You are in the official 2000-2001 General Catalog
for California State University, Fresno.
Department of Mathematics
COURSES
- Mathematics (MATH)
- Mathematics (MATH) --- Graduate Courses
- Mathematics (MATH) --- In-Service Courses
Mathematics (MATH)
4R. Entry Level Mathematics (4)
Covers all topics in the ELM exam. (I) Data Interpretation, Counting, Probability
and Statistics (reading, interpreting, and manipulating data, the Multiplication
Principle, permutations and combinations, basic probability laws, means,
medians, and expected values); (II) Geometry (basic Euclidean geometry,
congruence and similarity, coordinate geometry, basic right angle trigonometry);
and (III) Algebra (manipulating algebraic expressions, solving equations
and inequalities, investigating functions and their graphs). CR/NC grading
only; not applicable towards baccalaureate degree requirements.
4RA. Entry Level Mathematics (3)
Arithmetic review; Algebra - manipulating algebraic expressions (polynomial),
solving equations and inequalities (linear), and investigating functions
and their graphs (linear); Geometry - basic Euclidean geometry, congruence
and similarity, coordinate geometry, and basic right angle trigonometry.
Note: MATH 4RA together with MATH 4RB is equivalent to MATH 4R. Enrollment
is limited to first-time freshmen who score 370 and below on the ELM exam.
CR/NC grading only; not applicable toward baccalaureate degree requirements.
(Formerly MATH ILR)
4RB. Entry Level Mathematics (3)
Prerequisite: MATH 4RA. Arithmetic review; Algebra - manipulating algebraic
expressions (rational and radical), solving equations and inequalities (quadratic),
and investigating functions and their graphs (quadratic); Data Interpretation,
Probability, and Statistics - reading, interpreting, and manipulating data,
the Multiplication Principle, permutations and combinations, basic probability
laws, means, medians, and expected values. Note: MATH 4RB together
with MATH 4RA is equivalent to MATH 4R. Enrollment is limited to first-time
freshmen who score 370 and below on the ELM exam. CR/NC grading only; not
applicable toward baccalaureate degree requirements. (Formerly MATH ILR)
4RL. Entry Level Mathematics 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.
5. Trigonometry (3)
Prerequisite: students must meet the ELM requirement. 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 meet the ELM requirement. 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)
10A. Structure and Concepts in Mathematics I (3)
Prerequisite: students must meet the ELM requirement. Designed for prospective
elementary school teachers. Development of real numbers including integers,
rational and irrational numbers, computation, prime numbers and factorizations,
and problem-solving strategies. Meets Area B4 G.E. requirement for liberal
studies majors.
10B. Structure and Concepts in Mathematics II (3)
Prerequisite: MATH 10A. Designed for prospective elementary school teachers.
Counting methods, elementary probability and statistics. Topics in geometry
to include polygons, congruence and similarity, measurement, geometric transformations,
coordinate geometry, and connections between numbers and geometry with selected
applications.
11. Elementary Statistics (3)
Prerequisite: students must meet the ELM requirement. 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. (CAN STAT 2)
14. Introduction to Discrete Mathematics (3)
No credit if taken after MATH 75. Prerequisite: students must meet the ELM
requirement. Set theory, relations and functions, logic, proof techniques,
number systems.
25. Mathematica (1)
Prerequisites: MATH 70, 71, 75 (may be taken concurrently) or permission
of instructor. In addition, students must meet the ELM requirement. Use
of Mathematica software as an exploratory tool in Mathematics. Examples
drawn from a broad range of Mathematics. CR/NC grading only.
41. Number Systems (3)
Not open to mathematics majors. Prerequisite: students must meet the ELM
requirement. Designed for elementary credential students. 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 and operations; algorithms for operations; prime numbers,
divisibility tests; ratios. (CAN MATH 4)
43. Elementary Problem Solving (3)
Prerequisite: students must meet the ELM requirement. The purpose of this
course is to develop problem-solving skills using elementary mathematics.
45. What is Mathematics? (3)
Prerequisite: students must meet the ELM requirement. Covers topics from
the following areas: (I) The Mathematics of Social Choice; (II) Management
Science and Optimization; (III) The Mathematics of Growth and Symmetry;
and (IV) Statistics and Probability. G.E. Foundation B4.
