# Mathematics (MATH)

**MATH 090**

**Fundamentals of Mathematics**

**3.00**

Review of pre-algebra mathematics with an introduction to basic algebra. Topics include: real numbers, with an emphasis on fractions and decimals; percent notation; exponents; algebraic expressions; solving equations and inequalities; polynomials; factoring integers; unit conversions; and an introduction to graphing linear equations. Does not apply toward University Studies requirements or graduation requirements.

**MATH 095**

**Fundamentals of Algebra**

**3.00**

Review of elementary algebra topics typically topics include: the real number system; linear equations and inequalities and their graphs; systems of linear equations; polynomials, factoring polynomials; rational expressions; rational exponents; radical expressions. Does not apply toward University Studies requirements or graduation requirements.

Review of elementary algebra topics typically topics include: the real number system; functions; linear equations and inequalities and their graphs; systems of linear equations; polynomials, factoring polynomials; rational expressions; rational exponents; radical expressions. Does not apply toward University Studies requirements or graduation requirements.

Review of elementary algebra: the real number system; functions; linear equations and their graphs; polynomials; rational expressions; rational exponents; combinations and permutations. Does not apply toward University Studies requirements or graduation requirements.

**MATH 102**

**Intermediate Algebra**

**2.00**

Review of intermediate algebra topics typically studied in high school. Topics include: rational expressions and equations; rational exponents; radical expressions and equations; complex numbers; functions; quadratic equations and functions; graphing techniques, conic sections; exponential and logarithmic functions and equations.

**Prerequisites:**

- Adequate math placement score or completion of MATH 095 with a C- or better.

**MATH 112**

**Introduction to Contemporary Mathematics**

**3.00**

A liberal arts mathematics course presenting mathematics as a tool used by a wide range of professionals in modern society. Real-life examples are used to
promote understanding of mathematics and its relationship to other areas of
study. Examples will be chosen from graph theory (Traveling Salesman Problem and Euler Circuits), voting theory (fairness criteria and Arrow's impossibility theorem), elementary probability and statistics, logic, geometry, mathematics of growth, mathematics of finance, and mathematical modeling.

**Prerequisites:**

**University Studies Requirements:**

- Math/Computer Science

**MATH 113**

**Algebra with Applications**

**3.00**

Algebraic concepts, problem-solving techniques, and applications for students in business, natural and social sciences. Topics include linear, quadratic, exponential, logarithmic functions and their graphs; equations and inequalities; systems of equations and matrices; complex numbers.

**Prerequisites:**

**University Studies Requirements:**

- Math/Computer Science

**MATH 115**

**Precalculus**

**5.00**

Covers the algebra and trigonometry required for Calculus and Analytic Geometry. Topics include review of intermediate algebra; composite and inverse functions; systems of equations; partial fractions; matrices; polynomial and rational functions, exponential and logarithmic functions, trigonometric functions, identities, and equations; the binomial theorem; and fundamentals of analytic geometry.

**Prerequisites:**

- Adequate math placement score or completion of MATH 113 with a C- or better.

**University Studies Requirements:**

- Math/Computer Science

**MATH 130**

**Elementary Statistics**

**4.00**

Introductory course for students of all disciplines. Includes descriptive statistics, probability, the binomial and normal distributions, confidence intervals, correlation and linear regression, Central Limit Theorem, and one-sample (population mean and population proportion) and two-sample (population means) hypothesis testing. Problems are taken from various fields of study dependent on statistical decision making.

**Prerequisites:**

**University Studies Requirements:**

- Math/Computer Science

**MATH 151**

**Calculus for Business, Life, and Social Sciences**

**3.00**

A short course in calculus including concepts and problem-solving techniques for students in business, economics, biology and the social sciences. Topics include algebraic, exponential and logarithmic functions; derivatives, and optimization problems; integrals; partial derivatives and Lagrange multipliers as time permits.

**Prerequisites:**

- Adequate math placement score or completion of MATH 113 with a C- or better.

**University Studies Requirements:**

- Math/Computer Science

**MATH 189**

**Mathematics Elective**

**1.00-12.00**

Transfer credits ONLY from another accredited institution not equivalent to a UW-S course.

