# Mathematics Course Descriptions

## MATH-A 100 : Fundamentals of Algebra

Designed to provide algebraic skills needed for future mathematics courses. Integers, rational and real numbers, exponents, decimals, polynomials, equations, word problems, factoring, roots and radicals, quadratic equations, graphing, linear equations in more than one variable, and inequalities. Does not satisfy the College of Arts and Sciences distribution requirements nor general education mathematical reasoning requirement. (Fall, Spring, Summer)

## MATH-K 200 : Statistics for Teachers

The course serves as an introduction to statistical tools and spreadsheets or statistical packages used in everyday teaching practice. The emphasis is on understanding real-life applications of graphs of data, measures of central tendency, variation, probability, normal distributions, confidence intervals, hypothesis testing, and sampling. (Fall, Spring)

## MATH-K 300 : Statistical Techniques

An introduction to statistics. Nature of statistical data. Ordering and manipulation of data. Measures of central tendency and dispersion. Elementary probability. Concepts of statistical inference and decision, estimation, and hypothesis testing. Special topics discussed may include regression and correlation, analysis of variance, nonparametric methods. (Occasionally)

## MATH-M 015 : Arithmetic with Algebra

Integers, proportional reasoning, measurement systems, exponents, solving linear inequalities, polynomial operations, geometric concepts, rational numbers, ratios and percent, algebraic expressions, solving and writing linear equations, literal equations, graphs of linear equations, applications. Does not satisfy the College of Arts and Sciences distribution requirements nor general education mathematical reasoning requirement. (Fall, Spring)

## MATH-M 100 : Basic Mathematics

Topics in algebra, geometry, graphing, probability, statistics, and consumer mathematics. Emphasis on problem solving and constructing mathematical models. This course is designed for allied health students and liberal arts students who plan to take no additional mathematics courses. Does not count toward a major in mathematics. (Fall, Spring, Summer I, Summer II)

## MATH-M 110 : Excursions into Mathematics

A course designed to convey the flavor and spirit of mathematics, stressing reasoning and comprehension rather than technique. Not preparatory to other courses; explores the theory of games and related topics that may include the mathematics of politics and elections. This course does not count toward a major in mathematics. (Occasionally)

## MATH-M 117 : Intermediate Algebra

Designed to introduce nonlinear models and their applications, advanced linear systems, and function foundations. Does not satisfy the College of Arts and Sciences distribution requirements nor general education mathematical reasoning requirement. (Fall, Spring, Summer)

## MATH-M 118 : Finite Mathematics

Set theory, linear systems, matrices, probability, linear programming, Markov chains. Applications to problems from business and the social sciences. (Fall, Spring, Summer I, Summer II)

## MATH-M 119 : Brief Survey of Calculus

Introduction to calculus. Primarily for students in business and the social sciences. A student cannot receive credit for both MATH-M 119 and MATH-M 215. (Fall, Spring, Summer I, Summer II)

## MATH-M 125 : Precalculus Mathematics

Designed to prepare students for calculus (MATH-M 215). Algebraic operations, polynomial, rational exponential, and logarithmic functions and their graphs, conic sections, linear systems of equations. Does not satisfy the arts and sciences distributional requirements. (Fall, Spring, Summer II)

## MATH-M 126 : Trigonometric Functions

In-depth study of trigonmetic functions, definitions, unit circle, graphs, inverse functions, identities, trigonmetric equations and applications. This course, together with MATH-M 125 is designed to prepare students for calculus (MATH-M 215). (Occasionally)

## MATH-M 127 : Pre-calculus with Trigonometry

This course is designed to prepare students for calculus (M 215). Subject matter includes polynomial, rational, root, exponential, logarithmic, and trigonometric functions and their applications. (Fall, Spring, Summer)

## MATH-M 215 : Analytic Geometry and Calculus I

Differential calculus of functions of one variable, with applications. Functions, graphs, limits, continuity, derivatives of trigonometric, exponential and logarithmic functions, tangent lines, optimization problems, curve sketching, L'Hopital's Rule, definite integral, the Fundamental Theorem of Calculus. A student cannot receive credit for both MATH-M 119 and MATH-M 215. (Fall, Spring, Summer I)

## MATH-M 216 : Analytic Geometry and Calculus II

Integral calculus of functions of one variable. Antiderivatives, definite integrals, techniques of integration, areas, volumes, surface areas, arc length, parametric functions, polar coordinates, limits of sequences, convergence of infinite series, Taylor polynomials, power series, and applications. (Fall, Spring)

## MATH-M 295 : Readings and Research

Supervised problem solving. Admission only with permission of a member of the mathematics faculty, who will act as supervisor. (Occasionally)

## MATH-M 301 : Applied Linear Algebra

Emphasis on applications: systems of linear equations, vector spaces, linear transformations, matrices, simplex method in linear programming. Computer used for applications. Credit not given for both MATH-M 301 and MATH-M 303. (2-year cycle, see department for details)

