Mathematics (Math)
ILR. ELM Basic Mathematics Skills (3-6)
Prepares students for the ELM exam and for Math 4. The course takes two
semesters and reviews arithmetic, elementary algebra, and geometry. Note:
Enrollment is limited to freshmen who score lower than 370 on the ELM exam.
CR/NC grading only; not applicable toward baccalaureate degree requirements.
AR. ELM Basic Mathematics Skills (3)
Develops problem solving skills in arithmetic (integers and rational numbers),
elementary algebra (exponents, roots, polynomials and rational expressions,
linear and quadratic equations, and graphing), and geometry (perimeters,
areas, volumes, triangle properties, parallelism, and perpendicularity).
CR/NC grading only; not applicable toward baccalaureate degree requirements.
ARL. Elementary Algebra Laboratory (1)
Prerequisites: concurrently enrolled in Math AR and assigned to laboratory
after taking placement examination. Laboratory does not count toward baccalaureate
degree. Extra review and practice with skills essential to success in elementary
algebra. CR/NC grading only; not applicable toward baccalaureate degree
requirements. (Formerly Math 1AR)
4R. Intermediate Algebra (3)
Prerequisites: elementary algebra and geometry. Radicals, rational exponents,
quadratic equations, simultaneous linear equations, graphing inequalities,
complex numbers in rectangular form, introduction to exponential and logarithmic
functions, applications. CR/NC grading only; not applicable toward baccalaureate
degree requirements. (See Duplication of Courses.)
4RL. Intermediate Algebra Laboratory (1)
Prerequisites: concurrently enrolled in Math 4R and assigned to laboratory
after taking placement examination. Laboratory does not count toward baccalaureate
degree. Extra review and practice with skills essential to success in intermediate
algebra. CR/NC grading only; not applicable toward baccalaureate degree
requirements. (Formerly Math 4AR)
5. Trigonometry (3)
Prerequisite: Students must take the ELM exam; students who do not pass
the exam must record a grade of C or better in a college-taught 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.)
(CAN MATH 8)
6. Precalculus (4)
Prerequisite: Students must take the ELM exam; students who do not pass
the exam must record a grade of C or better in a college-taught intermediate
algebra course. Basic algebraic properties of real numbers; linear and quadratic
equations and inequalities; functions and graphs; polynomials; exponential
and logarithmic functions; analytic trigonometry and functions; conics;
sequences, and series. (CAN MATH 16)
11. Elementary Statistics (3)
Prerequisite: Students must take the ELM exam; students who do not pass
the exam must record a grade of C or better in a college-taught intermediate
algebra course. Illustration of statistical concepts: elementary probability
models, sampling, descriptive measures, confidence intervals, testing hypotheses,
chi-square, nonparametric methods, regression. It is recommended that students
with credit in Math 72 or 75 take Math 101. General Education CORE, Quantitative
Reasoning. (CAN STAT 2)
14. Introduction to Discrete Mathematics (3)
No credit if taken after Math 75. Prerequisite: Students must take the ELM
exam; students who do not pass the exam must record a grade of C or better
in a college-taught intermediate algebra course. Set theory, relations and
functions, logic, proof techniques, number systems.
41. Number Systems (3)
Not open to mathematics majors. Prerequisite: Students must take the ELM
exam; students who do not pass the exam must record a grade of C or better
in a college-taught intermediate algebra course. Designed for elementary
credential candidates. 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. (CAN MATH 4)
43. Elementary Problem Solving (3)
Prerequisite: Students must take the ELM exam; students who do not pass
the exam must record a grade of C or better in a college-taught intermediate
algebra course. The purpose of this course is to develop problem solving
skills using elementary mathematics.
45. What is Mathematics? (3)
Prerequisite: Students must take the ELM exam; students who do not pass
the exam must record a grade of C or better in a college-taught intermediate
algebra course. Intended primarily for liberal arts students. Topics: mathematics
and social science, mathematics of shape and growth, statistics, mathematics
of management science and mathematics of computers. General Education CORE,
Quantitative Reasoning.
70. Mathematical Analysis for Life Sciences (4)
No credit if taken after Math 72 or 75; one unit of credit if taken after
Math 71. Prerequisite: Students must take the ELM exam; students who do
not pass the exam must record a grade of C or better in a college-taught
intermediate algebra course. Functions and graphs, limits, derivatives,
antiderivatives, differential equations, and partial derivatives with applications
in the Life Sciences. General Education CORE, Quantitative Reasoning.
71. Elementary Mathematical Analysis I (3)
No credit if taken after Math 70, 72, or 75. Prerequisite: Students must
take the ELM exam; students who do not pass the exam must record a grade
of C or better in a college-taught intermediate algebra course. Review of
algebra, real numbers, inequalities, function, graph, finite induction,
limit, differentiation of algebraic functions and applications to extrema,
mean value theorem, I'Hôpital's rule.
