### Courses

#### Natural Sciences

##### Mathematics (MATH)

- MATH-A 118 Finite Mathematics for the Social and Biological Sciences (3 cr.) P: Placement by exam or MATH-M 101. Quantitative reasoning, probability, elementary combinations, reading and interpreting graphs and tables, measuring central tendency and variation, scatter plots, correlation, and regression. Intended to meet the finite math requirement for students who will be taking MATH-K 300. Course uses applied examples from psychology, sociology, biology, and political science. Credit given for only one of MATH-A 118 or MATH-M 118.

- MATH-K 300 Statistical Techniques for Health Professionals (3 cr.) P: Placement by exam or MATH-M 101. Recommended: MATH-M 118 or MATH-A 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 decision; estimation and hypothesis testing. Special topics may include regression and correlation, analysis of variance, and nonparametric methods. Credit not given for both ECON-E 280–E 281 and MATH-K 300.

- MATH-M 101 Topics in Algebra 4 (2 cr.) Topic: Linear Models and Graphs. Linear equations, inequalities, functions, graphs, systems, problem solving. Prepares students for MATH-M 102; MATH-M 110; MATH-M 112; MATH-M 114; MATH-A 118; MATH-M 118; MATH-T 101. Credit by examination not given.

- MATH-M 102 Topics in Algebra 5 (2 cr.) P: Placement by exam or MATH-M 101 with a C or better. Topic: Non-Linear Models and Graphs. Polynomials, factoring, rational expressions, radicals, quadratic equations and functions, problem solving. Prepares students for MATH-M 122; MATH-M 125; and MATH-M 126.

- MATH-M 110 Excursions into Mathematics (3 cr.) P: Placement by exam or MATH-M 101 with a C or better. Topics may include: Problem Solving, Logic, Set Theory, Numerations Systems (Historic and Other Bases Systems), Mathematics of Finance, Management Science, Apportionment and Voting Theory. This course does not count toward a major in mathematics.

- MATH-M 114 Quantitative Literacy II (3 cr.) P: Placement by exam or MATH-M 101 with a C or better. Introduction to statistics. Quantitative reasoning, probability, reading and interpreting graphs and tables, exploring shapes of distributions, measures or central tendency and variation.

- MATH-M 118 Finite Mathematics (3 cr.) P: Placement by exam or MATH-M 101 with a C or better. Set theory, logic, permutations, combinations, simple probability, conditional probability, Markov chains.

- MATH-M 119 Brief Survey of Calculus I (3 cr.) P: Placement by exam or MATH-M 122 with a C or better. Sets, limits, derivatives, integrals, and applications.

- MATH-M 120 Brief Survey of Calculus II (3 cr.) P: MATH-M 119 with a C or better. A continuation of MATH-M 119 covering topics in elementary differential equations, calculus of functions of several variables, and infinite series. Intended for nonphysical science students. Credit not given for both MATH-M 120 and MATH-M 216. For additional restrictions, refer to MATH-M 215-MATH-M 216.

- MATH-M 122 College Algebra (3 cr.) P: Placement by exam or MATH-M 102 with a C or better. Designed to prepare students for MATH-M 119 (Calculus). Includes solving and graphing linear, nonlinear, polynomial, radical, rational, exponential and logarithmic functions. Real life modeling and applications from business and economics. Credit not given for both MATH-M 122 and MATH-M 125.

- MATH-M 125 Precalculus Mathematics (3 cr.) P: Placement by exam or MATH-M 102 with a C or better. Designed to prepare students for MATH-M 215 (Calculus). Algebraic operations, polynomials, functions and their graphs, conic sections, exponential and logarithmic functions. Graphing calculators are not permitted in this course. Credit not given for both MATH-M 122 and MATH-M 125.

- MATH-M 126 Trigonometric Functions (3 cr.) C: MATH-M 125 or equivalent. Designed to develop the properties of the trigonometric functions and equation solving to prepare for courses in calculus (MATH-M 215; MATH-M 216).

- MATH-M 129 Business Algebra and Application (3 cr.) P: One of the following: MATH-M 101, M 102, M 117, M 118, M 122, M 125, M 126, or ALEKS score of 35 or higher. Designed to prepare students for mathematical problems they will encounter in business. Includes solving and graphing linear, nonlinear, quadratic, exponential and logarithmic functions. Real life modeling and applications from business and economics.

- MATH-M 215 Calculus I (5 cr.) Completion of MATH-M 125 and MATH-M 126 (or placement) are recommended prior to enrollment. Limits, continuity, derivatives, definite and indefinite integrals, applications, techniques of integration, infinite series.

- MATH-M 216 Calculus II (5 cr.) P: MATH-M 215 with a C or better. Limits, continuity, derivatives, definite and indefinite integrals, applications, techniques of integration, infinite series.

- MATH-M 295 Readings and Research (1-3 cr.) P: Instructor permission required. Supervised problem solving. Admission only with permission of a member of the mathematics faculty who will act as supervisor.

- MATH-M 303 Linear Algebra for Undergraduates (3 cr.) P: MATH-M 216 with a C or better. Introduction to the theory of real vector spaces. Coordinate systems, linear dependence, bases. Linear transformations and matrix calculus. Determinants and rank. Eigenvalues and eigenvectors.

- MATH-M 311 Calculus III (3 cr.) P: MATH-M 216 with a C or better. Elementary geometry of 2, 3, and n-space, functions of several variables, partial differentiation, minimum and maximum problems, and multiple integration.