## MATH-M 311 : Calculus III

Elementary geometry of 2, 3, and n-space; functions of several variables; partial differentiation; minimum and maximum problems; multiple integration. (Fall)

## MATH-M 312 : Calculus IV

Differential calculus of vector-valued functions, transformation of coordinates, change of variables in multiple integrals. Vector integral calculus: line integrals, Green's theorem, surface integrals, Stokes' theorem. Applications. (Occasionally)

## MATH-M 320 : Theory of Interest

Measurement of interest: accumulation and discount, equations of value, annuities, perpetuities, amortization and sinking funds, yield rates, bonds and other securities, installment loans, depreciation, depletion, and capitalized cost. This course covers topics corresponding to the society of Actuaries' Exam FM.(2-year cycle, see department for details)

## MATH-M 325 : Problem-solving Seminar in Actuarial Science

A problem- solving seminar to prepare students for the actuarial exams. May be repeated up to three times for credit. (2-year cycle, see department for details)

## MATH-M 343 : Introduction to Differential Equations with Applications I

Derivation of equations of mathematical physics, biology, etc. Ordinary differential equations and methods for their solution, especially series methods. Simple vector field theory. Theory of series, Fourier series, applications to partial differential equations. Integration theorems, Laplace and Fourier transforms, applications. A student may not receive credit for both MATH-M 313 and MATH-M 343. (2-year cycle, see department for details)

## MATH-M 360 : Elements of Probability

The study of probability models that involve one or more random variables. Topics include conditional probability and independence, gambler's ruin and other problems involving repeated Bernoulli trials, discrete and continuous probability distributions, moment generating functions, probability distributions for several random variables, some basic sampling distributions of mathematical statistics, and the central limit theorem. Course topics match portions of Exam for Course 1 of the Society of Actuaries. Credit not given for both MATH-M 360 and MATH-M 365. (2-year cycle, see department for details)

## MATH-M 366 : Elements of Statistical Inference

An introduction to statistical estimation and hypothesis testing. Topics include the maximum likelihood method of estimation and the method of moments, the Rao-Cramer bound, large sample confidence intervals, type I and type II errors in hypothesis testing, likelihood ratio tests, goodness of fit tests, linear models, and the method of least squares. This course covers portions of Actuarial Exam C. (2-year cycle, see department for details)

## MATH-M 371 : Elementary Computational Methods

Interpolation and approximation of functions, solution of equations, numerical integration and differentiation. Errors, convergence, and stability of the procedures. Students write and use programs applying numerical methods. (Occasionally)

## MATH-M 391 : Foundations of the Number Systems

Sets, functions and relations, groups, real and complex numbers. Bridges the gap between elementary and advanced courses. Recommended for students with insufficient background for 400-level courses, for M.A.T. candidates, and for students in education. Not open to students who have received credit for MATH M403 or MATH M413. Credit given only for one of MATH-M 391, MATH-M 393. (2-year cycle, see department for details)

## MATH-M 393 : Bridge to Abstract Mathematics

Preparation for 400-level math courses. Teaches structures and strategies of proofs in a variety of mathematical settings: logic, sets, combinatorics, relations and functions, and abstract algebra. Credit given only for one of MATH-M 391, MATH-M 393. (2-year cycle, see department for details)

## MATH-M 403 : Introduction to Modern Algebra I

Study of groups, rings, fields (usually including Galois theory), with applications to linear transformations. (2-year cycle, see department for details)

## MATH-M 405 : Number Theory

Numbers and their representation, divisibility and factorization, primes and their distribution, number theoretic functions, congruences, primitive roots, diophantine equations, quadratic residues, sums of squares, number theory and analysis, algebraic numbers, irrational and transcendental numbers. (Occasionally)

## MATH-M 406 : Topics in Mathematics

Selected topics in various areas of mathematics that are not covered by the standard courses. May be repeated for credit. (Occasionally)

## MATH-M 413 : Introduction to Analysis I

Modern theory of real number system, limits, functions, sequences and series, Riemann-Stieltjes integral, and special topics. (2-year cycle, see department for details)

## MATH-M 420 : Metric Space Topology

Topology of Euclidean and metric spaces. Limits and continuity. Topological properties of metric spaces, including separation properties, connectedness, and compactness. Complete metric spaces. Elementary general topology. (Occasionally)

## MATH-M 425 : Graph (Network) Theory and Combinatorial Theory

Graph theory: basic concepts, connectivity, planarity, coloring theorems, matroid theory, network programming, and selected topics. Combinatorial theory: generating functions, incidence matrices, block designs, perfect difference sets, selection theorems, enumeration, and other selected topics. (Occasionally)

