**A Mat 100 Precalculus Mathematics (3)**

This course provides a background in those topics that are needed for success in calculus. Topics include graphing techniques, systems of equations, functions, logarithms, and trigonometry. May not be taken for credit by students with credit in any calculus course. Student with credit for the former A Mat 103 (College Algebra) may not take A Mat 100 for credit). Prerequisite(s): three years of high school mathematics or permission of department.

**A Mat 101 Algebra and Calculus I (3)**

An integrated approach to pre-calculus and calculus. Elements of algebra and analytic geometry necessary to study calculus of one variable. Functions, limits, continuity, differentiation of algebraic functions, applications of differentiation. May not be taken for credit by students with credit for A Mat 100, 106, 112 or 118. Prerequisite(s): three years of high school mathematics or permission of the department.** **

A Mat 104 Topics in Contemporary Mathematics (3)

An introduction to application of mathematics to everyday life requiring a background of only standard high school mathematics (intermediate algebra and a little Euclidean geometry). Suggested topics include the mathematics of voting, management science through graph theory, and growth and symmetry. Prerequisite(s): two years of high school mathematics.

**A Mat 106 Survey of Calculus (3)**

An intuitive approach to differentiation and integration of algebraic and transcendental functions, intended only for students who plan to take no more calculus. Does not yield credit toward the major or minor in mathematics. May not be taken for credit by students with credit for A Mat 111, 112 or 118. Prerequisite(s): three years of high school mathematics.

**A Mat 108 Elementary Statistics (3)**

Frequency distributions, measures of central tendency and dispersion, probability and sampling, estimation, testing of hypotheses, linear regression and correlation. Prerequisite(s): three years of high school mathematics. Only one of A Mat 108 and B Itm 220 may be taken for credit. Not open for credit by students who have taken A Mat 308.

**A Mat 111 Algebra and Calculus II (4)**

The second semester of an integrated approach to pre-calculus and calculus; serves as a prerequisite to A Mat 113. Applications of differentiation, the definite integral, anti-derivatives, logarithms, trigonometry, exponential functions. Only one of A Mat 111, 112 & 118 may be taken for credit. Prerequisite(s): A Mat 101.

**A Mat 112 Calculus I (4)**

Calculus of one variable. Limits, continuity, differentiation of algebraic functions, applications of differentiation, anti-derivatives, the definite integral, transcendental functions. A MAT 118 is the honors version of A Mat 112 and substitutes for A Mat 112 toward the prerequisite in any course. Prerequisite(s): A Mat 100 or precalculus at the high school or college level. Students without precalculus should elect A Mat 101.

**A Mat 113 Calculus II (4)**

Techniques of integration, applications of the definite integral, conics, polar coordinates, improper integrals, infinite series. A Mat 119 is the honors version of A Mat 113 and substitutes for A Mat 113 toward the prerequisite in any course. Prerequisite(s): A Mat 111 or 112.

**T Mat 118 Honors Calculus (3)**

Honors version of first semester calculus. Same topics as A Mat 112, but topics are covered in greater depth. This course is for students with more than average ability and more than average interest in mathematics. Presidential Scholars with a strong interest in mathematics or the physical sciences should consider taking A Mat 118 instead of A Mat 112. A Mat 118 substitutes for A Mat 112 toward the prerequisite in any course. T Mat 118 is the Honors College version of A Mat 118. Only one of A Mat 112, A Mat 118, and T Mat 118 may be taken for credit. Prerequisite(s): three years of secondary school mathematics and permission of the instructor. Offered fall semester only. Open to Honors College students only.

**T Mat 119 Honors Calculus II (4)**

Honors version of second semester calculus. Same topics as A Mat 113, but topics are covered in greater depth. This course is for students with more than average ability and more than average interest in mathematics. Presidential Scholars with a strong interest in mathematics or the physical sciences should consider taking A Mat 119 instead of A Mat 113. A Mat 119 substitutes for A Mat 113 toward the prerequisite in any course. T Mat 119 is the Honors College version of A Mat 119. Only one of A Mat 113, A Mat 119, and T Mat 119 may be taken for credit. Prerequisite(s): A Mat 118, a grade of A in A Mat 112, or permission of the instructor. Open to Honors College students only.

**T Mat 214 Calculus of Several Variables (4)**

Curves and vectors in the plane, geometry of three-dimensional space, vector functions in three-space, partial derivatives, multiple integrals, line and surface integrals. Prerequisite(s): A Mat 113 or 119. T Mat 214 is the Honors College version of A Mat 214; only one may be taken for credit. Open to Honors College students only.

**A Mat 220 Linear Algebra (3)**

Linear equations, matrices, determinants, finite dimensional vector spaces, linear transformations Euclidean spaces. Prerequisite(s): A Mat 113.

