Resources for:

# Mathematics

### Contacts

Fe Evangelista
Department Chair
Phone: (262) 472-5684
Location: Laurentide 2207

## Course Descriptions

#### MATHEMATICAL IDEAS

##### Mathematics 140, Credits: 3

Designed to give students a broad understanding and appreciation of mathematics. Includes topics not usually covered in a traditional algebra course. Topics encompass some algebra, problem solving, counting principles, probability, statistics, and consumer mathematics. This course is designed to meet the University Proficiency Requirement in mathematics for those students who do not wish to take any course which has MATH 141 as a prerequisite. ACT Math subscore 19-23 (SAT 460-550)

#### FUNDAMENTALS OF COLLEGE ALGEBRA

##### Mathematics 141, Credits: 4

A functional approach to algebra with emphasis on applications to different disciplines. Topics include linear, exponential, logarithmic, quadratic, polynomial and rational equations and functions, systems of linear equations, linear inequalities, radicals and rational exponents, complex numbers, variation. Properties of exponents, factoring, and solving linear equations are reviewed. ACT Math subscore 19-23 (SAT 460-550)

#### FINITE MATHEMATICS FOR BUSINESS AND SOCIAL SCIENCES (GM)

##### Mathematics 143, Credits: 3

Mathematical preparation for the understanding of various quantitative methods in modern management and social sciences. Topics included are sets, relations, linear functions, interest, annuities, matrix theory, the solution of linear systems by the graphical, algebraic, Gauss-Jordan, and inverse methods, linear programming by graphical and simplex methods, counting and probability, and decision theory. College of Business and Economics majors must take this course on a conventional grade basis.

#### MATHEMATICS FOR THE ELEMENTARY TEACHER I (GM)

##### Mathematics 148, Credits: 3

A study of sets, whole numbers, fractions, integers, decimals and real numbers, basic arithmetic operations and their properties, standard and alternative algorithms and estimations strategies; problem-solving, proportional reasoning and algebraic thinking. Manipulatives and cooperative learning activities are used throughout the course. For elementary education majors.

#### MATHEMATICS FOR THE ELEMENTARY TEACHER II

##### Mathematics 149, Credits: 3

Topics in probability and statistics, with emphasis on descriptive techniques. Investigations in geometric figures, measurement, construction, transformations, congruent and similar geometric figures. Problem solving strategies, manipulatives, and cooperative learning activities are emphasized throughout the course. All students will prepare a mathematics based activity and present it at an area elementary school.

#### ELEMENTARY FUNCTIONS (GM)

##### Mathematics 152, Credits: 5

Review of algebraic functions, inequalities, mathematical induction, theory of equations, exponential and logarithmic functions, circular functions, trigonometric identities and equations, inverse trigonometric functions, solution of triangles.

#### THE LOGIC OF CHESS

##### Mathematics 177, Credits: 1

A study of logic particularly as it is used in the game of chess and, most particularly, in chess strategy and the end game of chess. The rules are taught to those who are not already acquainted with the game.

#### INTRODUCTION TO STATISTICAL REASONING AND ANALYSIS (GM)

##### Mathematics 230, Credits: 3

A course on the principles, procedures and concepts surrounding the production, summarization and analysis of data. Emphasis on critical reasoning and interpretation of statistical results. Content includes: probability, sampling, and research design; statistical inference, modeling and computing; practical application culminating in a research project. Unreq: ECON 245, PSYCH 215, SOCIOLGY 295

#### SHORT CALCULUS FOR BUSINESS AND SOCIAL SCIENCES (GM)

##### Mathematics 243, Credits: 3

A general survey of the calculus. Topics covered include limits, differentiation, max-min theory, exponential and logarithmic functions, and integration. Business and social science applications are stressed.

#### APPLIED CALCULUS SURVEY FOR BUSINESS AND SOCIAL SCIENCES (GM)

##### Mathematics 250, Credits: 5

An applied calculus course covering elementary analytic geometry, limits, differentiation, max-min theory, exponential and logarithmic functions, integration, functions of several variables, and elementary differential equations. Some computer topics may be included.

#### CALCULUS AND ANALYTIC GEOMETRY I (GM)

##### Mathematics 253, Credits: 5

Review of algebraic and trigonometric functions, transcendental functions, limits, study of the derivative, techniques of differentiation, continuity, applications of the derivative, L' Hopital's Rule and indeterminate forms, the Riemann integral, Fundamental Theorem of Calculus, and substitution rule.

