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Undergraduate Bulletin 2006-2007
 
Bulletin Homepage |College of Arts & Sciences | Courses in Mathematics

Courses in Mathematics


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. May not be offered in 2006-2007.

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. [MS]

A Mat 105 Finite Mathematics (3)

An introduction to topics of interest to students of the social sciences; sets and logic, partitions and counting, probability, vectors and matrices, theory of games. Prerequisite(s): three years of high school mathematics. [MS] 

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): A Mat 100 or satisfactory performance on the mathematics placement exam. [MS]

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. [MS]

A Mat 109 Applied Matrix Algebra (3)

Matrix algebra as applied to solving systems of linear equations. Markov chains, linear programming. Emphasizes calculations and applications rather than theory. Prerequisite(s): three years of high school mathematics. [MS]

A Mat 110 Introduction to Maple (2)

A hands-on introduction to the computer algebra system Maple. Basic commands are introduced by way of examples from the areas of algebra, calculus, number theory, graphics, business mathematics, and numerical analysis. Intended for transfer students having no background in Maple. Does not yield credit toward a major in mathematics. Prerequisite(s): A Mat 101 or a semester of calculus.

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. [MS]

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. Prerequisite(s): A Mat 100 or satisfactory performance on the mathematics placement exam. [MS]

A Mat 113 Calculus II (4)

Techniques of integration, applications of the definite integral, conics, polar coordinates, improper integrals, infinite series. Prerequisite(s): A Mat 111 or 112.

A Mat 118 Honors Calculus I (4)

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. Only one of A Mat 112 & 118 may be taken for credit. Prerequisite(s): three years of secondary school mathematics and permission of the instructor. Offered fall semester only. [MS]

A 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. Only one of A Mat 113 & 119 may be taken for credit. Prerequisite(s): A Mat 118, a grade of A in A Mat 112, or permission of the instructor. Offered spring semester only.

A Mat 180 Calculus Seminar (1)

Topics in mathematics that involve calculus and either elaborate concepts from calculus or apply calculus to problems in other areas or disciplines. The seminar is intended for freshmen who have just completed one semester of calculus and wish to enrich their understanding of calculus. Prerequisite(s): one semester of calculus and permission of instructor.

A 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.

A Mat 220 Linear Algebra (3)

Linear equations, matrices, determinants, finite dimensional vector spaces, linear transformations Euclidean spaces. Prerequisite(s): A Mat 113 or 119.

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 co-requisite(s): A Mat 113 or 119.

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 partial preparation for Actuarial Societyís Course 2 and Course 3 exams.

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): A Mat 108. Offered spring semester only.

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 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 312Z Basic Analysis (3)

A Mat 312Z is the writing intensive version of A Mat 312; only one may be taken for credit. Prerequisite(s): A Mat 214. [WI]

A Mat 313 Introduction to Numerical Methods (3)

Introduction to the theory and techniques in the numerical solution of mathematical problems. Topics include solutions of linear and nonlinear equations, interpolation, numerical integration, and numerical solution of differential equations. Only one of A Mat 313 or A Mat 401 may be taken for credit. Prerequisite(s): A Mat 220.

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 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 or 119.

A Mat 326Z Classical Algebra (3)

A Mat 326Z is the writing intensive version of A Mat 326; only one may be taken for credit. Prerequisite(s): A Mat 113 or 119. [WI]

A Mat 327 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 327Z Elementary Abstract Algebra (3)

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. [WI]

A Mat 331 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. Offered spring semester only.

A Mat 331Z Transformation Geometry (3)

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. [WI]

A Mat 342 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. Offered fall semester only.

A Mat 342Z Elementary Topology (3)

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. [WI]

A Mat 367 Discrete Probability (3)

Introduction to combinatorial methods and discrete probability models. Binomial, Poisson, hypergeometric, negative binomial distributions. Selected classical problems; e.g., gamblersí ruin. Expected value and variance. Conditional probability. Weak law of large numbers and the central limit theorem. Optional topics; joint probability mass functions, correlations, Markov chains. Mat 367Z is the writing intensive version of Mat 367; only one may be taken for credit. Prerequisite(s): A Mat 113 or 119 plus 6 credits at the 200 level or above in either mathematics or computer science.

