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. Symbolic Logic II (3)
Prerequisite: Math 110 or permission of instructor. 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 (3)
Prerequisite: Math 171. The real number system; function theory, continuity,
differentiability; partial differentiation.
173. Advanced Calculus (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 (3)
Prerequisite: Math 153 or permission of instructor. Semi-groups, groups
with operators, rings, fields, lattices.
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)