Department of Mathematics
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Undergraduate Level Courses

The department offers courses leading to a Bachelor of Science or a Bachelor of Arts Degree in Mathematics. A flowchart of the courses required or counting towards undergraduate math degrees is available [HERE].

In addition the department offers introductory courses to prepare undergraduate students for programs in premedical studies, management, the social sciences, and the natural sciences. A flowchart of the 100-and 200-level math courses is available [HERE].

Course Number and Title Credits Description Prerequisites Comments Sample Materials
MATH 114
Quantitative Reasoning
3 This course covers the basic algebra and technological tools used in the social, physical and life sciences to analyze quantitative information. The emphasis is on real world, open-ended problems that involve reading, writing, calculating, synthesizing, and clearly reporting results. Topics include descriptive statistics, linear, and exponential models. Technology used in the course includes computers (spreadsheets, internet) and graphing calculators. Math Placement Test. Degree students only
MATH 115
College Algebra
3 Topics include basic algebra concepts, linear equations and inequalities, properties of functions, linear and quadratic functions, absolute value equations and inequalities, systems of equations. Math Placement Test or MATH 125. Designed primarily but not exclusively for students seeking a stronger foundation in algebra before taking MATH 129 or MATH 130. Sample Materials
MATH 125
Introductory Statistics
3 Topics include introductory statistics, covering descriptive statistics; introductory probability sufficient to enable development of inferential statistics; and inferential statistics. Math Placement Test or MATH 114Q or 115 or 124 or 129 or 130 or 140. Sample Materials
MATH 129
Precalculus for Management and Social Sciences
3 This course teaches the algebraic and conceptual skills students need to master before they are ready for MATH 134 or MATH 135. The major part of the course then involves the application of linear, quadratic, and exponential models to problems in management and economics. Math Placement Test or MATH 115 with a grade of B or better in the previous semester. Students intending to take Calculus I and II (MATH 140 and 141) should take MATH 130 instead of MATH 129. Students may take MATH 130 after MATH 129, but only with the explicit permission of the department, and then only for two credits. Sample Materials
MATH 130
Precalculus
3 Preparation for first-year calculus. Covers symmetry, graphs, functions, lines, parabolas and max-min problems, exponential and logarithm functions, exponential growth, and the trigonometric functions and their inverses. Math Placement Test or MATH 115 with a grade of B or better in the previous semester. No student receives graduation credits for MATH 130 if it is taken after successful completion of any higher math course. Students who have successfully completed MATH 130 may not subsequently take MATH 129 for credit. Students may take MATH 130 after MATH 129 only with explicit permission of the department, and then only for two credits. Sample Materials
MATH 134
Managerial Calculus
3 A one-semester course in calculus, with particular emphasis on applications to economics and management. Topics covered include limits, continuity, derivatives, and integrals. Math Placement Test or successful completion of MATH 129 or MATH 130. Students may not receive graduation credit for both MATH 134 and MATH 135. Students may take MATH 140 after MATH 134, but only with the explicit permission of the department and then only for two credits. Sample Materials
MATH 135
Survey of Calculus
3 Calculus developed intuitively and applied to problems in biology, economics, psychology, and geometry. A course for non-physical science and non-mathematics majors. Suitable for some pre-medical programs. Math Placement Test or MATH 130. No student receives graduation credit for MATH 135 if it is taken after successful completion of MATH 134 or 140 or a higher Math course. Students may take MATH 140 after 135 only with explicit permission of the Department, and then only for two credits.
MATH 140
Calculus I
4 This course is an introduction to differential and integral calculus. It begins with a short review of basic concepts surrounding the notion of a function. Then it introduces the important concept of the limit of a function, and uses it to study continuity and the tangent problem. The solution to the tangent problem leads to the study of derivatives and their applications. Then it considers the area problem and its solution, the definite integral. The course concludes with the calculus of elementary transcendental functions. Math Placement Test or completion of MATH 130 within the past semester with a grade of B or higher. A student who has received credit for either MATH 134 or MATH 135 may not take MATH 140 for credit without the explicit permission of the department and then only for two credits. Sample Materials
MATH 141
Calculus II
4 Continuation of MATH 140. Topics include transcendental functions, techniques of integration, applications of the integral, improper integrals, l'Hospital's rule, sequences, and series. MATH 140 with grade of C- or better or MATH 145 with grade of C- or better. Because MATH 141 is the second part of a three-semester calculus sequence, it should be taken as soon as possible after MATH 140. Sample Materials
MATH 145
Calculus I for Life and Environmental Sciences
4 The course is the first in the sequence of calculus courses for science and math majors. The topics covered in this course parallel the topics covered in the other Math 140 sections; however, the applications presented in this course have origins in biological systems. The course begins with the basic concepts of functions, discrete time models and limits in the context of population models. Further topics covered include: derivatives along with their applications to biological modeling and definite and indefinite integrals with applications to geometric and biological problems. Math Placement Test or a grade of B or better in MATH 130 in the previous semester. Students who complete this course will be eligible for MATH 141, or MATH 146, as well as MATH 303.
