#### Mathematical Science | MATH

P Prerequisite | C Co-requisite | R Recommended

- MATH-A 100 Fundamentals of Algebra (4 cr.) P: ALEKS Assessment score greater than 15. Designed to introduce linear models and their applications, graphing of linear and quadratic equations, and to foster the growth of proficiency in a range of algebraic topics including factoring strategies. Does not satisfy the Campus General Education Mathematical Reasoning requirement.
- MATH-K 300 Statistical Techniques for Health Professions (3 cr.) P: C or higher in MATH-A 100 or ALEKS Assessment score greater than 35. C: MATH-M 125. Credit given for only one of MATH-K 300 and MATH-K 310. Course introduces nursing/health science students to the basic concepts and techniques of data analysis needed in professional health care practice. Measurements, data analysis and statistics are examined. Differences in types of qualitative data and methods of interpretation are explored. Procedures of estimation and hypothesis testing are also studied. Emphasis is on the application of fundamental conception to real situations in client care.
- MATH-K 310 Statistical Techniques (3 cr.) P: C- or higher in MATH-M 115, C- or higher in MATH-M 125, or ALEKS Assessment score greater than 60. Credit given for only one of MATH-K 300 and MATH-K 310. Introduction to probability and statistics. Elementary probability theory, conditional probability, independence, random variables, discrete and continuous probability distributions, measures of central tendency and dispersion. Concepts of statistical inference and decision: estimation, hypothesis testing, Bayesian inference, statistical decision theory. Special topics discussed may include regression and correlation, time series, analysis of variance, non-parametric methods.
- MATH-M 107 College Algebra (3 cr.) P: C or higher in MATH-A 100 or equivalent, or ALEKS Assessment score greater than 35. Designed to provide algebraic concepts and skills including sets of real numbers, exponents, complex fractions, linear equations and quadratic equations, rectangular coordinates, polynomial and rational expressions, complex numbers, and The Fundamental Theorem of Algebra.
- MATH-M 108 Quantitative Reasoning (3 cr.)
**Satisfiy CW Gen Ed Fund Lit QR**P: C or higher in MATH-A 100 or ALEKS Assessment score greater than 30. Topics include numerical reasoning, descriptive statistics, and linear and exponential modeling as used in solving problems typically encountered in everyday life. Emphasis is on analytic thinking, argumentation and mathematical writing. Computers (spreadsheets, internet) and graphing calculators are used. - MATH-M 111 Mathematics in the World (3 cr.)
**Satisfiy CW Gen Ed Fund Lit QR**P: C or higher in MATH-A 100 or ALEKS Assessment score greater than 30. MATH-M 111 grade can replace IU South Bend MATH-M 110 grade. Conveys spirit of mathematical languages of quantity; students apply concepts from algebra, geometry, management science, probability, and statistics, and use scientific software to analyze real world situations. - MATH-M 115 Precalculus and Trigonometry (5 cr.) P: Câ€“ or higher in MATH-M 107 or equivalent, or ALEKS Assessment score greater than 50. Equivalent to MATH-M 125/MATH-M 126. Credit not given for both MATH-M 115 and MATH-M 125/MATH-M 126. Satisfies Campuswide General Education Fundamental Literacies: Quantitative Reasoning. Designed to prepare students for higher numbered mathematics and computer science courses. Algebraic operations; polynomials; functions and their graphs; conic sections, linear systems of equations; trigonometric, exponential and logarithmic functions.
- MATH-M 118 Finite Mathematics (3 cr.) P: C or higher in MATH-A 100 or equivalent, or ALEKS Assessment score greater than 35. Set theory, logic, permutations, combinations, simple probability, conditional probability, Markov chains.
- MATH-M 119 Brief Survey of Calculus 1 (3 cr.) P: Câ€“ or higher in MATH-M 115, or Câ€“ or higher in MATH-M 125, or ALEKS Assessment score greater than 60. Primarily for students from business and the social sciences. Credit given for only one of the following: MATH-M 119, MATH-M 208, MATH-M 215. Sets, limits, derivatives, integrals, and applications.
