UNDERGRADUATE COURSES
MATH 006. College Algebra I. 3 crs. An intensive college
algebra course that emphasizes manipulative algebra, solutions of
equations and inequalities, and certain elementary functions. Prereq:
Satisfactory score on mathematics placement examination or completion
of ACAD015 (Basic Math II).
MATH 007. Precalculus. 4 crs. Exponential and logarithmic
functions; trigonometry, and systems of equations. Students planning
to take 156 should take this course. It is not intended for those
students planning to take 026; they may take 010 instead. Prereq:
006, or satisfactory score on Mathematics Placement Examination.
MATH 009. Introduction to Statistics. 4 crs. A first course
in statistics which may be followed by more specialized statistics
offered by other departments of the University. Not intended for
students who have taken calculus. Majors desiring a course in statistics
should take 189, non-major should take 167. Prereq: 006 or satisfactory
score on Mathematics Placement Examination.
MATH 010. College Algebra II. 4 crs. Exponential and logarithmic
functions; matrix theory, combinatorics, and probability. Students
planning to take 026 should take this course. It is not intended
for students planning to take 156, who should, instead, follow 006
with 007. Prereq: 006, or satisfactory score on Mathematics Placement
Examination.
MATH 012. Patterns in Mathematics. 3 crs. Introduction to
the art, nature and applications of mathematics. Emphasis is placed
on mathematical patterns occurring in real life situations. The course
is not intended for students planning to take any Calculus course.
Prereq.: 006 or a satisfactory score on the Mathematics Placement
Examination.
MATH 020. Fundamental Concepts of Mathematics for Education I. 3
crs. Fundamental concepts of mathematics needed by elementary school
teachers. Prereq: Satisfactory score on Mathematics Placement Examination..
MATH 026. Applied Calculus. 4 crs. Limits; differentiation;
integration; introduction to differential equations; and functions
of several variables. Prereq: 007 or 010 or outstanding score on
Mathematics Placement Examination.
MATH 084, 085. Directed Readings in Honors for Sophomores. 1
cr. ea.
MATH 088,089. Directed Readings in Honors for Juniors. 1
cr. ea.
MATH 092, 093 . Senior Departmental Honors. . 3 crs. ea.
MATH 101. Proof and Problem Seminar I.1 cr. This course and
MATH102 are designed to help mathematics majors make the transition
from the Calculus sequence to more advanced and abstract courses,
and is to be taken early, when a student declares a major. The topics
are sets, relations, functions, proofs by induction and contradiction,
complex numbers, and binomial coefficients. Coreq: 156.
MATH 102. Proof and Problem Seminar II. 1 cr. A continuation
of 101. The topics of 101 are reinforced by going more deeply into
one of number theory, dynamics, probability, graph theory, or modeling.
Prereq: 101. Coreq: 157.
MATH150. Modern Geometry. 3 crs. Deductive reasoning through
the study of selected topics from Euclidean and non-Euclidean geometrics.
Prereq.: 157.
MATH 156. Calculus I. 4 crs. Limits, continuity, and the
derivative and integral of functions of one variable, with applications.
Prereq: 007 or outstanding score on Mathematics Placement Examination.
MATH 157. Calculus II. 4 crs. Continuation of 156, including
more integration, sequences, series, Taylor's theorem, improper integrals,
and L'Hospital's rule. Prereq.: 156.
MATH 158. Calculus III. 4 crs. Continuation of 157, including
calculus of functions of several variables, with applications. Prereq.:
157
MATH 159. Differential Equations. 4 crs. Elementary techniques
of ordinary differential equations, including slope fields, equilibria,
separation of variables, linear differential equations, homogeneous
differential equations, undetermined coefficients, bifurcations,
power series, Laplace transforms, systems, and numerical methods.
Prereq.: 157.
MATH 160. Advanced Calculus for Science and Engineering 3
crs. Vector calculus in several dimensions. Generalizations of fundamental
theorem of calculus. Stokes theorem, divergence theorem, Inverse
and implicit functions theorems. req. 158.
MATH 161, 162. Seminar 1-3 crs. each. Offered on demand;
seminars in various topics in mathematics.
MATH 164. Introduction to Numerical Analysis. 3 crs. Treats
numerical integration and numerical solution of differential equations,
numerical linear algebra, matrix inversion, characteristic values;
error propagation; and stability. Prereq.: 159.
