Note: P-prerequisite; C - corequisite; R - recommended; Fall - offered fall semester; Spring - offered spring semester; Summer - offered in the summer session. For courses with no designated semester, consult the Master Schedule. Equiv. - course is equivalent to the indicated course taught at Indiana University Bloomington, or the indicated course taught at Purdue University, West Lafayette. For Statistics Courses, please click here.

Special Developmental Courses

M001 Introductory Algebra (6 cr.) P: Placement test or self elect for students who need more time on task. Fall, Spring. This is a first course in the study of algebra. Real numbers, algebraic expressions, solving equations, graphing equations, operations with polynomials, factoring polynomials, rational expressions and equations, solutions of systems of equations, radical expressions, and problem solving strategies are taught. Credit does not apply toward any degree.

001 Introduction to Algebra (4 cr.) P: Placement. Fall, spring, summer. Covers the material in the first year of high school algebra. Numbers and algebra, integers, rational numbers, equations, polynomials, graphs, systems of equations, inequalities, radicals. Credit does not apply toward any degree.

Undergraduate Level

Lower-Division Courses

110 Fundamentals of Algebra (4 cr.) P: 001 or M001 (minimum grade of C-) or placement. Fall, Spring, Summer. Intended primarily for liberal arts and business majors. Integers, rational and real numbers, exponents, decimals, polynomials, equations, word problems, factoring, roots and radicals, logarithms, quadratic equations, graphing, linear equations in more than one variable, and inequalities. This course satisfies the prerequisite needed for M118, M119, 130, and STAT 301.

111 Algebra (4 cr.) P: 001 or M001 (minimum grade of C) or placement. Fall, spring, summer. Real numbers, linear equations and inequalities, systems of equations, polynomials, exponents, logarithmic functions. Covers material in the second year of high school algebra.

M118 Finite Mathematics (3 cr.) P: 111 or 110 (minimum grade of C-) or equivalent. Fall, spring, summer. Logic, set theory, permutations, combinations, simple probability, conditional probability, and Markov chains. An honors option is available in this course.

M119 Brief Survey of Calculus I (3 cr.) P: 111 or 110 (minimum grade of C-) or equivalent. Fall, spring, summer. Sets, limits, derivatives, integrals, and applications. An honors option is available in this course.

130 Mathematics for Elementary Teachers I (3 cr.) P: 111 or 110 (minimum grade of C-) or equivalent and one year of high school geometry. Fall, spring, summer. Numeration systems, mathematical reasoning, integers, rationals, reals, properties of number systems, decimal and fractional notations, problem solving.

132 Mathematics for Elementary Teachers II (3 cr.) P: 130. Fall, spring, summer. Rationals, reals, geometric relationships, properties of geometric figures, one-, two-, and three-dimensional measurement and problem solving.

136 Mathematics for Elementary Teachers (6 cr.) P: 111 or 110 (minimum grade of C) or equivalent and one year of high school geometry. Fall, spring, summer. 136 is a one-semester version of 130 and 132. Not open to sudents with credit in 130 or 132.

153 Algebra and Trigonometry I (3 cr.) P: 111 (minimum grade of C) or placement. Fall, spring, summer. 153-154 is a two-semester version of 159. Not open to students with credit in 151 or 159. 153 covers college-level algebra and provides preparation for 165 and 221.

154 Algebra and Trigonometry II (3 cr.) P: 153 (minimum grade of C) Fall, spring, summer. 153-154 is a two-semester version of 159. Not open to students with credit in 151 or 159. 154 covers college-level trigonometry and provides preparation for 165 and 221.

159 Precalculus (5 cr.) P: 111 (with a minimum grade of B) or placement. Fall, Spring. 159 is a one-semester version of 153-154. Not open to students with credit in 153 or 154. 159 covers college-level algebra and trigonometry and provides preparation for 165 and 221.

163 Integrated Calculus and Analytic Geometry I (5 cr.) Effective Fall 2008, this course is being offered as Math 165.

S163 Honors Integrated Calculus and Analytic Geometry I (5 cr.) Effective Fall 2008, this course is being offered as Math S165.

164 Integrated Calculus and Analytic Geometry II (5 cr.) P: 163 (minimum grade of C-). Equiv. IU MATH M212, Purdue MA 162. Fall, spring, summer I. Transcendental functions, techniques of integration, indeterminant forms and improper integrals, conics, polar coordinates, sequences, infinite series, and power series. An honors option is available in this course.