#### CALCULUS AND ANALYTIC GEOMETRY II

##### Mathematics 254, Credits: 5

Techniques of integration, applications of the integral, introduction to differential equations, polar coordinates and conic sections, infinite sequences and series. This course includes a writing component.

#### CALCULUS AND ANALYTIC GEOMETRY III

##### Mathematics 255, Credits: 3

Solid analytic geometry, vectors and vector functions, functions of several variables, multiple integrals and their applications.

#### DISCRETE MATHEMATICS

##### Mathematics 280, Credits: 3

This course will supply a thorough grounding in the mathematical topics which are central to the study of computer science, and which form the basis for many modern applications of mathematics to the social sciences. Topics covered will include sets, logic, Boolean algebra and switching circuits, combinatorics, probability, graphs, trees, recursion, and algorithm analysis. Expressing mathematical ideas and writing proofs will be emphasized.

#### INTRODUCTION TO ANALYSIS

##### Mathematics 301, Credits: 3

A first course in real analysis. Topics include properties of the real numbers, convergence of sequences, monotone and Cauchy sequences, continuity, differentiation, the Mean Value Theorem, and the Riemann integral. Emphasis is placed on proof-writing and communicating mathematics.

#### APPLIED STATISTICS

##### Mathematics 342, Credits: 3

This course will cover the basics of statistical testing, regression analysis, experimental design, analysis of variance, and the use of computers to analyze statistical problems. This course contains a writing component.

#### THEORY OF INTEREST

##### Mathematics 346, Credits: 3

This course will cover the topics of interest theory listed in the Society of Actuaries/Casualty Actuarial Society syllabus for Exam FM/2. Topics include the time value of money, annuities, loans, bonds, general cash flows and portfolios, and immunization schedules.

#### INFINITE PROCESSES FOR THE ELEMENTARY TEACHER

##### Mathematics 352, Credits: 3

This course is primarily for pre-service elementary and middle school teachers. Students will be introduced to the concepts of calculus, which include infinite precesses, limits, and continuity. In addition, dirivatives and integrals, and their relationship to area and change will be covered.

#### COLLEGE GEOMETRY

##### Mathematics 353, Credits: 5

The topics included in this course are foundations of Euclidean geometry, Euclidean transformational geometry, modern synthetic geometry that builds on Euclidean geometry, selected finite geometries, and an introduction to non-Euclidean and projective geometry, including their relationship to Euclidean geometry. Although the course is adapted to the prospective teacher of geometry, it will also meet the needs of those in other majors needing a background in geometry. Standards and guidelines of appropriate national and local bodies will be implemented.

#### MATRICES AND LINEAR ALGEBRA

##### Mathematics 355, Credits: 3

Systems of linear equations, matrices and determinants, finite dimensional vector spaces, linear dependence, bases, dimension, linear mappings, orthogonal bases, and eigenvector theory. Applications stressed throughout.

#### PROBABILITY & STATISTICS FOR TEACHERS

##### Mathematics 359, Credits: 3

An introduction to probability and statistics for teachers. Topics covered include counting techniques, basic probability theory, exploratory data analysis, simulation, randomization, and statistical inference. This course contains a writing component.

#### DIFFERENTIAL EQUATIONS

##### Mathematics 361, Credits: 3

Ordinary differential equations: general theory of linear equations, special methods for nonlinear equations including qualitative analysis and stability, power series and numerical methods, and systems of equations. Additional topics may include transformation methods and boundary value problems. Applications stressed throughout.

#### PROBLEM SOLVING FOR THE ELEMENTARY TEACHER

##### Mathematics 370, Credits: 3

This course is primarily for pre-service elementary and middle school teachers. Students will learn a variety of problem solving strategies applicable in elementary and middle school. The applications will cover many different areas of mathematics.

#### DEVELOPMENT OF MATHEMATICS

##### Mathematics 375, Credits: 3

A study of the development of mathematical notation and ideas from prehistoric times to the present. Periods and topics will be chosen corresponding to the backgrounds and interests of the students.

#### PRE-ALGEBRA

##### Mathematics 40, Credits: 3

A course for students who need a review of basic mathematics or who lack the computational skills required for success in algebra and other University courses. Topics include fractions, decimals, percent, descriptive statistics, English and metric units of measure, and measures of geometric figures. Emphasis is on applications. A brief introduction to algebra is included at the end of the course. This course does count toward the semester credit load and will be computed into the grade point average. It will not be included in the 120 credits required for graduation. It may be taken for a conventional grade or on a satisfactory/no credit basis. Not available to students who have satisfied the University Proficiency requirement in mathematics. ACT Math subscore 14 or below (SAT 340 or below) Arithmetic skills test required.

