MATHEMATICS — COURSES
“Q” Courses
Courses with a “Q” prefix meet the Quantitative Reasoning Requirement. This requirement may also be met in other ways. For complete information on the Quantitative Reasoning Requirement, see the CSM “Graduation Requirements” section of this catalog.
Mathematics Courses
MATH Q114
Quantitative Reasoning
For a complete description of this course, see the “First-year and Intermediate Seminars” section of this publication.
MATH 115
College Algebra
Designed primarily but not exclusively for students seeking a stronger foundation in algebra before taking MATH 129 or MATH 130. Topics include basic algebra concepts, linear equations and inequalities and inequalities, properties of functions, linear and quadratic functions, absolute value equations and inequalities, systems of equations.
: A suitable score in math placement test A or MATH 125.
: Mathematics and Computer Languages.
3 Lect Hrs, 3 Credits
MATH 125
Introductory Statistics
Topics include introductory statistics, covering descriptive statistics; introductory probability sufficient to enable development of inferential statistics; and inferential statistics.
: A suitable score in math placement test B or MATH Q114 or MATH 115.
: Mathematics and Computer Languages.
: Mathematics.
3 Lect Hrs, 3 Credits
MATH 129
Pre-Calculus for Management and Social Science Students
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.
Note: 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.
: A suitable score on the math placement test B only.
: Mathematics and Computer Languages.
3 Lect Hrs, 3 Credits
MATH 130
Precalculus
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.
Note: 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.
: A suitable score on the math placement test B only.
: Mathematics and Computer Languages.
: Mathematics.
3 Lect Hrs, 3 Credits
MATH 134
Managerial Calculus
A one-semester course in calculus, with particular emphasis on applications to economics and management. Topics covered include limits, continuity, derivatives, and integrals. 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.
: A suitable score on the mathematics placement test D or successful completion of MATH 129.
: Mathematics and Computer Languages.
3 Lect Hrs, 3 Credits
MATH 135
Survey of Calculus
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.
Note: 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. (Course offered in the spring only.)
: Successful completion of MATH 129 or MATH 130, or a suitable score on math placement test D.
: Mathematics and Computer Languages.
: Mathematics.
3 Lect Hrs, 3 Credit
MATH 140
Calculus I
The first in the sequence of calculus courses for science and math majors. Starts with the basic concepts of functions and limits. Topics covered include: derivatives and their applications, definite and indefinite integrals with applications to geometric and physical problems, and discussion of algebraic and transcendental functions.
Note: 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.
Prerequisite: A suitable score on math placement test C, or completion of MA 130 within the past semester with a grade of B or higher.
: Mathematics and Computer Languages.
: Mathematics.
4 Lect Hrs, 4 Credits
MATH 141
Calculus II
Continuation of MATH 140. Topics include transcendental functions, techniques of integration, applications of the integral, improper integrals, l’Hospital’s rule, sequences, and series. Please note: Because MATH 141 is the second part of the integrated calculus sequence, it should be taken as soon as possible after MATH 140.
: MATH 140 or equivalent.
: Mathematics and Computer Languages.
: Mathematics.
4 Lect Hrs, 4 Credits
MATH 240
Calculus III
Calculus of functions of several variables. Topics include partial derivatives, transformations, the derivative as a matrix, chain rule, directional derivatives, gradients, second derivatives; and multiple integrals, substitution rule, and Jacobians. Please note: Because MATH 240 is the final part of a three-semester calculus sequence, it should be taken as soon as possible after MATH 141.
: MATH 141.
: Mathematics and Computer Languages.
3 Lect Hrs, 3 Credits
MATH 260
Linear Algebra I
Elementary theory of vector spaces. Topics include linear independence, bases, dimension, linear maps and matrices, determinants, orthogonality, eigenvalues and eigenvectors.
: MATH 140
: Mathematics and Computer Languages.
