Undergraduate Courses
in the Mathematical Sciences

MATHEMATICS (MATH)

Non-Credit Courses

3010 Introductory Algebra (2-2)

The course begins with a review of signed numbers, rational numbers, and exponents. Major topics include variables, linear equations and inequalities, word problems, and operations with polynomials. This course is designed as an introduction to MATH 3011. Credit hours received for MATH 3010 may count toward removal of provisional status, but may not be used to satisfy any institutional degree requirements. Prerequisite: Placement by examination.

3011 Intermediate Algebra (3-0)

The course begins with a review of polynomials. Major topics include rational expressions and equations, radical expressions, rational exponents, complex numbers, quadratic equations, graphing lines, and geometry. The course is designed as an introduction to MATH 4109 or 3120. Credit hours received for MATH 3011 may count toward removal of provisional status, but may not be used to satisfy any institutional degree requirements. Prerequisite: MATH 3010 or placement by examination.

Lower Division Courses

4109 Precalculus I (4-0)

(Common Course Number MATH 1314)
Topics include the algebra of real functions, graphs of functions, analytic geometry of first and second degree curves, rational functions, exponential and logarithmic functions, and polynomial equations, sequences, series, and mathematical induction. A one hour per week laboratory is mandatory for problem solving, testing, concept development, and course enrichment. Prerequisite: MATH 3011, or an acceptable score on a placement examination.

4110 Precalculus II (4-0)

(Common Course Number MATH 2412)
Topics include trigonometry, vectors in two dimensions, rotations of coordinate axes, trigonometric form for complex numbers, polar coordinates, systems of equations, matrices, and analytic geometry of three dimensional space. A one hour per week laboratory session is mandatory for problem solving, testing, concept development, and course enrichment. Prerequisite: MATH 4109, or an acceptable score on a placement examination.

4111 Calculus (4-0)

(Common Course Number MATH 2413)
Topics include limits, continuity, differentiation, and integration of functions of a single variable. Prerequisites: Four years of high school mathematics including trigonometry and analytic geometry and an adequate score on a placement examination, or MATH 4110.

3112 Calculus II (3-0)

(Common Course Number MATH 2314)
Continuation of MATH 4111. Topics include special methods of integration and applications; infinite series. Prerequisite: MATH 4111.

3120 Mathematics for Social Sciences I (3-0)

(Common Course Number MATH (1324)
Topics of college algebra and geometry including the algebra of sets; linear, quadratic, exponential and logarithmic functions; systems of linear equations and inequalities; matrix algebra; probability and statistics. Prerequisites: Three years of high school mathematics and an adequate score on a placement examination, or MATH 3011.

3200 Discrete Mathematics (3-0)

(Common Course Number MATH 2305)
Topics in discrete mathematics including introduction and recursion, sets and relations, combinatorics, graph theory, finite automata, and logic. Prerequisite: MATH 4110 or equivalent.

3201 Mathematics for Social Sciences II (3-0)

(Common Course Number MATH 1325)
Topics include linear programming and an introduction to differential and integral calculus with applications to business and the social sciences. Prerequisite: MATH 3120 or 4110.

3203 Properties of the Real Numbers I (3-0)

A study of the arithmetic structure of the real numbers from an advanced point of view. Relations with concepts from set theory, groups, rings, and fields will be included. Prerequisites: MATH 4109 or 3120 or an acceptable score on a placement examination.

3213 Calculus III (3-0)

(Common Course Number MATH 2315)
Continuation of Math 3112. Topics include solid analytic geometry, partial differentiation, and multiple integrals. Prerequisite: MATH 3112.

3220 Mathematics of Interest (3-0)

Mathematical foundations - a calculus based development of the theory of interest with applications including annuities, bonds, depreciation, sinking funds, amortization schedules, insurance and yield rates. Prerequisite: Math 3201 or Math 3112.

3226 Differential Equations (3-0)

(Common Course Number MATH 2320)
A study of first order equations, linear equations with constant coefficients; general linear equations, the method of variation of parameters, the Laplace transform, and power series solutions. Prerequisite: MATH 3112.

Upper Division Courses

3300 History of Mathematics to 1650 (3-0)

A historical development of precalculus mathematics and the branch of mathematics culminating in the development of the calculus. Mathematical contributions for various cultures and eras from ancient Babylonia to 17th century Europe are reviewed with a special focus on greek mathematics. The course views the history through the problems of the various epics studied. Prerequisite: MATH 4111 or consent of the instructor.

3303 Properties of the Real Numbers II (3-0)

Additional topics in the structure of the real numbers. Basic number theory including divisibility and congruences. Topics in finite mathematics. Prerequisite: MATH 3203.

3304 Fundamentals of Geometry from an Advanced Standpoint (3-0)

An axiomatic treatment of Euclidean geometry including some historical perspectives. Informal treatment of other geometries such as distance and hyperbolic geometry. Prerequisite: MATH 3203.

3319 Elementary Number Theory (3-0)

An introduction to some of the classical topics in number theory including divisibility, congruences, quadratic reciprocity. Diophantine equations and the distribution of primes. Prerequisite: MATH 3112.

3320 Actuarial Mathematics (3-0)

Individual and collective risk models. Survival distributions and life contingency tables. Models for life insurance and multiple life functions. Prerequisite: STAT 3330.

3323 Matrix Algebra (3-0)

Systems of linear equations, matrices, determinants, eigenvalues and eigenvectors, diagonalization, vector spaces and linear transformations. Prerequisite: MATH 3112.