- MATH-M 120 Brief Survey of Calculus 2 (3 cr.) P: C- or higher in MATH-M 119. Credit not given for both MATH-M 216 and MATH-M 120. A continuation of M119 covering topics in elementary differential equations, calculus of functions of several variables and infinite series. Intended for nonphysical science students.
- MATH-M 125 Pre-Calculus Mathematics (3 cr.) P: Câ€“ or higher in MATH-M 107 or equivalent, or ALEKS Assessment score greater than 50. Credit not given for both MATH-M 125 and MATH-M 115. Designed to prepare students for MATH-M 215. Algebraic operations; polynomial, exponential, and logarithmic, functions and their graphs; conic sections; systems of equations; and inequalities.
- MATH-M 126 Trigonometric Functions (2-3 cr.) P: Câ€“ or higher in MATH-M 125 or ALEKS Assessment score greater than 60. Credit not given for both MATH-M 126 and MATH-M 115. Satisfies Campuswide General Education Fundamental Literacies: Quantitative Reasoning. Designed to develop the properties of the trigonometric, exponential, and logarithmic functions and to prepare for course in calculus.
- MATH-M 208 Technical Calculus I (3 cr.) P: C- or higher in MATH-M 115 or C- or higher in MATH-M 125 and MATH-M 126. An introduction to differential and integral calculus for today's technology students. It covers analytic geometry, limits, derivatives, applications of the derivatives, the integrals, and transcendental functions and technical applications. The approach is semi-rigorous with emphasis on the applications of calculus to technology.
- MATH-M 209 Technical Calculus II (3 cr.) P: C- or higher in MATH-M 208 or C- or higher in MATH-M 215. This is the second semester of differential and integral calculus for today's technology students. It covers application of the integral, limited techniques, integration techniques, infinite series, differential equations, and the Laplace transform. The approach is semi-rigorous with emphasis on the applications of calculus to technology.
- MATH-M 215 Calculus I (5 cr.) P: Câ€“ or higher in MATH-M 115, or Câ€“ or higher in both MATH-M 125 and MATH-M 126 or ALEKS Assessment score greater than 75. Credit given for only one of the following: MATH-M 119, MATH-M 208, MATH-M 215. Limits, continuity, derivatives, definite and indefinite integrals, applications, techniques of integration, infinite series.
- MATH-M 216 Calculus II (5 cr.) P: Câ€“ or higher in MATH-M 211, or Câ€“ or higher in MATH-M 215. Credit given for only one of the following: MATH-M 209, MATH-M 120, MATH-M 216. Limits, continuity, derivatives, definite and indefinite integrals, applications, techniques of integration, infinite series.
- MATH-M 260 Combinatorial Counting and Probability (3 cr.) P: One of the following; MATH-M 208, MATH-M 215, or MATH-M 211. Credit not given for both MATH-M 260 and MATH-M 365. Permutations, combinations, counting principles, tree diagrams, binomial theorem, statistical experiments, conditional probability, independent events, random variables, probability density, cumulative distribution, expected values, standard deviations, binomial, Poisson, normal distribution, and the central limit theorem.
- MATH-M 261 Statistical Inferences (2 cr.) P: MATH-M 260. Credit not given for both MATH-M 261 and MATH-M 366. Estimates for population parameters, estimation judged by unbiasedness and mean square error, t-distribution, chi-square distribution, philosophy of hypothesis testing, probabilities in making conclusions after testing, estimation and hypothesis testing, linear and nonlinear least square regression equation for prediction and forecast.
- MATH-M 301 Linear Algebra and Applications (3-4 cr.) P: MATH-M 208, MATH-M 211, MATH-M 215, or consent of instructor. Solving systems of linear equations, matrix algebra, determinants, vector spaces, eigenvalues and eigenvectors. Selection of advanced topics. Applications throughout. Computer used for theory and applications.
