MATHEMATICS
(MTH)
College
of Science and Allied Health
Department
Chair: Bruce Riley
1034
Cowley Hall, 608-785-8382
e-mail:
riley.bruc@uwlax.edu
Professors: Bange, Barkauskas, Breiter,
Host, Riley, B., Scheidt, Senger, Skala, Sobota; Associate Professors:
Boyle, Hoar, Kelly, S., Lewin, Koster, Matchett, O’Brien,
Assistant
Professors:
Baggett, Elfessi, Kattchee, Lang, Nelson, P., Niedfeldt, Reineke.
Major
and/or minor requirements differ for students in the College of Business
Administration, the College of Liberal Studies, and the College of Science and
Allied Health, from those in the School of Education and the College of Health,
Physical Education and Recreation. See separate listings below.
Credit
by Examination:
The
mathematics department awards credit by examination in MTH 150, College
Algebra; MTH 151, Precalculus; MTH 207, Calculus I; and MTH 208, Calculus II.
The exams may be taken by new freshmen and are scheduled for the second week of
semester I. Students may not earn credit by examination in both MTH 150 and MTH
151. Credit for MTH 205 will be granted to entering freshmen with a College
Board Advanced Placement Statistics Examination score of three or better.
Credit for MTH 207 will be granted to entering freshmen with a College Board
Advanced Placement AB exam score of three or better. Entering freshmen with a
score of three or better on the BC form of this exam will receive credit for
MTH 207 and should consult the mathematics department chair about additional
credit and placement in mathematics courses.
Retroactive
Credits:
Students
taking MTH 207, 208, or 309, and earning a grade of “B” or better, will be
given retroactive credit for MTH 151 provided that the student’s transcript
shows no record of prior or concurrent enrollment in MTH 151, 207, 208, or 309.
(All
colleges, excluding Teacher Certification programs) — 38 credits, including MTH
207, 208, 225, 309, 310, one two-course sequence chosen from MTH 353 and 480,
353 and 461, 407 and 408, 411 and 412, 441 and 442, and 12 additional credits
selected from 311, 317, 320, 331, 341, 353, 371, 407, 408, 410, 411, 412, 413,
441, 442, 461, 480, C-S 453, and PHY 470. MTH 151 may be used to fulfill three
of the 12 additional credits. In addition, C-S 120 must be taken. Mathematics–
computer science double majors may count MTH 317, MTH 371, and C-S 453 for credit in both majors.
Mathematics–physics double majors may count MTH 461 and PHY 470 for credit in
both majors.
(All
colleges, excluding Elementary/Middle Education) — 22 credits, including MTH
207, 208, 309, and nine additional credits selected from MTH 225, 250, and MTH
courses numbered 310 and above. Credit for MTH 151 may be used to fulfill three
of the nine additional credits. Computer science majors may count MTH 317, 371
and C-S 453 for credit in both the computer science major and the mathematics
minor. Physics majors may count MTH 461 and PHY 470 for credit in both the
physics major and the mathematics minor.
(All
colleges, excluding Teacher Certification programs) — 39 credits, including MTH
207, 208, 309, 310, 341, 441, 442, 445, 446, and six additional credits
selected from MTH 371, 407, 410, 444, 447, and 448. In addition, C-S 120 must
be taken.
(Teacher
Certification programs) — 36 credits, including MTH 207, 208, 225, 309, 310,
331, 341, 411 and six additional credits selected from MTH 311, 317, 320, 353,
371, 407, 408, 410, 412, 413, 441, 442, 461, and 480. MTH 151 may be used to fulfill
three of the six additional credits. In addition, C-S 120 must be taken.
(Elementary/Middle
Education) — 22 credits, including MTH 125, 171, 280 and 12 additional credits
selected from MTH 151, 205, 175 or 207, 208, and MTH courses numbered 300 and
above.
