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 units 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.

Unreq: MATH 140 or MATH 141

**MATH 041 BEGINNING ALGEBRA
4 u**

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 units 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. Unreq: MATH 140 or 760
141.

**MATH 140 MATHEMATICAL IDEAS (Proficiency)
3 u**

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.

Prereq: Satisfactory completion of MATH 041, with a grade of C or better, or demonstration of equivalent capability. This course cannot be taken for credit after completing any mathematics course above 141.

**MATH 141 INTERMEDIATE ALGEBRA
(Proficiency)
4 u**

Introduction to college algebra. Topics and concepts extend beyond those taught in a beginning algebra course. A proficiency course for those who have not had sufficient preparation in high school to allow them to take MATH 143 or MATH 152. Students may not take for credit any course for which they have received a waiver, nor may they take for credit any course in the same department that is a prerequisite for a course that has been waived (e.g., if a student has been waived from Math 143, he may not take Math 141 for credit).

Prereq: Satisfactory completion of MATH 041 with a grade of C or better, or demonstration of equivalent capability.

Unreq: MATH 140 OR MATH 141B

**MATH 143 FINITE MATHEMATICS FOR BUSINESS
AND SOCIAL SCIENCES** ** GM
3 u**

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.

Prereq: Waiver of or a grade of C or better in MATH 141.

**MATH 148 MATHEMATICS FOR THE ELEMENTARY TEACHER
I GM
3 u**

A study of sets, whole numbers, fundamental operations of arithmetic, fundamental algorithms and structural properties of arithmetic, fractions, problem solving and introduction to inductive and deductive logic stressing the structure of mathematics. All students will prepare a mathematics based activity and present it at an area elementary school. For elementary education prekindergarten-6 and elementary education elementary/middle school emphasis students.

Prereq: A grade of C or better in MATH 141 or MATH 141B or a waiver from the university mathematics proficiency requirement.

**MATH 149 MATHEMATICS FOR THE ELEMENTARY
TEACHER II 3 u**

Selected topics in logic. The computer as a useful tool in mathematical
explorations is introduced and applied throughout the course. Topics in
probability and statistics, with emphasis on descriptive techniques. Investigations
in geometric figures, measurement, construction, congruent and similar
geometric figures. An introduction to coordinate geometry. Problem solving,
discovery, and student projects are emphasized throughout. All students
will prepare a mathematics based activity and present it at an area elementary
school.

Prereq: MATH 148 with a grade of C or better.

**MATH 152 ELEMENTARY FUNCTIONS
GM
5 u**

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.

Prereq: Waiver of or a grade of C or better in MATH 141.

**MATH 177 THE LOGIC OF CHESS
1 u**

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.

Prereq: Fulfillment of University Proficiency requirement in mathematics.

**MATH 230 INTRODUCTORY STATISTICS
***GM***
3 u**

A pre-calculus course in statistics. Descriptive statistics, probability
distributions, prediction, hypothesis testing, correlation, and regression.
This course does not count towards a mathematics major or minor in either
liberal arts or secondary education or towards a mathematics minor in elementary
education. This course may not be taken for credit if credit has been or
is being earned in any other statistics course.

Prereq: Waiver or a grade of C or better in MATH 141. Unreq: Any other
statistics course.

**MATH 231 UNDERSTANDING PROBABILITY
AND STATISTICS GM
3 u**

A pre-calculus course in probability and statistics. Descriptive statistics, classical probability, probability distributions, prediction, parametric and nonparametric hypothesis testing, correlation, regression, and use of some statistical software. This course does not count towards a mathematics major or minor in liberal arts or towards a mathematics major in secondary education. This course may not be taken for credit if credit has been or is being earned in any other statistics course.

Prereq: Completion, with a grade of C or better, of either MATH 143 or MATH 152. Unreq: Any other statistics course.

**MATH 243 SHORT CALCULUS FOR BUSINESS
AND SOCIAL SCIENCES GM
3 u**

A general survey of the Calculus. Topics covered include limits, differentiation, max-min theory, exponential and logarithmic functions, integration and functions of several variables. As in MATH 143, business and social science applications are stressed. College of Business and Economics majors must take this course on a conventional grade basis.

Prereq: Completion with a grade of C or better in either of the courses MATH 143 or MATH 152. Unreq: MATH 250. Students should check with their major department for advice on whether to take MATH 243 or MATH 250.

