A description of the mathematics
curriculum may be found in Specialization Descriptions.
MATH 009
Introductory Algebra (0)
A comprehensive review of fractions, percentages, operations
with signed numbers, and geometric formulas. Basic algebraic topics covered
include exponents, polynomials, and linear equations. Although this course
carries no credit toward any degree in the University System of Maryland,
its cost is equivalent to that of a 3-credit course.
MATH 102
College Math and Problem-Solving Techniques (3)
(Fulfills the prerequisite for MATH 107.) Prerequisites:
MATH 009 or satisfactory performance on a placement test. A study of problem-solving
techniques for math and statistics. Numbers and algebraic properties,
graphing skills, and applications drawn from a variety of areas (such
as statistics, computing, and discrete mathematics) are emphasized. Topics
include polynomials; factoring; exponents and their notation; linear,
quadratic, and other equations; and inequalities. Students may receive
credit for only one of the following courses: MATH 101 (not offered at
all sites), MATH 102, MATH 102M, or (former courses) MATH 199A or MATH
199M.
MATH 102M
College Math and Problem-Solving Techniques (4)
(For students whose academic progress is being blocked by
anxiety about their mathematics coursework. Fulfills the prerequisite
for MATH 107.) Prerequisites: MATH 009 or satisfactory performance on
a placement test. A study of problem-solving techniques for math and statistics.
Numbers and algebraic properties, graphing skills, and applications drawn
from a variety of areas (such as statistics, computing, and discrete mathematics)
are emphasized. Topics include polynomials; factoring; exponents and their
notation; linear, quadratic, and other equations; and inequalities. Students
may receive credit for only one of the following courses: MATH 101 (not
offered at all sites), MATH 102, MATH 102M, or (former courses) EDCP 108M,
MATH 199A, or MATH 199M.
MATH 105
Mathematics: Contemporary Topics and Applications (3)
Prerequisites: MATH 102 or satisfactory performance on a
placement test. A survey of contemporary topics in mathematics, covering
applications and projects. Topics include problem solving, sequences and
series, financial management, geometry, probability, and statistics.
MATH 107
College Algebra (3)
(The first course in the two-course series MATH 107–108.
An alternative to MATH 115 Pre-Calculus.) Prerequisites: MATH 102 or satisfactory
performance on a placement test. An introduction to equations, inequalities,
and absolute values and a study of functions and their properties, including
the development of graphing skills with polynomial, rational, exponential,
and logarithmic functions. Applications are also covered. Students may
receive credit for only one of the following courses: MATH 107 or MATH
115.
MATH 108
Trigonometry and Analytical Geometry (3)
(The second course in the two-course series MATH 107– 108.
An alternative to MATH 115 Pre-Calculus.) Prerequisites: MATH 107 or satisfactory
performance on a placement test. An introduction to trigonometric functions,
identities, and equations and their applications. Analytical geometry
and conic sections are covered. Additional topics may include matrices,
determinants, sequences, and series. Students may receive credit for only
one of the following courses: MATH 108 or MATH 115.
MATH 115
Pre-Calculus (3)
(Preparation for MATH 140 or MATH 220. Not open to students
who have completed MATH 140 or any course for which MATH 140 is a prerequisite.)
Prerequisites: MATH 102 or satisfactory performance on a placement test.
Explication of elementary functions and graphs. Topics include polynomials,
rational functions, exponential and logarithmic functions, and trigonometric
functions. Algebraic techniques preparatory for calculus are presented.
Students may receive credit for only one of the following courses: MATH
107– 108 or MATH 115.
MATH 140
Calculus I (4)
(Especially recommended for students specializing in mathematics)
Prerequisite(s): MATH 107–108, MATH 115, or satisfactory performance on
a placement test. An introduction to calculus. Major topics include functions,
the sketching of graphs of functions, limits, continuity, derivatives
and applications of the derivative, definite and indefinite integrals,
and calculation of area. Students may receive credit for only one of the
following courses: MATH 140 or MATH 220.
MATH 141
Calculus II (4)
(A continuation of MATH 140.) Prerequisite: MATH 140. A study
of integration and functions, with application, and coverage of other
topics. Focus is on techniques of integration, improper integrals, and
applications of integration (such as volumes, work, arc length, and moments);
inverse, exponential, and logarithmic functions; and sequences and series.
Students may receive credit for only one of the following courses: MATH
141 or MATH 221.
MATH 220
Elementary Calculus I (3)
(For students not specializing in mathematics.) Prerequisite:
MATH 107, MATH 115, or satisfactory performance on a placement test. A
presentation of the basic ideas of differential and integral calculus.
Emphasis is on elementary techniques of differentiation, as well as applications.
Students may receive credit for only one of the following courses: MATH
140 or MATH 220.
MATH 221
Elementary Calculus II (3)
(For students not specializing in mathematics.) Prerequisite:
MATH 140 or MATH 220. A study of differential and integral calculus. Emphasis
is on elementary techniques of integration and various applications. Students
may receive credit for only one of the following courses: MATH 141 or
MATH 221.