- MATH-M 311 Calculus 3 (3-5 cr.) P: MATH-M 212, MATH-M 216, or consent of instructor. C: MATH-M 301. Elementary geometry of 2, 3, and n-space, functions of several variables, partial differentiation, minimum and maximum problems, multiple integration.
- MATH-M 325 Problem Seminar in Actuarial Science (1-6 cr.) P: MATH-M 463 for Exam P preparation (even years) and MATH-M 451 for Exam FM preparation (odd years); or consent of instructor. A problem-solving seminar to prepare students for the actuarial examinations. May be repeated up to three times for up to six credits.
- MATH-M 343 Introduction to Differential Equations with Applications I (3 cr.) P: MATH-M 212 or MATH-M 216. Ordinary differential equations and methods for their solution, including series methods and the Laplace transform. Applications of differential equations. Systems, stability, and numerical methods. Partial differential equations of mathematical physics, Fourier series.
- MATH-M 344 Introduction to Differential Equations with Applications II (3 cr.) P: MATH-M 311 and MATH-M 343. Ordinary differential equations and methods for their solution, including series methods and the Laplace transform. Applications of differential equations. Systems, stability, and numerical methods. Partial differential equations of mathematical physics, Fourier series.
- MATH-M 347 Discrete Mathematics (3 cr.) P: MATH-M 212 or MATH-M 216. Injective and surjective functions; inverse functions; composition; reflexive, symmetric, and transitive relations; equivalence relations; sets including complements, products, and power sets; cardinality; introductory logic including truth tables and quantification; elementary techniques of proof including induction and recursion; counting techniques; graphs and trees; discrete probability.
- MATH-M 365 Introduction to Probability and Statistics (3-4 cr.) P: MATH-M 209 or MATH-M 212, or MATH-M 216. Credit not given for MATH-M 365 and MATH-M 463/MATH-M 466. Elementary concepts of probability and statistics. Combinatorics, conditional probability, independence, random variables, discrete and continuous distributions, moments. Statistical inference, point estimation, confidence intervals, test of hypotheses. Applications to social and natural sciences.
- MATH-M 380 History of Mathematics (3 cr.) P: MATH-M 208, MATH-M 211, or MATH-M 215. Brief study of the development of algebra and trigonometry; practical, demonstrative, and analytic geometry; calculus, famous problems, calculating devices; famous mathematicians and chronological outlines in comparison with outlines in the sciences, history, philosophy, and astronomy.
- MATH-M 391 Introduction to Mathematical Reasoning (3 cr.) P: MATH-M216 required; MATH-M301 strongly recommended. Elementary logic, techniques of proof, basic set theory, functions, relations, binary operations, number systems, counting. Bridges the gap between elementary and advanced courses. Not open to students who have received credit for MATH-M 403, MATH-M 413, or MATH-M 420.
- MATH-M 403 Introduction to Modern Algebra I (3 cr.) P: MATH-M 301 and MATH-M 347 or MATH-M 391. Study of groups, rings, field extensions, with applications to linear transformations.
- MATH-M 404 Introduction to Modern Algebra 2 (3 cr.) P: MATH-M 403 or consent of instructor. Study of groups, rings, field extensions, with applications to linear transformations.
- MATH-M 405 Number Theory (3 cr.) P: MATH-M 212 or MATH-M 216. Numbers and their representation, divisibility and factorization, primes and their distribution, number theoretic functions, congruence, primitive roots, Diophantine equations, quadratic residues, sums of squares.
- MATH-M 409 Linear Transformations (3 cr.) P: MATH-M 301. The study of linear transformations of a finite dimensional vector space over the complex field. Canonical forms similarity theory; inner products and diagonalization of normal transformations.