## MATH-M 436 : Introduction to Geometries

Non-Euclidean geometry, axiom systems. Plane projective geometry, Desarguesian planes, perspectivities coordinates in the real projective plane. The group of projective transformations and subgeometries corresponding to subgroups. Models for geometries. Circular transformations. (Occasionally)

## MATH-M 447 : Mathematical Models and Applications I

Formation and study of mathematical models used in the biological, social, and management sciences. Mathematical topics include games, graphs, Markov and Poisson processes, mathematical programming, queues, and equations of growth. (2-year cycle, see department for details)

## MATH-M 448 : Mathematical Models and Applications II

Formation and study of mathematical models used in the biological, social, and management sciences. Mathematical topics include games, graphs, Markov and Poisson processes, mathematical programming, queues, and equations of growth. (2-year cycle, see department for details)

## MATH-M 451 : The Mathematics of Finance

R: Math-M 343. Course covers probability theory, Brownian motion, Ito's Lemma, stochastic differential equations, and dynamic hedging. These topics are applied to the Black-Scholes formula, the pricing of financial derivatives, and the term theory of interest rates. (Occasionally)

## MATH-M 463 : Introduction to Probability Theory

Idealized random experiments, conditional probability, independence, compound experiments. Univariate distributions, countable additivity, discrete and continuous distributions, Lebesgue-Stieltjes integral (heuristic treatment), moments, multivariate distribution. Generating functions, limit theorems, normal distribution. (Occasionally)

## MATH-M 469 : Applied Statistical Techniques

Linear regression, multiple regression, applications to credibility theory, time series and ARIMA models, estimation, fitting, and forecasting. This course covers the Applied Statistics portion of the actuarial VEE requirements and portions of Exam C. (2-year cycle, see department for details)

## MATH-M 477 : Mathematics of Operations Research

Introduction to the methods of operations research. Linear programming, dynamic programming, integer programming, network problems, queuing theory, scheduling, decision analysis, simulation. (2-year cycle, see department for details)

## MATH-M 483 : Historical Development of Modern Mathematics

The development of modern mathematics from 1660 to 1870 will be presented. The emphasis is on the development of calculus and its ramifications and the gradual evolution of mathematical thought from mainly computational to mainly conceptual. (Occasionally)

## MATH-M 485 : Life Contingencies I

Measurement of mortality, life annuities, life insurance, net annual premiums, net level premium reserves, the joint life and last- survivor statuses, and multiple-decrement tables. (2-year cycle, see department for details)

## MATH-M 486 : Life Contingencies II

Population theory, the joint life status, last- survivor and general multilife statuses, contingent functions, compound contingent functions, reversionary annuities, multiple-decrement tables, tables with secondary decrements. (Occasionally)

## MATH-M 493 : Senior Thesis in Mathematics

Student must write and present a paper, relating to 400-level mathematics study, on a topic agreed upon by the student and the department chair or advisor delegated by the chair.

## MATH-T 101 : Mathematics for Elementary Teachers I

Elements of set theory, counting numbers. Operations on counting numbers, integers, rational numbers, and real numbers. Open only to elementary education majors. Does not count toward arts and sciences distribution requirement. (Fall, Spring)

## MATH-T 102 : Mathematics for Elementary Teachers II

Sets, operations, and functions. Prime numbers and elementary number theory. Elementary combinatorics, probability, and statistics. Open only to elementary education majors. Does not count toward arts and sciences distribution requirement. (Spring, Summer I)

## MATH-T 103 : Mathematics for Elementary Teachers III

Descriptions and properties of basic geometric figures. Rigid motions. Axiomatics. Measurement, analytic geometry, and graphs of functions. Discussion of modern mathematics. Open only to elementary education majors. Does not count toward arts and sciences distribution requirement. (Fall, Summer II)

## MATH-T 336 : Topics in Euclidean Geometry

Axiom systems for the plane; the parallel postulate and non-Euclidean geometry; classical theorems. Geometric transformation theory vectors and analytic geometry; convexity; theory of area and volume. (2-year cycle, see department for details)

## MATH-T 490 : Topics for Elementary Teachers

Development and study of a body of mathematics specifically designed for experienced elementary teachers. Examples may include probability, statistics, geometry, and algebra. Open only to graduate elementary teachers with permission of the instructor. Does not count toward arts and sciences distribution requirement. (Occasionally)

## MATH-T 493 : Mathematics of Middle and High School, Advanced Perspective

Team-taught capstone course for mathematics education majors. Mathematics of grades 6-12 and methods of instruction. Topics explored from a college perspective. (Occasionally)

## MATH-Y 398 : Internship in Professional Practice

Professional work experience involving significant use of mathematics or statistics. Evaluation of performance by employer and Department of Mathematics. Does not count toward requirements. May be repeated with approval of Department of Mathematics for a total of 6 credits.