(All
colleges) — 20 credits, including MTH 175 or 207, 205, 305, and nine additional
credits selected from MTH 444, 445, 446, 447, and 448. With the approval of the
mathematics department chair, a research methods course from another department
may be substituted for three of the nine additional credits. MTH 250 or 341 may
be substituted for MTH 205. This minor is not available to mathematics majors.
+ above a course number indicates a General Education course.
MTH 050
Cr. 3 transcript*
Basic
Algebra
A
review of beginning algebra. Topics include an elementary treatment of real
numbers, polynomials, linear equations, inequalities, rational expressions,
systems of linear equations, radicals, and quadratic equations. Letter grade,
but only F calculated in GPA.
Topics
in Intermediate Algebra
A
course to enhance the student’s skills in selected areas of intermediate
algebra; areas
covered
include polynomials, rational expressions, exponents, equations, and
inequalities. Prerequisite: MTH 050 or an appropriate placement test score.
Letter grade, but only F calculated in GPA.
MTH 125 Cr.
4
Mathematics
for Elementary Teachers
A
study of the mathematical concepts and techniques that are fundamental to, and
form the basis for, elementary school mathematics. Topics include: sets, logic,
functions, numeration systems, real numbers, number theory, geometry and
statistics. Prerequisite: MTH 050 or equivalent placement.
+
MTH
150 Cr.
4
College
Algebra
A
college algebra course on the properties, graphs, and applications of
elementary functions. Topics include the real and complex numbers, concepts
from analytic geometry, solutions to equations and inequalities, the elementary
algebraic functions, and the logarithmic and exponential functions.
Prerequisite: MTH 051 or two years of high school algebra and a satisfactory
placement test score.
+
MTH
151 Cr.
4
Precalculus
A
precalculus course on properties, graphs, and applications of elementary
transcendental functions. Topics include concepts from analytic geometry;
theory of equations; the logarithmic, exponential, trigonometric, and inverse
trigonometric functions; and analytic trigonometry. Prerequisite: MTH 150 or
two years of high school algebra and a satisfactory placement test score.
(Successful completion of MTH 151 precludes taking MTH 150 for credit.
Successful completion of MTH 207 precludes taking MTH 151 for credit.)
MTH 171 Cr.
3
Geometry
for Elementary Teachers
Analysis
and description of 2- and 3-dimension geometric concepts. Intuitive, direct,
and indirect proofs and applications of geometric principles.Transformations,
similarities and symmetry. Some topics from measurement. Prerequisite: MTH 125
and either MTH 150 or math placement above MTH 150. Offered
Sem.
I.
+
MTH 175 Cr.
4
Applied
Calculus
Basic
concepts and methods from differential, integral, and multivariate calculus.
Logarithmic and exponential functions are included, but not trigonometric
functions. Emphasis of the course is on models and applications in business and
the social, life, and physical sciences. Prerequisites: MTH 150 or two years of
high school algebra and a satisfactory placement test score. (Successful
completion of MTH 175 precludes taking MTH 150 for credit. Successful
completion of MTH 207 precludes taking MTH 175 for credit.)
+
MTH 205 Cr.
4
Elementary
Statistics
An
introductory course covering fundamentals of modern statistical methods. Topics
include descriptive statistics, the binomial and normal distributions,
estimation, and hypothesis testing. The z, t, F and chi-square test statistics
are introduced. Instruction in computer use is included, and statistics
software is used throughout the course for analyzing data files and carrying
out statistical procedures. Prerequisite: MTH 050 or equivalent placement.
+
MTH 207 Cr.
5
Calculus
I
A
rigorous introduction to calculus. Topics include limits, derivatives of
algebraic and trigonometric functions, and integration. Applied problems from
related rates, extrema, volumes. Prerequisite: MTH 151 or four years of high
school mathematics, including trigonometry.
+
MTH 208 Cr.