- MATH-M 413 Introduction to Analysis 1 (3 cr.) P: MATH-M 391 or three courses at or above the 300-level. It is strongly recommended that students who have had little experience writing proofs take MATH-M 391 before taking MATH-M 413. Modern theory of real number system, limits, functions, sequences and series, Riemann-Stieltjes integral, and special topics.
- MATH-M 414 Introduction to Analysis 2 (3 cr.) P: MATH-M 413. Continuation of Math-M 413. Functions of several variables, Taylor series, extreme values. Manifolds in Euclidean space, Implicit function Theorem, Inverse Function Theorem. Divergence Theorem and other classical theorems of vector calculus. Special topics.
- MATH-M 415 Elementary Complex Variables (3 cr.) P: MATH-M 311. Algebra and geometry of complex numbers, elementary function of a complex variable, power series, integration, calculus of residues, conformal mappings. Applications to physics.
- MATH-M 420 Metric Space Topology (3 cr.) P: MATH-M 347 or MATH-M 391. 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.
- MATH-M 427 Combinatorics (3 cr.) P: MATH-M 391. An introduction to combinatorics, the study of discrete mathematical structures. Topics include enumerative methods, generating functions, famous number families, elementary graph theory, and strategies for combinatorial problem solving.
- MATH-M 435 Introduction to Differential Geometry (3 cr.) P: MATH-M 301 and MATH-M 311. An introduction to the geometry or curves and surfaces. Topics will include arc length torsion, Frenet formulae, metrics, curvatures, and classical theorems in these areas.
- MATH-M 436 Introduction to Geometries (3 cr.) P: MATH-M 347 or MATH-M 391. R: MATH-M 403. 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.
- MATH-M 446 Financial Mathematics (3 cr.) P: MATH-M 451 with a grade of C- or better or instructor's consent. This course is a continuation of Math-M451, the Mathematics of Finance,and prepares students for the second professional actuarial examination, Exam2/Financial Mathematics(FM). Topics include the rate of return of an investment, term structure of interest rates, cash flow duration, cash flow convexity and immunization. This course will also offer an introduction to derivative securities such as forwards, options and futures. Basic insurance strategies will also be covered.
- MATH-M 447 Mathematical Models and Applications 1 (3 cr.) P: MATH-M 301. 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.
- MATH-M 448 Mathematical Models and Applications II (3 cr.) P: MATH-M 447. 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.
- MATH-M 451 The Mathematics of Finance (3 cr.) P: Two courses from the following MATH-M 301, MATH-M 311, MATH-M 343, MATH-M 365, MATH-M 447, MATH-M 463. Course covers probability theory, Brownian motion, Ito's Lemma, stochastic differential equations, and dynamitic hedging. These topics are applied to the Black-Scholes formula, the pricing of financial derivatives, and the term theory of interest rates. I (even years)
- MATH-M 463 Introduction to Probability Theory I (3-4 cr.) C: MATH-M 311. The meaning of probability. Random experiments, conditional probability, independence. Random variables, expected values and standard deviations, moment generating functions, Important discrete and continuous distributions. Poisson processes. Multivariate distributions, basic limit laws such as the central limit theorem.
- MATH-M 466 Introduction to Mathematical Statistics (3 cr.) P: MATH-M 463. Rigorous mathematical treatment of problems in sampling and statistical inference. Sufficient statistics, exponential distributions, monotone likelihood ratio, most powerful tests, minimum variance estimates, shortest confidence intervals, linear models and analysis of variance, nonparametric methods.
- MATH-M 467 Advanced Statistical Techniques I (3 cr.) P: MATH-M 466 or consent of instructor. Statistical techniques of wide application, developed from the least-squares approach: fitting of lines and curves to data, multiple regression, analysis of variance of one-way and two-way layouts under various models, multiple comparison.