**MATH 250 APPLIED CALCULUS SURVEY FOR
BUSINESS AND THE SOCIAL SCIENCES GM
5 u**

An applied calculus course covering elementary analytic geometry, limits, differentiation, max-min theory, transcendental functions, integration, functions of several variables, and elementary differential equations. Some computer topics may be included. College of Business and Economics majors must take this course on a conventional grade basis.

Prerequisite: MATH 143, with a grade of C or better, or equivalent preparation as determined by the Mathematics Department. Unreq: MATH 243, MATH 253.

**MATH 253 CALCULUS AND ANALYTIC GEOMETRY
I GM
5 u**

Review of algebraic and trigonometric functions, transcendental functions, limits, study of the derivative, techniques of differentiation, continuity, applications of the derivative, L' Hospital's Rule and indeterminate forms, the Riemann integral, Fundamental Theorem of Calculus, substitution rule. Conventional grade basis only if course is required in the College of Business for major.

Prereq: MATH 152 or equivalent high school preparation as determined by the Mathematics Department. Unreq: MATH 243 and MATH 250.

**MATH 254 CALCULUS AND ANALYTIC GEOMETRY
II 5 u**

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.

Prereq: MATH 250 with a grade of B or better, or MATH 253.

**MATH 255 CALCULUS AND ANALYTIC GEOMETRY
III 3 u**

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

Prereq: MATH 254.

**MATH 280 DISCRETE MATHEMATICS
3 u**

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.

Prereq: MATH 250 with a grade of C or better, or MATH 253.

**MATH 290 SPATIAL ANALYSIS
3 u**

Presentation and interpretation of data, use descriptive statistics
and measures of spatial patterns, introduction to statistical inference
and measures of association, with particular reference to geographic examples.
Students will become proficient in using computers to achieve these skills.

Prereq: MATH 143

**MATH 301 INTRODUCTION TO ANALYSIS
3 u**

The main emphasis of this course is to introduce students to mathematical
proofs. Students will learn to read and write proofs in mathematics by
writing proofs of theorems about limits, sets of real numbers, and continuous
functions. If time permits, other topics may include derivative and integration
theorems, theory of open and closed sets, and cardinality of sets.

Prereq: MATH 255 and MATH 280

**MATH 342/542 APPLIED STATISTICS
3 u**

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.

Prereq: MATH 253 or MATH 250 or cons instr. Unreq: ECON 245.

**MATH 353 COLLEGE GEOMETRY
5 u**

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.

Prereq: MATH 253 and MATH 280 or consent of instructor.

**MATH 355/555 MATRICES AND LINEAR ALGEBRA
3 u**

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.

Prereq: MATH 250 or MATH 253.

**MATH 359 MATHEMATICAL MODELING & STATISTICS
3 u**

An introduction to mathematical modeling and descriptive statistics.
Students will develop the basic skills of formulation, simplification,
and analysis of mathematical models for describing and predicting physical
phenomena. The basic tools of descriptive statistics will also be introduced;
the use of descriptive statistics in formulating and interpreting mathematical
models will be emphasized.

Prereq: MATH 255 or consent of instructor.

**MATH 361 DIFFERENTIAL EQUATIONS
3 u**

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.

Prereq: MATH 255.

**MATH 365/565 LINEAR PROGRAMMING
3 u**

A study of the vector-matrix theory and computational techniques of
the simplex method, duality theorem, degeneracy problem, transportation
problems and their applications to engineering and economics. Machine solution
of large linear programming problems.

Prereq: COMPSCI 171 and MATH 355.

**MATH 375/575 DEVELOPMENT OF MATHEMATICS
3 u**

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.

Prereq: MATH 152 or cons instr.

**MATH 380/580 PATTERNS OF PROBLEM SOLVING
3 u**

This course will expose students to a variety of techniques useful
in solving mathematics problems. The experiences gained from this course
can be applied to problems arising in all fields of mathematics. The student
will have the chance to see how some general techniques can be used as
tools in many areas. Homework for this course will consist mostly of solving
a large number of mathematics problems. Consent will be given to students
with substantial interest in problem solving, and adequate preparation.

Prereq: MATH 280 or cons instr.

**MATH 415/615 MODERN ALGEBRA AND NUMBER
THEORY FOR THE ELEMENTARY TEACHER
3 u**

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.

Prereq: MATH 112 and MATH 152. Unreq: MATH 452.

**MATH 416/616 GEOMETRY FOR THE ELEMENTARY
TEACHER 3 u**

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.

Prereq: MATH 112 and MATH 152

**MATH 417/617 THEORY OF NUMBERS
3 u**

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.

