You are in the official 2008-2009 General Catalog
for California State University, Fresno.
You are in the official 2008-2009 General Catalog
for California State University, Fresno.
COURSES
Mathematics (MATH)
MATH 1RA. Developmental Mathematics I (3)
The first semester in a two semester sequence preparing students for college
level mathematics. See the online Schedule
of Courses for restrictions on enrollment based on the Entry Level Math
test. Properties of ordinary arithmetic, integers, rational numbers and
linear equations. CR/NC grading only; not applicable towards baccalaureate
degree requirements. F
MATH 1RB. Developmental Mathematics II (3)
Prerequisite: MATH 1RA. The second semester in a two semester sequence preparing
students for college level mathematics. Systems of linear equations, exponents,
rational expressions, polynomials and quadratic equations. CR/NC grading
only; not applicable toward baccalaureate degree requirements. S
MATH 3. College Algebra (3)
Prerequisite: students must meet the ELM requirement. Equations and inequalities;
rectangular coordinates; systems of equations and inequalities; polynomial,
rational, exponential, and logarithmic functions and their graphs; complex
numbers. FS
MATH 4R. Intermediate Algebra (3)
Prerequisite: see the online Schedule
of Courses for restrictions on enrollment based on the Entry Level Math
test. Covers radicals, rational exponents, quadratic equations, simultaneous
linear equations, graphing, inequalities, and complex numbers. CR/NC grading
only; not applicable towards baccalaureate degree requirements. FS
MATH 4RA. Intermediate Algebra (3)
Focuses on arithmetic review, linear equalities, inequalities, and graphing.
Note: MATH 4RA together with MATH 4RB is equivalent to MATH 4R. Enrollment
is limited to first-time freshmen who score 30 and below on the ELM exam.
CR/NC grading only; not applicable towards baccalaureate degree requirements.
MATH 4RB. Intermediate Algebra (3)
Prerequisite: MATH 4RA. Focuses on radicals, rational exponents, and quadratic
equations. Note: MATH 4RB together with MATH 4RA is equivalent to
MATH 4R. Enrollment is limited to first-time freshmen who score 30 and below
on the ELM exam. CR/NC grading only; not applicable towards baccalaureate
degree requirements.
MATH 4RL. Intermediate Algebra Laboratory (1)
Prerequisites: concurrently enrolled in MATH 4RA, 4RB, or 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.
MATH 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)
MATH 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)
FS
MATH 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 B4 G.E. requirement only for liberal
studies majors. FS
MATH 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. FS
MATH 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
or 75A and B take MATH 101. (CAN STAT 2) FS
MATH 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.
MATH 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. FS
MATH 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.
MATH 70. Calculus for Life Sciences (4)
No credit if taken after MATH 75 or 75A and B. Prerequisite: students must
meet the ELM requirement. Functions and graphs, limits, derivatives, antiderivatives,
differential equations, and partial derivatives with applications in the
Life Sciences. FS
MATH 75. Calculus I (4)
Prerequisite: passing score on the departmentŐs Calculus Readiness Test required prior to enrollment. In addition, students must meet the ELM requirement. Functions, graphs, limits, continuity, derivatives and applications, definite and indefinite integrals. G.E. Foundation B4. FS
MATH 75A. Calculus with Review IA (4)
Prerequisite: passing score on the department's Calculus Readiness Test
required prior to enrollment. In addition, students must meet the ELM requirement.
Functions, graphs, limits, continuity, derivatives, and applications, with
extensive review of algebra and elementary functions. FS
MATH 75B. Calculus with Review IB (4)
Prerequisite: MATH 75A. Further applications of derivatives and definite
and indefinite integrals, with extensive review of algebra and elementary
functions. With MATH 75A, equivalent to MATH 75. FS
MATH 76. Calculus II (4)
Prerequisite: MATH 75 or 75A and B. Techniques and applications of integration,
improper integrals, conic sections, polar coordinates, infinite series.
(CAN MATH 20) FS
MATH 77. Calculus III (4)
Prerequisite: MATH 76. Vectors, three-dimensional calculus, partial derivatives,
multiple integrals, Green's Theorem, Stokes' Theorem. (CAN MATH 22) FS
MATH 81. Applied Analysis (3)
Prerequisite: MATH 77. Introduction to ordinary linear differential equations
and linear systems of differential equations; solutions by Laplace transforms.
Solution of linear systems of equations; introduction to vector spaces;
eigenvalues and eigenvectors. Using computer software as an exploratory
tool. FS
MATH 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)
MATH 100. Exploring Mathematics (3)
Prerequisite: MATH 10B. A problem-solving approach to topics from game theory,
combinatorics, mathematical modeling, and finite geometries. FS
MATH 101. Statistical Methods (4)
Prerequisite: MATH 70 or 75 or 75A and B; 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. FS
MATH 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. F
MATH 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. S
even
MATH 109. Applied Probability (3)
Prerequisite: MATH 107. Introduction to stochastic processes and their applications
in science and industry. Markov chains, queues, stationary time series.
S odd
MATH 110. Symbolic Logic (3)
(Similar to PHIL 145; consult department.) Prerequisite: MATH 75 or 75A
and B. An informal treatment of the theory of logical inference, statement
calculus, truth-tables, predicate calculus, interpretations applications.
