You are in the official 1985-86 General Catalog for California State University, Fresno.

COURSES

 

Mathematics (Math)

1. Elementary Algebra (3)
Fundamental operations, linear equations, polynomials, factoring, rational expressions, graphing of linear equations, introduction to inequalities, quadratic equations, and systems of linear equations. CR/NC grading only. (See Duplication of Courses)

1AR. Elementary Algebra Laboratory (1)
Prerequisite; concurrently enrolled in Math 1 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.

2R. Elementary Geometry (3)
Prerequisite; elementary algebra. Postulates concerning points, lines, planes. Definitions. Congruence; properties of triangles. Parallel lines. Properties of quadrilaterals. Area formulae. Similar figures. Circles. Volumes of certain solids. CR/NC grading only; not applicable toward baccalaureate degree requirements.

4A. Intermediate Algebra (3)
Prerequisite: 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. )

4AR. Intermediate Algebra Laboratory (1)
Prerequisite: 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 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.)

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.

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.

11L. Elementary Statistics Laboratory (1)
Concurrent enrollment in Math 11. (Not required for Math 11.) Computational techniques pertinent to elementary statistics with emphasis on calculator programming and formula derivation.

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.

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.

51. Elements of Modern Mathematics (3)
Prerequisite: passing score on the Entry Level Mathematics (ELM) Exam and intermediate algebra. Logic, set theory, vectors and matrices, linear programming, permutations and combinations, probability, Markov chains, applications to business and social sciences.

52. Elementary Linear Algebra (3)
Prerequisite: passing score on the Entry Level Mathematics (ELM) Exam and intermediate algebra. Elementary properties of matrices, determinants; systems of linear equations; linear transformations.

70. Mathematis 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.

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.

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.

76. Mathematical Analysis II (4)
Prerequisite: Math 72 or 75. Transcendental functions, techniques of integration, improper integrals, conic sections, polar coordinates, introduction to vectors.

77. Mathematical Analysis III (4)
Prerequisite: Math 76. Three dimensional calculus, partial derivatives, multiple integrals, infinite series, and applications. (

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)

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.

102. Sampling Theory and Methods (3)
Prerequisite: one semester of statistics, and Math 70 or 72 or 75. Basic concepts of sampling; probability sampling, stratification, clusters, single and multiple-stage designs; estimation procedures, non- sampling errors; illustrations from agriculture, biology, and social sciences.

103. Linear Statistical Models and Their Application (4)
Prerequisite: Math 101. Elements at matrix algebra. Components of experimental design. Common linear statistical models including factorial designs, split-plot, Latin square. Multiple regressional analysis, residual analysis, path diagrams. Analysis including both continuous and classification variables. Simple, multiple and partial correlation.

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)
rerequisite: 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 (3)
Prerequisite: Math 72 or 75. Divisibility, greatest common divisor, Euler's function, continued fractions, congruences, quadratic residues, Diophantine equations, different forms of the Prime Number Theorem, Mobius inversion formula.

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.

122. Numerical Analysis II (3)
Prerequisite: Math 121. Advanced topics from numerical linear algebra, function approximation, fast Fourier transforms, and numerical partial differential equations. 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.

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. Complex Analysis (3)
Prerequisite: Math 77. Analytic functions of a complex variable, contour integration, series, singularities of analytic functions, the residue theorems, conformal mappings; applications to engineering and physics.

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.

132. Mathematical Methods of Operations Research (3)
Prerequisite: Math 131 or permission of instructor. Simplex method, parametric programming, goal programming, dynamic programming, integer programming, nonlinear programming, and network models, with applications.

132L. Mathematical Methods of Operations Research (1)
Concurrent enrollment in Math 132. (Not required for Math 132.) Use of computers in setting up and solving problems in operations research.

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.

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. Groups, cyclic groups, normal subgroups; rings,integral domains and polynomials; fields.

152. Linear Algebra (4)
Prerequisite: Math 151. Linear transformations, matrices, determinants, linear functionals, bilinear forms, quadratic forms, orthogonal and unitary transformations, selected applications of linear algebra.

153T. Topics in Algebra (3)
Prerequisite: Math 151. Topics may include such algebraic theories as Galois Theory, permutation groups, modules, lattices, etc.

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.

167. Catastrophe Theory (3)
Prerequisite: Math 77. Structural stability, morphogenesis and Thorn's classification of the seven elementary catastrophes with applications to the physical, biological and social sciences.

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.

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.

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.

173T. Topics in Real Analysis (3)
Prerequisite: Math 172. Topics will vary according to needs and interests of students. May include elementary measure theory. Fourier series and integrals; Dirac delta function and elementary distribution theory.

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.

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.



GRADUATE COURSES

(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.

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 (3; max total 6 if topic not repeated)


 

Computer Science (C Sci)

10. Introduction to BASIC Programming (1)
Prerequisite: elementary algebra. Introduction to structured programming techniques using the programming language BASIC. Topics include input/output, branching, looping, subroutines, and computer graphics. No prior experience required.

