Mathematics (Math)
27. Elementary Algebra (3)
Transition from arithmetic to symbolism and generalization of algebra,
fundamental operations, equations, formulas, sets, graphs. (See Duplication
of Courses.)
28. Plane Geometry (3)
Prerequisite: elementary algebra. POints, lines, angles, triangles,
polygons, circles; axioms, theorems, problems; proofs and constructions.
(See Duplication of Courses.)
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.
51. Elements of Modern Mathematics (3)
Prerequisite: two years high school algebra or Math 29. Logic, set theory,
probability, Markov chains, matrices, linear programming, inroduction to
differential calculus, applications to business, economics, psychology and
sociology. (2 lecture, 1 discussion hour)
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.. Definite integrals, indefinite integrations,
vectors, polar coordinates, solid analytic geometry, multiple integrals.
77. Mathematical Analysis III (4)
Prerequisite: Math 76. Partial derivatives, line integrals, Green's theorem,
Taylor's theorem, L'Hospital's rules, sequences, convergence tests for infinite
series, introduction to differential equations.
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)
(See Phil 110.)
111. Symbolic Logic II (3)
(See Phil 111.)
116. Theory of Numbers (3)
Prerequisite: Math 72 or 75. Divisibility, greatest common divisor, Euler's
function, continued fractions, congruences, quadratic residues, Diophantine
equations.
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.
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.
140. Arithmetic and Algebra of the Rational Number System (3)
Not open to mathematics majors. Meets general education mathematics require-
mcnt for elementary credential candidates. Prerequisite: elementary algebra
and geometry. Development of the rational number system and its subsystems
from the informal point of view; sets, relations and operations, equivalence
classes; definitions of number systems, isomorphism; algorithms for operations
with numbers; prime numbers and divisibility; ratios; applications.
151. Principles of Algebra (4) (Former Math 102)
Prerequisite: Math 76. Integral domains; ordered fields; rational, real,
and complex numbers; polynomials and theory of equations.
152. Linear Algebra (4) (Former Math 114)
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) (Former Math 115)
Prerequisite: Math 152. Group theory, field theory, elements of Galois theory.
161. Principles of Geometry (3) (Former Math 101)
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) (Former Math 160)
Prerequisite: Math 151 or 161. Synthetic and analytic projective geometry;
axioms; duality; perspective and projective correspondence; hannonic sets;
coordinatization; projective collineations and correlations; polarities
and conics; groups of projective, affine and Euclidean transformations.
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. Introduction to Complex Analysis (3)
Prerequisite: Math 171, or 81 and permission of instructor. Introduction
to com- plex analysis including Cauchy's integral theorem and formula, Taylor's
and Laurent's series, contour integration, elementary conformal mappings;
applications.
181. Differential Equations (3)
Prerequisite or concurrently: Math 172. Definition and classification of
differential equations; general, particular, and singular solutions; existence
theorems; theory and technique of solving cen= differential equations; applications.
182. Partial Differential Equations (3)
Prerequisite: Math 181. 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.
(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.
221. Advanced Numerical Analysis (3)
Prerequisite: Math 121. Linear equations and matrices; parabolic, hyperbolic,
and elliptic differential equations; constructive function theory.
251. Abstract Algebra (3)
Prerequisite: Math 153 or permission of instructor. Semi-groups, groups
with operators, rings, fields, lattices.
252. Linear Algebra (3) (Former Moth 232)
Prerequisite: Math 153. Vector spaces, linear transformations, sets of linear
trans- formations, 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)
Prerequisite or concurrently: Math 173 or 182. Study of geometry in Euclidean
space by means of calculus, including theory of cur-ves and surfaces, curvature
theory of surfaces, and intrinsic geometry on a surface.
271. Real Variables (3)
Prerequisite: Math 173. Theory of sets; cardinals; ordinals; function spaces,
linear spaces; measure theory; modern theory of integration and differentiation.
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)
Prerequisite: permission of instructor. Topics in modern mathematics
with special emphasis for teachers.