3325 Principles of Mathematics (3-0)

Logic and proofs, elements of set theory, relations and functions: application of these ideas. Cardinality, groups and their quotients, the field of real numbers. Prerequisite: MATH 3112.

3327 Applied Algebra (3-0)

Study of problems from one of the following subjects: Automata Theory; Formal Languages; Information Theory; Theory of Algorithms; Artificial Intelligence. This course deals with the theoretical components of computer science and is also of interest to students of structural/theoretical features in such disciplines as biology, linguisitcs, social science, and in learning theory. Prerequisite: Junior standing. May be repeated for credit if subjects differ.

3328 Foundations of Mathematics (3-0)

Study of principles of mathematical thinking and of common objects of mathematical thought. Emphasis on one of these aspects: Logic; Set Theory; Geometry; topology. May be repeated for credit if subjects differ. Prerequisite: Junior standing or permission of instructor.

3335 Applied Analysis I (3-0)

Line and surface integrals, change of variable in multiple integrals, vector analyis and an introduction to complex variables. Prerequisite: MATH 3213.

3341 Intoduction to Analysis (3-0)

A theoretical study of the foundations of the calculus of functions of one variable. Includes the real number system, convergence, continuity, differentiability and elementary integration theory. Prerequisite: MATH 3112.

1499 Individual Studies in Mathematics (0-0-1)

Studies of topics not included in or going beyond the regular course offerings. May be repeated for credit. Prerequisite: Departmental approval.

3425 Modern Algebra (3-0)

Groups, rings, integral domains, and fields. Prerequisite: MATH 3325.

3426 Linear Algebra (3-0)

Vector spaces, linear transformations and matrix representations, canonical forms, eigenvalues, invariant subspaces, orthogonal and unitary trasnformations, bilinear and quadratic forms. Prerequisite: MATH 3325.

3429 Numerical Analyis (3-0)

The course covers numerical algorithms for approximation of functions, quadrature, solution of ordinary differential equations, solution of nonlinear equations, solution of linear systems of equations, computing eigenvalues and eigenvectors. Many computer applications will be required. Prerequisites: MATH 3323 adn CS 4120 or equivalent.

3436 Applied Analysis II (3-0)

Series solutions of differential equations. Fourier series and Fourier integrals. Bessels's equation and Bessel functions. Legendre's equation and Legendre polynomials, the Sturm-Liouville problem and eigen function expansions, and an introduction to partial differential equations. Prerequisite: MATH 3226.

3441 Real Analysis (3-0)

Convergence of series of constant terms; convergence of sequences and series of functions; and analysis of functions of several variables to include the differential approximation theorem, the inverse function theorem and the implicit function theorem. Prerequisite: MATH 3341.

3470 Topics Seminar (3-0)

Organized lectures in mathematics on topics not represented among the other course offerings. Prerequisite: Junior standing; additional prerequisites may be announced as required by the topic. May be repeated for credit.

3499 Individual Studies in Mathematics (0-0-3)

Studies of topics not included in or going beyond the regular course offerings. May be repeated for credit. Prerequite: Departmental approval.

STATISTICS (STAT)

Minor in Statistics: Students may minor in Statistics by taking 18 hours (six advanced) as follows: CS 4120 or equivalent, MATH 3201 or 4111, plus 12 units from STAT 3280, 3281, 3330, 3380, 3480. Students who plan to pursue graduate studies in statistics-related areas are urged to take STAT 3480.

3180 Basics of Descriptive and Inferential Statistics (3-0)

A course in ststistical literacy. Emphasis will be on standard descriptive measures of location, spread, and association. Regression, probability and sampling, and binomial distribution. Interpretation of data which occur in daily life (polls, weather forecasting, surveys, quality control, etc.) will be stressed. Prerequisite: MATH 3120 or equivalent.

3280 Statistical Methods I (3-0)

(Common Course Number MATH 1342) An elemaentary introduction to statistical concepts and methods. Descriptive statistics , elementary probability, binomial distribution, normal distribution, estimation and hypothesis testing for one- and two-sample problems, simple linear regression, and correlation. Must be taken concurrently wit STAT 1282. Prerequisite: MATH 3011 or equivalent.

3281 Statistical Methods II (3-0)

A continuation of Statistics 3280 with treatment of more advanced statistical methods. Chi-square goodness-of-fit and contingency table analysis, analysis of variance and multiple comparisons, multiple linear regression and correlation and analysis. Prerequisite: STAT 3280.

1282 Computing Laboratory for Statistics 3280 (1-1)

Practical exercises in the handling of statistical data and experimental sampling as related to the coursework in STAT 3280. Includes an introduction to data processing.

3330 Probability (3-0)

Theory and applications of probability models. Sample space, combinatorics, conditional probability, random variables, discrete and continuous prbability distributions, expectation, moment generating functions, law of large numbers, central limit theorem. Prerequisite: MATH 3213.

3380 Sampling Techniques (3-0)

An account of sampling theory with practical applications; the role of sampling theory, simple random sampling, sampling for proportions, the estimation of sample size, stratified random sampling, systematic sampling. Prerequisite: STAT 3280 or 3330 or equivalent.

3381 Nonparametric Statistical Methods (3-0)

Distribution-free procedures; nonparametric one-and two-sample tests for location and scale; nonparametric analysis of variance; nonparametric correlation. Prerequisite: STAT 3280 or equivalent.

3480 Statistics I (3-0)

A calculus-based development of statistical concepts and methods. Distribution theory, point and interval estimation and hypothesis testing in parametric statistical models, chi-square goodness of fit and contingency table analysis, simple linear regression analysis, introduction to analysis of variance. Prerequisite: STAT 3330.


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Updated 11/1/96