**Mathematics (MATH) **

**MATH K200 Statistics for Teachers (3 cr.)**

P: one year of high school algebra or MATH M007. The course serves as an introduction to statistical tools and spreadsheets or statistical packages used in every-day 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)

**MATH K300 Statistical Techniques (3 cr.) **

P: at least a C in MATH M014 or equivalent. R: MATH M118. 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 M007 Elementary Algebra (4 cr.)**

P: placement according to IU Northwest Mathematics Placement Test. Signed numbers, operations with polynomials, solving equations, factoring, introduction to graphing. (Grades earned in MATH M007 will appear on the transcript, but will not be included in the grade point average. Credit for MATH M007 may not be applied toward any degree.) (Fall, Spring, Summer I)

**MATH M014 Basic Algebra (3 cr.) **

P: proficiency in elementary algebra or at least a C in MATH M007. Designed to provide algebraic skills needed for courses such as MATH M125, MATH M118, or MATH M119. Polynomials, factoring, and solving equations. Algebraic fractions, radicals, exponents, linear and quadratic equations, inequalities, graphs, word problems. (Grades earned in MATH M014 will appear on the transcript, but will not be included in the grade point average. Credit for MATH M014 may not be applied toward any degree.) (Fall, Spring, Summer I)

**MATH M100 Basic Mathematics (4 cr.) **

P: one year of high school algebra or at least a C in MATH M007. 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 M110 Excursions into Mathematics (3 cr.) **

P: one year of high school algebra or at least a C in MATH M007. 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 M118 Finite Mathematics (3 cr.) **

P: proficiency in two years of high school algebra or at least a C in MATH M014. 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 M119 Brief Survey of Calculus I(3 cr.)**

P: proficiency in two years of high school algebra or at least a C in MATH M014. Introduction to calculus. Primarily for students in business and the social sciences. A student cannot receive credit for both MATH M119 and MATH M215. (Fall, Spring, Summer I, Summer II)

**MATH M125 Precalculus Mathematics (3 cr.) **

P: proficiency in two years of high school algebra or at least a C in MATH M014. Designed to prepare students for calculus (MATH M215). Algebraic operations, polynomial, 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 M126 Trigonometric Functions (2 cr.) **

P or C: MATH M125 or equivalent. Designed to develop the properties of the trigonometric and prepare for courses in calculus (MATH M215). Does not satisfy arts and sciences distributional requirements. (Fall)

**MATH M215 Analytic Geometry and Calculus I(5 ****cr.) **

P: either two years of high school algebra and trigonometry or MATH M125 and MATH M126 (MATH M126 may be taken concurrently with MATH M215). Functions, limits, continuity, derivative, definite integral, applications, exponential and logarithmic functions. A student cannot receive credit for both MATH M119 and MATH M215. (Fall, Spring, Sumer I)

**MATH M216 Analytic Geometry and Calculus II (5 cr.)**

P: either two years of high school algebra and trigonometry or MATH M125 and MATH M126. Definite integral, applications, L’Hopital’s Rule, techniques of integration, limits of sequence, infinite series, polar coordinates. (Fall, Spring)

**MATH M295 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 M301 Applied Linear Algebra (3 cr.) **

P: MATH M216 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. (Spring—odd year)

**MATH M311 Calculus III (4 cr.) **

P: MATH M216. Elementary geometry of 2,3, and n-space, functions of several variables, partial differentiation, minimum and maximum problems, multiple integration. (Fall)

**MATH M312 Calculus IV (3 cr.) **

P: MATH M311. 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 M315 Advanced Calculus for Applications (3 ****cr.) **

P: MATH M311. Properties of real numbers, sequences and series of functions, vector analysis, line and surface integrals, integral theorems. (Occasionally)

**MATH M320 Theory of Interest (3 cr.) **

P: MATH M216. 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. (Fall—odd year)

**MATH M325 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. (Spring)

**MATH M343 Introduction to Differential Equations ****with Applications I(3 cr.) **

P: MATH M216. 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 M313 and MATH M343. (Spring—even year)

**MATH M360 Elements of Probability (3 cr.)**

P: MATH M216 and MATH M311, which may be taken concurrently. R: MATH M118. 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 M360 and MATH M365. (Fall— even year)

**MATH M366 Elements of Statistical Inference (3 cr.) **

P: MATH M360. R: ECON E270. An introduction to statistical estimation and hypothesis testing. Topics include the maximum likelihood method of estimation and the method of moments, the Rao-Carmer 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. (Spring—odd year)