S
MATH 111. Transition to Advanced Mathematics (3)
Prerequisite: MATH 76. Introduction to the language and problems of mathematics.
Topics include set theory, symbolic logic, types of proofs, and mathematical
induction. Special emphasis is given to improving the student's ability
to construct, explain, and justify mathematical arguments. FS
MATH 114. Discrete Structures (3)
Prerequisite: MATH 111. Counting techniques, matrix algebra, graphs, trees
and networks, recurrence relations and generating functions, applied modern
algebra. F
MATH 116. Theory of Numbers (4)
Prerequisite: MATH 111. Divisibility theory in the integers, primes and
their distribution, congruence theory, Diophantine equations, number theoretic
functions, primitive roots, indices, the quadratic reciprocity law. FS
MATH 118. Graph Theory (3)
Prerequisite: MATH 111. Trees, connectivity, Euler and Hamilton paths, matchings,
chromatic problems, planar graphs, independence, directed graphs, networks.
S even
MATH 121. Numerical Analysis I (3)
Prerequisites: MATH 77 and CSCI 40. Zeros of nonlinear equations, interpolation,
quadrature, systems of equations, numerical ordinary differential equations,
and eigenvalues. Use of numerical software libraries. S
MATH 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. S
odd
MATH 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. F
MATH 133. Number Theory for Liberal Studies (3)
Prerequisite: MATH 10B or permission of instructor. 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. F
MATH 134. Geometry for Liberal Studies (3)
Prerequisite: MATH 10B or permission of instructor. 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.
S
MATH 137. Exploring Statistics (3)
Prerequisite: MATH 10B or permission of instructor. 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. F
MATH 138. Exploring Algebra (3)
Prerequisite: MATH 10B or permission of instructor. 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. S
MATH 143. History of Mathematics (4)
Prerequisite: MATH 75 or 75A and B. 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.
S
MATH 145. Problem Solving (3)
Prerequisite: MATH 111; EHD 50 (may be enrolled concurrently). 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. F
MATH 151. Principles of Algebra (4)
Prerequisite: MATH 111. Equivalence relations; groups, cyclic groups, normal
subgroups, and factor groups; rings, ideals, and factor rings; integral
domains and polynomial rings; fields and field extensions. FS
MATH 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. FS
MATH 161. Principles of Geometry (3)
Prerequisite: MATH 111. 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. S
MATH 165. Differential Geometry (3)
Prerequisite: MATH 111 or permission of instructor. 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. F
MATH 171. Intermediate Mathematical Analysis I (4)
Prerequisite: MATH 111. 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. FS
MATH 172. Intermediate Mathematical Analysis II (4)
Prerequisite: MATH 77 and 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. S
MATH 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. F
MATH 182. Partial Differential Equations (3)
Prerequisites: MATH 81 or 123. 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. S
even
MATH 190. Independent Study (1-3; max total 6)
See Academic Placement -- Independent
Study. Approved for RP grading.
MATH 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.
MATH 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.
(See Catalog Numbering System.)
Mathematics (MATH)
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.
MATH 216T. 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.
MATH 223. Principles and Techniques of Applied Mathematics (3)
Prerequisite: graduate standing or permission of instructor. Linear spaces
and spectral theory of operators.
MATH 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.
MATH 232. Mathematical Models with Technology (3)
Prerequisite: graduate standing in mathematics or permission of instructor.
A technology-assisted study of the mathematics used to model phenomena in
statistics, natural science, and engineering.
MATH 250. Perspectives in Algebra (3)
Prerequisite: graduate standing in mathematics or permission of instructor.
Study of advanced topics in algebra, providing a higher perspective to concepts
in the high school curriculum. Topics selected from, but not limited to,
groups, rings, fields, and vector spaces.
MATH 251. Abstract Algebra I (3)
Prerequisite: undergraduate abstract algebra. Groups, rings, integral domains,
and fields.
MATH 252. Abstract Algebra II (3)
Prerequisite: MATH 251. Rings and ideals, modules, linear and multilinear
algebras, representations.
MATH 260. Perspectives in Geometry (3)
Prerequisite: graduate standing in mathematics or permission of instructor.
Geometry from a transformations point of view. Euclidean and noneuclidean
geometries in two and three dimensions. Problem solving and proofs using
transformations. Topics chosen to be relevant to geometrical concepts in
the high school curriculum.
MATH 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.
MATH 270. Perspectives in Analysis (3)
Prerequisite: graduate standing in mathematics or permission of instructor.
An overview of the development of mathematical analysis, both real and complex.
Emphasizes interrelation of the various areas of study , the use of technology,
and relevance to the high school mathematics curriculum.
MATH 271. Real Variables (3)
Prerequisite: MATH 172. Theory of sets; cardinals; ordinals; function spaces,
linear spaces; measure theory; modern theory of integration and differentiation.
MATH 290. Independent Study (1-3; max total 6)
See Academic Placement -- Independent
Study. Approved for RP grading.
MATH 291T. Seminar (1-3; max total 6)
Prerequisite: graduate standing. Seminar covering special topics in
an area of mathematical research. (Formerly MATH 291)
MATH 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 RP
grading.
(See Catalog Numbering System.)
Mathematics (MATH)
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.
Mathematics
Degrees