Mathematics and Statistics
College of Arts & Sciences
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Elementary Statistics
CAS MA 113
Basic concepts of estimation and tests of hypotheses, ideas from probability; one-, two-, and multiple-sample problems. Applications are in the social sciences, and students will be able to understand the basics of using a sample to predict uncertainty. CAS MA 113 may not be taken for credit by any student who has completed any CAS MA course numbered 300 or higher. Students may receive credit for not more than one of the following courses: CAS MA 113, CAS MA 115, or CAS MA 213. Carries MCS divisional credit in CAS. Effective Fall 2020, this course fulfills a single unit in each of the following BU Hub areas: Quantitative Reasoning II, Critical Thinking. 4 cr.
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Statistics I
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. CAS MA 115 may not be taken for credit by any student who has completed any CAS MA course numbered 300 or higher. Students may receive credit for not more than one of the following courses: CAS MA 113, CAS MA 115, or CAS MA 213. Carries MCS divisional credit in CAS. Effective Fall 2020, this course fulfills a single unit in each of the following BU Hub areas: Quantitative Reasoning II, Critical Thinking. 4 cr.
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Statistics II
CAS MA 116
Undergraduate Prerequisites: (CASMA115) or equivalent. - Introduces basic statistical modeling techniques. One- or two- sample inference for unknown means, proportions and variances, categorical data analysis, introduction to design of experiments and analysis of variance, analysis of simple and multiple linear regression models, non-parametric methods. CAS MA 116 may not be taken for credit by any student who has completed any CAS MA course numbered 300 or higher. Students may receive credit for not more than one of the following courses: CAS MA 116, CAS MA 214, or CAS MA 614. Carries MCS divisional credit in CAS. Effective Fall 2020, this course fulfills a single unit in each of the following BU Hub areas: Quantitative Reasoning II, Critical Thinking. 4 cr.
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Applied Mathematics for Personal Finance
CAS MA 119
Applications of mathematics for personal financial decision-making. Systems of equations, exponential functions, logarithms, probability, descriptive statistics, and numerical simulation for modeling saving, borrowing, inflation, purchasing power, taxation, government benefits, risk management, insurance, annuities, and investments. Carries MCS divisional credit in CAS. This course also fulfills the learning outcomes for Life Skills. Effective Fall 2020, this course fulfills a single unit in each of the following BU Hub areas: Quantitative Reasoning I, Social Inquiry I, Critical Thinking. 4 cr.
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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 applications. Especially suitable for students concentrating in the biological and social sciences. Students may receive credit for not more than one of the following courses: CAS MA 121 or CAS MA 123. Carries MCS divisional credit in CAS. Students must register for two sections: lecture and discussion. Effective Fall 2020, this course fulfills a single unit in each of the following BU Hub areas: Quantitative Reasoning II, Social Inquiry II, Critical Thinking. 4 cr.
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Calculus for the Life and Social Sciences II
CAS MA 122
Undergraduate Prerequisites: (CASMA121 OR CASMA123) - 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, CAS MA 124, or CAS MA 129. Carries MCS divisional credit in CAS. Effective Fall 2020, this course fulfills a single unit in each of the following BU Hub areas: Quantitative Reasoning II, Social Inquiry II, Critical Thinking. 4 cr.
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Calculus I
CAS MA 123
Limits; derivatives; differentiation of algebraic and transcendental functions. Applications to maxima, minima, and convexity of functions. The definite integral; the fundamental theorem of integral calculus. Students may receive credit for not more than one of the following courses: CAS MA 121 or CAS MA 123. Carries MCS divisional credit in CAS. Effective Fall 2020, this course fulfills a single unit in each of the following BU Hub areas: Quantitative Reasoning II, Critical Thinking. 4 cr.
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Calculus II
CAS MA 124
Undergraduate Prerequisites: (CASMA121 OR CASMA123) - 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, CAS MA 124, or CAS MA 129. Carries MCS divisional credit in CAS. Effective Fall 2020, this course fulfills a single unit in each of the following BU Hub areas: Quantitative Reasoning II, Scientific Inquiry II, Critical Thinking. 4 cr.
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Basic Statistics and Probability
CAS MA 213
Undergraduate Prerequisites: good background in high school algebra. - Elementary treatment of probability densities, means, variances, correlation, independence, the central limit theorem, confidence intervals, and p-values. Students learn to answer questions such as how can a pollster use a sample to predict the uncertainty of an election? Students may receive credit for not more than one of the following courses: CAS MA 113, CAS MA 115, or CAS MA 213. Carries MCS divisional credit in CAS. Effective Fall 2020, this course fulfills a single unit in each of the following BU Hub areas: Quantitative Reasoning II, Critical Thinking, Teamwork/Collaboration. 4 cr.
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Applied Statistics
CAS MA 214
Undergraduate Prerequisites: CASMA 213 or CASMA 115 or CASMA 113 or CDSDS 120 or CASCS 237 or consent of instructor. - Students may receive credit for not more than one of the following courses: CASMA 116, MA 214, or MA 614. 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. Effective Fall 2018, this course fulfills a single unit in each of the following BU Hub areas: Quantitative Reasoning II, Teamwork/Collaboration. Effective Fall 2020, this course fulfills a single unit in each of the following BU Hub areas: Quantitative Reasoning II, Critical Thinking, Teamwork/Collaboration. 4 cr.