S164 Honors Integrated Calculus and Analytic Geometry II (5 cr.) P: S163 (with a minimum grade of B-) or 163 (with a minimum grade of A-), and consent of instructor. This course covers the same topics as Math 164. However, it is intended for students having a strong interest in mathematics who wish to study the concepts of calculus in more depth and who are seeking a mathematical challenge.

165 Analytic Geometry and Calculus I (4 cr.) P: 159 or 154 (minimum grade of C) or equivalent, and one year of high school geometry. Equiv. IU MATH M211, Purdue MA 161. Fall, spring, summer I. Introduction to differential and integral calculus of one variable, with applications. The Fundamental Theorem of Calculus.

S165 Honors Analytic Geometry and Calculus I (4 cr.) P: Precalculus or trigonometry and consent of instructor. This course has the same topics as Math 165. However, it is intended for students having a strong background in mathematics who wish to study the concepts of calculus in more depth and who are seeking mathematical challenges.

171 Multidimensional Mathematics (3 cr.) P: 159 or 154 (minimum grade of C) or equivalent, and one year of high school geometry. An introduction to mathematics in more than two dimensions. Graphing of curves, surfaces and functions in three dimensions. Two and three dimensional vector spaces with vector operations. Solving systems of linear equations using matrices. Basic matrix operations and determinants.

190 Topics in Applied Mathematics for Freshmen (3 cr.) Treats applied topics in mathematics at the freshman level. Prerequisites and course material vary with the applications.

221 Calculus for Technology I (3 cr.) P: 159 or 154 (minimum grade of C-) or equivalent, and one year of geometry. Fall, spring, summer 1. Analytic geometry, the derivative and applications, the integral and applications.

222 Calculus for Technology II (3 cr.) P: 221 (minimum grade of C-). Fall, spring, summer 2. Differentiation of transcendental functions, methods of integration, power series, Fourier series, differential equations.

231 Calculus for the Life Sciences I (3 cr.) P: 154 or 159 (with a minimum grade of C-) or equivalent and one year of geometry. Limits, derivatives and applications. Exponential and logarithmic functions. Integrals, antiderivatives, and the Fundamental Theorem of Calculus. Examples and applications are drawn from the life sciences.

232 Calculus for the Life Sciences II (3 cr.) P: 231 (with a minimum grade of C-) or equivalent. Matrices, functions of several variables, differential equations and solutions with applications. Examples and applications are drawn from the life sciences.

261 Multivariate Calculus (4 cr.) P: 164. Equiv. IU MATH M311, Purdue MA 261. Fall, spring, summer 1. Spatial analytic geometry, vectors, curvilinear motion, curvature, partial differentiation, multiple integration, line integrals, Green's theorem. An honors option is available in this course. Note: Students taking Math 261 starting in the Fall 2009 must complete both Math 164 (or 166) AND Math 171 prior to registering for Math 261.

262 Linear Algebra and Differential Equations (4 cr.) P: 164. R: 261. Fall, spring, summer 1. First-order equations, higher-order linear equations, initial and boundary value problems, power series solutions, systems of first-order equations, Laplace transforms, applications. Requisite topics of linear algebra: vector spaces, linear independence, matrices, eigenvalues, and eigenvectors.

276 Discrete Mathematics (3 cr.) P or C: 163, 165 or consent of instructor. Spring. Logic, sets, functions, integer algorithms, applications of number theory, mathematical induction, recurrence relations, permutations, combinations, finite probability, relations and partial ordering, and graph algorithms.

290 Topics in Applied Mathematics for Sophomores (3 cr.) Treats applied topics in mathematics at the sophomore level. Prerequisites and course material vary with the applications.

Upper-Division Courses

300 Logic and the Foundations of Algebra (3 cr.) P: 163 or 165. Fall. Logic and the rules of reasoning, theorem proving. Applications to the study of the integers; rational, real, and complex numbers; and polynomials. Bridges the gap between elementary and advanced courses. Recommended for prospective high school teachers.

333 Chaotic Dynamical Systems (3 cr.) P: 164 or 222. Spring. The goal of the course is to introduce some of the spectacular new discoveries that have been made over the past twenty years in the field of Mathematics known as Dynamical Systems. It is intended for undergraduate students in Mathematics, Science, or Engineering. It will include a variety of computer experiments using software that is posted on the web.

