INDIANA UNIVERSITY SOUTH BEND 2003 - 2005 BULLETIN

IUSB Course Descriptions

P = Prerequisite, R = Recommended, C = Concomitant
I = Fall Semester, II = Spring Semester, S = Summer Session(s)

MATH: Mathematics

MATH K300 Statistical Techniques for Health Professions (3 cr.) P: MATH M014 or level III on mathematics placement examination. R: MATH M125. 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 concepts to real situations in client care. I

MATH K310 Statistical Techniques (3 cr.) P: MATH M115, MATH M125, or level V on mathematics placement examination. An introduction to probability and statistics. Elementary probability theory, conditional probability, independence, random variables, discrete probability distributions, binomial, Poisson and hypergeometric distributions, continuous probability distributions, normal and t-distributions, measures of central tendency and dispersion, central limit theorem. Concepts of statistical inference, estimation, hypothesis testing, regression, tolerancint, quality control. Special topics discussed may include time series, analysis of variance, nonparametric methods, statistical decision theory, Bayesian inference. Credit given for only one of MATH K300 or MATH K310. II

MATH M004 Introduction to algebra (3 cr.) P: Level I on the mathematics placement examination. Designed for remediation of advanced arithmetic and beginning algebra skills. Arithmetic of fractions and signed numbers. Beginning equations in one variable. S/F grading. Credit may not be used toward a degree. I, II, S

MATH M014 Basic Algebra (4 cr.) P: MATH M004 or level II on the mathematics placement examination. Designed to provide algebraic skills needed for future mathematics courses. Algebraic fractions, exponents, linear equations, quadratic equations, inequalities, factoring, elementary graphs. S/F grading. Credit may not be used toward a degree. I, II, S

MATH M107 College Algebra (3 cr.) P: M014 or level III on mathematics placement examination. 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. Does not satisfy liberal arts and sciences general education requirement. I, II, S

MATH M108 Quantitative Reasoning (3 cr.) P: MATH M014 or Level III on the Mathematics placement examination. Number sense, operations, mathematical relationships, functions, data interpretation, geometry, measurement, reasoning. Emphasis on building conceptual understanding and developing problem solving skills. Does not satisfy liberal arts and sciences general education requirements.

MATH M110 Excursions in Mathematics (3 cr.) P: MATH M014 or level III on mathematics placement examination. A course designed to convey the flavor and spirit of mathematical languages of quantity. Probability and statistics, including the use of MINITAB; topics from management science; special topics discussed may include the use of mathematics in coding and in social choice and decision making. I, II, S

MATH M115 Pre-Calculus and Trigonometry (5 cr.) P: MATH M107, or level IV on mathematics placement examination. Designed to prepare students for higher numbered mathematics and computer science courses, including calculus MATH M215. Graphing equations in two variables; functions and their graphs; linear, quadratic, polynomial, and rational functions; exponential and logarithmic functions; trigonometric and inverse trigonometric functions. Equivalent to MATH M125-MATH M126. Credit not given for both MATH M115 and MATH M125-MATH M126. Does not satisfy liberal arts and sciences general education requirement. I, II, S

MATH M118 Finite Mathematics (3 cr.) P: MATH M014 or level III on mathematics placement examination. Set theory, linear systems, matrices, probability, linear programming. Applications to problems from business and the social sciences. I, II, S

MATH M119 Brief Survey of Calculus I (3 cr.) P: MATH M115, MATH M125 or level V on mathematics placement examination. Introduction to calculus. Primarily for students from business and the social sciences. Credit not given for both MATH M119 and MATH M215. I, II, S

MATH M120 Brief Survey of Calculus II (3 cr.) P: MATH M119. A continuation of MATH M119 covering topics in elementary differential equations, calculus of functions of several variables, trigonometric functions, techniques of integration. Credit not given for both MATH M216 and MATH M120. I, II

MATH M125 Pre-Calculus Mathematics (3 cr.) P: MATH M107 or level IV on mathematics placement examination. Designed to prepare students for higher-level mathematics and computer science courses including calculus MATH M119. Graphing equations in two variables; functions and their graphs; linear, quadratic, polynomial, and rational functions; exponential and logarithmic functions. Does not satisfy the liberal arts and sciences general education requirements. Credit not given for both MATH M125 and MATH M115. I, II, S

MATH M126 Trigonometric Functions (2 cr.) P: MATH M125 or level V on mathematics placement examination. Designed to develop the properties of the trigonometric and inverse trigonometric functions and to prepare for courses in calculus MATH M215. Credit not given for both MATH M126 and MATH M115. Does not satisfy liberal arts and sciences general education requirement. I, II, S

