Mathematics and Statistics
CAS MA 113
Basic concepts of estimation and tests of hypotheses, ideas from probability; one-, two-, and multiple-sample problems. Applications in social sciences. Primarily for students in the social sciences who require a one-semester introduction to statistics; others should consider CAS MA 115 or MA 213. MA 113 may not be taken for credit by any student who has completed any MA course numbered 300 or higher. Students may receive credit for not more than one of the following courses: CAS MA 113, MA 115, or MA 213. Carries MCS divisional credit in CAS. 4 cr.
CAS MA 115
Numerical and graphical summaries of univariate and bivariate data. Basic probability, random variables, binomial distribution, normal distribution. One-sample statistical inference for normal means and binomial probabilities. Primarily for students in the social sciences with limited mathematics preparation. MA 115 may not be taken for credit by any student who has completed any MA course numbered 300 or higher. Students may receive credit for not more than one of the following courses: CAS MA 113, MA 115, or MA 213. Carries MCS divisional credit in CAS. 4 cr.
CAS MA 116
Prereq: (CAS MA 115) or equivalent. One- or two-sample inference for normal means and binomial probabilities, analysis of variance, simple linear regression, multiple regression, analysis of categorical data. Introduction to survey design and design of experiments. Primarily for students in the social sciences with limited mathematics preparation. MA 116 may not be taken for credit by any student who has completed any MA course numbered 300 or higher. Students may receive credit for not more than one of the following courses: CAS MA 116, MA 214, or MA 614. Carries MCS divisional credit in CAS. 4 cr.
College Algebra and Trigonometry
CAS MA 118
Functions and graphs. Linear and quadratic equations. Exponents; logarithms. Right and oblique triangles; trigonometric functions. Optimization. Specifically intended to prepare students with insufficient background in mathematics for the study of calculus. This course may not be used in fulfillment of the divisional studies requirement. Satisfies the mathematics requirement in the College program. MA 118 may not be taken for credit by any student who has completed any MA course numbered 121 or higher. 4 cr.
Applied Mathematics for Social and Management Sciences
CAS MA 120
Linear equations, systems of linear equations, matrix algebra, exponential functions and logarithms, elements of differential calculus, optimization, probability. Applications in economics, finance, and management. Satisfies both mathematics requirement and divisional studies requirement. MA 120 may not be taken for credit by any student who has completed any MA course numbered 124 or higher. Carries MCS divisional credit in CAS. 4 cr.
Calculus for the Life and Social Sciences I
CAS MA 121
Differentiation and integration of functions of one variable. Same topics as CAS MA 123, but with less emphasis on mathematical generality and more on application. Especially suitable for students concentrating in the biological and social sciences. Students may receive credit for either CAS MA 121 or 123, but not both. Carries MCS divisional credit in CAS. 4 cr.
Calculus for the Life and Social Sciences II
CAS MA 122
Prereq: (CAS MA 121 or CAS MA 123). Continuation of CAS MA 121. Review of univariate calculus, calculus of the elementary transcendental functions, elementary differential equations, elementary multivariate calculus. Applications to exponential growth, optimization, equilibrium, and dynamic modeling problems. Students may receive credit for not more than one of the following courses: CAS MA 122, MA 124, MA 127, or MA 129. Carries MCS divisional credit in CAS. 4 cr.
CAS MA 123
Limits; derivatives; differentiation of algebraic functions. Applications to maxima, minima, and convexity of functions. The definite integral; the fundamental theorem of integral calculus; applications of integration. Students may receive credit for either CAS MA 121 or 123, but not both. Carries MCS divisional credit in CAS. 4 cr.
CAS MA 124
Prereq: (CAS MA 121 or CAS MA 123). Logarithmic, exponential, and trigonometric functions. Sequences and series; Taylor's series with the remainder. Methods of integration. Calculus I and II together constitute an introduction to calculus of a function of a single real variable. Students may receive credit for not more than one of the following courses: CAS MA 122, MA 124, MA 127, or MA 129. Carries MCS divisional credit in CAS. 4 cr.
Introduction to Linear Algebra
CAS MA 142
Systems of linear equations; matrices. Vector spaces and linear transformations. Determinants. Eigenvalues and eigenvectors. Applications. Cannot be taken for credit in addition to CAS MA 242, CAS MA 442, or ENG EK 102. 2 cr.
Basic Statistics and Probability
CAS MA 213
Prereq: good background in high school algebra. Elementary treatment of probability densities, means, variances, correlation, independence, the binomial distribution, the central limit theorem. Stresses understanding and theoretical manipulation of statistical concepts. Students may receive credit for not more than one of the following courses: CAS MA 113, MA 115, or MA 213. Carries MCS divisional credit in CAS. 4 cr.
CAS MA 214
Prereq: (CAS MA 213) or consent of instructor. Inference about proportions, goodness of fit, student's t-distribution, tests for normality; two-sample comparisons, regression and correlation, tests for linearity and outliers, residual analysis, contingency tables, analysis of variance. Students may receive credit for not more than one of the following courses: CAS MA 116, MA 214, or MA 614. Carries MCS divisional credit in CAS. 4 cr.
