr & dept chair.
601 Advanced Engineering Mathematics I. 3 cr. U/G. Sequences and series, elementary complex analysis; Fourier series; linear and nonlinear ordinary differential equations; matrix theory, elementary functional analysis; elementary solution of partial differential equations.|Prereq: jr st; Math 234(P) or ElecEng 234(P); 3 cr Math at 300-level or above; or cons instr.
602 Advanced Engineering Mathematics II. 3 cr. U/G. Continuation of Math 601. Partial differential equations, Fourier and Laplace transforms, convolutions, special functions, mathematical modeling.|Prereq: jr st; Math 601(P).
615 (effective 09/02/2014) Numerical Solution of Partial Differential Equations. 3 cr. U/G. Finite difference solution of elliptic boundary value problems and of evolution problems; solution of hyperbolic conservation laws; finite volume methods; finite element methods.|Prereq: jr st; Math 413(P), 415(414)(P), or 417(416)(P); Math 322(P) or 602(P); or cons instr.
617 (effective 09/02/2014) Optimization. 3 cr. U/G. Unconstrained and constrained optimization: linear, nonlinear, and dynamic programming; barrier, penalty, and Lagrangian methods; Karush-Kuhn-Tucker theory, quadratic, and sequential quadratic programming; evolutionary algorithms.|Prereq: jr st; Math 321(P) or 602(P); or grad st or cons instr.
621 Introduction to Analysis. 3 cr. U/G. Topology of Euclidean space; continuity; differentiation of real and vector-valued functions; Riemann-Stieltjes integration.|Prereq: jr st, Math 233(P) 234(P), & 341(241)(P); or grad st.
622 Introduction to Analysis. 3 cr. U/G. Continues Math 621. Sequences and series of functions; uniform convergence; power series; functions of several variables; inverse and implicit function theorems; differential forms; Stokes' theorem.|Prereq: jr st & Math 621(P); or grad st.
623 Complex Analysis. 3 cr. U/G. Complex numbers; definition and properties of analytic functions of a complex variable; conformal mapping; calculus of residues; applications to mathematics and physics. See also Math 713.|Prereq: jr st & either Math 321(P) OR 521(P); or grad st.
631 Modern Algebra. 3 cr. U/G. Group theory, including normal subgroups, quotients, permutation groups, Sylow's theorems, Abelian groups; field theory; linear algebra over general fields.|Prereq: jr st, Math 531(P) or cons instr; or grad st.
632 Modern Algebra. 3 cr. U/G. Continuation of Math 631. Ring theory, including ideals, quotient rings, Euclidean rings, polynomial rings, unique factorization; modules, including vector spaces, linear transformations, canonical forms; bilinear forms.|Prereq: jr st & Math 631(P) or cons instr; or grad st.
675 Topics in Modern Mathematics: (Subtitled). 3 cr. U/G. Instructor and student presentations of modern topics. Specific topics and any additional prerequisites announced in Schedule of Classes each time course is offered.|Retakable w/chg in topic to 9 cr max. Prereq: jr st, Math 233(P) & cons instr; or grad st.
699 Independent Reading. 1-3 cr. U. See Advanced Independent Study. For further information, consult dept chair.|Retakable w/chg in topic. Prereq: jr st; 2.5 gpa, & writ cons instr, dept chair, & asst dean for SAS.

This course information produced at 01:00 on 08/29/2014.