MATH M208 Technical Calculus I (3 cr.) P: MATH M115 or MATH M125 and MATH M126. 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 M209 Technical Calculus II (3 cr.) P: MATH M208 or MATH M215. This is the second semester of differential and integral calculus for today’s technology students. It covers application of the integral, limit 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 M215 Analytic Geometry and Calculus I (5 cr.) P: MATH M115, MATH M125-MATH M126 or level VI on mathematics placement examination. Functions, limits, continuity, derivative, definite integral, applications, exponential and logarithmic functions. A student cannot receive credit for both MATH M119 and MATH M215. I, II, S

MATH M216 Analytic Geometry and Calculus II (5 cr.) P: MATH M211 or MATH M215. Definite integral, applications, L'Hapital's Role, techniques of integration, limits of sequence, infinite series, polar coordinates. Credit not given for both MATH M120 and MATH M216. I, II, S

MATH M260 Combinatorial Counting and Probability (2 cr.) P: One of the following; MATH M208, MATH M215 or MATH M211. 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. Credit not given for both MATH M260 and MATH M365.

MATH M261 Statistical Inferences (2 cr.) P: MATH M260. 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. (Credit not given for both M261 and M366).

MATH M301 Linear Algebra AND APPLICATIONS (3-4 cr.) P: MATH M211 or MATH M215. Systems of linear equations, the vector space Rn, abstract vector spaces, linear dependence, bases, linear transformations, matrices, eigenvalues and eigenvectors, applications. I, II

MATH M311 Calculus III (5 cr.) P: MATH M212 or MATH M216. R: MATH M301. Solid analytic geometry, functions of several variables, partial differentiation, multiple integration, vector fields, line and surface integrals, Stokes' and Green's theorems. I

MATH M325 topics course: problem-solving seminar in actuarial science (1-3 cr.) P: Consent of instructor. A problem-solving seminar to prepare students for the actuarial examinations. May be repeated up to three times for credit.

MATH M343 Introduction to Differential Equations with Applications I (3 cr.) P: MATH M212 or MATH M216. 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. I

MATH M344 Introduction to Differential Equations with Applications II (3 cr.) P: MATH M311 and MATH M343. 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. II (odd years)

MATH M347 discrete mathematics (3 cr.) P: MATH M212 or MATH M216. 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 M360 Elements of Probability (3 cr.) P: MATH M212 or MATH M216. Introduction to mathematical theory of probability. Probability models, combinatoric problems, conditional probability and independence, random variables, distributions, densities, expectation, moments. Chebyshev inequality, generating functions of random variables, binomial, hypergeometric, Poisson, uniform, gamma, normal, and related distributions, joint distributions, law of large numbers, normal approximation, characteristic of sample means and variances, t-distribution, F-distribution, applications. I (odd years)

MATH M365 Introduction to Probability and Statistics (3-4 cr.) P: MATH M212 or MATH M216. Elementary concepts of probability and statistics. Combinatorics, conditional probability, independence, random variables, moments, Chebyshev inequality, law of large numbers, discrete and continuous distributions. Statistical inference, point and interval estimation, tests of hypotheses. Applications to social, behavioral and natural sciences. Credit not given for MATH M365 and MATH M360-MATH M366. I (even years)

MATH M366 Elements of Statistical Inference (3 cr.) P: MATH M360. Estimation theory, sufficient statistics, confidence intervals; hypothesis testing, including power function, error types, Neyman-Pearson Lemma, likelihood ratio tests, and hypothesis tests for means and variances; nonparametric tests, including goodness-of-fit tests, sign test, signed-rank test; linear regression and correlation; multiple linear regression; analysis of variance. II (even years)

MATH M380 History of Mathematics (3 cr.) P: MATH M211 or MATH M215. The development of mathematics with emphasis on the modern period; role of proof and truth; discovery of non-Euclidian geometry; rigorization of calculus; the rise of algebra; the paradoxes of set theory; logicist, formalist, and intuitionist responses. I (odd years)

MATH M403 Introduction to Modern Algebra I (3 cr.) P: MATH M347 or three 300-level MATH courses. Study of groups, rings, and fields. It is strongly recommended that students who have had little experience writing proofs take MATH M347 before taking MATH M403. Study of groups, including subgroups, normal subgroups, factor groups, homomorphisms, isomorphisms, finite abelian groups, and beginning the study of rings, including subrings, ideals, and polynomial rings. In those years when MATH M405 is taught rather than MATH M404, some topics may be omitted and replaced by others from MATH M404 to provide a survey course in modern algebra. I (even years)

MATH M404 Introduction to Modern Algebra II (3 cr.) P: MATH M403 or three 300-level courses. It is strongly recommended that students who have had little experience writing proofs take MATH M347 and MATH M413 before taking MATH M404. Study of groups, rings, and fields. II (odd years)

MATH M405 Number Theory (3 cr.) P: MATH M212 or 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, coding theory, cryptography, or other selected applications.