A Mat 367Z Discrete Probability (3)

Writing intensive version of A Mat 367; only one of the two courses may be taken for credit. Prerequisite(s): A Mat 113 or 119 plus 6 credits at the 200 level or above in either mathematics or computer science. Prerequisite(s): A Mat 113 or 119 plus 6 credits at the 200 level or above in either mathematics or computer science. [WI]

A Mat 368 Statistics and Continuous Probability (3)

Continuous random variables, including the normal, exponential, t, and chi-square. Maximum likelihood and unbiased estimators. Confidence intervals and hypothesis tests, mainly for normal means and variances, based on one and two samples. F distribution. Behrens-Fisher problem. May not be taken for credit by students with credit for Mat 362 or Mat 362Z. Mat 368Z is the writing intensive version of Mat 368; only one of Mat 368 and Mat 368Z may be taken for credit. Prerequisite(s): A Mat 214 or A Mat 367 or A Mat 367Z.

A Mat 368Z Statistics and Continuous Probability (3)

Writing intensive version of A Mat 368; only one may be taken for credit. Mat 368Z may not be taken for credit by students with credit for Mat 362 or Mat 362Z. Prerequisite(s): A Mat 214 or A Mat 367 or A Mat 367Z. [WI]

A Mat 369 Statistics and Data Analysis (3)

Continuation of Mat 368. Chi-squared tests for goodness-of-fit and for independence. Introduction to regression (cf. A Mat 465). Analysis of variance. Distribution free methods. Robustness, transformations of data. Students will use a statistical computer package (usually Minitab), no prior knowledge of which is assumed. The course will normally be taught in a computer classroom. Normally offered spring semester only. Prerequisite(s): A Mat 368 or A Mat 368Z and A Mat 214.

A Mat 372 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. Usually offered in the summer .

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

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. . [WI]

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. Offered spring semester only.

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.

A Mat 403 Life Contingencies I (3)

Treatment of the contingencies of a single life including: mortality functions, life annuities, life insurance functions, annual premiums, net level premium reserves, the expense factor, and more complex benefits. Recommended as partial preparation for Course 3 actuarial exam. Prerequisite(s): A Mat 301, 367.

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. Recommended as partial preparation for Course 3 actuarial exam. 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 Complex Variables for Applications (3)

The elementary functions, differentiation, conformal transformations, power series, integral theorems, Taylorís theorems, Taylorís and Laurentís 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. Offered fall semester only.

A Mat 412Z Complex Variables for Applications (3)

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. [WI]

A Mat 413/413Z and 414 Advanced Calculus (3, 3)

A rigorous presentation of the traditional topics in the calculus of several variables and their applications. Topics include the implicit function theorem, Taylorís theorem, Lagrange multipliers, Stieltjes integral, Stokesí 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 414. [WI]

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, Greenís 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 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 432Z Foundations of Geometry (3)

A Mat 432Z is the writing intensive version of A Mat 432; only one may be taken for credit. Prerequisite(s): A Mat 220. Normally only the writing intensive version of this course is offered. [WI]

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 fall semester only.

A Mat 442 Introduction to Algebraic Topology (3)

Two-dimensional manifolds, the fundamental group and Van Kampenís theorem, covering spaces, graphs, and applications to group theory. Prerequisite(s): A Mat 214 and 220.

A Mat 452 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.

A Mat 452Z History of Mathematics (3)

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. Offered fall semester only. [WI]

A Mat 464 Applied Stochastic Processes (3)

An overview of various stochastic processes found in practice with particular emphasis on Markov chains. Introduction to queuing theory. Particular attention given to estimation. Examples of applications. Recommended as partial preparation for Course 3 actuarial exam. Prerequisite(s): A Mat 367 or 367Z or 467. Offered spring semester only.

A Mat 465 Applied Statistics (3)

A second or third course in statistics. Central theme is forecasting; i.e., simple and multiple regression and time series. Recommended as partial preparation for Course 3 and Course 4 actuarial exams. Offered in fall semester only.

A Mat 465Z Applied Statistics (3)

Writing intensive version of A Mat 465; only one of the two courses may be taken for credit. Prerequisite(s): A Mat 220 and either A Mat 368 or A Mat 468. [WI]

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 Course 1 actuarial exam. Prerequisite(s): A Mat 367 or Mat 367Z, Mat 214 and Mat 220. 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. Prerequisite: A Mat 467. Offered spring semester only.

A Mat 469 Actuarial Probability and Statistics (1)

Drill in problem solving for Course 1 exam of The Society of Actuaries. Prerequisite(s): A Mat 467. Offered spring semester only. S/U Graded.

A Mat 481 Senior Seminar I (3)

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

A Mat 482 Senior Seminar II (3)

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

A Mat 497 Independent Study in Mathematics (1Ė3)

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. [WI]