72. Elementary Mathematical Analysis II (3)
No credit if taken after Math 75; 2 units of credit if taken after Math
70. Prerequi sites: Math 71 and trigonometry. Analytic geometry and calculus
of polynomials, rational functions, transcendental functions; polar coordinates,
conic sections, integration and applications. General Education CORE, Quantitative
Reasoning.
75. Mathematical Analysis I (4)
No credit if taken after Math 72; 2 units of credit if taken after Math
71; 3 units of credit if taken after Math 70. Prerequisite: Students must
take the ELM exam. Additionally,beginning in the fall of 1994, a passing
score on the Precalculus Diagnostic Test or a grade of C or better in Math
6 will be required prior to registration. Inequalities, functions, graphs,
limits, continuity, derivatives, antiderivatives, the definite integral
and applications. General Education CORE, Quantitative Reasoning. (CAN MATH
18)
76. Mathematical Analysis II (4)
Prerequisite: Math 72 or 75. Transcendental functions, techniques of integration,
improper integrals, conic sections, polar coordinates, infinite series.
(CAN MATH 20)
77. Mathematical Analysis III (4)
Prerequisite: Math 76. Vectors, three dimensional calculus, partial derivatives,
multiple integrals, Green's Theorem, Stokes' Theorem. Use of the microcomputer
as an exploratory tool in the calculus. (3 lecture, 2 lab hours) (Computer
lab fee, $15) (CAN MATH 22)
81. Applied Analysis (4)
Prerequisite: Math 77. Introduction to ordinary linear differential equations;
solutions by power series and Laplace transforms. Solution of systems of
equations. Introduction to Fourier series. Use of the microcomputer as an
exploratory tool. (3 lecture, 2 lab hours) (Computer lab fee, $15)
90. Directed Study (1-3; max total 3)
Independently arranged course of study in some limited area of mathematics
either to remove a deficiency or to investigate a topic in more depth. (1-3
hours, to be arranged)
101. Statistical Methods (4)
Prerequisite: Math 70, 71, or equivalent; no credit if taken after Math
108. Application of statistical procedures to examples from biology, engineering,
and social science; one- and two-sample normal theory methods; chi-square,
analysis of variance, and regression; nonparametric methods. Computerized
statistical packages are used.
107. Introduction to Probability and Statistics (3)
Prerequisite: Math 77 or concurrently. Basic concepts required for applications
of probability theory; standard discrete and continuous models; random variables;
conditional distributions; limit theorems.
108. Statistics (3)
Prerequisite: Math 107. Criteria used for selecting particular procedures
of data analysis; derivation of commonly used procedures; topics from sampling,
normal theory, nonparametrics, elementary decision theory.
109. Applied Probability (3)
Prerequisite: Math 107. Introduction to stochastic processes and their applications
in science and industry. Markov chains, queues, stationary time series.
110. Symbolic Logic (3)
(Similar to Phil 145; consult department.) Prerequisite: 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.
114. Discrete Structures (3)
Prerequisite: Math 76. Counting techniques, matrix algebra, graphs, trees
and networks, recurrence relations and generating functions, applied modern
algebra.
116. Theory of Numbers (4)
Prerequisite: Math 72 or 75. Divisibility theory in the integers, primes
and their distribution, congruence theory, Diophantine equations, number
theoretic functions, primitive roots, indices, the quadratic reciprocity
law.
118. Graph Theory (3)
Prerequisite: Math 77. Trees, connectivity, Euler and Hamilton paths, matchings,
chromatic problems, planar graphs, independence, directed graphs, networks.
121. Numerical Analysis I (3)
Prerequisites: Math 77 and working knowledge of C, Fortran, or Pascal. Zeros
of nonlinear equations, interpolation, quadrature, systems of equations,
numerical ordinary differential equations, and eigenvalues. Use of numerical
software libraries.
121L. Numerical Analysis Laboratory (1)
Prerequisite: concurrently enrolled in Math 121. Optional computer laboratory
for Numerical Analysis I. Use of microcomputers to implement numerical algorithms.
(2 lab hours)
122. Numerical Analysis II (4)
Prerequisite: Math 121. Advanced topics from numerical linear algebra, function
approximation, fast Fourier transforms, and numerical partial differential
equations. Use of numerical software libraries. (3 lecture, 2 lab hours)
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.
124. Applied Matrix Analysis (3)
Prerequisite: Math 77. Matrix algebra, systems of equations, eigenvalues,
eigenvectors, diagonalizations, functions of ma-trices with applications
to differential equations, optimization, and Markov chains.
128. Applied Complex Analysis (3)
Prerequisite: Math 77. Analytic functions of a complex variable, contour
integration, series, singularities of analytic functions, the residue theorems,
conformal mappings; emphasis on engineering and physics applications.
131. Game Theory and Linear Programming (3)
Prerequisites: Math 72 and permission of instructor; or Math 76. Introduction
to linear programming, problem formulation, adaptation of the Dantzig simplex
algorithm to linear programming problems, duality theory, transportation
problems. Games of chance, strategy, minimax theorem for two-person zero-sum
games, relationship to linear programming.
