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.)
1. Mathematical Analysis (3)
Prerequisites: intermediate algebra and trigonometry. Algebraic-rapid review
of fundamentals, graphs, quadratic equations, exponents, theory of logarithms,
third order determinants, systems of equations, binomial theorem. Trigonometric-functions,
special angles, identities, conditional equations, reduction formulas, multiple
and half angles.
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. Analytic Geometry (5)
Prerequisites: Math. B, C. Functions and their graphs, straight line
and plane, conic sections, surfaces; graphs of trigonometric, logarithmic
and exponential functions; development of algebraic techniques; introduction
to calculus.
4. Calculus I (5)
Not open to students with credit in former Math. 4A. Prerequisite: analytic
geometry. Limits, theory and technique of differentiation, differentials,
law of the mean, inverse differentiation, definition and theory of the definite
integral, technique of integration; applications.
4A. Integral Calculus (3)
For students with 3 units credit in Math. 3b (differential calculus). Students
with credit in Math. 4 (Calculus I) should take Math. 6. Further application
of the derivative and differential, inverse of differentiation, definition
and theory of integrals, technique of integration; applications.
6. Analytic Geometry and Calculus II (3)
Prerequisite: Math. 4. Infinite series, partial derivatives, multiple integrals;
applications.
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.)
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.
110. Symbolic Logic (3)
(See Phil 110.)
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.
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.
120. Vector Analysis (3)
Prerequisites: Math 6; Physics 2A or 4A. Algebra and calculus of vectors,
line integrals, surface integrals; Green's theorem, Gauss' theorem, Stokes'
theorem; introduction to tensors; applications to geometry and dynamics.
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.
190. Independent Study (1-5)
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.
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.