20. Introduction to Computer Programming (4)
Prerequisite; ELM Exam, intermediate algebra and trigonometry. Introduction to programming in FORTRAN with emphasis on program design, debugging and documentation. Elementary applications and structured programming for algorithm development. (3 lecture, 2 lab hours)

40. Computer Programming I (4)
Prerequisites: ELM exam, intermediate algebra, and trigonometry. Introduction to problem solving, algorithm development, procedural and data abstraction; program design, coding, debugging, testing, and documentation; programming language Pascal. No credit if taken after C Sci 20. (3 lecture, 2 lab hours)

41. Computer Programming II (4)
Prerequisite: C Sci 40. Programming methodology, program correctness. Review of data types. Data structures: linear and nonlinear structures, files. Implementation of data structures. Recursion. Searching and sorting. (3 lecture, 2 lab hours)

112. Assembly Language Programming (4)
Prerequisite: C Sci 41. Boolean algebra, combinational logic, elementary digital circuits. A comparison of several assembly languages with an in-depth study of the organization of a particular computer. (3 lecture, 2 lab hours)

115. Data Structures (3)
Prerequisites: C Sci 41. Review of basic data structures. Graph, search paths, and spanning trees. Algorithm design and analysis of sorting, merging, and searching. Memory management, hashing, dynamic storage allocation. Integration of data structures into system design.

117. Programming Languages (3)
Prerequisites: C Sci 41 and 112. Examination of general concepts and paradigms of programming languages; scope and binding rules. A study oftwo or more of the following languages: ADA, ALGOL, APL, PL/1, MODULA II, PROLOG, SNOBOL.

124. Introduction to File Processing (3)
Prerequisite: C Sci 115. Definition of file components, access methods, and file operations. Algorithms for efficient implementation of data structures; characteristics of bulk storage media for mainframe and microcomputers. Introduction to database management systems. (Spring semester)

126. Database Systems (3)
Prerequisite: C Sci 115. Database concepts; hierarchical, relational, and network models. Data normalization, data description languages, data manipulation languages, and query design. (Fall semester)

134. Compiler Design (3)
Prerequisites: C Sci 112, 115, 119. Syntax and semantics of programming languages. Lexical analysis, parsing techniques, parser generator, SLR and LALR parsing. Introduction to symbol table organization and semantic routines. Compiler generators. (Spring semester)

136. Compiler Construction (3)
Prerequisite: C Sci 134. Advanced topics in compiler design. Type checking. Run-time storage management. Intermediate code generation. Interpreters. Error recovery techniques. Code generation and optimization. (Spring semester)

144. Operating Systems and Computer Architecture I (3)
Prerequisites: C Sci 112, 115. Review o1 system architecture. Dynamic procedure activation. Process management'-interrupt hardware, process control blocks, concurrent processes, semaphores, monitors, deadlock. Storage management -- real and virtual. Processor management-job and processor scheduling, multiprocessing.

146. Operating Systems and Computer Architecture II (3)
Prerequisites: C Sci 113A, 144. Auxiliary storage management, disk scheduling, file and database systems. Performance measuring, monitoring and evaluation, analytic modeling. Networks, security and case studies.

148. Systems Programming (3)
Prerequisites: C Sci 113A, 144. Topics include implementation of operating system components and modification of existing systems. Device drivers, memory management, communication networks, and file systems will be examined. Projects will be emphasized.

154. Simulation (3)
Prerequisites: C Sci 41, 60; Math 75. Simulation as a tool for the study of complex systems in computer science, statistics and operations research. Generating random variables. Review of principles behind and examples of simulation languages.

164. Artificial Intelligence Programming (3)
Prerequisite: C Sci 117. Introduction to functional programming and applicative languages via LISP. Production systems. Knowledge-based systems. Examples from: game playing, theorem proving, language processing. Introduction to logic programming and declarative languages via PROLOG. Introduction to expert systems. (Fall semester)

166. Principles of Artificial Intelligence (3)
Prerequisite: C Sci 164. Automated reasoning including nonmonotonic logic. Topics from: robot planning, natural language processing, perception (computer vision, speech), learning.

172. Computer Graphics (4)
Prerequisites: Math 76, C Sci 41. Hardware devices, raster graphics, device in dependence, graphic data structure and representations, interactive techniques, and algorithms for the display of two- and three-dimensional objects, graphic transformations, graphics standards, modeling, animation, and scientific visualization. (3 lecture, 2 lab hours)

174. Design and Analysis of Algorithms (3)
Prerequisites: C Sci 115, 119. Models of computation and measures of complexity, algorithms for sorting and searching, set representation and manipulation, branch and bound, integer and polynomial arithmetic, pattern-matching algorithms, parsing algorithms, graph algorithms, NP-complete problems. (Spring semester)

186. Automata Theory and Formal Languages (3)
Prerequisite: C Sci 119. Introduction to formal language theory. Regular grammars, context-free grammars, context-sensitive grammars, unrestricted grammars; properties of context-free languages, push-down automata.

188. Theory of Computation (3)
Prerequisite: C Sci 186. Compatibility, effective procedures, algorithms; finite-state and infinite machines; Turing machines, recursive functions, limitations of effective compatibility, the halting problem, the debugging problem, computable and noncomputable real numbers. (Former Math 113 and C Sci 113A and C Sci 184)

190. Independent Study in Computer Science (1-3)

191T. Proseminar (1-3)

Prerequisite: permission of instructor. Presentation of selected topics in computer science.

194. Cooperative Education (1-4; max total 8)
Prerequisites: courses appropriate to the work experience; approval by major department cooperative education coordinator. Integration of work experience with academic program, individually planned through coordinator. CR/NC grading only.

198. Project (3)
Prerequisite: senior standing in computer science or permission of instructor and approved subject. See Criteria for Thesis and Project. Study of a problem under the supervision of a faculty member. Presentation by the student in a seminar setting and a final report are required. Satisfies the senior major requirement for the B.S. in Computer Science.

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