- MATH-M 312 Calculus IV (3 cr.) P: MATH-M 311 with C or better. Intended for students majoring in the physical sciences and applied mathematics. Vector integral calculus (line integrals, Green's theorem, surface integrals, Stokes' theorem and applications). Topics in series expansions, including Fourier series and some applications. Introduction to functions of a complex variable (Cauchy-Riemann equations, Cauchy integral theorem, Laurent expansions and applications).

- MATH-M 313 Elementary Differential Equations with Applications (3 cr.) P: MATH-M 216 with a C or better. Ordinary differential equations of first order and linear equations of higher order with applications, series solutions, operational methods, Laplace transforms, and numerical techniques.

- MATH-M 320 Theory of Interest (3 cr.) 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.

- MATH-M 363 Sample Survey Techniques (3 cr.) P: Two years of high school mathematics including algebra, MATH-K 300 or equivalent, or consent of instructor. Techniques; simple random, stratified, systematic, cluster, proportions, ratios, percentages; sample size, and sources of error in surveys.

- MATH-M 366 Elements of Statistical Inference (3 cr.) P: MATH-M 360 with a C or better. Introduction to statistical theory. Basic sampling distributions. Order statistics. Point estimation, maximum likelihood estimation, the Cramer-Rao bound, least squares method, confidence intervals, hypothesis-testing concepts, Neyman-Pearson lemma, likelihood ratio tests, linear models, large sample theory, contingency tables, goodness-of-fit tests.

- MATH-M 371 Elementary Computational Methods (3 cr.) 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.

- MATH-M 380 History of Mathematics (3 cr.) P: MATH-M 216 with a C or better. 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-M 216 with a C or better. Elementary logic, techniques of proof, basic set theory, functions, relations, binary operations, number systems, counting. Bridges the gap between elementary and advanced courses.

- MATH-M 403 Introduction to Modern Algebra I (3 cr.) P: MATH-M 303 and MATH-M 391 with a C or better or consent of instructor. Study of groups, rings, field extensions, with applications to linear transformations.

- MATH-M 404 Introduction to Modern Algebra II (3 cr.) P: MATH-M 403 with a C or better. Study of groups, rings, fields (usually including Galois theory), with applications to linear transformations.

- MATH-M 405 Number Theory (3 cr.) P: MATH-M 216 with a C or better. 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.

- MATH-M 406 Topics in Mathematics (3 cr.) P: Instructor permission required. Selected topics in various areas of mathematics not covered by the standard courses. May be repeated for credit.

- MATH-M 413 Introduction to Analysis I (3 cr.) P: MATH-M 311 and MATH-M 391 with a C or better. Modern theory of real number system, limits, functions, sequences and series, Riemann-Stieljes integral, and special topics.

- MATH-M 414 Introduction to Analysis II (3 cr.) P: MATH-M 413 with a C or better. Modern theory of real number system, limits, functions, sequences and series, Riemann-Stieljes integral, and special topics.

- MATH-M 421 Introduction to Topology I (3 cr.) P: MATH-M 303 and MATH-M 311 with a C or better. Introduction to point set topology with emphasis on metric spaces. Continuity, Cortesian products, connectedness, compactness, completeness. Elements of homotopy theory, fundamental group and covering spaces, elementary homology theory, applications to simplicial complexes and manifolds.

- MATH-M 425 Graph (Network) Theory and Combinatorial Theory (3 cr.) P: MATH-M 216 with a C or better. 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.

- MATH-M 436 Introduction to Geometries (3 cr.) P: MATH-M 391 with a C or better or consent of instructor. Non-Euclidean geometry, axiom system. 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-M 466 Introduction to Mathematical Statistics (3 cr.) 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 447 Mathematical Models and Applications I (3 cr.) P: MATH-M 303, MATH-M 311, and MATH-M 360 or consent of instructor. C: MATH-M 303, MATH-M and MATH-M 360. 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-M 471 Numerical Analysis I (3 cr.) P: MATH-M 303 and MATH-M 313, or consent of instructor. 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 490 Problem Seminar (3 cr.) P: MATH-M 303, MATH-M 403, or MATH-M 413 and consent of instructor. C: MATH-M 403 or MATH-M 413 Introduction to research techniques for advanced undergraduates, based on problems from parts of the regular curriculum, such as linear algebra, topology, probability, and analysis. Emphasis will be on problems of both current and historical interest but usually not in the standard literature.

- MATH-M 493 Senior Thesis in Mathematics (1 cr.) P: MATH-M 403 or MATH-M 413 and permission of instructor. The student must write and present a paper (senior thesis) on a topic agreed upon by the student and the department chairperson or advisor delegated by the chairperson.

- MATH-T 101 Mathematics for Elementary Teachers I (3 cr.) P: Placement by exam. Elements of set theory, counting numbers. Operations on counting numbers, integers, rational numbers, and real numbers. Only open to elementary education majors.s.

- MATH-T 102 Mathematics for Elementary Teachers II (3 cr.) P: MATH-T 101 with a C or better. Prime numbers and elementary number theory. Elementary combinatorics, probability, and statistics.

- MATH-T 103 Mathematics for Elementary Teachers III (3 cr.) P: MATH-T 101 with a C or better. Descriptions and properties of basic geometric figures. Rigid motions. Axiomatics. Measurement, analytic geometry, and graphs of functions. Discussion of modern mathematics.

- MATH-T 610 Topics in Analysis (3 cr.) This course will cover graduate-level knowledge in Analysis applications, including Real Analysis, Complex Analysis, Fourier Analysis, and other topics in Analysis.