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# Department of Mathematics and Actuarial Science

## Course Descriptions

MATH-A 100 Fundamentals of Algebra (4 cr.)
P: Level MA102 on Placement Exam. 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 (3 cr.)
P: Level MA103 on Placement Exam or at least a C in MATH-A 100 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 (3 cr.)
P: at least a C in MATH-M 117 or equivalent. MATH-M 118. 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 15 Arithmetic with Algebra (0-5 cr.) Integer's, 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 (4 cr.)
P: Level MA103 on Placement Exam  or at least a C in MATH-A 100 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 (3 cr.)
P: Level MA103 on Placement Exam  or at least a C in MATH-A 100. 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 (3 cr.)
P: Level MA103 on Placement Exam or MATH A 100. 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 (3 cr.)
P: Level MA104 on Placement Exam  or at least a C in MATH M 117. 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 (3 cr.)
P: Level MA104 on Placement Exam or at least a C in MATH M 117. 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 (3 cr.)
P: Level MA104 on Placement Exam or at least a C in MATH M 117. 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 (2-3 cr.)
P: Level MA104 on Placement Exam  or at least a C in MATH M 117. In-depth study of trigonometric functions: definitions, unit circle, graphs, inverse functions, identities, trigonometric equations and applications.  This course together with M 125 is designed to prepare students for calculus (M 215). Does not satisfy arts and sciences distributional requirements. (Occasionally)

MATH-M127 Pre-calculus with Trigonometry (5 cr.)
P: Level MA104 on Placement Exam or MATH-M 117 (with C or better). 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 Calculus I (5 cr.) P: Level MA105 on Placement Exam or MATH-M 125 and MATH-M 126 or MATH-M 127.  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 Calculus II (5 cr.) P: MATH-M 215  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 (1-3 cr.) 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 (3 cr.)
P: Math-M 216 or consent of instructor. 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 M301 and MATH M303. (2-year cycle, see department for details)

MATH-M 311 Calculus III (4 cr.) P: MATH M 216. 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 (3 cr.) P: MATH-M 311. 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 (3 cr.)
P: MATH-M 216. 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 (1-3 cr.) P: Consent of instructor. 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 (3 cr.) P: MATH-M 216. 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 (3 cr.)
P: MATH-M 216 and MATH-M 311, which may be taken concurrently. R: MATH-M 118. 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 (3 cr.) P: MATH-M 360.R: ECON-E 270. 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 (3 cr.) P: CSCI-C 201, or equivalent or consent of instructor, MATH-M 215, MATH-M 216. 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 (3 cr.) P: MATH M 216. 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. 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 (3 cr.) P: MATH M 216 or consent of instructor. 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 (3 cr.) P: MATH M 301. 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 (3 cr.)
P: MATH-M 216. 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 (3 cr.) 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 (3 cr.)
P: MATH-M 301 or MATH-M 303, and MATH-M 311, or consent of instructor. 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 (3 cr.)
P: MATH-M 301 or MATH-M 303. 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 (3 cr.) P: MATH-M 301 or MATH-M 303. 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 (3 cr.)
P: MATH M391 or its equivalent. 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 (3 cr.) P: MATH-M 311and MATH-M 360, or consent of instructor. 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 (3 cr.) P: MATH-M 311 and MATH-M 360, or consent of instructor. 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 (3 cr.)
P: MATH-M 311 and MATH-M 366, 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 (3 cr.) P: MATH-M 301 or MATH-M 303, and MATH-M 311, or consent of instructor. 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 (3 cr.) P: MATH-M 366 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 (3 cr.) P: MATH-M 301 or MATH-M 303, MATH-M 311, MATH-M 360. 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 (3 cr.) P: MATH-M 301, MATH-M 311, and at least 3 additional credit hours in mathematics at the 300 level or above. 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 (3 cr.)
P: MATH-M 320 and MATH-M 360. 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 (3 cr.)
P: MATH-M 485 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 (3 cr.) P: At least one 400-level mathematics course. At least one 400- level mathematics course. 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 (3 cr.) P: Proficiency in elementary algebra (demonstrated by placement exam or a grade of C or better in MATH-A 100) and proficiency in geometry (one year, high school, C or better).
R: Proficiency in intermediate algebra MATH-M 117. 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 (3 cr.) P: MATH-T 101 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 (3 cr.) P: MATH-T 102. 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 (3 cr.)
P: MATH-M 391.  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 (3 cr.) P: MATH-T 103. 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 (3 cr.) P: Junior or senior standing in mathematics education or consent of instructor. 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 (3 cr.) P: Approval of Department of Mathematics. 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.