This course on mathematical methods, including calculus and algebraic technique, is suitable for students who wish to take at least a service paper in mathematical methods and do not yet have a background in mathematics sufficiently strong to join MATH 160. Emphasis is placed on understanding via examples, and the methods taught are used to study a variety of practical problems. In the process, students’ manipulation skills in algebra and calculus will improve.
Assessment
Written assignments (x5) and computer tests (x3): 35%
Final examination (2 hours): 65%
This course consists of half algebra and half calculus, and is the main entry point to 100-level mathematics. The course provides the basis for progression to MATH 170 and then to 200-level mathematics as well as an adequate background to support other subjects.
Assessment
Marked assignments (x10): 16.7% (if they help)
Computer skills tests (x5 each in Algebra and Calculus): 33.3%
Final examination (3 hours): 67.7% (or 50%, if assignments help)
To pass terms, a student must gain at least 5/10 in each of the first four skills tests.
This course covers descriptive statistics, probability distributions, estimation, hypothesis testing, regression, analysis of variance, experimental design, sampling and design principles. The program R will be used throughout the course.
This paper will provide a head start for students wishing to advance in statistics as well as those requiring only the statistical background represented by STAT 110 to proceed in their own disciplines.
Assessment
Online assignment and mastery tests: 33%
Final examination (3 hours): 67%
Grades achieved in the online assignment and mastery tests will count towards the final grade only if this is to the student’s advantage.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Prereq: (CAS MA 123).
Propositional logic, set theory. Elementary probability theory. Number theory. Combinatorics with applications.
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.
Prereq: (MET CS546 and (MET CS520 or MET CS521)) or equivalent knowledge, or instructor’s consent.
Provides students with the mathematical and practical background required in the field of data analytics. Starting with an introduction to probability and statistics, the R tool is introduced for statistical computing and graphics. Different types of data are investigated along with data summarization techniques and plotting. Data populations using discrete, continuous, and multivariate distributions are explored. Errors during measurements and computations are analyzed in the course. Confidence intervals and hypothesis testing topics are also examined. The concepts covered in the course are demonstrated using R. Laboratory Course.
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.
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.
Prereq: (CAS PS 101).
Introduction to the logic and processes involved in descriptive and inferential statistics for psychology. Topics include statistical inference, significance, t-tests, ANOVAs, correlation, and statistical software analysis. This is a hybrid class: class time is reserved for hands on activities.
This course fulfills a single unit in each of the following BU Hub areas: Scientific Inquiry II, Quantitative Reasoning I.
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.
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.
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.
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.
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.
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.
Prereq: (QST QM 221 & CAS EC 101). Sophomore standing.
Examines the use of economic and statistical tools for making business decisions. Topics include optimization (including linear programming), multiple regression, demand modeling, cost modeling, industry analysis (including models of perfect competition, monopoly, and oligopoly), and game theory. Emphasizes modeling with spreadsheets.
This course fulfills a single unit in the following BU Hub area: Quantitative Reasoning II.
Basic properties of groups, Sylow theorems, basic properties of rings and ideals, Euclidean rings, polynomial rings.
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.
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.
Exposes students to the fundamentals of probability, decision analysis, and statistics, and their application to business. Topics include probability, decision analysis, distributions, sampling, estimation, hypothesis testing, and chi-square.
This course fulfills a single unit in the following BU Hub area: Quantitative Reasoning I.
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.
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.
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.
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.
Pre-requisite: MATH 115A.
Ring of integers, integral domains, fields, polynomial domains, unique factorization.
Pre-requisite: MATH 32B, 33B.
Rigorous introduction to foundations of real analysis; real numbers, point set topology in Euclidean space, functions, continuity.
Pre-requisite: MATH 31A.
Introduction to differential calculus of several variables, vector field theory.
Pre-requisite: MATH 32B, 33B.
Introduction to basic formulas and calculation procedures of complex analysis of one variable relevant to applications. Topics include Cauchy/Riemann equations, Cauchy integral formula, power series expansion, contour integrals, residue calculus.
Pre-requisite: Successful completion of Mathematics Diagnostic Test.
Differential calculus and applications; introduction to integration.
Pre-requisite: MATH 31A, 31B.
Discrete structures commonly used in computer science and mathematics, including sets and relations, permutations and combinations, graphs and trees, induction.
Pre-requisite: MATH 33A.
Techniques of proof, abstract vector spaces, linear transformations, and matrices; determinants; inner product spaces; eigenvector theory.
Pre-requisite: MATH 3B or 31B or 32A.
Introduction to linear algebra: systems of linear equations, matrix algebra, linear independence, subspaces, bases and dimension, orthogonality, least-squares methods, determinants, eigenvalues and eigenvectors, matrix diagonalization, and symmetric matrices.
Pre-requisite: MATH 33B.
Dynamical systems analysis of nonlinear systems of differential equations. One- and two- dimensional flows. Fixed points, limit cycles, and stability analysis. Bifurcations and normal forms. Elementary geometrical and topological results. Applications to problems in biology, chemistry, physics, and other fields.
Pre-requisite: MATH 115A.
Quantitative modeling of strategic interaction. Topics include extensive and normal form games, background probability, lotteries, mixed strategies, pure and mixed Nash equilibria and refinements, bargaining; emphasis on economic examples. Optional topics include repeated games and evolutionary game theory.
Pre-requisite: MATH 33A, 33B.
Introduction to fundamental principles and spirit of applied mathematics. Emphasis on manner in which mathematical models are constructed for physical problems. Illustrations from many fields of endeavor, such as physical sciences, biology, economics, and traffic dynamics.
Pre-requisite: MATH 33A, 33B.
Selected topics in differential equations. Laplace transforms, existence and uniqueness theorems, Fourier series, separation of variable solutions to partial differential equations, Sturm/Liouville theory, calculus of variations, two-point boundary value problems, Green’s functions.
Pre-requisite: MATH 3B.
Multivariable modeling, matrices and vectors, eigenvalues and eigenvectors, linear and nonlinear systems of differential equations, probabilistic applications of integration.
Pre-requisite: Successful completion of Mathematics Diagnostic Test.
Linear and polynomial functions and their graphs, applications to optimization. Inverse, exponential, and logarithmic functions. Trigonometric functions.
Basic statistical procedures and their application to research and practice in various areas of psychology.
Lecture, four hours. Requisites: course 10 with a grade of C or better, and one course from Mathematics 2, Program in Computing 10A, Statistics 10, or one term of calculus. Designed for pre-majors.
Pre-requisites: Mathematics 31A, 31B.
Introduction to probability and statistics for economists, with emphasis on rigorous arguments. Not open to students with credit for former Statistics 11.
