# Mathematics and Statistics

**Note:** Course details for Summer 2018 will be available on December 15. The courses below were offered in Summer 2017 and can serve as a guide to what is typically offered.

Colleges: College of Arts & Sciences | Metropolitan College

## College of Arts & Sciences

#### Elementary 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.

#### 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. 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.

#### Statistics II

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

Topics chosen from linear equations, systems of linear equations, matrix algebra, exponential functions and logarithms, elements of differential calculus, optimization, probability. Some sections focus on 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.

#### Calculus I

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.

#### Calculus II

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.

#### Applied Statistics

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.

#### Multivariate Calculus

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.

#### Differential Equations

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.

#### Linear Algebra

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 of this course 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.

#### Discrete Mathematics

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.

#### Advanced Calculus

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.

#### Complex Variables

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.

#### Probability

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.

#### Introduction to Stochastic Processes

CAS MA 583

Prereq: (CAS MA 581 or CAS MA 381) 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

#### 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.

#### Discrete Mathematics

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.

### Courses of Related Interest

- CAS EC 203 - Empirical Economics 1
- CAS EC 204 - Empirical Economics 2
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