Mathematics (Math)
B. 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.)
C. Trigonometry (3)
Prerequisite: Math B. Concept of a function, sine and cosine functions,
tables and graphs, other trigonometric functions, identities and equations,
trigonometric functions of solution of triangles. (See Duplication of Courses.)
2. Mathematics of Finance (3)
Prerequisite: Math B or 2 years high school algebra. Development of mathematical
relations between investment and income; compound interest, annuities, sinking
fund, depreciation, amortization, and bond.
3. Mathematical Analysis I (5)
Prerequisite: two years of high school algebra, one year of plane geometry,
trigonometry. Analytic geometry, limits and derivatives, applications of
differentiation, differentials, elementary transcendental functions, the
definite integral.
4. Mathematical Analysis II (5)
Prerequisite: Math 3. Definite integrals, indefinite integrations, vectors,
polar coordinates, solid analytic geometry, multiple integrals.
6. Mathematical Analysis III (3)
Prerequisite: Math 4. Partial derivatives, line integrals, Green's theorem,
Taylor's theorem, L'Hospital's rules, sequences, convergence tests for infinite
series, introduction to differential equations.
10. Mathematics of the Elementary School (3)
Not open to students with credit in Ed 107. Prerequisite: elementary algebra
and geometry. For prospective teachers of elementary school mathematics.
The natural number system as developed through sets; algorithms for operations
with natural numbers; prime numbers and divisibility; ratios, rational numbers,
fractions; decimal fractions and percents.
21. Elementary Astronomy (3)
Prerequisite: elementary algebra and geometry. Nontechnical fundamental
principles and facts of astronomy; appreciation of the wonders of the universe.
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.)
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.
101. Principles of Geometry (3)
Prerequisite: Math 3. Fundamental concepts of synthetic geometry from
the modem point of view; axioms of collinearity, order, congruence; theorems
of Ceva, Menelaus, Desargues; loci; transformations of the plane; selected
topics from geometry of the circle and triangle.
102. Principles of Algebra (3)
Prerequisite: Math 4. Integral domains; ordered fields; rational, real,
and complex numbers; polynomials and theory of equations.
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.
106. Projective Geometry (3)
Prerequisite: Math 101 or 102. Synthetic and analytic projective geometry:
axioms; duality; perspective and projective correspondence; harmonic sets;
coordinization; projective couineations and correlations; polarities and
conics; groups of projective, affine and Euclidean transformations.
107. Probability and Statistics (3)
Prerequisite: Math 4. Introduction to statistics, mathematical development
of probability, measures of central tendency and variability, moments, normal
distribution, linear correlation.
108. Advanced Statistics (3)
Prerequisite: Math 107. Theory of sampling; problem of estimation; tests
of significance; statistical hypotheses; confidence limits; the t, F, and
chi-square distributions; analysis of variance and covariance; application
of certain tools and techniques.
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.)
114. Linear Algebra (4)
Prerequisite: Math 102. Group theory; vectors and vector spaces, transformation
of coordinates, linear transformations, geometry of real vector spaces,
matrices, algebra and matrices, eigenvalues, quadratic forms, unitary and
hermitian matrices.
115. Modern Algebra (3)
Prerequisite: Math 114. Determinants and canonical forms; Boolean algebra;
partial orderiiigs and lattices, transfinite arithmetic; rings and ideals;
algebraic number fields; Galois theory.
116. Theory of Numbers (3)
Prerequisite: Math 72 or 75. Divisibility, greatest common divisor, Euler's
function, continued fractions, congruences, quadratic residues, Diophantine
equations.
117. Advanced Engineering Mathematics (3)
Prerequisite: Math 6. Vectors and matrices; introduction to ordinary differential
equations, Laplace transforms, orthogonal functions, Fourier series; introduction
to functions of a complex variable; partial differential equations.
118A-B. Advanced Calculus (3-3)
Prerequisite: Math 7. The real number system; function theory, continuity,
differentiability; partial differentiation; multiple integrals; line and
surface integrals; Fourier series and integrals; infinite series.
119. Differential Equations (3)
Prerequisite: Math 6, Physics 4A. Definition and classification of differential
equations; general, particular, and singular solutions; existence theorems;
theory and technique of solving certain differential equations; applications.
121. Numerical Analysis I (3)
Prerequisite: Math 6, 102. Finite difference and Lagrangian interpolation
formulas; numerical solution of equations, systems of equations, and differential
equations.
130. Introduction to Modern Mathematics (3)
Prerequisite: Math B. Logic, set theory, probability, linear programniing,
Markov chains, applications to economics, psychology, and sociology.
190. Independent Study (1-3; max see reference)
See Regulations and Proceedures -- Independent Study.
(See Course Numbering System.)
Mathematics (Math)
200. Foundations of Mathematics (3)
Prerequisite: Math 102 or 110 or permission of instructor. Mathematical
logic with applications to the development of the real number system and
philosophy of mathematics.
202. Fundamental Concepts of Mathematics (3)
Prerequisite: Math 6 or 7. Fundamental notions regarding number theory,
number system, algebra of number fields; functions, limits, calculus, and
differential equations. Primarily for those planning to teach mathematics.
205. Functions of a Complex Variable (3)
Prerequisite or concurrently: Math 118A. Analytic functions, conformal mapping,
analytic continuation, meromorphic functions, contour integration and the
residue theorm, Laplace transform.
207. Real Variables (3)
Prerequisite or concurrently: Math 118B. Theory of sets; cardinals; ordinals;
function spaces, linear spaces; measure theory; theory of modern integration
and differentiation.
211. Point Set Topology (3)
Prerequisite or concurrently: Mah 205 or 207. 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.
215. Differential Geometry (3)
Prerequisite or concurrently: Math 118B or 122. 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.
221. Advanced Numerical Analysis (3)
Prerequisite: Math 121. Linear equations and matrices; parabolic, hyperbolic,
and elliptic differential equations; constructive function theory.
231. Rings and Fields (3)
Prerequisite: Math 115. Sets, groups, groups with operators, rings, fields,
factorization, Galois theory.
232. Linear Algebra (3)
Prerequisite: Math 231. Modules, representation theory, ideal theory, polynomial
ideals, real fields.
241. Seminar (3)
Prerequisite: two graduate courses in mathematics. Presentation of current
mathematical research in field of student's interest.
290. Independent Study (1-5)
See Regulations and Proceedures -- Independent Study.
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.