MATH M409 Linear Transformations (3 cr.) P: MATH M301. The study of linear transformations on a finite dimensional vector space over the complex field. Canonical forms, similarity theory; inner products, dual spaces and diagonalization of normal transformations.

MATH M413 Introduction to Analysis I (3 cr.) P: MATH M347 or three courses at or above the 300 level. It is strongly recommended that students who have had little experience writing proofs take MATH M347 and MATH M413 before taking MATH M414. The real numbers, topology of Cartesian spaces, continuity, derivatives, sequences and series of functions, the Riemann-Stieltjes integral. I (odd years)

MATH M414 Introduction to Analysis II (3 cr.) P: MATH M413. The real numbers, topology of Cartesian spaces, continuity, derivatives, sequences and series of functions, the Riemann-Stieltjes integral. MATH M414-MATH M415 II (even years)

MATH M415 ELEMENTARY COMPLEX VARIABLES WITH APPLICATIONS (3 cr.) P: MATH M311. Algebra and geometry of complex numbers, elementary functions of a complex variable, power series, integration, calculus of residues, conformal mappings and applications. MATH M414-MATH M415 II (even years)

MATH M420 Metric Space Topology (3 cr.) P: MATH M347. 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 M435 Introduction to Differential Geometry (3 cr.) P: MATH M311 and MATH M301. 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.

MATH M436 Introduction to Geometries (3 cr.) P: MATH M347. R: MATH M403. Non-Euclidean geometry, axiom systems. Plane projective geometry, Desarguesian planes. Perspectives, coordinates in the real projective plane. The group of projective transformations and subgeometries corresponding to subgroups. Models for geometries. Circular transformations.

MATH M447 Mathematical Models and Applications I (3 cr.) P: MATH M301. 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. Suitable for secondary school teachers. I (even years)

MATH M448 Mathematical Models and Applications II (3 cr.) P: MATH M447. 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. Suitable for secondary school teachers.

MATH M451 the Mathematics of finance and interest theory (3 cr.) P: Two courses from the following MATH M301, MATH M311, MATH M343, MATH M360, MATH M365, MATH M447. Interest theory, introduction to theory of options pricing, Black-Scholes theory of options, general topics in finance as the time value of money, rate of return of an investment, cash-flow sequence, utility functions and expected utility maximization, mean variance analysis, optimal portfolio selection, and the capital assets pricing model, topics in measurement of interest. II (odd years)

MATH M471 Numerical Analysis I (3 cr.) P: MATH M301, MATH M311, CSCI C101, knowledge of a programming language such as C, C++, or Fortran, or consent of instructor. R: MATH M343. Numerical solutions of nonlinear equations; interpolation, including finite difference and splines; approximation, using various Hilbert spaces; numerical differentiation and integration; direct methods for linear systems; iterative techniques in matrix algebra. I (odd years)

MATH M472 Numerical Analysis II (3 cr.) P: MATH M471 and MATH 343. Numerical solutions of nonlinear systems; solution of ordinary differential equations: initial-value problems, boundary-value problems; computation of eigenvalues and eigenvectors; introduction of numerical solutions for partial differential equations.

MATH M491 PUTNAM EXAMINATION SEMINAR (1 cr.) P: MATH M211 or MATH M215. The Putnam Examination is a national mathematics competition for college undergraduates at all levels of study. It is held in December each year. This problem seminar is designed to help students prepare for the examination. May be repeated twice for credit.

MATH M5xx transform methods (3 cr.) Basic transform methods in problem solving; Laplace transforms, Fourier transforms, other integral transforms, inversion of transforms; introduction to wavelets and their applications. (Courses without complete numbers are currently under development.)

MATH M5xx sampling (3 cr.) Survey designs, simple random, stratified, and systematic samples, systems of sampling, methods of estimation, ratio and regression estimates, costs. Other topics as time permits. (Courses without complete numbers are currently under development.)

MATH M546 Control theory (3 cr.) Examples of control problems; control and observability of discrete and continuous systems; optimal control, the maximum principle; state-space and frequency domain approaches; stochastic control.