4
Calculus
II: Calculus with Linear Algebra and Differential Equations
A
continuation of Calculus I with an introduction to linear algebra and
differential equations. Topics include: differentiation and integration of
transcendental functions, indeterminate forms, improper integrals, techniques
of integration, applications to the physical sciences, first order linear
differential equations, and an introduction to vectors, matrices, and systems
of linear equations. Prerequisite: MTH 207.
MTH 225 Cr.
3
Mathematical
Logic
An
introduction to mathematical reasoning. Mathematical logic, including
quantification and the predicate calculus is introduced and used to discuss set
theory, relations, functions and the natural number system. Elementary proofs,
including proofs by induction are stressed. Prerequisite: MTH 151 or four years
of high school mathematics.
+
MTH 250 Cr.
3
Statistics
An
initial course in statistics for students strong in mathematics. It covers the
fundamentals of modern statistical methods. Topics include descriptive
statistics, random variables, and inferential statistics. This course exceeds
Math 205 in depth and breadth. A student may not receive credit for both MTH
205 and MTH 250. Prerequisite: MTH 207. Offered Sem. II.
MTH 280 Cr.
3
Problem
Solving for Elementary Teachers
A
high activity course designed to enhance skills in problem solving. Includes
methods of representing problems, general strategies for solving problems,
creative problem posing and ways to evaluate progress in problem solving
skills. Examples taken from the
elementary school curriculum. Prerequisite: MTH 125 and either MTH 150 or math
placement above MTH 150.Offered Sem. II.
MTH 305/505 Cr.
3
Statistical
Methods
A
survey of statistical methods from the point of view of how these methods are
implemented with a standard statistics software package. Topics include
descriptive statistics, graphical methods, tests of location, goodness of fit,
simple and multiple regression, design of experiments, ANOVA, multiple
comparisons, chi-square tests. Both parametric and nonparametric methods are
treated. Computer use is an integral part of the course. Prerequisite: MTH 205
or 250 or 341. Not applicable to a mathematics major. May be applied only to
mathematics and statistics minors. Offered
Sem. I.
MTH 309 Cr.
4
Calculus
III: Calculus with Linear Algebra and Differential Equations
A
continuation of the study of calculus and linear algebra, with applications to
differential equations. Topics include: determinants, vector spaces, subspaces,
basis and dimension, linear transformations and their matrix representations,
similar matrices and diagonalization, infinite sequences and series, and
solutions of second and higher order differential equations. Prerequisite: MTH
208.
MTH 310 Cr.
4
Calculus
IV: Multivariate Calculus
The
final course in the introductory calculus-linear algebra-differential equations
sequence. Topics include: parametric equations and polar coordinates, partial
derivatives, multiple integrals and an introduction to vector calculus.
Applications to differential equations. Prerequisite: MTH 309.
MTH 311 Cr.
3
Number
Theory
Topics
are selected from such areas as: divisibility and factorization, congruence,
distribution of prime numbers, Diophantine equations. Problem-solving
strategies and unsolved problems are stressed. Applications to areas such as
coding theory. Prerequisites: MTH 225 and 309. Offered Sem. I, even-numbered
years.
MTH 317 Cr.
3
Graph
Theory
An
introduction to graph theory emphasizing algorithms. Topics include graphs and
subgraphs, isomorphism, degree sequences, digraphs, networks, algorithm
complexity and NP-completeness, trees, Euler circuits and Hamilton cycles,
planarity and graph coloring. Prerequisites: MTH 225, 309 and C-S 120. Offered
Sem. I, odd numbered years.
MTH 320 Cr.
3
History
of Mathematics
A
study of the evolution of mathematics. Discussion and evaluation of major
periods of development including the lives and works of preeminent
mathematicians. A sampling of problem solving methods from various historical
periods. Emphasis is on Western mathematics from earliest recorded history
through the initial developments of calculus and modern mathematics.
Prerequisite: MTH 309. Offered Sem. II, odd-numbered years.
MTH 331 Cr.