351 Elementary Linear Algebra (3 cr.) P: 261. Not open to students with credit in 511. Fall, spring. Systems of linear equations, matrices, vector spaces, linear transformations, determinants, inner product spaces, eigenvalues, applications.

375 Theory of Interest (3 cr.) P: 261. Spring. An introduction to the theory of finance including such topics as compound interest, annuities certain, amortization schedules, sinking funds, bonds, and related securities.

390 Topics in Applied Mathematics for Juniors (3 cr.) Treats applied topics in mathematics at the junior level. Prerequisites and course material vary with the applications.

398 Internship in Professional Practice (1-3 cr.) P: Approval of Department of Mathematical Sciences. Professional work experience involving significant use of mathematics or statistics. Evaluation of performance by employer and Department of Mathematical Sciences. May count toward major requirements with approval of the Department of Mathematical Sciences. May be repeated with approval of the Department of Mathematical Sciences for a total of 6 credits.

414 Numerical Methods (CSCI 414) (3 cr.) P: 262 and a course in a high-level programming language. Fall. Not open to students with credit in CSCI 512. Error analysis, solution of nonlinear equations, direct and iterative methods for solving linear systems, approximation of functions, numerical differentiation and integration, numerical solution of ordinary differential equations.

417 Discrete Modeling and Game Theory (3 cr.) P: 262 and 351 or 511 or consent of instructor. Linear programming; mathematical modeling of problems in economics, management, urban administration, and the behavioral sciences.

426 Introduction to Applied Mathematics and Modeling (3 cr.) P: 262 and PHYS 152. Spring. Introduction to problems and methods in applied mathematics and modeling. Formulation of models for phenomena in science and engineering, their solution, and physical interpretation of results. Examples chosen from solid and fluid mechanics, mechanical systems, diffusion phenomena, traffic flow, and biological processes.

441 Foundations of Analysis (3 cr.) Effective Fall 2007, MATH 441 is offered as MATH 444.

444 Foundations of Analysis I (3 cr.) P: 261. Fall. Set theory, mathematical induction, real numbers, completeness axiom, open and closed sets in Rm, sequences, limits, continuity and uniform continuity, inverse functions, differentiation of functions of one and several variables. (Formerly offered as MATH 441.)

442 Foundations of Analysis II (3 cr.) Effective Spring 2008, MATH 442 is offered as MATH 445.

445 Foundations of Analysis II (3 cr.) P: 444. Spring. Continuation of differentiation, the mean value theorem and applications, the inverse and implicit function theorems, the Riemann integral, the fundamental theorem of calculus, point-wise and uniform convergence, convergence of infinite series, series of functions. (Formerly offered as MATH 442.)

453 Beginning Abstract Algebra (3 cr.) P: 351 or consent of the instructor. Fall. Basic properties of groups, rings, and fields, with special emphasis on polynomial rings.

456 Introduction to the Theory of Numbers (3 cr.) P: 261. Divisibility, congruences, quadratic residues, Diophantine equations, the sequence of primes.

462 Elementary Differential Geometry (3 cr.) P: 351. Calculus and linear algebra applied to the study of curves and surfaces. Curvature and torsion, Frenet-Serret apparatus and theorem, fundamental theorem of curves. Transformation of R2, first and second fundamental forms of surfaces, geodesics, parallel translation, isometries, fundamental theorem of surfaces.

463 Intermediate Euclidean Geometry for Secondary Teachers (3 cr.) P: 300 or equivalent and one year of high school geometry, or consent of instructor. Spring. History of geometry. Ruler and compass constructions, and a critique of Euclid. The axiomatic method, models, and incidence geometry. Presentation, discussion and comparison of Hilbert's, Birkhoff's, and SMSG's axiomatic developments.

490 Topics in Mathematics for Undergraduates (1-5 cr.) By arrangement. Open to students only with the consent of the department. Supervised reading and reports in various fields.

S490 Senior Seminar (3 cr.)

491 Seminar Competitive Math Prolem Solving (1-3 cr.) Approval of the Director of Undergraduate Programs is required. This seminar is designed to prepare students for various national and regional mathematics contests and examinations such as the Putnam Mathematical Competition, the Indiana College Mathematical Competition and the Mathematical Contest in Modeling (MCM), among others. May be repeated twice for credit.

492 Capstone Experience (1-3 cr.) By arrangement.