**A Mat 221 (= I Csi 221) Introduction to Discrete Mathematics (3)**

Topics chosen from sets, relations, induction, binomial theorem, permutations and combinations, counting, and related topics in discrete mathematics. Only one of A Mat 221 & I Csi 221 may be taken for credit. Prerequisite(s) or corequisite(s): A Mat 113**.**

A Mat 301 (= A Eco 351) Theory of Interest (3)

The basic measures of interest, annuities, sinking funds, amortization schedules, bonds, and installment loans. Recommended as preparation for Actuarial Society exam FM.

**A Mat 308 Topics in Statistical Inference (3)**

Various statistical techniques such as chi-square tests, multiple regression and correlation; nonparametric statistics, and the analysis of variance as applied to physical, biological, and social sciences. Prerequisite(s): some prior experience with elementary statistics**.**

A Mat 311 Ordinary Differential Equations (3)

Linear differential equations, systems of differential equations, series solutions, boundary value problems, existence theorems, applications to the sciences. Prerequisite(s): A Mat 214.

**A Mat 312/312Z Basic Analysis (3)**

Theoretical aspects of calculus including construction of the real numbers, differentiation and integration of functions in one variable, continuity, convergence, sequences and series of functions. A Mat 312Z is the writing intensive version of A Mat 312; only one may be taken for credit. Prerequisite(s): A Mat 214.

**A Mat 314 Analysis for Applications I (3)**

Introduction to topics in mathematical analysis which traditionally have been applied to the physical sciences, including vector analysis, Fourier series, ordinary differential equations, and the calculus of variations. Prerequisite(s): A Mat 214 and 220. Offered fall semester only.

**A Mat 315 Analysis for Applications II (3)**

Continuation of A Mat 314. Series solutions of differential equations, partial differential equations, complex variables, and integral transforms. Prerequisite(s): A Mat 314. Offered spring semester only.

**A Mat 326/326Z Classical Algebra (3)**

Elementary number theory. Elementary theory of equations over rational, real, and complex fields. A Mat 326Z is the writing intensive version of A Mat 326; only one may be taken for credit. Prerequisite(s): A Mat 113 .

**A Mat 327/327Z Elementary Abstract Algebra (3)**

Basic concepts of groups, rings, integral domains, fields. A Mat 327Z is the writing intensive version of A Mat 327; only one may be taken for credit. Prerequisite(s): A Mat 220, and either 326 or 326Z.

**A Mat 331/331Z Transformation Geometry (3)**

Classical theorems of Menelaus, Ceva, Desargues, and Pappus. Isometries, similarities, and affine transformations for Euclidean geometry. A Mat 331Z is the writing intensive version of A Mat 331; only one may be taken for credit. Prerequisite(s): A Mat 220. Usually offered spring semester only.

**A Mat 342/342Z Elementary Topology (3)**

Networks, map coloring problems, surfaces, topological equivalence, the Euler number, the polygonal Jordan curve theorem, homotopy, the index of a transformation, and the Brouwer Fixed Point Theorem. A Mat 342Z is the writing intensive version of A Mat 342; only one may be taken for credit. Prerequisite(s): A Mat 214 and 220. Usually offered fall semester only.

**A Mat 362 Probability for Statistics (3)**

Introduction to discrete and continuous probability models, including probability mass functions, density functions and cumulative distribution functions. Discrete examples will include the binomial, negative binomial, Poisson, and hypergeometric distributions. Continuous distributions will include the normal and exponential distributions, the family of gamma and beta densities, and, if time permits, t and chi-square distributions. Other topics are the probability axioms, equally likely sample spaces (combinatorics), conditional probability, joint distributions, marginal distributions, conditional distributions, covariance, correlation, moment generating functions and the Central Limit Theorem. A Mat 362 constitutes substantial preparation for Actuarial Exam P. A student may not apply both A Mat 362 and A Mat 367 towards a major or minor in mathematics or a minor in statistics. Prerequisite(s): calculus through A Mat 214 or the equivalent.

**A Mat 363/363Z Statistics (3)**

A calculus-based introduction to statistics. Confidence intervals and hypothesis tests for means and variances, differences of means and ratios of variances, including P-values, power functions and sample size estimates and involving normal, binomial, t, chi-square and F distributions. Additional topics may include introductions to simple linear regression, Bayesian statistics, sample survey methods, goodness of fit tests, non-parametric tests or analysis of variance. A MAT 363Z is the writing intensive version of A MAT 363; only one may be taken for credit. Students with credit for A Mat 367 but who have not taken A Mat 362 may take A Mat 363 only with permission of instructor. Students with credit for A Mat 368 may not take A Mat 363. Prerequisite(s): A Mat 362.