3 Lect Hrs, 3 Credits
MATH 261
Linear Algebra II
Topics include the problem of similarity, Jordan canonical form, Euclidean and Hermitian spaces, orthogonality, normal operators, spectral theorem; and multilinear algebra, quadratic forms. (This course is offered as demand requires.)
: MATH 260.
: Mathematics and Computer Languages.
3 Lect Hrs, 3 Credits
MATH 303
Introduction to Mathematical Biology
Mathematical models of population growth and other biological processes. Use of math order linear difference equations will be used to model propagation of annuals 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.
3 Lect Hrs, 3 Credits
MATH 310
Applied Ordinary Differential Equations
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 either MATH 260 or PHYSIC 114.
3 Lect Hrs, 3 Credits
MATH L320 (CS L320)
Applied Discrete Mathematics
This is a cross-listing of CS 320. See the course description and prerequisites as they are given in the Computer Science Department section of this publication.
MATH 345
Probability and Statistics I
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.
3 Lect Hrs, 3 Credits
MATH 346
Probability and Statistics II
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. (This course is normally offered once in two years.)
: MATH 140, 141 and 345.
3 Lect Hrs, 3 Credits
MATH 350
Applied Partial Differential Equations
Study of heat flow and other physical problems and the partial differential equation problems that arise from them, using the mathematical techniques of separation of variables, fundamental solutions, superposition, and characteristics. Use of Dirac delta function; asymptotics. Classification of partial differential equations. (This course is normally offered every third semester, in rotation with MATH 354 and MATH 358.)
: MATH 240, MATH 260, and MATH 310.
3 Lect Hrs, 3 Credits
MATH 354
Vector Calculus
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. (This course is normally offered every third semester, in rotation with MATH 350 and MATH 358.)
: MATH 240 and MATH 260.
3 Lect Hrs, 3 Credits
MATH 358
An Introduction to Complex Analysis
Complex numbers; complex functions; power series; trigonometric functions; Moebius transformations; differentiation and integration of analytic functions; Cauchy’s theorem; residues; singularities; meromorphic functions. (This course is normally offered every third semester, in rotation with MATH 350 and MATH 354.)
: MATH 310 or MATH 354.
3 Lect Hrs, 3 Credits
MATH 360
Abstract Algebra I
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. (Course offered in the fall only.)
: MATH 260.
3 Lect Hrs, 3 Credits
MATH 361
Abstract Algebra II
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. (Course is offered in the spring only.)
: MATH 360.
3 Lect Hrs, 3 Credits
MATH 370
History of Mathematics
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. (This course is offered as demand requires.)
: Junior standing in mathematics or permission of instructor.
: Mathematics.
3 Lect Hrs, 3 Credits
MATH 425
Numerical Analysis
Approximations of roots. Finite differences. Interpolation. Numerical solutions of differential and algebraic equations. (This course is offered as demand requires.)
: CS 260, and either MATH 310 or 354, or permission of the instructor.
3 Lect Hrs, 3 Credits
MATH 450
An Introduction to Real Analysis
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. (Course offered in the spring only.)
: MATH 310 or MATH 354.
3 Lect Hrs, 3 Credits
MATH 458
Theory of Numbers
Prime numbers; congruences and residues; approximation of real numbers by rationals; diophantine equations. (Course offered in the spring only.)
: MATH 260 or CS 320 or equivalent.
3 Lect Hrs, 3 Credits
MATH 460
Survey of Geometry
Topics taken from classical Euclidean geometry and the non Euclidean geometries; projective geometry; lattices; finite geometries. (This course is normally offered at least once every three semesters.)
: MATH 260.
3 Lect Hrs, 3 Credits
MATH 470
Mathematical Logic
Syntax and semantics of propositional and first order predicate logic. Axiomatic theories and completeness. Brief discussion of incompleteness results.
: MATH 360 or CS 320, or equivalent.
3 Lect Hrs, 3 Credits
MATH 478
Independent Study
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.
3 Lect Hrs, 3 Credits
MATH 479
Independent Study See MATH 478.
MATH 480
Special Topics
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 department.
3 Lect Hrs, 3 Credits