# Mathematics and Statistics

## 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 are in the social sciences and students will be able to understand the basics of using a sample to predict uncertainty. 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. This course fulfills a single unit in the following BU Hub area: Quantitative Reasoning II. 4 cr. Tuition: \$2800

Summer 1 (May 21-June 27)

Summer 2 (July 1-August 8)

Seven-week course (July 1-August 16)

Summer 2 Section OL: Only for first year students entering BU as of Fall 2018.

For information about technology requirements for online courses at Boston University, see bu.edu/online/online-learning/technology . The Distance Education office can be reached at 617-358-1960 for additional information.

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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. 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. This course fulfills a single unit in the following BU Hub area: Quantitative Reasoning II. 4 cr. Tuition: \$2800

Summer 1 (May 21-June 27)

Summer 2 (July 1-August 8)

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#### Statistics II

CAS MA 116

Prereq: (CAS MA 115) 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. 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. This course fulfills a single unit in the following BU Hub area: Quantitative Reasoning II. 4 cr. Tuition: \$2800

Summer 1 (May 21-June 27)

Summer 2 (July 1-August 8)

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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 fulfills a single unit in each of the following BU Hub areas: Social Inquiry I, Quantitative Reasoning I. This course also fulfills the learning outcomes for Life Skills. 4 cr. Tuition: \$2800

Summer 1 (May 21-June 27)

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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 either CAS MA 121 or 123, but not both. Carries MCS divisional credit in CAS. This course fulfills a single unit in the following BU Hub area: Quantitative Reasoning II. 4 cr. Tuition: \$2800

Summer 1 (May 21-June 27)

Summer 2 (July 1-August 8)

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#### 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. This course fulfills a single unit in the following BU Hub area: Quantitative Reasoning II. 4 cr. Tuition: \$2800

Summer 2 (July 1-August 8)

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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 either CAS MA 121 or 123, but not both. Carries MCS divisional credit in CAS. This course fulfills a single unit in the following BU Hub area: Quantitative Reasoning II. 4 cr. Tuition: \$2800

Summer 1 (May 21-June 27)

Summer 2 (July 1-August 8)

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#### 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. This course fulfills a single unit in the following BU Hub area: Quantitative Reasoning II. 4 cr. Tuition: \$2800

Summer 1 (May 21-June 27)

Summer 2 (July 1-August 8)

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#### 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 103. 2 cr. Tuition: \$1400

Summer 2 (July 1-August 7)

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#### Investigations in Geometry

CAS MA 150

An immersion experience in mathematical thinking and mathematical habits of mind. Students investigate topics in Euclidean and non-Euclidean geometry starting from basic elementary material and leading to an overview of current research topics. Does not satisfy MCS Divisional requirement. Does satisfy CAS WR 150 requirement. This course fulfills a single unit in each of the following BU Hub areas: Quantitative Reasoning II, Writing: Research & Inquiry, Research and Information Literacy. 4 cr. Tuition: \$2800

Summer 2 (July 1-August 8)

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#### Basic Statistics and Probability

CAS MA 213

Prereq: good background in high school algebra. Elementary treatment of probability densities, means, variances, correlation, independence, the central limit theorem, confidence intervals, and p-values. 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. This course fulfills a single unit in each of the following BU Hub areas: Quantitative Reasoning II, Teamwork/Collaboration. 4 cr. Tuition: \$2800

Summer 1 (May 21-June 27)

Summer 2 (July 1-August 8)

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#### 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. This course fulfills a single unit in each of the following BU Hub areas: Quantitative Reasoning II, Teamwork/Collaboration. 4 cr. Tuition: \$2800

Summer 1 (May 21-June 27)

Summer 2 (July 1-August 8)

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#### 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. This course fulfills a single unit in the following BU Hub area: Quantitative Reasoning II. 4 cr. Tuition: \$2800

Summer 1 (May 21-June 27)

Summer 2 (July 1-August 8)

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#### 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. Tuition: \$2800

Summer 1 (May 21-June 27)

Summer 2 (July 1-August 8)

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#### 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. Tuition: \$2800

Summer 1 (May 21-June 27)

Summer 2 (July 1-August 8)

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#### 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. Tuition: \$2800

Summer 1 (May 21-June 27)

A sample of student projects from previous offerings of this course can be found here.

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#### Discrete Mathematics

CAS MA 293

Prereq: (CAS MA 123). Propositional logic, set theory. Elementary probability theory. Number theory. Combinatorics with applications. 4 cr. Tuition: \$2800

Summer 1 (May 21-June 27)

Summer 2 (July 1-August 8)

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#### 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. Tuition: \$2800

Summer 2 (July 1-August 8)

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#### 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. Tuition: \$2800

Summer 1 (May 21-June 27)

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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. Tuition: \$2800

Summer 1 (May 21-June 27)

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#### 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. Tuition: \$2800

Summer 2 (July 1-August 8)

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#### Analysis of Variance

CAS MA 416

Prereq: (CAS MA 116 or CAS MA 214) or equivalent. Fundamental concepts and analytical skills in analysis of variance, including crossed and nested designs, as well as fixed- and random- effect models. Trend analysis for repeated measures, expected mean squares, and non- parametric techniques. SAS is used throughout the course. 4 cr. Tuition: \$2800

Summer 1 (May 21-June 27)

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#### Graph Theory

CAS MA 433

Prereq: (CAS MA 242 and CAS MA 293) or consent of instructor. Focus on learning the basic concepts of graph theory and enhancing the ability to read and write rigorous mathematical proofs. Topics covered include graph connectivity, planarity, graph colorings, and Euler's formula. 4 cr. Tuition: \$2800

Summer 1 (May 21-June 27)

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#### Introduction to Analysis 1

CAS MA 511

Prereq: (CAS MA 225 or CAS MA 230). 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. Tuition: \$2800

Summer 1 (May 21-June 27)

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#### Modern Algebra I

CAS MA 541

Basic properties of groups, Sylow theorems, basic properties of rings and ideals, Euclidean rings, polynomial rings. 4 cr. Tuition: \$2800

Summer 1 (May 21-June 27)

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#### 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. Tuition: \$2800

Summer 2 (July 1-August 8)

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#### 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. Tuition: \$2800

Summer 1 (May 21-June 27)

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#### 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. Tuition: \$2800

Summer 1 (May 21-June 27)

Summer 2 (July 1-August 8)

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#### Mathematical Statistics

CAS MA 582

Prereq: (CAS MA 581 or CAS MA 381). 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. Tuition: \$2800

Summer 1 (May 21-June 27)

Summer 2 (July 1-August 8)

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#### 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. Tuition: \$2800

Summer 2 (July 1-August 8)

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## 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. Tuition: \$3520

Summer 1 (May 22-June 26)

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#### 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. 4 cr. Tuition: \$2800

Summer 1 (May 22-June 26)

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