A Mat 367/367Z Discrete Probability (3)

Introduction to discrete probability models (including the binomial, negative binomial, Poisson, and hypergeometric distributions, their means, variances and cumulative distribution functions). Other topics include probability axioms, equally likely sample spaces (combinatorics), conditional probability, the gamblers' ruin problem, finite state Markov chains, moment generating functions, joint distributions (including the multinomial distribution), marginal distributions, conditional distributions, covariance and correlation, the weak law of large numbers, and, if time permits, the Central Limit Theorem. Students who intend to take A Mat 363 should take A Mat 362, not A Mat 367. Students who have taken A Mat 367 and who wish to take a first statistics course can take A Mat 308. Actuarial students who need continuous as well as discrete probability, should take A Mat 362 (which constitutes substantial preparation for Actuarial Exam P). A Mat 367Z is the writing intensive version of A Mat 367; only one may be taken for credit. Prerequisite(s): A Mat 113 or 119 plus 6 credits at the 200 or higher level in either mathematics or computer science.

**A Mat 369 Statistics and Data Analysis (3)**

A topics course whose content will vary somewhat from semester to semester. In the recent past the course has focused on analysis of variance, categorical data analysis, distribution free methods and survey sampling. Other possible topics include Bayesian statistics, bootstrap methods, log-linear models, lifetime distributions, Meier-Kaplan estimators and the Mantel-Haenszel test. Topics covered in Math 465 (multiple regression and time series) would be avoided. May be repeated for credit with permission of instructor. Prerequisite(s): A Mat 363.

**A Mat 372/372Z Linear Programming and Game Theory (3)**

Operation and theory of the simplex algorithm for solving linear programming problems, duality theory, and matrix games. A Mat 372Z is the writing intensive version of A Mat 372; only one may be taken for credit. Prerequisite(s): A Mat 109 or 220.

**A Mat 374 Operations Research (3)**

Operations research techniques and applications, linear programming, queuing theory, including birth and death processes, decision theory, network analysis, simulation. Prerequisite(s): A Mat 367 or 367Z or permission of instructor. May not be offered in 2008-2009.

**A Mat 401 Numerical Analysis (3)**

Error analysis, numerical solution of nonlinear equations, interpolation and polynomial approximation, numerical differentiation and integration, direct methods for solving linear systems. Not more than one of A Mat 313 or A Mat 401 may be taken for credit. Prerequisite(s): A Mat 220. Offered fall semester only. May not be offered in 2008-2009.

**A Mat 403 Life Contingencies I (3)**

Treatment of single and joint lives including mortality functions, various kinds of annuities and life insurance, premiums, reserves and standard actuarial notations for these concepts. Recommended as partial preparation for actuarial exam M. Prerequisite(s): A Mat 301, 367, 368.

**A Mat 404 Life Contingencies II (3)**

Expansion of Mat 403 with emphasis on two or more lives in combination and on multiple causes of decrement. Topics include population theory, multi-life statuses, multi-life functions, reversionary annuities, multiple-decrement functions, primary and secondary decrements, and applications of multiple-decrement functions. Prerequisite(s): A Mat 403.

**A Mat 409 Vector Analysis (3)**

Classical vector analysis presented heuristically and in physical terms. Topics include the integral theorems of Gauss, Green, and Stokes. Prerequisite(s): A Mat 214. Offered spring semester only.

**A Mat 412/412Z Complex Variables for Applications (3)**

The elementary functions, differentiation, conformal transformations, power series, integral theorems, Taylor’s theorems, Taylor’s and Laurent’s expansions, applications of residues. A Mat 412Z is the writing intensive version of A Mat 412; only one may be taken for credit. Prerequisite(s): A Mat 214. Usually offered fall semester only.

**A Mat 413/413Z and 414 Advanced Calculus I & II (3, 3)**

A rigorous presentation of the traditional topics in the calculus of several variables and their applications. Topics include the implicit function theorem, Taylor’s theorem, Lagrange multipliers, Stieltjes integral, Stokes’ theorem, infinite series, Fourier series, special functions, Laplace transforms. A Mat 413Z is the writing intensive version of A Mat 413; only one may be taken for credit. Prerequisite(s): A Mat 312 or 312Z; A Mat 413 or 413Z is a prerequisite for A Mat 414.

**A Mat 416 Partial Differential Equations (3)**

The partial differential equations of classical mathematical physics. Separation of variables, eigenvalue problems, Fourier series and other orthogonal expansions. First order equations, Green’s functions, Sturm-Liouville theory, and other topics as time permits. Prerequisite(s): a course in Ordinary Differential Equations. Offered fall semester only**.**

A Mat 420 Abstract Algebra (3)

Topics in group theory, especially finite group theory, algebraic field extensions, and Galois theory. Prerequisite(s): A Mat 327 or 327Z.