#### BEGINNING ALGEBRA

##### Mathematics 41, Credits: 4

A course for those who have a sound background in basic arithmetic, but who have not been exposed to algebra, or who need to strengthen their basic algebra skills. Topics include properties of the real numbers, linear and quadratic equations, linear inequalities, exponents, polynomials, rational expressions, the straight line, and systems of linear equations. The course counts towards the semester credit load and will be computed into the grade point average. It will not, however, be included in the credits necessary for graduation. It may be taken for a conventional grade or on a satisfactory/no credit basis. Prereq: MATH 040 or equivalent demonstration of capability. Students cannot receive credit for MATH 041 if they have been waived from the Mathematics Proficiency Requirement. Not available to students who have satisfied the University Proficiency requirement in mathematics.

#### MODERN ALGEBRA AND NUMBER THEORY FOR THE ELEMENTARY TEACHER

##### Mathematics 415, Credits: 3

An introduction to modern algebra with special emphasis on the number systems and algorithms which underlie the mathematics curriculum of the elementary school. Topics from logic, sets, algebraic structures, and number theory.

#### GEOMETRY FOR THE ELEMENTARY TEACHER

##### Mathematics 416, Credits: 3

A study of the intuitive, informal geometry of sets of points in space. Topics include elementary constructions, coordinates and graphs, tessellations, transformations, problem solving, symmetries of polygons and polyhedra, and use of geometry computer software.

#### THEORY OF NUMBERS

##### Mathematics 417, Credits: 3

A study of the properties of integers, representation of integers in a given base, properties of primes, arithmetic functions, module arithmetic. Diophantine equations and quadratic residues. Consideration is also given to some famous problems in number theory.

#### APPLIED REGRESSION ANALYSIS

##### Mathematics 420, Credits: 3

This is a second course in regression analysis and its applications. Topics include correlation, simple and multiple linear regression, model assumptions, inference of regression parameters, regression diagnostics and remedial measures, categorical predictors, multicollinearity,and model selection. Real data re emphasized and analyzed using statistical software such as R or SAS.

#### MATHEMATICS FOR HIGH SCHOOL TEACHERS I

##### Mathematics 421, Credits: 3

The course revisits the high school curriculum from an advanced perspective. The focus is on deepening understanding of concepts, highlighting connections and solving challenging problems. The mathematical content includes number systems, functions, equations, integers, and polynomials. Connections to geometry are emphasized throughout the course.

#### MATHEMATICS FOR HIGH SCHOOL TEACHERS II

##### Mathematics 422, Credits: 3

The course continues the exploration of the high school curriculum from an advanced perspective that was started in MATH 421. The focus is on deepening understanding of concepts, highlighting connections and solving challenging problems. The mathematical content includes congruence, distance, similarity, trigonometry, area, and volume. Connections to algebra are emphasized throughout the course.

#### TOPOLOGY

##### Mathematics 431, Credits: 3

An introduction to point-set topology, including such topics as topological spaces, mappings, connectedness, compactness, separation axioms, metric spaces, complete spaces, product spaces and function spaces.

#### PROBABILITY THEORY

##### Mathematics 441, Credits: 3

Probability spaces, discrete and continuous random variables, mathematical exceptation, discrete and continuous distributions.

#### MATHEMATICAL STATISTICS

##### Mathematics 442, Credits: 4

This course will cover moment generating functions, moments of linear combinations of random variables, conditional expection, functions of random variables, sampling distributions, the theory of estimation, Bayesian estimation, hypothesis testing, nonparametric tests, and linear models.

#### ACTUARIAL EXAMINATION PREPARATION FOR EXAM P/1

##### Mathematics 448, Credits: 1

The course is designed to prepare students for Exam P/1, the first actuarial exam which tests students' knowledge of and ability to use and apply fundamental probability tools in assessing risk. Basic concepts from risk theory are introduced, probability theory is reviewed, and sample questions from previous exams are discussed.

#### ACTUARIAL EXAMINATION PREPARATION

##### Mathematics 449, Credits: 1

This course is designed to prepare students for Exam FM/2, the second acturial exam which tests students' knowledge and understanding of the fundamental concepts of financial mathematics. Derivatives are introduced, interest theory is reviewed, and sample questions from previous exams and practice exams from other sources are discussed.