CAS MA 225
Prereq: (CAS MA 124 or CAS MA 127 or CAS MA 129). Vectors, lines, planes. Multiple integration, cylindrical and spherical coordinates. Partial derivatives, directional derivatives, scalar and vector fields, the gradient, potentials, approximation, multivariate minimization, Stokes's and related theorems. Cannot be taken for credit in addition to CAS MA 230. 4 cr.
CAS MA 226
Prereq: (CAS MA 225 or CAS MA 230). First-order linear and separable equations. Second-order equations and first-order systems. Linear equations and linearization. Numerical and qualitative analysis. Laplace transforms. Applications and modeling of real phenomena throughout. Cannot be taken for credit in addition to CAS MA 231. 4 cr.
CAS MA 242
Matrix algebra, solution of linear systems, determinants, Gaussian elimination, fundamental theory, row-echelon form. Vector spaces, bases, norms. Computer methods. Eigenvalues and eigenvectors, canonical decomposition. Applications. Cannot be taken for credit in addition to CAS MA 142, MA 442, or ENG EK 102. 4 cr.
The Mathematics of Sustainability
CAS MA 267
Prereq: (CAS MA 121 or CAS MA 123) or consent of instructor. The goal is to develop models for sustainability. "Just-in-time" mathematics/statistics techniques are taught with immediate application, for example: geometry for flight routes; graph theory for social networks; linear algebra for operations research; fractal measures for earthquakes and tsunamis. 4 cr.
CAS MA 293
Prereq: (CAS MA 123). Propositional logic, set theory. Elementary probability theory. Number theory. Combinatorics with applications. 4 cr.
Applied Abstract Algebra
CAS MA 294
Prereq: (CAS MA 293) or consent of instructor. Abstract algebra and its applications to combinatorics. A first exposure to groups, rings, and fields via significant combinatorial applications. Students who have already received credit for MA 541 or MA 542 may not subsequently receive credit for MA 294. 4 cr.
Introduction to Number Theory
CAS MA 341
Prereq: (CAS MA 242) or consent of instructor. Study of integers and basic results of number theory. Topics include Linear Diophantine equations, prime numbers and factorization, congruences, and quadratic reciprocity. 4 cr.
CAS MA 411
Prereq: ((CAS MA 225 or CAS MA 230) & (CAS MA 242 or CAS MA 442)). Extends concepts and techniques of calculus and develops further applications. Topics include higher dimensional calculus, applications of vector analysis, uniform convergence of series, complex series, improper integrals, gamma and beta functions, Stirling's formula, Fourier series and transform. 4 cr.
CAS MA 412
Prereq: (CAS MA 225 or CAS MA 230). Basic concepts, results, and applications of complex analysis. Emphasis on computation and applications. Complex plane and functions, differentiability, Cauchy-Riemann conditions, contour integrals, Cauchy formulas, complex series, residue calculus, applications. Extends the concepts of the calculus to the complex setting. 4 cr.
Modern Algebra I
CAS MA 541
Basic properties of groups, Sylow theorems, basic properties of rings and ideals, Euclidean rings, polynomial rings. 4 cr.
Geometry and Symmetry
CAS MA 549
Prereq: consent of instructor. Problem-oriented seminar in modern geometry focusing on invariants of transformation groups. Specific topics may include Euclidean and plane geometry, Hilbert's Axioms, conics, tilings, finite, projective, spherical and/or hyperbolic geometry, tessellations, applications to number theory, Platonic Solids. 4 cr.
Optimization Methods of Operations Research
CAS MA 569
Prereq: ((CAS MA 225 or CAS MA 230) & (CAS MA 242 or CAS MA 442)). Optimization of linear functions: linear programming, simplex method; transportation, assignment, and network problems. Optimization of non-linear functions: unconstrained optima, constrained optima and Lagrange multipliers, Kuhn-Tucker conditions, calculus of variations, and Euler's equation. 4 cr.
CAS MA 581
Prereq: (CAS MA 225 or CAS MA 230) or consent of instructor. Basic probability, conditional probability, independence. Discrete and continuous random variables, mean and variance, functions of random variables, moment generating function. Jointly distributed random variables, conditional distributions, independent random variables. Methods of transformations, law of large numbers, central limit theorem. Cannot be taken for credit in addition to CAS MA 381. 4 cr.
Mathematics for Management
MET AD 510
An overview of fundamental mathematical concepts, with emphasis on the solution of word problems. Topics covered include quadratic equations, signed numbers, polynomials, graphs, roots and radicals, and basic concepts of differential and integral calculus. Prerequisite course which may not be used toward graduate credit. 2 cr.
Pension Mathematics and Mortality Tables
MET AT 782
Prereq: (MET MA 581 or CAS MA 581) and MET AT 721. Covers pension actuarial funding methods and the use of life contingencies. Included are analyses of the funding methods allowable under ERISA, their computation, and uses. Also reviews the use of mortality tables and discusses the various actuarial functions that are used in pension actuarial calculations. Finally, reviews implications for pension funding under the IRS. 4 cr.
MET CS 248
Fundamentals of logic (the laws of logic, rules of inferences, quantifiers, proofs of theorems). Fundamental principles of counting (permutations, combinations), set theory, relations and functions, graphs, trees and sorting, shortest path and minimal spanning trees algorithms. Monoids and Groups. 4 cr.
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