**A Mat 424 Advanced Linear Algebra (3)**

Duality, quadratic forms, inner product spaces, and similarity theory of linear transformations. Prerequisite(s): A Mat 220. Offered fall semester only.

**A Mat 425 Number Theory (3)**

Divisibility, congruencies, quadratic reciprocity, Diophantine equations, sums of squares, cubes, continued fractions, algebraic integers. Prerequisite(s): A Mat 326 or 326Z. Offered spring semester only.

**A Mat 432/432Z Foundations of Geometry (3)**

Axiomatic development of absolute geometry, theory of parallels, introduction to non-Euclidean geometry, isometries of the Bolyai-Lobachevsky plane. A Mat 432Z is the writing intensive version of A Mat 432; only one may be taken for credit. Prerequisite(s): A Mat 220. Offered fall semester only.

**A Mat 441 Introduction to Differential Geometry (3)**

Differential geometry of curves and surfaces in Euclidean space, frames, isometries, geodesics, curvature, and the Gauss-Bonnet theorem. Prerequisite(s): A Mat 214 and 220. Offered spring semester only.

**A Mat 442 Introduction to Algebraic Topology (3)**

Two-dimensional manifolds, the fundamental group and Van Kampen’s theorem, covering spaces, graphs, and applications to group theory. Prerequisite(s): A Mat 214 and 220. May not be offered in 2008-2009.

**A Mat 452/452Z History of Mathematics (3)**

History of the development of mathematics, emphasizing the contributions of outstanding persons and civilizations. A Mat 452Z is the writing intensive version of A Mat 452; only one may be taken for credit. Prerequisite(s): A Mat 214, 326 or 326Z, and either 331 or 331Z or 432 or 432Z. Normally only the writing intensive version of this course is offered**. **Offered fall semester only.

**A Mat 464 Applied Stochastic Processes (3)**

An overview of stochastic processes with particular emphasis on Markov chains. Introduction to queuing theory. Particular attention given to estimation. Recommended as partial preparation for actuarial exams M and C. Prerequisite(s): A Mat 367 or 367Z or 467. Offered spring semester only.

**A Mat 465/465Z Applied Statistics (3)**

A** **second or third course in statistics, focusing on simple and multiple regression and time series. Course carries VEE credit from the Society of Actuaries in applied statistics. A Mat 465Z is the writing intensive version of A Mat 465; only one may be taken for credit. Prerequisite(s): A Mat 220 and one of A Mat 308, A Mat 363 or A Mat 468. Offered in fall semester only.

**A Mat 467 Continuous Probability and Mathematical Statistics (3)**

One and two dimensional calculus applied to probability. Continuous random variables in one and two dimensions, including the normal, bivariate normal, exponential, gamma (including chi-square) and beta. Density functions of transformations of random variables. Moment generating functions, weak law of large numbers, central limit theorems, convergence of random variables. Maximum likelihood and unbiased estimators. Confidence intervals, mainly for normal means and variances. Recommended as partial preparation for actuarial exam P. Prerequisite(s): A Mat 214 and 220 and one of A Mat 362 or A Mat 367 or 367Z. Offered fall semester only.

**A Mat 468 Mathematical Statistics (3)**

Neyman-Pearson theory (hypothesis testing), type I and II errors, power functions, generalized likelihood ratio tests. Two-sample confidence intervals and hypothesis tests. Sampling distributions, including the t, chi-square and F, all rigorously defined. Sufficient statistics, Fisher information, minimum variance estimators. Introduction to regression and Bayesian estimators. Some listed topics are tested on actuarial exam C. Prerequisite: A Mat 467. Offered spring semester only**.**

A Mat 469 Actuarial Probability and Statistics (1)

Drill in problem solving for one of the following actuarial exams: P, FM or M. May be repeated for credit with permission of instructor. Prerequisites depend on which of the three actuarial exam is featured. S/U Graded.

**A Mat 482 Senior Seminar (3)**

Study of topics in mathematics, chosen at the discretion of the instructor. Prerequisite(s): permission of instructor.

**A Mat 487 Topics in Modern Mathematics (3)**

Selected topics in mathematics. The topic of the course will be indicated in the course schedule and in departmental announcements. The course may be repeated for credit when the topic differs. Prerequisites for A Mat 487 will be as indicated on the departmental announcements.

**A Mat 497 Independent Study in Mathematics (1–3)**

Individual, independent study of selected topics not covered in a regularly scheduled course. Open only to majors in mathematics. May be repeated for credit. Prerequisite(s): junior or senior class standing, and permission of instructor with whom student wishes to study.

**A Mat 499Z Undergraduate Thesis (3)**

Individual, independent study leading to an undergraduate thesis under the direction of faculty chosen by the student. The thesis may be used to fulfill the thesis requirement in the honors program with the approval of the department. Prerequisite(s): permission of instructor.