- MATH-M 468 Advanced Statistical Techniques II (3 cr.) P: MATH-M 466 or consent of instructor. Analysis of discrete data, chi-square tests of goodness of fit and contingency tables, Behrens-Fisher problem, comparison of variances, nonparametric methods, and some of the following topics: introduction to multivariate analysis, discriminant analysis, principal components.
- MATH-M 471 Numerical Analysis 1 (3 cr.) P: MATH-M 301, MATH-M 311, CSCI-C 101, or consent of instructor. Knowledge of a programming language such as C, C++, or Fortran is a prerequisite of this course. C: MATH-M 343. Interpolation and approximation of functions, numerical integration and differentiation, solution of nonlinear equations, acceleration and extrapolation, solution of systems of linear equations, eigenvalue problems, initial and boundary value problems for ordinary differential equations, and computer programs applying these numerical methods.
- MATH-M 472 Numerical Analysis 2 (3 cr.) P: MATH-M 471 and MATH-M 343. Interpolation and approximation of functions, numerical integration and differentiation, solution of nonlinear equations, acceleration and extrapolation, solution of systems of linear equations, eigenvalue problems, initial and boundary value problems for ordinary differential equations, and computer programs applying these numerical methods.
- MATH-M 491 Putnam Examination Seminar (1 cr.) P: MATH-M 211 or MATH-M 215, or consent of instructor or department chair. The Putnam Examination is a national mathematics competition for college undergraduates at all levels of mathematics study. It is held in December each year. This problem seminar is designed to help student prepare for the examination.
- MATH-M 546 Control Theory (3 cr.) P: MATH-M 301, MATH-M 343. Examples of control problems; optimal control of deterministic systems; linear and nonlinear. The maximal principle; Stochastic control problems.
- MATH-M 551 Markets and Asset Pricing (3 cr.) P: Two courses from the following: MATH-M 301, MATH-M 311, MATH-M 343, MATH-M 365, MATH-M 447. The concept of arbitrage and risk-neutral pricing are introduced within the context of dynamical models of stock prices, bond prices and currency exchange rates. Specific models include multi-period binomial models, Markov processes, Brownian motion and martingales.
- MATH-M 560 Applied Stochastic Processes (3 cr.) P: MATH-M 301, MATH-M 463 or MATH-M 365, or consent of instructor. Simple random walk as approximation of Brownian motion. Discrete-time Markov chains. Poisson, compound Poisson, and birth-and-death chains; Kolmogorov's backward and forward equations; steady state. Diffusions as limits of birth-and-death processes. Examples drawn from diverse fields of application.
- MATH-M 562 Statistical Design of Experiments (3 cr.) P: MATH-M 365, MATH-M 466, or consent of instructor. Latin square, incomplete blocks, and nested designs. Design and analysis of factorial experiments with crossing and nesting of factors, under fixed, random, and mixed effects models, in the balanced case. Blocking and fractionation of experiments with many factors at two levels. Exploration of response surfaces.
- MATH-M 565 Analysis of Variance (3 cr.) P: MATH-M 466 and some matrix algebra. General linear hypothesis. Least squares estimation. Confidence regions. Multiple comparisons. Analysis of complete layouts. Effects of departures from underlying assumptions. Analysis of covariance.
- MATH-M 571 Analysis of Numerical Methods I (3 cr.) P: CSCI-C 101, MATH-M 301, MATH-M 311, or consent of instructor. C: MATH-M 343. Solution of systems of linear equations, elimination and iterative methods, error analyses, eigenvalue problems; numerical methods for integral equations and ordinary differential equations; finite difference, finite element, and Galerkin methods for partial differential equations; stability of methods.
- MATH-M 572 Analysis of Numerical Methods II (3 cr.) P: MATH-M 343, MATH-M 571. Solution of systems of linear equations, elimination and iterative methods, error analyses, eigenvalue problems; numerical methods for integral equations and ordinary differential equations; finite difference, finite element, and Galerkin methods for partial differential equations; stability of methods.