3
Introduction
to Modern Geometry
A
thorough discussion of transformations and their use in proving congruence of
geometric figures; selected theorems concerning the triangle and circle, and
constructions possible given different parts of a triangle. Prerequisites: MTH
225 and 309. Offered Sem. II.
MTH 341 Cr.
4
Probability
and Statistics
Chance
experiments and sample spaces, sophisticated counting, random variables and
their distributions, independence, binomial and other discrete distributions
and their applications. Continuous random variables with emphasis on the
normal, uniform and exponential. An introduction to basic concepts of
statistics, estimation theory, hypothesis testing, and the role of probability
in statistical inference. Prerequisite: MTH 309.
MTH 353 Cr.
3
Differential
Equations
Fundamental
existence and uniqueness theory, linear independence and the Wronskian, series
solutions near regular singular points, Laplace transforms and systems of first
order linear equations. Fourier Series and the method of separation of
variables will be applied to the heat equation, wave equation and Laplace’s
equation. Prerequisite: MTH 310. Offered Sem. I.
MTH 371 Cr.
3
Introduction
to Numerical Methods
Techniques
devised for use with computing machinery are applied to problems such as:
solving non-linear equations and linear systems, curve-fitting and function
approximation, numerical integration. Prerequisites: MTH 309 and C-S 120.
Offered Sem. II.
MTH 395 Cr.
1-3
Special
Topics in Mathematics
Special
topics in mathematics not covered by regular courses taught in this department.
The particular topic is decided mutually by the student and instructor.
Prerequisite: written consent of department chair. Repeatable for credit —
maximum 6.
MTH 407 Cr.
3
Analysis
I
A
careful examination of the structure of the real number system and of
differentiation and integration for real-valued functions. Prerequisites: MTH
225 and 310. Offered Sem. I.
MTH 408 Cr.
3
Analysis
II
Continuation
of MTH 407. Sequences and series of functions, followed by an introduction to
areas such as Fourier Analysis where the ideas and methods of real analysis are
usefully applied. Prerequisite: MTH 407. Offered Sem. II, odd-numbered years.
MTH 410 Cr.
3
Complex
Analysis
Introduction
to complex numbers and complex functions. Analytical functions are developed
via power series and Cauchy’s Theorem. Topics include: Cauchy-Riemann
conditions, integration theorems, residues, conformal mapping and applications.
Prerequisites: MTH 225 and 310. Offered Sem. II, even-numbered years.
MTH 411 Cr.
3
Abstract
Algebra I
A
rigorous approach to algebraic systems including the study of groups, rings,
integral domains and fields with primary emphasis on the study of groups.
Prerequisites: MTH 225 and 309. Offered Sem. I.
MTH 412 Cr.
3
Abstract
Algebra II
Continuation
of MTH 411. Further study of rings, integral domains and fields with
application to polynomials. Prerequisite: MTH 411. Offered Sem. II,
even-numbered years.
MTH 413 Cr.
3
Topics
in Linear Algebra
A
thorough study of selected topics such as abstract vector spaces, linear
transformations and their matrix representations, inner product spaces,
canonical forms; selected applications. Prerequisites: MTH 225 and 309. Offered
Sem. II, odd-numbered years.
MTH 441 Cr.
3
Mathematical
Statistics I
Review
of discrete and continuous random variables. Moment generating functions,
multivariate probability distributions, marginal and conditional probability
distributions, functions of random variables, order statistics, Central Limit
Theorem, point estimation and confidence intervals. Prerequisites: MTH 310 and
341. Offered Sem. I.
MTH 442 Cr.
3
Mathematical
Statistics II
Methods
of estimating, including method of moments and maximum likelihood. Sufficient
statistics, hypothesis testing, power of tests, likelihood ratio tests and
introduction to regression and analysis of variance. Prerequisite: MTH 441.
Offered
Sem.
II, even-numbered years.
MTH 444/544 Cr.