MATH 146
Calculus II for Life and Environmental Sciences
4 The course is the second in the sequence of calculus courses for life science and environmental science majors. The topics covered in this course do not parallel the topics covered in the Math 141: Calculus II sections; however, the material covered in this course introduces the student to mathematical fields that are commonly applied in the study of life and environmental sciences. Applications presented in this course have origins in biological and environmental systems. The course begins with a brief review of integration techniques learned in Calculus I, and continues with a thorough analysis of integration. Computational methods, differential equations, linear algebra and multivariable calculus are introduced so that the student may examine dynamical systems that are central to understanding the behavior of many physical models. MATH 140 or MATH 145. This course does not fulfill the Calculus II (Math 141) requirement and does not serve as a prerequisite for Multivariable Calculus (Math 240). This course satisfies the following GenEd requirements: Quantitative Reasoning, Distribution II: MT.
MATH 240
Multivariable Calculus
3 Differential and integral calculus of functions of several variables and of vector fields. Topics include Euclidean, polar, cylindrical, and spherical coordinates; dot product, cross-product, equations of lines and planes; continuity, partial derivatives, directional derivatives, optimization in several variables; multiple integrals, iterated integrals, change of coordinates, Jacobians, general substitution rule. MATH 141. Because MATH 240 is the final part of a three-semester calculus sequence, it should be taken as soon as possible after MATH 141. No student receives graduation credit for MATH 240 if it is taken after successful completion of MATH 242. Students may take MATH 242 after MATH 240 only with the explicit permission of the Department and then only for one credit.
MATH 242
Multivariable and Vector Calculus
4 Differential and integral calculus of functions of several variables and of vector fields. Topics include Euclidean, polar, cylindrical, and spherical coordinates; dot product, cross-product, equations of lines and planes; continuity, partial derivatives, directional derivatives, optimization in several variables; multiple integrals, iterated integrals, change of coordinates, Jacobians, general substitution rule; curves and surfaces, parametrizations, line integrals, surface integrals; gradient, circulation, flux, divergence; conservative, solenoidal vector fields; scalar, vector potential; Green, Gauss, and Stokes theorems. MATH 141. Because MATH 242 is the final part of a three-semester calculus sequence, it should be taken as soon as possible after MATH 141. No student receives graduation credit for MATH 240 if it is taken after successful completion of MATH 242. Students may take MATH 242 after MATH 240 only with the explicit permission of the Department and then only for one credit.
MATH 260
Linear Algebra
3 Elementary theory of vector spaces. Topics include linear independence, bases, dimension, linear maps and matrices, determinants, orthogonality, eigenvalues and eigenvectors. MATH 140. Sample Materials
MATH 280
Introduction to Proofs
3 The course is designed to aid students in making the transition from calculus, differential equations and linear algebra to the more advanced and more abstract mathematics courses, such as abstract algebra and real analysis. The course will cover mathematical logic, mathematical proofs, mathematical induction, set theory, relations, functions, cardinality and applications of proofs in the study of such areas as number theory, calculus and group theory, as time permits. MATH 141. Sample Materials
MATH 303
Introduction to Mathematical Biology
3 Mathematical models of population growth and other biological processes and nth order linear difference equations will be used to model propagation of annual plants; growth of segmental organisms; red blood cell production; and population growth and destiny dependence in single-species populations. Continuous models will be constructed from among several possibilities, including the logistic equation, simple exponential growth, the Chemostat, Michaelis-Menten kinetics, drug delivery, glucose-insulin kinematics, Gompertz growth in tumors, and the Fitzhugh-Magumo model for neural impulses. Appropriate software will be used throughout the course. MATH 140.
MATH 310
Applied Ordinary Differential Equations
3 A comprehensive study of the nature of ordinary differential equations. The course includes qualitative analysis of properties of solutions, as well as standard methods for finding explicit solutions to important classes of differential equations. It presents many applications, particularly for linear equations. [MATH 240] AND [MATH 260 or PHYSICS 114].