MATH 165, 166. Directed Readings. 1-3 crs. each. Readings
under a faculty member whose approval is required for admission to
course.
MATH 168. Actuarial Science Laboratory I.1 cr. Systematic
methods and approaches for rapid and accurate solutions of problems
arising in elementary algebra, calculus, and analysis. Prereq.: Consent
of instructor or 158.
MATH 169. Actuarial Science Laboratory II.1 cr. Continuation
of 168 with the problems to be solved coming from thematical statistics.
Prereq.: Consent of instructor or 190.
MATH 180. Introduction to Linear Algebra. 3 crs. Vector spaces,
linear transformations, the Gram-Schmidt process, determinants, eigenvectors
and eigenvalues, diagonalization and applications. Prereq: 157.
MATH 181. Discrete Structures. 3 crs. Algebraic structures
applicable to computer science; semigroups, graphs, lattices, Boolean
algebras, and combinatorics. Prereq.: 157.
MATH 183. Intermediate Differential Equations. 3 crs. Initial
value problems, existence and uniqueness of solutions. Properties
of solutions boundary value problems, Sturm-Liouville systems, and
orthogonal expansions. Prereqs.: MATH 159 and 180.
MATH 184. Introduction to Number Theory. 3 crs. Elementary
algebraic number theory. Prereq.: 197.
MATH 185. Introduction to Complex Variables. 3 crs. Complex
numbers and their geometry, plane topology, limits, continuity, differentiation,
Cauchy-Riemann equations, analytic functions, series, Cauchy theorems,
contour integration, and residue theory. Prereq.: 195.
MATH 186. Introduction to Differential Geometry. 3 crs. Calculus
in Euclidean space, vector fields, geometry of surfaces, and curves.
Prereqs.: 158 and 180.
MATH 187. Introduction to Algebraic Topology. 3 crs. Complexes,
homology, surface topology, and the classical groups. Prereq.: 197
and 199.
MATH 189. Probability and Statistics I. 3 crs. Sample spaces,
random variables, distributions, expectation, independence, law of
large numbers. Prereq.: 158.
MATH 190. Probability and Statistics II. 3 crs. Continuation
of 189. Includes estimation, order statistics, sufficient statistics,
test of hypotheses, and analysis of variance. Prereq.: 189.
MATH 191. Foundations of Applied Mathematics. 3 crs. Introduction
to the concepts and methods of applied mathematics, including gravitational
motion, calculus of variations, Lagrange's and Hamilton's equations;
approximation techniques, partial differential equations, Fourier
series, and Fourier integrals. Prereqs.: 147,148,159.
MATH 192. Topics In Applied Mathematics. 3 crs. Topics are
selected from the following areas: combinatorics, computer science,
control theory, fluid dynamics, game theory, information theory,
mathematical biology, and statistical mechanics. Prereq.: 191. Prereq.:
permission of instructor.
MATH 193. Actuarial Science Seminar.3 crs. Treats life contingency,
or the theory of interest, or other applications of mathematics to
actuarial science as required. Prereq.: 190.
MATH 194. Introduction to Set Theory. 3 crs. Axiomatic foundations;
relations and functions; ordered and well-ordered sets; ordinals
and cardinals and axiom of choice with its equivalents. Prereq.:
195.
MATH 195. Introduction to Analysis I.3 crs. Set theory, logic,
real and complex numbers, introductory topology, and continuous function.
Required for mathematics majors. Prereq.:157.
MATH 196. Introduction to Analysis II. 3 crs. Sequences;
series; limits; continuity; uniform continuity and convergence; differentiation
and integration of functions of one variable. Prereq.: MATH 195.
MATH 197. Introduction to Modern Algebra I.3 crs. Groups,
rings, fields and homomorphisms. Prereq.: 180.
MATH 198. Introduction to Modern Algebra II.3 crs. Continuation
of 197, including isomorphism theorems, Cayley's theorem, the Sylow
theorems, p-groups, abelian groups, unique factorization domains,
and Galois theory. Prereq.: 197.
MATH 199. Introduction to General Topology. 3 crs. Topological
spaces; relative topology and subspaces, finite product spaces; quotient
spaces; continuous and topological maps; compactness; connectedness;
and separation axioms. Prereq.:157 and 195.