61. Geometry and the Imagination (3)
Prerequisite: students must meet the ELM requirement. Topics in Geometry.
May include, but is not restricted to, tilings and tessellations, regular
polyhedra in 3 and 4 dimensions, ruler and compass constructions, map coloring.
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 meet the ELM requirement. Functions
and graphs, limits, derivatives, antiderivatives, differential equations,
and partial derivatives with applications in the Life Sciences.
71. Elementary Mathematical Analysis I (3)
No credit if taken after MATH 70, 72, or 75. Prerequisite: students must
meet the ELM requirement. Review of algebra, real numbers, inequalities,
functions, graphs, finite induction, limits, differentiation of algebraic
functions and applications to extrema, mean value theorem, l'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. Prerequisites: MATH 71 and trigonometry. Analytic geometry and calculus
of polynomials, rational functions, transcendental functions; polar coordinates,
conic sections, integration and applications.
75. Mathematical Analysis I (4)
Two units of credit if taken after MATH 70; 3 units of credit if taken after
MATH 71; 2 units of credit if taken after MATH 72. Prerequisite: elementary
geometry, intermediate algebra, trigonometry, or MATH 6. In addition, students
must meet the ELM requirement. Inequalities, functions, graphs, limits,
continuity, derivatives, antiderivatives, the definite integral, and applications.
Using Mathematica software as an exploratory tool. G.E. Foundation B4. (CAN
MATH 18)
76. Mathematical Analysis II (4)
Prerequisite: MATH 75. Transcendental functions, techniques of integration,
improper integrals, conic sections, polar coordinates, infinite series.
Using Mathematica software as an exploratory tool. (CAN MATH 20)
77. Mathematical Analysis III (4)
Prerequisite: MATH 76. Vectors, three dimensional calculus, partial derivatives,
multiple integrals, Green's Theorem, Stokes' Theorem. Using Mathematica
software as an exploratory tool. (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. Using Mathematica software as
an exploratory tool.
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)
100. Exploring Mathematics (3)
Prerequisite: MATH 10B. A problem-solving approach to topics from game theory,
combinatorics, mathematical modeling, and finite geometries.
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 (may be taken 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 75. An informal
treatment of the theory of logical inference, statement calculus, truth-tables,
predicate calculus, interpretations 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 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.
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.
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.
133. Number Theory for Liberal Studies (3)
Prerequisite: completion of at least one university-level mathematics course
(MATH 5 or above). The historical development of the concept of number and
arithmetic algorithms. The magnitude of numbers. Basic number theory. Special
numbers and sequences. Number patterns. Modular arithmetic. (Formerly N
SCI 140T section)
134. Geometry for Liberal Studies (3)
Prerequisite: completion of at least one university-level mathematics
course (MATH 5 or above). The use of computer technology to study and explore
concepts in Euclidean geometry. Topics include, but are not restricted to,
properties of polygons, tilings, and polyhedra.
137. Exploring Statistics (3)
Prerequisite: at least one university-level mathematics course (MATH 5 or
above). Descriptive and inferential statistics with a focus on applications
to mathematics education. Use of technology and activities for student discovery
and understanding of data organization, collection, analysis, and inference.
138. Exploring Algebra (3)
Prerequisite: at least one university-level mathematics course (MATH 5 or
above). Designed for prospective school teachers who wish to develop a deeper
conceptual understanding of algebraic themes and ideas needed to become
competent and effective mathematics teachers.
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: MATH 76. 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 77. 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.
171. 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 171A)
172. Intermediate Mathematical Analysis II (4)
Prerequisite: MATH 171. 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 171. 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 total 6)
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, 171,
and 152. Independent investigation and presentation of an advanced topic
in mathematics. Satisfies the senior major requirement for the B.A. in Mathematics.
GRADUATE COURSES
(See Course Numbering System.)
Mathematics (MATH)
202. Fundamental Concepts of Mathematics (3)
Prerequisites: MATH 151, 161 and 171. 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: graduate standing or permission of instructor. Linear spaces
and spectral theory of operators.
224. Optimization Methods (3)
Prerequisite: graduate standing or permission of instructor. 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. 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; 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 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 total 6)
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.
IN-SERVICE COURSE
(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.
