Mathematics (Math)
29. Intermediate Algebra (3)
Prerequisite: elementary algebra and geometry. Sets, functions,
graphs, quadratic equations, inequalities, simultaneous equations,
matrices and determinants, mathematical induction, binomial theorem,
progressions, exponents and logarithms. (See Duplication of Courses.)
30. Trigonometry (3)
Prerequisite: intermediate algebra course. Concept of a function,
sine and cosine functions, tables and graphs, other trigonometric
functions, identities and equations. Trigonometric functions of
angles, solution of triangles. (See Duplication of Courses.)
40. Elements of Statistics (3)
Not open to students with credit in MAth 107, 109. Prerequisite:
elementary algebra and geometry. Organization of data, descriptive
measures, sampling, statistical inference, testing hypotheses,
chi-square, correlation and regression.
41. Number Systems I (3) (Former Math 140)
Not open to mathematics majorsor to students with credit in Math
141; designed for elementary credential. Prerequisite: elementary
algebra and geometry. Development of rational number system and
its subsystems from the informal point of view; sets, relations
and operations, equivalence classes; definitions of number systems
and operations; algorithms for operations; prime numbers, divisibility
tests; ratios.
51. Elements of Modern Mathematics (3)
Prerequisite: two years high school algebra or Math 29. Logic,
set theory, vectors and matrices, linear programming, permutations
and combinations, probability, Markov chains, applications to
business and social sciences.
71. Elementary Mathematical Analysis I (3)
Prerequisite:two years high school algebra one year high school
geometry. Review of algebra, analytic geometry, introduction to
set theory, mathematical induction, vectors, complex numbers,
limits, derivatives. (2 lecture, 1 discussion hour)
72. Elementary Mathematical Analysis II (3)
Prerequisite: Math 71 and trigonometry. Applications of differentiation,
polynomials, rational fractions, trigonometric functions, exponential
and logarithmic functions, conic sections, definite integral.
(2 lecture, 1 discussion hour)
75. Mathematical Analysis I (4)
Not open to students with credit in Math 72; one unit allowed
for students with credit in Math 71. Prerequisite: two years of
high school algebra, one year of plane geometry and trigonometry.
Analytic geometry, functions, limits and derivatives, applications
of the derivative, anti-derivative, the definite integral.
76. Mathematical Analysis II (4)
Prerequisite: Math 72 or 75. Applications of the definite integral,
transcendental functions, techniques of integration, polar coordinates,
conic sections, multiple integrals.
77. Mathematical Analysis III (4)
Prerequisite: Math 76. Vectors, improper integrals, three dimensional
analytical geometry, functions of several variables, infinite
series.
81. Advanced Engineering Mathematics (3)
Prerequisite: Math 77. Vector functions, gradient line, surface
and volume integrals, Green's and Stoke's theorems. Introduction
to complex variables; introduction to linear differential equationswith
constant coefficients; solution by series, LAplace transforms.
Introduction to Fourier series; matrices.
103. History of Mathematics (3)
Prerequisite: Math 72 or 75. History of the development of mathematical
concepts in algebra, geometry, number theory, analytical geometry,
and calculus from ancient times through the 17th century, and
selected topics from more recent times.
107. Probability and Statistics (3)
Prerequisite: Math 171. Theory of probability and mathematical
statistics, introduction to estimation theory and sets of simple
hypotheses.
108. Advanced Statistics (3)
Prerequisite: Math 107. Estimation theory and sampling, tests
of simple and composite hypotheses.
109. Probability (3)
Prerequisite: Math 171. Axiomatic development of the theory of
probability, discrete and absolutely continuous probability distributions,
Markov chains, limit theorems.
110. Symbolic Logic (3)
rerequisite: Math 71 or 75. An informal treatment of the theory
of logical inference, statement calculus, truth-tables, predicate
calculus, interpretations applications.
111. Theory of Sets (3)
Prerequisite: Math 71 or 75. Set theory from an informal axiomatic
foundation, relations and functions, cardinal numbers, ordinal
numbers, applications.
116. Theory of Numbers (3)
Prerequisite: Math 72 or 75. Divisibility, greatest common divisor,
Euler's function, continued fractions, congruences, quadratic
residues, Diophantine equations, different forms of the Prime
Number Theorem, Mobius inversion formula.
121. Numerical Analysis I (3)
Prerequisites: Math 77, 152..Finite differences and Lagrangian
interpolation formulatas; numerical solution of equations, systems
of equations, and differential equations; principles of coding
and programming computers.
123. Topics in Applied Mathematics (3)
Prerequisite: Math 77. Vector spaces and linear transformations,
eigenvalues and eigen functions. Special types of linear and nonlinear
differential equations; solution by series. Fourier transforms.
Special functions, including gamma, hypergeometric, Legendre,
Bessel, Laguerre, and Hermite functions. Introduction to partial
differential equations.
131. Game Theory and Linear Programming (3)
Prerequisites: Math 72 and permission of instructor; or Math 76.
Games of strategy, normal form of a game, minimax theorem for
two-person games, n-person games, solutions of n-person games
and equilibrium points linear programming, applications.
141. Number Systems II (3)
Prerequisite: Math 41 or 71. Especially recommended for prospective
teachers. and minors. Development of the real number system and
its subsystems from the formal point of view. Mathematical induction
and definition by recursion. Axiomatic development of the various
number systems and their interrelation.
151. Principles of Algebra (4)
Prerequisite: Math 76 or 141. Rings,integral domains and polynomials;
fields.