MATH 240
Introduction to Linear Algebra (4)
Prerequisite: MATH 141. An explanation of the basic
concepts of linear algebra. Topics include vector spaces, applications
to line and plane geometry, linear equations, and matrices, as well as
linear transformations, changes of basis, diagonalization, similar matrices,
Jordan canonical forms, eigenvalues, determinants, and quadratic forms.
Students may receive credit for only one of the following courses: MATH
240 or (former courses) MATH 400 or MATH 461.
MATH 241
Calculus III (4)
Prerequisites: MATH 141. An introduction to multivariable
calculus. Exposition covers vectors and vector-valued functions; partial
derivatives and applications of partial derivatives (such as tangent planes
and Lagrangian multipliers); multiple integrals; volume; surface area;
and the classical theorems of Green, Stokes, and Gauss.
MATH 246
Differential Equations (3)
Prerequisite: MATH 141. An introduction to the basic methods
of solving differential equations. Separable, exact, and especially linear
differential equations are addressed. The main techniques considered are
undetermined coefficients, series solutions, Laplace transforms, and numerical
methods. Students may receive credit only once under this course number.
MATH 301
Concepts of Real Analysis I (3)
(The first semester of a yearlong course.) Prerequisites:
MATH 240 and 241. An approach to real analysis. Subjects include sequences
and series of numbers, continuity and differentiability of real-valued
functions of one variable, the Riemann integral, sequences of functions,
and power series. Also discussed are the functions of several variables,
including partial derivatives, multiple integrals, line and surface integrals,
and the implicit-funtion theorem. Students may receive credit for only
one of the following courses: MATH 301 or (former course) MATH 410.
MATH 302
Concepts of Real Analysis II (3)
(The second semester of a yearlong course; continuation
of MATH 301.) Prerequisite: MATH 301. Further study of real analysis.
Students may receive credit for only one of the following courses: MATH
302 or (former course) MATH 411.
MATH 370
Actuarial Science (3)
Prerequisite: MATH 241. A study of the computation of rates
based on statistical probabilities. Focus is on measurement of interest,
force of interest, term-certain annuities, and mathematical techniques
in analyzing life insurance settlement options. Topics may also include
materials from the mathematics of compound interest in the associateship
examinations of various actuarial organizations.
MATH 381
Operations Research (3)
Prerequisite: MATH 240. An exploration of linear programming
models and applications, simplex algorithms, sensitivity analysis, integer
programming, and network flow models.
MATH 390
Mathematics of Communication (3)
Prerequisite: MATH 240. An overview of the mathematics
of electronic communication. Topics include signaling and modulation;
filtering and signal noise ratio; encoding for error correction/detection
and compression; Fourier analysis; congestion in networks, queuing, routing,
and flow control; and cryptography.
MATH 402
Algebraic Structures (3)
Prerequisite: MATH 240. An overview of groups, rings, integral
domains, and fields; detailed study of several groups; and exploration
of properties of integers and polynomials. Topics may include introduction
to computer algebra and Boolean algebra.
MATH 432
Point Set Topology (3)
Prerequisite: MATH 241. A survey of connectedness, compactness,
transformations, and homomorphisms. The concepts are applied to various
spaces. Particular attention is paid to the Euclidean plane. Students
may receive credit only once under this course number.
MATH 436
Modern Geometry (3)
Prerequisites: MATH 240 and 241. A survey of the basic concepts
of modern geometry. Topics include curves in the plane and Euclidean space;
surfaces in Euclidean space and orientability of surfaces; Gaussian and
mean curvatures; surfaces of revolution and ruled and minimal surfaces;
special curves on surfaces; Theorema Egregium; and the intrinsic geometry
of surfaces.
MATH 450
Logic for Computer Science (3)
(Also listed as CMSC 450. Accessible to advanced undergraduates
specializing in computer science.) Prerequisites: CMSC 150 and MATH 241.
Elementary development of prepositional logic (including the resolution
method) and first-order logic (including Hebrand’s unsatisfiability theorem).
Discussion covers the concepts of truth and interpretation; validity,
provability, and soundness; completeness and incompleteness; and decidability
and semidecidability. Students may receive credit for only one of the
following courses: CMSC 450, MATH 450, or (former courses) MATH 444 or
MATH 445.
MATH 463
Complex Variables (3)
Prerequisite: MATH 241. A survey of analytic functions, mapping
properties of the elementary functions, the algebra of complex numbers,
and the Cauchy integral formula. Further topics include conformal mapping
as well as theory of residues and its application to evaluation of integrals.
Students may receive credit only once under this course number.
MATH 466
Numerical Analysis (3)
Prerequisites: MATH 240 and 241. A study of various methods
of numerical analysis. Topics include solutions of equations in one variable,
interpolation and polynomial approximation, and numerical integration.
Also discussed are direct methods for solving linear systems and applications
to finance and actuarial science.
MATH 475
Combinatorics and Graph Theory (3)
(Also listed as CMSC 475.) Prerequisites: MATH 240 and 241.
An exploration of general enumeration methods, difference equations, and
generating functions. Focus is on elements of graph theory, matrix representations
of graphs, and applications of graph theory to transport networks. Matching
theory and graphical algorithms are also considered. Students may receive
credit for only one of the following courses: CMSC 475 or MATH 475.