- MATH-M 574 Applied Regression Analysis (3 cr.) P: MATH-M 466 or MATH-M 365 or MATH-M 261. Least square estimates of parameters; single linear regression; multiple linear regression; hypothesis testing and confidence intervals in linear regression models; testing of models, data analysis and appropriateness of models; optional topics about nonlinear regression, i.e. logistic regression, Poisson regression, and generalized linear regression models.
- MATH-M 575 Simulation Modeling (3 cr.) P: MATH-M 209 or MATH-M 216; MATH-M 365, MATH-M 463, or CSCI-C 455; CSCI-C 101. The statistics needed to analyze simulated data; examples such as multiple server queuing methods, inventory control, and exercising stock options; variance reduction variables and their relation to regression analysis. Monte Carlo method, Markov chain, and the alias method for generating discrete random variables.
- MATH-M 576 Forecasting (3 cr.) P: MATH-M 301, MATH-M 365, or MATH-M 466. Forecasting systems, regression models, stochastic forecasting, time series, smoothing approach to prediction, model selection, seasonal adjustment, Markov chains, Markov decision processes, and decision analysis.
- MATH-M 577 Operations Research: Modeling Approach (3 cr.) P: MATH-M 209, MATH-M 212, MATH-M 216, or MATH-M 301. Credit not given for both MATH-M 577 and MATH-M 447. Mathematical methods of operations research used in the biological, social, management sciences. Topics include modeling, linear programming, the simplex method, duality theory, sensitivity analysis, and network analysis.
- MATH-N 390 The Natural World (3 cr.) P: MATH-M 215. Explores an important scientific or technological issue in modern society. Applies scientific methods and interdisciplinary perspectives in an examination of the subject. Investigates the broader implications and ethical dimensions of scientific research and technological advancement.
- MATH-T 101 Mathematics for Elementary Teachers 1 (3 cr.) P: C or higher in MATH-A 100 or equivalent, or ALEKS Assessment score greater than 35. Elements of set theory, counting numbers. Operations on counting numbers, integers, rational numbers, and real numbers. Only open to elementary education majors.
- MATH-T 102 Mathematics for Elementary Teachers II (3 cr.) P: C or higher in MATH-T 101. Prime numbers and elementary number theory. Elementary combinatorics, probability, and statistics.
- MATH-T 103 Mathematics for Elementary Teachers III (3 cr.) P: C or higher in MATH-T 101. Descriptions and properties of basic geometric figures. Rigid motions. Axiomatics. Measurement, analytic geometry, and graphs of functions. Discussion of modern mathematics.
- MATH-T 201 Problem Solving (3 cr.) P: Either C or higher in MATH-T 102 and MATH-T 103; or MATH-M 118 and MATH-M 125; or consent of instructor. Provides experiences in mathematical problem solving for future teachers of mathematics, and for others interested in mathematical thinking. Exploration and development of the general processes of mathematical thinking, including monitoring and reflection, conjecturing, justifying and convincing.
- MATH-T 336 Topics in Euclidean Geometry (3 cr.) P: MATH-M 301. A study of the central aspects of two-dimensional Euclidean geometry from historical and axiomatic points of view as well as through hands-on and/or computer-based exploration of geometric concepts and constructions.
- MATH-T 436 Secondary Mathematics for Teachers (3 cr.) P: MATH-M 216 and one 300-level mathematics course. Emphasizes developing a deeper understanding of secondary mathematics by examining its fundamental ideas from an advanced perspective. Topics selected from real and complex number systems, functions, equations, integers, polynomials, congruence, distance and similarity, area and volume, and trigonometry.
- 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 include probability, statistics, geometry, and algebra. Open only to graduate elementary teachers with permission of the instructor.
- MATH-W 109 Mathematical Typesetting (1-2 cr.) This course introduces the creation of mathematical and scientific documents in the universal typesetting software LATEX.