**MATH 189MC**

**Mathematics Elective Math/Computer Science**

**1.00-12.00**

Transfer credits ONLY from another accredited institution not equivalent to a UW-S course.

**MATH 240**

**Calculus and Analytic Geometry I**

**4.00**

A first course in the fundamentals of calculus. Topics include: real numbers; functions; limits; continuity; derivatives, integrals; the use of computational tools in calculus; transcendental functions; and applications.

**Prerequisites:**

- Adequate math placement score or completion of MATH 115 with a C- or better.

**University Studies Requirements:**

- Math/Computer Science

**MATH 241**

**Calculus and Analytic Geometry II**

**4.00**

Continuation of MATH 240. Topics include: conic sections; techniques and applications of integration; parametric curves and polar coordinates; indeterminate forms; improper integrals; and infinite series.

**Prerequisites:**

- Completion of MATH 240 with a grade of C- or better.

**MATH 242**

**Calculus and Analytic Geometry III**

**4.00**

Continuation of MATH 241. Topics include: three-dimensional analytic geometry; vectors; partial derivatives; multiple integrals; line integrals; and surface integrals.

**Prerequisites:**

- Completion of MATH 241 with a grade of C- or better.

**MATH 289**

**Mathematics Elective**

**1.00-12.00**

Transfer credits ONLY from another accredited institution not equivalent to a UW-S course.

**MATH 289MC**

**Math Elective Math/Computer Science**

**1.00-12.00**

Transfer credits ONLY from another accredited institution not equivalent to a UW-S course.

**MATH 310**

**Introduction to Abstract Mathematics**

**3.00**

Fundamentals of formal mathematics emphasizing mathematical writing and
types of formal proof. Includes significant coverage of topics in logic, set
theory, basic number theory, relations and functions.

**Prerequisites:**

- Completion of MATH 240 with a C- or better or instructor permission.

**MATH 315**

**Linear Algebra**

**3.00**

Introduction to the algebra and geometry of two-and three-dimensional real vector space and extension to n-dimensional space. Topics include: line and coordinate vectors; systems of linear equations and their solution by reduction methods; matrix algebra; determinants; fundamentals of abstract vector spaces; linear independence, dimension theorems; linear transformations; eigenvalues and eigenvectors; diagonal matrices; quadratic forms; inner products; and the Gram-Schmidt orthogonalization.

**Prerequisites:**

- Successful completion of MATH 310.

**MATH 320**

**Discrete Structures**

**4.00**

Continuation of MATH 310. Investigation of concepts of non-calculus mathematics of interest in computer and other areas. Topics include: recurrence relations, enumerative combinatorics, partially ordered sets, graph theory, and related algorithms.

**Prerequisites:**

- Successful completion of MATH 310.

**MATH 344**

**Differential Equations**

**4.00**

Introduction to the theory of ordinary differential equations including some coverage of series solutions, as time permits. Also covers various classical applications, such as spring mass systems.

**Prerequisites:**

- Successful completion of MATH 241.

**MATH 362**

**Topics In Geometry**

**3.00**

A proof-based course in modern geometry with an emphasis in Euclidean Geometry. Topics include: lines, polygons, circles, congruence and similarity, area of shapes, compass and straight edge constructions, axioms of incidence, and Playfrair's axiom.

**Prerequisites:**

- Successful completion of MATH 310.

**MATH 370**

**Probability**

**3.00**

A first course in Calculus-based probability theory. Topics include: axioms of probability; combinatorial analysis; conditional probability; independence; discrete and continuous random variables; probability distributions; expectation; variance; Poisson processes; and limit theorems.

**MATH 371**

**Statistics**

**4.00**

Calculus-based statistics emphasizing applications intended for students in mathematics, economics and the sciences. Topics include: the use of statistical software; estimation and prediction; hypothesis testing; linear and multiple regression; F and t tests; analysis of variance; and non-parametric statistics.

**MATH 381**

**Special Projects**

**1.00-4.00**

Various individual and small-group projects carried out under the supervision of one or more instructors. Requires weekly progress reports plus a final report and/or a final exam. May be repeated, but no more than a total of four credits may be earned from both MATH 381 and CSCI 381. Pass-Fail only. Preliminary project plan and an independent study contract required prior to enrollment.