#### GRAPH THEORY

##### Mathematics 450, Credits: 3

This course will examine basic concepts and applications of graph theory. Topics covered will be selected from trees, connectivity, paths and cycles, coloring, matching and covering problems, digraphs, and network flows.

#### INTRODUCTION TO ABSTRACT ALGEBRA

##### Mathematics 452, Credits: 3

An introductory survey of abstract algebra and number theory with emphasis on the development and study of the number systems of integers, integers mod n, rationals, reals, and complex numbers. These offer examples of and motivation for the study of the classical algebraic structures of groups, rings integral domains and fields. Applications to algebraic coding theory and crystallography will be developed if time allows.

#### ABSTRACT ALGEBRA

##### Mathematics 453, Credits: 3

This course is a continuation of MATH 452 with emphasis on ring and field theory. Topics include a review of group theory, polynomial rings, divisibility in integral domains, vector spaces, extension fields, algebraic extension fields, finite fields, etc.

#### APPLIED MATHEMATICAL ANALYSIS

##### Mathematics 458, Credits: 3

Selected topics in ordinary differential equations: series solutions, stability, transform methods, special functions, numerical methods, vector differential calculus, line and surface integrals.

#### PARTIAL DIFFERENTIAL EQUATIONS

##### Mathematics 459, Credits: 3

Fourier analysis, partial differential equations and boundary value problems, complex variables, and potential theory.

#### COMPLEX VARIABLES

##### Mathematics 463, Credits: 3

This course is a study of the algebra and geometry of complex numbers, the properties of analytic functions, contour integration, the calculus of residues and the properties of power series.

##### Mathematics 464, Credits: 3

This course presents a rigorous treatment of the differential and integral calculus of single variable functions, convergence theory of numerical sequences and series, uniform convergence theory of sequences and series of functions, metric spaces, functions of several real variables, and the inverse function theorem. This course contains a writing component.

#### NUMERICAL ANALYSIS

##### Mathematics 471, Credits: 3

Emphasis on numerical algebra. The problems of linear systems, matrix inversion, the complete and special eigenvalue problems, solutions by exact and iterative methods, orthogonalization, gradient methods. Consideration of stability and elementary error analysis. Extensive use of microcomputers and programs using a high level language. This course contains a writing component.

#### WORKSHOP

##### Mathematics 49, Credits: 1-3

Variable credit course offering with a defined topic. Repeatable with a change of topic.

#### WORKSHOP

##### Mathematics 490, Credits: 1-3

Variable topics. Group activity oriented presentations emphasizing `hands on` and participatory instructional techniques. Repeatable. Prereq: Consent of instructor

#### FIELD STUDY

##### Mathematics 492, Credits: 1-3

A study for which data is obtained or observations are made outside the regular classroom. Repeatable. Instructor Consent required.

#### SEMINAR

##### Mathematics 494, Credits: 2

Variable topics. Group activity. An advanced course of study in a defined subject matter area emphasizing a small group in intense study with a faculty member. Repeatable. Instructor Consent required.

#### SPECIAL STUDIES

##### Mathematics 496, Credits: 1-3

Variable topics. Group activity. Not offered regularly in the curriculum but offered on topics selected on the basis of timeliness, need, and interest, and generally in the format of regularly scheduled Catalog offerings. Repeatable three times maximum in 6 years. Instructor Consent required.

#### EXCHANGE STUDY

##### Mathematics 497, Credits: 1-12

Variable topics

#### INDEPENDENT STUDY

##### Mathematics 498, Credits: 1-5

Study of a selected topic or topics under the direction of a faculty member. Repeatable. Department Consent required.

#### INDEPENDENT STUDY - UNDERGRADUATE RESEARCH

##### Mathematics 498R, Credits: 1-3

Study of a selected topic or topics under the direction of a faculty member. Repeatable. Department Consent required.

#### PROJECT FOR MAJORS

##### Mathematics 499, Credits: 1

This course is designed to give students experience and to improve their skill in reading, writing, and understanding mathematics by requiring them to research one or more mathematical topics and then write a report about their activities and discoveries. The focus is on the learning and communication of mathematics: how to read with understanding, write with clarity and precision, and in the process discover how writing can aid in understanding.

#### Location

College of Letters & Sciences
Laurentide Hall 4100
University of Wisconsin-Whitewater
800 W. Main Street
Whitewater, WI 53190-1790

#### Contact

Office of the Dean
Rebecca Reichert
Phone: (262) 472-1621
E-mail:reicherr@uww.edu