136. Coding Theory (3)
Prerequisite: Math 114. Mathematical properties of error correcting codes;
information rate, error. detecting and error correcting capacities, encoding
and decoding algorithms. Linear, cyclic, Hamming, BCH, and Golay codes.
140. Applications of Calculus (4)
Prerequisite: intermediate algebra. Designed to give liberal arts students
the crucial ideas of calculus in an informal way. Applications in biology,
medicine, business, economics, psychology, engineering, and athletics will
be stressed. Open to all credential candidates except math majors.
142. General Mathematics (4)
Prerequisites: intermediate algebra, Math 140. The role of arithmetic, algebra,
and geometry in the development of modern mathematics will be studied, as
well as an informal treatment of rational number system. Introduction to
the nature of mathematics for students in arts, humanities, and social sciences.
Open to all credential candidates except math majors.
143. History of Mathematics (4)
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 modern times. Theorems with historical significance
will be studied as they relate to the development of modern mathematics.
145. Problem Solving (3)
Prerequisite: at least ine 100-200 series mathematics course. A study of
formulation of problems into mathematical form; analysis of methods of attack
such as specialization, generalization, analogy, induction, recursion, etc.
applied to a variety of non-routine problems. Topics will be handled through
student presentation.
151. Principles of Algebra (4)
Prerequisite: Math 76. Equivalence relations; groups, cyclic groups, normal
subgroups, and factor groups; rings, ideals, and factor rings; integral
domains and polynomial rings; fields and field extensions.
152. Linear Algebra (4)
Prerequisite: Math 151. Vector spaces, linear transformations, matrices,
determinants, eigenvalues and eigenvectors, linear functions, inner-product
spaces, bilinear forms, quadratic forms, orthogonal and unitary transformations,
selected applications.
161. Principles of Geometry (3)
Prerequisite: Math 77. 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.
165. Differential Geometry (3)
Prerequisite: Math 77. 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.
168. Geometric Topology (3)
Prerequisite: Math 77. Topology of surfaces the Euler characteristic, homeomorphism:
the fundamental group, Vector fields on surfaces, knot theory and introduction
to differentiable manifolds.
171A. Intermediate Mathematical Analysis I (4)
Prerequisite: Math 77. Sets, real numbers as a complete ordered field, its
usual topology, functions of a real variable, limits, continuity, uniform
continuity, differentiability, generalized mean value theorem, Riemann integrals,
series of functions, uniform convergence, and Fourier series of integrable
functions. (Formerly Math 171)
171B. Intermediate Mathematical Analysis I (4)
Prerequisite: Math 171A. Analytic functions of a complex variable, contour
integration, series, singularities of analytic functions, the residue theorems,
conformal mappings.
172. Intermediate Mathematical Analysis II (4)
Prerequisite: Math 171A. Differentiation of functions of several variables,
applications of partial differentiation, functions of bounded variation,
rectifiable curves, theory of Riemann-Stieltjes integration, multiple integrals
and line integrals, improper Riemann-Stieltjes integrals. Inverse and implicit
function theorems.
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 Academic Placement -- Independent Study. Approved for SP grading.
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.
198. Senior Project (3)
Prerequisites: senior standing or permission of instructor; Math 151, 171A
and 124 or 152. Independent investigation and presentation of an advanced
topic in mathematics. Satisfies the senior major requirement for the B.A.
in Mathematics.
(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.
224. Optimization Methods (3)
Prerequisite: Math 123. Techniques for optimizing static and dynamic systems,
calculus of variations, Hamiltonian canonical form, maximum principle, with
applications.
228. Functions of a Complex Variable (3)
Prerequisite: Math 128, 171B. Representation theorems of Weierstrass and
Mittag-Leffler, normal families, conformal mapping and Riemann mapping theorem,
analytic continuation, Dirichlet problem.
251. Abstract Algebra I (3)
Prerequisite: undergraduate abstract algebra. Groups, rings, integral domains,
and fields.
252. Abstract Algebra II (3)
Prerequisite: Math 251. Rings and ideals, modules, linear and multilinear
algebras, representations.
263. Point Set Topology (3)}
Prerequisite: Math 172. Basic concepts of point set topology, set theory,
topological spaces, continuous functions; connectiv-ity, 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 172. 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).
290. Independent Study (1-3; max see reference)
See Academic Placement -- Independent Study. Approved for SP grading.
291. Seminar (3)
Prerequisite: graduate standing. Presentation of current mathematical research
in field of student's interest.
298. Research Project in Mathematics (3)
Prerequisite: graduate standing. Independent investigation of advanced character
as the culminating requirement for the master's degree. Approved for SP
grading.
(See Course Numbering System.)
Mathematics (Math)
302. Topics in Mathematics for Teachers (1-3; max total 6 if
topic not repeated)
Prerequisite: permission of instructor. Topics in modern mathematics with
special emphasis for teachers.