MATH M562 statistical design of experiments (3 cr.) Fundamentals, completely randomized design, randomized complete blocks. Latin squares, multi-classification, factorial, nested factorial, incomplete blocks, fractional replications, confounding, general mixed factorial, split-plot and optimum design. Use of existing statistical computing packages.

MATH M569 statistical decision theory (3 cr.) Foundation of statistical analysis, Bayesian and decision theoretic formulation of problems; construction of utility functions and quantifications of prior information; methods of Bayesian decision and inference, with applications; empirical Bayes; combination of evidence; game theory and minimax rules, Bayesian design and sequential analysis. Comparison of statistical paradigms.

MATH M571 analysis of numerical methods I (3 cr.) P: MATH M301, MATH M311, CSCI C201. 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 M572 analysis of numerical methods ii (3 cr.) P: MATH M471, MATH M343. 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 M575 simulation modeling (3 cr.) P: MATH M216; MATH M365, MATH M360 or CSCI C455; CSCI C101. 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 M576 forecasting (3 cr.) Forecasting systems, regression models, stochastic forecasting, time series, smoothing approach to prediction, model selection, seasonal adjustment.

MATH M577 OPERATIONS RESEARCH: modeling APPROACH (3 cr.) P: MATH M301, MATH M212 or MATH M216. 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. Credit not given for both MATH M577 and MATH M447.

MATH T101 Mathematics for Elementary Teachers I (3 cr.) P: MATH M014 or level III on mathematics placement examination. The foundations of arithmetic, including elements of set theory, numeration systems, operations, elementary number theory, integers and rational numbers. Emphasis is on explaining, illustrating, and communicating mathematical ideas. Does not satisfy liberal arts and sciences general education requirements. I, II, S

MATH T102 Mathematics for Elementary Teachers II (3 cr.) P: C or better in MATH T101. Real numbers, equations, and inequalities, functions and graphs, measurement concepts, problem solving elementary combinatorics, probability, and statistics. Emphasis is on applying problem-solving strategies in a variety of mathematical situations. Does not satisfy liberal arts and sciences general education requirement. I, II, S

MATH T103 Mathematics for Elementary Teachers III (3 cr.) P: C or better in MATH T101. Topics include analysis and measurement of two and three dimensional figures; congruent and similar triangles, compass and straight-edge constructions. Emphasis is on the transition from visual and informal reasoning to formal reasoning about geometric objects and relationships. Does not satisfy liberal arts and sciences general education requirements. I, II, S

MATH T201 problem solving (3 cr.) P: Either C or better in MATH T102 and MATH T103 or MATH M118 and MATH M125 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 T336 Topics in Euclidean Geometry (3 cr.) P: MATH M301. Rigorous treatment of high school geometry topics, some advanced theorems and constructions, impossible constructions; transformations, dissection theory, projective geometry; formalization and non-Euclidean geometry. I

MATH T436 Secondary Mathematics for Teachers: An Advanced Perspective (3 cr.) P: MATH M216 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 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 include probability, statistics, geometry and algebra. Open only to graduate elementary teachers.

MATH Y790 graduate independent study-thesis (1-3 cr.) Graduate independent study.

MICR: Microbiology

(See ANAT, BIOL, PHSL, PLSC, and ZOOL for additional biological sciences courses.)

MICR M250 Microbial Cell Biology (3 cr.) R: One college-level biology course; one college-level chemistry course. Introduction to microorganisms: cytology, nutrition, reproduction, and physiology. Importance of microorganisms in infectious disease. Host defense mechanisms against disease. Credit not allowed toward a biology major. I, II, S

MICR M255 Microbiology: Laboratory (2 cr.) P or concurrent: MICR M250. Exercises in the principles and techniques of microscopy, cultivation, identification and detection of microorganisms. Credit not allowed toward a biology major. I, II, S

MICR M310 Microbiology (3 cr.) P: BIOL L101, BIOL L102. R: CHEM C341, MICR M315 concurrently. Application of fundamental biological principles to the study of microorganisms. Significance of microorganisms to humans and their environment. II (even years)

MICR M315 Microbiology Laboratory (2 cr.) P or concurrent: MICR M310. Exercises and demonstrations in principles and techniques of cultivation and utilization of microorganisms. II (even years)

MICR M440 Medical Microbiology: Lecture (3 cr.) P: MICR M310. Microorganisms as agents of disease, host-parasite relationships, epidemiology, chemotherapy, immunology. II (odd years)

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Last updated: 07/10/2003