**MATH M371 Elementary Computational Methods (3 cr.) **

P: CSCI C201, or equivalent or consent of instructor. R: MATH M215-MATH M216. 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. (Fall—even year)

**MATH M391 Foundations of the Number Systems ****(3 cr.)**

P: MATH M216. 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 M391, MATH M393. (Spring—even year)

**MATH M393 Bridge to Abstract Mathematics (3 cr.)**

P: MATH M216 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 M391, MATH M393. (Spring—even year)

**MATH M403 Introduction to Modern Algebra I(3 cr.) **

P: MATH M301 or MATH M307. Study of groups, rings, fields (usually including Galois theory), with applications to linear transformations. (Fall—odd year)

**MATH M405 Number Theory (3 cr.) **

P: MATH M216. 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 M406 Topics in Mathematics (3 cr.)**

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

**MATH M413 Introduction to Analysis I(3 cr.) **

P: MATH M301 or MATH M303, and MATH M311, or consent of instructor. Modern theory of real number system, limits, functions, sequences and series, Riemann-Stieltjes integral, and special topics. (Spring— even year)

**MATH M420 Metric Space Topology (3 cr.) **

P: MATH M301 or MATH M303. 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 M425 Graph (Network) Theory and Combinatorial Theory (3 cr.)**

P: MATH M301 or MATH M303. 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 M435 Introduction to Differential Geometry ****(3 cr.) **

P: MATH M301 or MATH M303, and MATH M311. An introduction to the geometry of curves and surfaces. Topics will include arc length, torsion, Frenet formulae, metrics, curvatures, and classical theorems in these areas. (Occasionally)

**MATH M436 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. (Spring—odd year)

**MATH M447 Mathematical Models and Applications ****I(3 cr.) **

P: MATH M311 and MATH M360, 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. (Fall—odd year)

**MATH M448 Mathematical Models and Applications ****II(3 cr.) **

P: MATH M311 and MATH M360, 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. (Spring—even year)

**MATH M451 The Mathematics of Finance (3 cr.)**

P: consent of instructor. Course covers probability theory, Brownian motion, Ito’s Lemma, Stochastic differential equations, convexity, Hahn-Banach theorem, Lagrange multipliers, Bellman equations, dynamic programming and the application of these topics to Black-Scholes formula, capital assets pricing model, the term theory of interest rates and the relation of Martingale measures to arbitrage. (Occasionally)

**MATH M463 Introduction to Probability Theory (3 ****cr.) **

P: MATH M301 or MATH M303, and MATH M311, 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 M477 Mathematics of Operations Research ****(3 cr.)**

P: MATH M301 or MATH M303, MATH M311, MATH M360. Introduction to the methods of operations research. Linear programming, dynamic programming, integer programming, network problems, queuing theory, scheduling, decision analysis, simulation. (Fall—odd year)

**MATH M483 Historical Development of Modern Mathematics (3 cr.) **

P: MATH M301, MATH M311, 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 M485 Life Contingencies I(3 cr.) **

P: MATH M320 (may be taken concurrently), MATH M360. Measurement of mortality, life annuities, life insurance, net annual premiums, and net level premium reserves. (Fall—odd year)

**MATH M486 Life Contingencies II(3 cr.) **

P: MATH M485. Population theory, the joint life status, last-survivor and general multi-life statuses, contingent functions, compound contingent functions, reversionary annuities, multiple-decrement tables, tables with secondary decrements. (Spring—even year)

**MATH M493 Senior Thesis in Mathematics (1-3 cr.) **

P or C: at least one 400-level mathematics course. Student must write a paper, relating to 400-level mathematics study, on a topic agreed upon by the student and the department chairman or advisor delegated by the chairman.

**MATH T101 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 M007) and proficiency in geometry (one year, high school, C or better). R: proficiency in basic algebra M014. 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 T102 Mathematics for Elementary Teachers II (3 cr.) **

P: MATH T101. 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. (Fall, Spring)

**MATH T103 Mathematics for Elementary Teachers ****III (3 cr.) **

P: MATH T102. 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, Spring)

**MATH T336 Topics in Euclidean Geometry (3 cr.) **

P: MATH M391. 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. (Fall—even year)

**MATH T490 Topics for Elementary Teachers (3 cr.)**

P: MATH T103. 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 T493 Mathematics of Middle and High School, Advanced Perspective (4 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. (Summer, even years)

**MATH Y398 Internship in Professional Practice (1-3 ****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.

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