Prereq: MATH 280 or MATH 415 or cons instr.

**MATH 431/631 TOPOLOGY
3 u**

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.

Prereq: MATH 255 and either MATH 280 or cons instr.

**MATH 441/641 PROBABILITY THEORY
3 u**

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

Prereq: MATH 255 and either MATH 280 or cons instr.

**MATH 442/642 MATHEMATICAL STATISTICS
4 u**

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

Prereq: MATH 441 and either MATH 355 or cons instr.

**MATH 446/646 ACTUARIAL MATHEMATICS
3 u**

This course will discuss the actuarial profession and the insurance
industry, provide direction to students wishing to take the first few actuarial
examinations, thoroughly cover the theory of interest, and introduce the
basic concepts of actuarial mathematics.

Prereq: MATH 441 or concurrent registration

**MATH 452/652 INTRODUCTION TO ABSTRACT
ALGEBRA 3 u**

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.

Prereq: MATH 280.

Unreq: MATH 415.

**MATH 453/653 ABSTRACT ALGEBRA
3 u**

This course is a continuation of MATH 452/652 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.

Prereq: MATH 355 and MATH 452.

**MATH 458/658 APPLIED MATHEMATICAL ANALYSIS
I 3 u**

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

Prereq: MATH 361.

**MATH 459/659 PARTIAL DIFFERENTIAL EQUATIONS
3 u**

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

Prereq: MATH 361.

**MATH 463 COMPLEX VARIABLES
3 u**

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.

Prereq: MATH 255

**MATH 464/664 ADVANCED CALCULUS I
3 u**

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.

Prereq: MATH 301.

**MATH 471/671 NUMERICAL ANALYSIS I
3 u**

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, such as PASCAL.

Prereq: COMPSCI 171 and MATH 355.

**MATH 473 LIGHTNING RADIATIVE TRANSFER
4 u**

This course will introduce the students to the field of Mathematical
Lightning Radiative Transfer. It will provide the students with the background
needed to analyze lightning events and to discriminate cloud to ground
discharges from intra-cloud discharges. In addition, this course will introduce
the students to the area of Ground Detection of Lightning.

Prereq: MATH 361 and PHYSICS 174 or consent of instructor.

**MATH 475 DATA INTERPRETATION OF SPACE SCIENCE
3 u**

This course will continue the study of Mathematical Space Science.
The course will teach and train students on how to read and interpret data
from Space and ground instruments. Students will learn how to access and
work with satellite data.

Prereq: MATH 361 and COMPSCI 171 or consent of instructor.

**MATH 477 MATHEMATICAL SCATTERING THEORY AND
APPLICATIONS 3 u**

This course will address the fundamental theory and applications of
mathematical scattering. Students will be exposed to the scalar, vector,
and tensor scattering. In addition, the course will introduce the students
to diverse techniques of statistical and mathematical scattering inversion.
Applications from earth system and space sciences will be studied throughout
the course.

Prereq: MATH 458, MATH 459, MATH 463 AND PHYSCS 322 or consent of instructor.

**MATH 483 MATHEMATICAL WAVES PROPAGATION
THEORY AND APPLICATIONS 3 u**

This course will address the fundamental theory and applications
of mathematical wave propagation. Students will be exposed to the scalar,
vector, and tensor wave nature of matter. In addition, the course will
introduce diverse techniques of linear and non-linear modeling of natural
occurrences and their role in understanding mathematical inversion. Applications
from earth system and space sciences will be studied throughout the course.

Prereq: MATH 458, MATH 459, MATH 463 AND PHYSCS 322 or consent of instructor.

**MATH 490/690 WORKSHOP
1-3 u**

Repeatable. Prereq: Consent of instructor.

**MATH 492 FIELD STUDY
1-3 u**

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

Prereq: Consent of instructor.

**MATH 494/694 SEMINAR
2 u**

Repeatable. Prereq: Consent of instructor.

**MATH 496/696 SPECIAL STUDIES
1-3 u**

Repeatable three times maximum in 6 years. Prereq: Consent of instructor.

**MATH 498 INDEPENDENT STUDY
1-3 u**

Repeatable. Prereq: Consent of instructor and consent of department
chairperson.

**MATH 499 PROJECT
FOR MAJORS 1 u**

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.

Prereq: Jr st or cons dept chp.

Registrar's
Office - UW-Whitewater
For comments: registrar@mail.uww.edu. Last revised on May 20, 2002 by MAR URL: http://www.uww.edu/catalog |