MATH 320L
Applied Discrete Mathematics
3 An introduction to the mathematical structures and concepts used in computing: sets, mathematical induction, ordered sets, Boolean algebras, predicate calculus, trees, relations and lattice theory. Formal and informal theories and corresponding mathematical proofs are taught. CS110 and MATH 260; or permission of instructor.
MATH 345
Probability and Statistics I
3 This course presents the mathematical laws of random phenomena, including discrete and continuous random variables, expectation and variance, and common probability distributions such as the binomial, Poisson, and normal. Topics also include basic ideas and techniques of statistical analysis. MATH 141 or permission of instructor. Sample Materials
MATH 346
Probability and Statistics II
3 This is a statistics course for students with a firm mastery of calculus, emphasizing the mathematical and conceptual bases of statistics, with a view to understanding the proper application of standard methods. The course includes thorough treatments of the Central Limit Theorem, the theory of estimation, hypothesis testing, and regression. MATH 345. Sample Materials
MATH 350
Applied Partially Differential Equations
3 Applied Partial Differential Equations is an introduction to the basic properties of partial differential equations and to some of the techniques that have been developed to analyze the solutions to these equations. The equations that describe the dynamics of waves, diffusion, flow and vibrations will be the main focus of this course. Initial value and boundary value problems of first and second-order equations will be considered. A geometric and analytic analysis of the solutions to these equations will be explored. Specific topics covered include classification of partial differential equations, well posed problems, the maximum principles for the diffusion equation and Laplace's equation, Dirichlet, Neumann and Robin boundary conditions, the method of characteristic coordinates, and separation of variables. The theory of Fourier Series will be introduced to the student and used to approximate solutions to inhomogeneous boundary value problems using the expansion method. Additional topics specific to the instructor's preference may be included in the course if time permits. MATH 240 and MATH 260 and MATH 310.
MATH 354
Vector Calculus
3 Differential and integral calculus of vector fields. Topics include line integrals, surface-area integrals, and smoothness; oriented curves and surfaces; circulation and flux of fields; Stokes' theorem; conservative, solenoidal fields; scalar, vector potentials; independence of path, surfaces, Maxwell's equations; and differential forms, exterior derivatives. MATH 240 and MATH 260.
MATH 356
Differential Geometry
3 Differential geometry of curves and surfaces in Euclidean spaces, as an introduction to the geometry of Riemannian manifolds. The course presents intrinsic and extrinsic properties, both from a local and global point of view. Topics include; plane and space curves, surfaces, metrics on surfaces, Gaussian curvature, surfaces of constant curvature, shape operator, mean curvature and minimal surfaces, vector fields on surfaces. MATH 242 and MATH 260.
MATH 358
Complex Analysis
3 Complex numbers; complex functions; power series; trigonometric functions; Moebius transformations; differentiation and integration of analytic functions; Cauchy's theorem; residues; singularities; meromorphic functions. MATH 240 or MATH 354.
MATH 360
Abstract Algebra I
3 Review of set theory and introduction to mathematical proof. Introduction to concepts and techniques of group theory, including but not limited to: symmetric groups, axiomatic definitions of groups, important classes of groups, subgroups, group homomorphisms, coset theory, normal subgroups, quotient groups, direct products, Sylow theorems. Possible applications include number theory, geometry, physics and combinatorics. MATH 260. Course offered in the fall only.
MATH 361
Abstract Algebra II
3 Introduction to ring and field theory. Topics include: commutative rings, ideals, integral domains, polynomial fields, the theory of extension fields, vector spaces, Galois groups, and the fundamental theorem of Galois theory. Applications include insolvability of certain higher degree polynomials, and other topics as time permits. MATH 360. Course is offered in the spring only.
MATH 370
History of Mathematics
3 This course traces the development of mathematics from ancient times up to and including 17th century developments in the calculus. Emphasis is on the development of mathematical ideas and methods of problem solving. Junior standing in mathematics or permission of instructor.
MATH 380
Introduction to Computational Algebraic Geometry
3 This course is an introduction to the geometry of affine algebraic varieties, with emphasis on the algebra-geometry dictionary and on computation via Groebner bases and Buchberger's algorithm. MATH 260 Sample Materials
MATH 384L
Game Theory and Evolution
3 Fundamental concepts of evolutionary game theory and their application in biology. Topics include: the strategy and payoff matrix, the game tree, strategic and extensive form games, symmetric games, Nash equilibria. Evolutionary game theory concepts are discussed for two-strategy games (Prisoner's Dilemma, Hawk-Dove) and three-strategy games (Rock-Scissors-Paper). Biological examples are studied, such as blood sharing in vampire bats, competition in bacteria, or the evolution of altruistic punishment.