152. Linear Algebra (4)
Prerequisite: Math 151. Linear transformations, matrices, determinants,
linear functionals, bilinear forms, quadratic forms, orthogonal
and unitary transformations, selected applications of linear algebra.
153. Modern Algebra (3)
Prerequisite: Math 152. Group theory, field theory, elements of
Galois theory.
161. Principles of Geometry (3)
Prerequisite: Math 72 or 75. The classical elliptic, parabolic,
and hyperbolic geometries developed on a framework of incidence,
order and separation, congruence; coordinatization. Theory of
parallels for parabolic and hyperbolic geometries. Selected topics
of modern Euclidean geometry.
162. Projective Geometry (3)
Prerequisite: Math 77. Synthetic and analytic projective geometry;
axioms; duality; perspective and projective correspondence; harmonic
sets; coordinalization; projective collineations and correlations;
polarities and conics; groups of projective, affine and Euclidean
transformations
165. Differential Geometry (3)
Prerequisite: Math 77, 152. Study of geometry in Euclidean space
by means of calculus, including theory of curves and surfaces,
curvature, theory of surfaces, and intrinsic geometry on a surface.
171. Intermediate Mathematical Analysis I (4)
Prerequisite: Math 77. The complete and ordered foeld and its
usual topography; extensions to the plane; continuity and uniform
continuity; characterization of the differential; extended mean
value theorem; intermediate value property of derivatives; characterization
of Riemann integrable functions as functions continuous almost
anywhere.
172. Advanced Calculus I (3)
Prerequisite: Math 171. The real number system; function theory,
continuity, differentiability; partial differentiation.
173. Advanced Calculus II (3)
Prerequisite: Math 172. Multiple integrals; line and surface integrals;
Fourier series and integrals; infinite series.
174. Complex Analysis (3)
Prerequisite: Math 77. Analytic functions of a complex variable,
contour integration, series, singularities of analytic functions,
the residue theorems with applications to the definite integral.
181. Differential Equations (3)
Prerequisite: Math 81 or 123. Definition and classification of
differential equations; general, particular, and singular solutions;
existence theorems; theory and technique of solving certain differential
equations: phase plane analysis, elementary stability theory;
applications.
182. Partial Differential Equations (3)
Prerequisites: Math 81 or 123, and 171A. Classical methods for
solving partial differential equations including separation of
variables, Green's functions, the Riemann-Volterra method and
Cauchy's problem for elliptic, parabolic, and hyperbolic equations;
applications to theoretical physics.
190. Independent Study (1-3; max see reference)
See Regulations and Procedures -- Independent Study.
191T. Proseminar (1-3; max total 9)
Prerequisite: permission of instructor. Presentation of advanced
topics in mathematics in the field of the student's interest.
(See Course Numbering System.)
Mathematics (Math)
202. Fundamental Concepts of Mathematics (3)
Prerequisites: Math 151, 161 and 171A. Fundamental notions regarding
number theory, number systems, algebra of number fields; functions.
210. Foundations of Mathematics (3)
Prerequisite: Math 110 or 151. Formal introduction to theories
of inference, first order theories, completeness metatheorems,
consistency metatheorems, decision problems.
216. Topics in Number Theory (3; max total 6)
Prerequisite: Math 116. An investigation of topics having either
historical or current research interest in the field of number
theory.
221. Advanced Numerical Analysis (3)
Prerequisite: Math 121. Linear equations and matrices; parabolic,
hyperbolic, and elliptic differential equations; constructive
function theory.
223. Principles and Techniques of Applied Mathematics (3)
Prerequisite: Math 123. Linear spaces and spectral theory of operators.
251. Abstract Algebra I (3)
Prerequisite: Math 153 or permission of instructor. Semi-groups,
groups with operators, rings, fields, lattices.
252. Abstract Algebra II (3)
Prerequisite: Math 153, 251. Vector spaces, linear transformations,
sets of linear transformations, Euclidean and unitary spaces,
infinite dimensional vector spaces.
263. Point Set Topology (3)
Prerequisite: Math 172. Basic concepts of point set topology,
set theory, topological spaces, continuous functions; connectivity,
compactness and separation properties of spaces. Topics selected
from function spaces, metrization, dimension theory.
265. Differential Geometry (3)
Prerequisites: Math 165, 172. Study of geometry of curves and
surfaces in Euclidean space; including an introduction to Riemannian
geometry and theory of manifolds.
271. Real Variables (3)
Prerequisite: Math 173. Theory of sets; cardinals; ordinals; function
spaces, linear spaces; measure theory; modern theory of integration
and differentiation.
272. Functional Analysis (3)
Prerequisite: Math 271. The Lebesgue-Stieltjes integral and its
generalizations, integral equations, Hilbert and Banach spaces,
linear transformations (bounded and unbounded).
274. Functions of a Complex Variable (3)
Prerequisite: Math 171, 174. Representation theorems of Weierstrass
and Mittag-Leffler, normal families, conformal mapping and Riemann
mapping theorem, analytic continuation, Dirichlet problem.
290. Independent Study (1-3; max see reference)
See Regulations and Procedures -- Independent Study.
291. Seminar (3)
Prerequisite: graduate standing. Presentation of current mathematical
research in field of student's interest.
299. Thesis (2-6; max total 6)
Prerequisite: See Criteria for Thesis and Project. Preparation,
completion, and submission of an acceptable thesis for the master's
degree.
(See Course Numbering System.)
Mathematics (Math)
302. Topics in Mathematics for Teachers (3; max total
6 if topic not repeated)