3
Introduction
to Sampling
Methodology
of simple random sampling, stratified sampling, systematic sampling, cluster
sampling, and multistage sampling is developed and applications related to
physical, social, and biological sciences are given. Single and two variable
estimation techniques are discussed. Prerequisite: MTH 305 or 341. Offered Sem.
I, odd-numbered years.
MTH 445/545 Cr.
3
Correlation
and Regression Analysis
An
introduction to simple linear regression, multiple regression, polynomial
regression. Inferences, appropriateness of model, model diagnostics/adequacy,
difficulties in the application of models are discussed. A computer package
will be used. Course participants will be involved with hands-on statistical
applications and consulting. Prerequisite: MTH 305 or 341. Offered Sem. I,
even-numbered years.
MTH 446/546 Cr.
3
Analysis
of Variance and Design of Experiments
An
introduction to single factor, multiple factor, and randomized block designs in
analysis of variance. Inferences, appropriateness of model, model diagnostics/adequacy,
difficulties in the application of models are discussed. Design or structure of
an experiment will be discussed. A computer package will be used. Course
participants will be involved with hands-on statistical applications and
consulting. Prerequisite: MTH 305 or 341. Offered Sem. II, odd-numbered years.
MTH 447/547 Cr.
3
Nonparametric
Statistics
An
introductory course presenting the theory and procedures for using
distribution-free methods in data analysis. Standard procedures, such as the
Wilcoxon tests, Kruskal-Wallis, Kolmogorov-Smirnov, nonparametric confidence
intervals, regression analysis, and powers of the tests will be included.
Computer programs will be used when appropriate. Prerequisite: MTH 305 or 341.
Offered Sem. II, even-numbered years.
MTH 448 Cr.
3
Operations
Research
An
introductory course which applies mathe-matics/statistics to management
decision making. Included are methods of optimizing systems, inventory and
production control, scheduling, game theory bidding, queuing, quality control,
reliability and time series. Various programming, analysis and Monte Carlo
techniques are introduced with the computer used as a tool where appropriate.
Prerequisite: MTH 305 or 341. Offered Sem. II, odd-numbered years.
MTH/PHY
461 Cr.
3
Mathematical
Physics
In
depth study of topics from vector analysis, Fourier analysis and special
functions with emphasis on modeling physical phemomena involving conservative
fields, fluid flow, heat conduction, and wave motion. Prerequisite: MTH 353.
(Cross-listed with PHY; may only earn credit in MTH or PHY.) MTH 461 may be
counted towards both a MTH and PHY major. Offered Sem. II, odd numbered years.
MTH 480 Cr.
3
Studies
in Applied Mathematics
Advanced
studies of applications of mathematics and computation to solve problems and
understand processes from a variety of fields (for example, industry, medicine
and the physical and life sciences.) Requirements include an application/
modeling project with a written report and class presentation. Prerequisite:
MTH 353. Offered Sem. II.
MTH 495/595 Cr.
1-3
Special
Topics in Mathematics
Special
topics in mathematics not covered by regular courses taught in this department,
such as topology, set theory and advanced numerical analysis. The particular
topic is decided mutually by the students and the instructor. Prerequisite:
written consent of the department chair. Repeatable for credit — maximum 6.
MTH 498 Cr.
1-3
Independent
Study
Directed
readings or presentation of material not available in formal departmental
courses under the supervision of a faculty member. Prerequisites: written
consent of the supervising faculty member and the department chair. Repeatable
for credit — maximum 6.
MTH 499 Cr.
1-3
Research
Topics
An
opportunity to pursue individual research topics under the direction of a
faculty member. Depending on the nature of the research project, study is
expected to involve substantial computational or theoretical work in addition
to literature review and instruction. In addition to a written report to the
supervising faculty member, expected outcomes may include: software, papers and
presentations to the department and regional meetings. Prerequisite: written
consent of the supervising faculty member and the department chair. Not
applicable to a mathematics major or minor. Repeatable for credit — maximum 6.