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Multivariate Calculus
CAS MA 225
Undergraduate Prerequisites: (CASMA124 OR CASMA129) - 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. Effective Fall 2020, this course fulfills a single unit in each of the following BU Hub areas: Quantitative Reasoning II, Critical Thinking. 4 cr.
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Differential Equations
CAS MA 226
Undergraduate Prerequisites: (CASMA225 OR CASMA230) - 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. Effective Fall 2020, this course fulfills a single unit in the following BU Hub area: Critical Thinking. 4 cr.
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Linear Algebra
CAS MA 242
Undergraduate Prerequisites CASMA 121 or CASMA 123 or CASMA 129 or consent of instructor. - Cannot be taken for credit in addition to CAS MA 442 or ENG EK 103. 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. Effective Fall 2019, this course fulfills a single unit in the following BU Hub area: Quantitative Reasoning II. Effective Fall 2020, this course fulfills a single unit in each of the following BU Hub areas: Quantitative Reasoning II, Critical Thinking. 4 cr.
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Discrete Mathematics
CAS MA 293
Propositional logic, set theory. Elementary probability theory. Number theory. Combinatorics with applications. Effective Fall 2020, this course fulfills a single unit in the following BU Hub area: Critical Thinking. 4 cr.
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Applied Abstract Algebra
CAS MA 294
Undergraduate Prerequisites: (CASMA293) 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 CAS MA 541 or CAS MA 542 may not subsequently receive credit for CAS MA 294. Effective Fall 2020, this course fulfills a single unit in the following BU Hub area: Critical Thinking. 4 cr.
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Introduction to Number Theory
CAS MA 341
Undergraduate Prerequisites: (CASMA242) 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. Effective Fall 2020, this course fulfills a single unit in the following BU Hub area: Critical Thinking. 4 cr.
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Advanced Calculus
CAS MA 411
Undergraduate Prerequisites: ( (CASMA225 OR CASMA230) & (CASMA242 OR CASMA442)) - Prereq: (CAS MA 225 or CAS MA 230) and (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, and Fourier series and transform. 4 cr.
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Complex Variables
CAS MA 412
Undergraduate Prerequisites: (CASMA225 OR CASMA230) - 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.
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Introduction to Analysis I
CAS MA 511
Undergraduate Prerequisites: (CASMA225 OR CASMA230) - Graduate Prerequisites: (CASMA225 OR CASMA230) - Fundamental concepts of mathematical reasoning. Properties of the real-number system, elementary point-set theory, metric spaces. Limits, sequences, series, convergence, uniform convergence, continuity. Differentiability for functions of a single variable, Riemann-Stieltjes integration. 4 cr.
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Optimization Methods of Operations Research
CAS MA 569
Undergraduate Prerequisites: (CASMA225 OR CASMA230) , CASMA242 OR CASMA442 - Graduate Prerequisites: (CASMA225 OR CASMA230 OR CASMA242 OR CASMA442) - Prereq: (CAS MA 225 or CAS MA 230) and (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.
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Probability
CAS MA 581
Undergraduate Prerequisites: (CASMA225 OR CASMA230) or consent of instructor. - Graduate Prerequisites: (CASMA225 OR CASMA230) 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.
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Mathematical Statistics
CAS MA 582
Undergraduate Prerequisites: (CASMA581) - Graduate Prerequisites: (CASMA581) - Prereq: (CAS MA 581). Point estimation including unbiasedness, efficiency, consistency, sufficiency, minimum variance unbiased estimator, Rao-Blackwell theorem, and Rao-Cramer inequality. Maximum likelihood and method of moment estimations; interval estimation; tests of hypothesis, uniformly most powerful tests, uniformly most powerful unbiased tests, likelihood ratio test, and chi-square test. 4 cr.
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Introduction to Stochastic Processes
CAS MA 583
Undergraduate Prerequisites: (CASMA581) or consent of instructor. - Graduate Prerequisites: (CASMA581) or consent of instructor. - Prereq: (CAS MA 581) or consent of instructor. Basic concepts and techniques of stochastic process as they are most often used to construct models for a variety of problems of practical interest. Topics include Markov chains, Poisson process, birth and death processes, queuing theory, renewal processes, and reliability. 4 cr.
Metropolitan College
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Pension Mathematics and Mortality Tables
MET AT 782
Undergraduate Prerequisites: (MET MA581 or CAS MA581) and MET AT721 - Covers the mathematics of actuarial funding methods as used by pension actuaries. General pension concepts are introduced, and the calculation of benefits under pension plans is discussed. Reviews the development of mortality tables and the use of life contingencies in developing pension models. Computations under actuarial funding methods are addressed, including the use of these methods in pension plans worldwide. The use of mortality tables is addressed, as are modifications to those tables to reflect expected changes to mortality in the future. Alternative ways to receive pension payments at retirement are discussed. 4 cr.
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Discrete Mathematics
MET CS 248
Undergraduate Prerequisites: high school algebra. - 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. 4 cr.