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MATHEMATICS I 261
116. Theory of Numben (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.
121 . Numerical Analysis (3)
Prerequisite: Math 77. Finite difference and Lagrangian interpolation formulas; numerical
solution of equations, systems of equations, and differential equations; principles of coding
and programming computers.
123. Topics in Applied Mathematics (3)
Prerequisite: Math 77. Vector spaces and linear transformations, eigen values 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.
131. Game Theory and Linear Programming (3)
Prerequisite: Math 72 and permission of instructor; or Math 76. Carnes of strategy, normal
form of a game, minimax theorem for two-person games, a-person games, solutions of
n-person games and equilibrium points, linear programming, applications.
141. Number Systems II (3)
Not open to students with credit in Math 151 or 171. Prerequisite: Math 41 or 71. Especially
recommended for prospective teachers and minors. Development of the real number system
and its subsystems from the formal point of view. Mathematical induction and definition by
recursion. Axiomatic development of the various number systems and their interrelation.
151. Principles of Algebra (3)
Prerequisite: Math 76 or 141. Rings, integral domains, fields, polynomials.
152. Linear Algebra (3)
Prerequisite: Math 151 or permission of instructor. Linear transformations, matrices,
determinants, linear functionals, bilinear forms, quadratic forms, orthogonal and unitary
tnnsformations, selected applications of linear algebra.
153. Modern Algebra (3)
Prequisite: Math 152. Group theory, field theory, elements of Galois theory.
161. Principles of Geometry (3)
Prerequisite: Math 72 or 75. The classical elliptic, parabolic, and hyperbolic geometries
developed on a common framework of incidence, order and sep,ration, congruence;
coordinatization. Theory of parallels for parabolic and hyperbolic geometries. Selected topics
of modem Euclidean geometry.
162. Projedlve Geometry (3)
Prerequisite: Math 77. Synthetic and analytic projective geometry; axioms; duality;
perspective and projective correspondence; harmonic sets; coordinatization; projective
collineations and correlations; polarities and conics; groups of projective, affme and
Euclidean transformations.
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 (3)
Prerequisite: Math 77. The complete ordered field and its usual topology; extensions to the
plane; continuity and uniform continuity; characterization of the differential; extended
mean value theorem; intermedi.ate value property of derivatives; characterization of
Riemann integrable functions as functions continuous almost everywhere.
Object Description
| Title | 1973-74 General Catalog |
| Creator | California State University, Fresno |
| Format | PDF Document |
| Date of publication | 1973-05 |
| Subjects | California State University, Fresno. Curricula. Catalogs |
| Object type | Document |
| Location | Fresno, California |
| Language | eng |
Description
| Title | Page 261 |
| Full Text Search | MATHEMATICS I 261 116. Theory of Numben (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. 121 . Numerical Analysis (3) Prerequisite: Math 77. Finite difference and Lagrangian interpolation formulas; numerical solution of equations, systems of equations, and differential equations; principles of coding and programming computers. 123. Topics in Applied Mathematics (3) Prerequisite: Math 77. Vector spaces and linear transformations, eigen values 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. 131. Game Theory and Linear Programming (3) Prerequisite: Math 72 and permission of instructor; or Math 76. Carnes of strategy, normal form of a game, minimax theorem for two-person games, a-person games, solutions of n-person games and equilibrium points, linear programming, applications. 141. Number Systems II (3) Not open to students with credit in Math 151 or 171. Prerequisite: Math 41 or 71. Especially recommended for prospective teachers and minors. Development of the real number system and its subsystems from the formal point of view. Mathematical induction and definition by recursion. Axiomatic development of the various number systems and their interrelation. 151. Principles of Algebra (3) Prerequisite: Math 76 or 141. Rings, integral domains, fields, polynomials. 152. Linear Algebra (3) Prerequisite: Math 151 or permission of instructor. Linear transformations, matrices, determinants, linear functionals, bilinear forms, quadratic forms, orthogonal and unitary tnnsformations, selected applications of linear algebra. 153. Modern Algebra (3) Prequisite: Math 152. Group theory, field theory, elements of Galois theory. 161. Principles of Geometry (3) Prerequisite: Math 72 or 75. The classical elliptic, parabolic, and hyperbolic geometries developed on a common framework of incidence, order and sep,ration, congruence; coordinatization. Theory of parallels for parabolic and hyperbolic geometries. Selected topics of modem Euclidean geometry. 162. Projedlve Geometry (3) Prerequisite: Math 77. Synthetic and analytic projective geometry; axioms; duality; perspective and projective correspondence; harmonic sets; coordinatization; projective collineations and correlations; polarities and conics; groups of projective, affme and Euclidean transformations. 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 (3) Prerequisite: Math 77. The complete ordered field and its usual topology; extensions to the plane; continuity and uniform continuity; characterization of the differential; extended mean value theorem; intermedi.ate value property of derivatives; characterization of Riemann integrable functions as functions continuous almost everywhere. |
