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. Not open to students eligible for math courses that carry graduation credit. 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. Prereq: math placement level D.
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.
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.
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 Trigonometry. 2 cr. U.
Trigonometric functions; graphs, indentities, 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 Freshman Seminar: (Subtitled). 3 cr. U.
Specific topics are announced in the Schedule of Classes each time the class is offered. Open only to freshmen. Retakable w/chg in topic to 6 cr max. 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.
201 Computer Calculus Laboratory. 1 cr. U.
Review of elementary Fortran; study of some of the concepts of calculus such as limits, continuity, differentiation, and integration by the use of computer programs. Prereq: Math 211(C) or 231(C).
202 Computer Calculus Laboratory. 1 cr. U.
Study of some of the concepts of calculus in the use of computer programs such as partial differentiation, max-min problems, Taylor series, and integration. Prereq: knowledge of Fortran; Math 232(C).
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.
214 Computational Models and Problem Solving. 3 cr. U.
Statistical calculations, simulation of random and nonrandom processes, and other numerical problems. Prereq: grade of C or better in CompSci 132(R) & 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. 5 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.
225 Calculus with Precalculus I. 4 cr. U.
Half of Math 231 correlated with material from algebra, coordinate geometry, trigonometry, and elementary functions. Prereq: math placement level AB.
226 Calculus with Precalculus II. 4 cr. U.
Continuation of Math 225. Remaining portions of Math 231 correlated with material from algebra, coordinate geometry, trigonometry, and elementary functions. Repeats Math 227; repeats Math 228 & 231 only if Math 225 also completed w/grade of C or better. Prereq: grade of C or better in Math 225(P).
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).
240 Matrices and Applications. 3 cr. U.
Vectors, matrices, linear transformations, quadratic forms, eigenvalues, and applications. Prereq: 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.
305 Vectors and Matrices. 3 cr. U/G.
Systems of linear equations and determinants, vector geometry and linear transformations in three dimensions, with emphasis on the development of computational tools. Not open for cr to students w/cr in Math 234(ER). Does not carry cr toward Math Sci major or grad cr in Math Sci. Prereq: jr st, math placement level B; or grad st.
311 Theory of Interest. 3 cr. U/G.
Simple and compound interest, annuities, amortization schedules, sinking funds, bonds, miscellaneous topics. Designed to prepare students for interest theory portion of second examination of Society of Actuaries. Does not carry grad cr in Math Dept. Prereq: jr st, Math 211(P) or 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.
337 Introduction to Number Theory. 3 cr. U/G.
Divisibility; primes; congruences; continued fractions; Pell's equation; Pythagorean triples; magic squares. Applies toward math major only in School of Education. Does not carry grad cr in math sciences. Prereq: jr st, Math 211(P) or math placement level A; 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.
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.
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.
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.
471 Introduction to the Theory of Probability. 3 cr. U/G.
Probability in discrete & continuous sample spaces; combinatorial analysis; conditional probabilities; stochastic independence; Laplace limit theorem; Poisson distribution; laws of large numbers. Applications to physics, statistics. Prereq: jr st & Math 233(P); 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 40 hrs in the 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.
520 Non-Linear Differential Equations. 3 cr. U/G.
Two dimensional autonomous systems, fixed point theory, Lyapunov functions, limit cycles, normal forms, bifurcation theory. Introduction to higher dimensional systems, invariant manifolds, Poincare maps. Prereq: jr st, Math 320(P) or cons instr; or grad st.
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.
525 Introductory Theory of Differential Equations. 3 cr. U/G.
Basic course in the theory of ordinary differential equations. Existence and uniqueness theorems; series methods; Bessel and Legendre equations. Prereq: jr st & Math 521(P); or grad st.
529 Structure of Real and Complex Numbers. 3 cr. U/G.
Construction of the real and complex number systems; topology of the real line and the complex plane; sequences and series of complex numbers. Prereq: jr st & Math 341( 241)(P); or grad st.
531 Modern Algebra. 3 cr. U.
Integers; groups; rings; fields; emphasis on proofs. Prereq: Math 234(P) & 341(241)(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.
555 Projective Geometry. 3 cr. U/G.
Axiomatic and analytic methods; relation to affine geometry; coordinatization; conics; real projective plane; projective spaces. Prereq: jr st, Math 232(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).
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 01:01 on 05/16/2008.
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