MATH 390
Problem Solving Seminar
3 This course is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. MATH 280 or permission of instructor. Although this course is repeatable up to six credits, Mathematics majors (who are required to take a certain number of mathematics courses at the 300-level or higher) may count this course at most once toward their upper-level elective requirement. Sample Materials
MATH 420
Introduction to Combinatorics
3 This course is an introduction to combinatorics: a branch of mathematics that studies the existence, enumeration, analysis, and optimization of discrete structures that satisfy certain properties. Topics include counting distributions and colorings, sieve methods (such as inclusion-exclusion, for example), generating functions, partially ordered sets, and Ramsey theory. Additional topics may be included, such as permutation spaces, matching theory, and elementary graph theory. [MATH 141 and MATH 260] or Permission of Instructor.
MATH 425
Numerical Analysis
3 Approximations of roots. Finite differences. Interpolation. Numerical solutions of differential and algebraic equations. Numerical integration. MATH 141 and MATH 260.
MATH 440
General Topology
3 This course is an introduction to the abstract theory of continuity and convergence, otherwise known as general (or point-set) topology. Topics include metric spaces and topological spaces, continuity, subspaces, product and quotient spaces, sequences, nets and filters, separation and countability, compactness, connectedness, and the fundamental group. MATH 360 or permission of instructor.
MATH 447
Probability Models
3 This is an introductory course on probability models with a strong emphasis on stochastic processes. The aim is to enable students to approach real-world phenomena probabilistically and build effective models. The course emphasizes models and their applications over the rigorous theoretical framework behind them, yet critical theory that is important for understanding the material is also covered. Topics include: discrete Markov chains, continuous-time Markov chains, Poisson processes, renewal theory, Brownian motion and martingales. Optional topics: queuing theory, reliability theory, and random sampling techniques. Applications to biology, physics, computer science, economics, and engineering will be presented. MATH 345.
MATH 448
An Introduction to Statistical Learning
3 This course will provide an introduction to methods in statistical learning that are commonly used to extract important patterns and information from data. Topics include, linear methods for regression and classification, regularization, kernel smoothing methods, statistical model assessment and selection, and support vector machines. Unsupervised learning techniques such as principal component analysis and generalized principal component analysis will also be discussed. The topics and their applications will be illustrated using the statistical programing language R. [MATH 260 and MATH 345 and CS 110] or Permission of Instructor.
MATH 450
Real Analysis
3 A rigorous treatment of the calculus of functions of one real variable. Emphasis is on proofs. Includes discussion of topology of real line, limits, continuity, differentiation, integration and series. [MATH 310 or MATH 354] AND [MATH 280] Course offered in the spring only.
MATH 454
Analysis on Manifolds
3 This course is an introduction to the framework for modern advanced analysis. Topics include differentiable maps between Euclidean spaces, Implicit and Inverse Function Theorems, manifolds, differential forms, differentiation and integration on manifolds. Math 242 and Math 260
MATH 458
Theory of Numbers
3 Prime numbers; congruences and residues; approximation of real numbers by rationals; diophantine equations; other topics as time permits. MATH 260 or MATH/CS 320L or equivalent.
MATH 460
Topics in Geometry
3 Topics taken from classical Euclidean geometry and the non Euclidean geometries; projective geometry; lattices; finite geometries. MATH 260.
MATH 470
Mathematical Logic
3 Syntax and semantics of propositional and first-order predicate logic. Axiomatic theories and completeness. Brief discussion of incompleteness results. MATH 360 or MATH/CS 320L, or equivalent.
MATH 478
Independent Study
3 Work done by a student or group of students under faculty supervision on material not currently offered in a regularly scheduled course. Students wishing to undertake such work must first find a faculty member willing to supervise it; the work to be completed must be approved by the department chair. Permission of instructor.
MATH 480
Special Topics
3 An advanced course offering intensive study of selected topics in mathematics. A course offered as MATH 480 is an advanced undergraduate mathematics course being given for the first time and covering topics not available in current courses. Such a course is offered either to fulfill a one-time need or to try out material with the intention of developing a new course. Course content varies each semester and will be announced prior to registration. Permission of instructor. Sample Materials
MATH 490
Thesis Research
1-6 An opportunity for qualified, advanced students to work on a specialized research project under the guidance of a faculty advisor. Permission of Instructor. Although this course is repeatable up to six credits, Mathematics majors (who are required to take a certain number of mathematics courses at the 300-level or higher) may count this course at most once toward their upper-level elective requirement.


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University of Massachusetts Boston
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