**MATH 385**

**Introduction to Operations Research**

**3.00**

Topics include mathematical programming, (programming problems, transportation problems, dynamic programming, game theory), queuing theory, inventory theory, reliability theory, and simulation techniques. Look at capitalization

**MATH 389**

**Mathematics Elective**

**1.00-9.00**

Transfer credits ONLY from another accredited institution not equivalent to a UW-S course.

**MATH 390**

**Mathematical Sciences Internship**

**1.00-4.00**

Work in an approved position to gain experience in solving real problems using computer science, mathematics, and statistics. Interns may receive salaried appointments with cooperating companies. Pass-Fail only.

**MATH 391**

**Putnam Mathematical Competition**

**3.00**

Preparation for the national Putnam Mathematics Contest. Includes review of previous examination problems and lectures on selected topics. May be repeated for a total of up to six credits. Pass-Fail only.

**MATH 421**

**Theory of Computation**

**4.00**

Thorough introduction to automata, formal languages and computability. Topics include: models of computation; regular and context-free languages; finite and pushdown automata; Turing machines; unsolvable decision problems; and fundamentals of computational complexity.

**Prerequisites:**

- Successful completion of MATH 320.

**MATH 425**

**Algorithm Design and Analysis**

**4.00**

Study of the design and analysis of algorithms that are based on elementary data structures such as queues, stacks and trees. Some graph and network algorithms (shortest paths, connectivity, coloring, flows, matchings), geometric algorithms (convex hulls, range search, nearest neighbors), NP-complexity, approximation algorithms (vertex cover, traveling salesman, scheduling), and introduction to randomized algorithms. Introduction to algorithm design techniques, including greedy algorithms, divide-and-conquer, and dynamic programming. Lower and upper bounds of program complexity are analyzed. Introduction to algorithms used in the area of information security.

**Prerequisites:**

- Successful completion of MATH 320.

**MATH 437**

**Cryptography**

**4.00**

Study of the theory of cryptography together with applied programming projects. Topics include: discrete probability spaces; Shannon's theory of information and perfect secrecy; classical cryptosystems and cryptanalysis; authentication and key exchange; public key cryptosystems; elementary number theory, primality checking, the RSA cryptosystem; and Advanced Encryption Standard (AES).

**MATH 440**

**Real Analysis**

**4.00**

Fundamental concepts of limit, continuity, differentiability, and integrability of functions of one variable and sequences and series.

**MATH 450**

**Topology**

**4.00**

Topology of Euclidean space, metric spaces, topological spaces, bases and neighborhoods, Hausdorff property, continuity, homeomorphisms and embeddings, connectivity, and compactness.

**MATH 455**

**Abstract Algebra**

**4.00**

Introduction to algebraic systems including groups, rings, integral domains and fields, homomorphisms and isomorphisms.

**Prerequisites:**

- Successful completion of MATH 310.

**MATH 471**

**Introduction to Complex Variables**

**4.00**

Introduction to the study of analytic functions including differentiation, integration and series.

**MATH 475**

**Numerical Analysis**

**4.00**

Study of theory and applications of computational techniques for mathematical solutions emphasizing rapid approximation and error analysis. Topics include: solution to equations in one variable; polynomial approximations to functions; error analysis; numerical solutions to ordinary differential equations; boundary value problems.

**MATH 481**

**Special Topics**

**1.00-4.00**

In-depth study of selected topics in mathematical sciences. May be repeated when topics are different.

**MATH 489**

**Mathematics Elective**

**1.00-9.00**

Transfer credits ONLY from another accredited institution not equivalent to a UW-S course.

**MATH 489MC**

**Math Elective Math/Computer Science**

**1.00-12.00**

Transfer credits ONLY from another accredited institution not equivalent to a UW-S course.

**MATH 498**

**Mathematics Capstone**

**1.00**

Senior year students carry out individual investigations into chosen topics of mathematics. A written paper of their findings will be presented to the Mathematics and Computer Science department. Instructor consent is required.