Page 416 |
Previous | 416 of 569 | Next |
|
|
This page
All
|
Mathematics
416 2009-2010 California State University, Fresno General Catalog
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)
Prerequisites: MATH 111; EHD 50 (may
be enrolled concurrently). A study of for-mulation
of problems into mathematical
form; analysis of methods of attack such
as specialization, generalization, analogy,
induction, recursion, etc. applied to a vari-ety
of non-routine problems. Topics will be
handled through student presentation. F
MATH 149. Capstone Mathematics for
Teachers (4)
Prerequisites: MATH 151, 161, and 171.
(MATH 161 and MATH 171 may be
taken concurrently.) Secondary school
mathematics from an advanced viewpoint.
Builds on students’ work in upper-division
mathematics to deepen their understand-ing
of the mathematics taught in second-ary
school. Students will actively explore
topics in number theory, algebra, analysis,
geometry.
MATH 151. Principles of Algebra (4)
Prerequisite: MATH 111. Equivalence
relations; groups, cyclic groups, normal
sub-groups, and factor groups; rings, ide-als,
and factor rings; integral domains and
polynomial rings; fields and field exten-sions.
FS
MATH 152. Linear Algebra (4)
Prerequisite: MATH 77. Vector spaces, lin-ear
transformations, matrices, determinants,
eigenvalues and eigenvectors, linear func-tions,
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 el-liptic,
parabolic, and hyperbolic geometries
developed on a framework of incidence,
order and separation, congruence; coor-dinatization.
Theory of parallels for par-abolic
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 sur-face.
F
MATH 171. Intermediate
Mathematical Analysis I (4)
Prerequisite: MATH 111. Natural and ra-tional
numbers, real numbers as a complete
ordered field, its usual topology, sequences
and series of real numbers, functions of a real
variable, limits, continuity, uniform continu-ity,
differentiability, generalized mean value
theorem, Riemann integrals, and power
series. FS
MATH 172. Intermediate
Mathematical Analysis II (4)
Prerequisite: MATH 77 and 171. Pointwise
and uniform convergence of sequences
and series of functions, convergence of
sequences in higher dimensions, continuity
and differentiability of functions of several
variables. Inverse and implicit function
theorems; topics in integration theory in
higher dimensions. 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; appli-cations
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. Pre-sentation
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 presenta-tion
of an advanced topic in mathematics.
Satisfies the senior major requirement for
the B.A. in Mathematics.
GRADUATE COURSES
(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.
Object Description
| Title | 2009-10 General Catalog |
| Creator | California State University, Fresno |
| Format | PDF Document |
| Date of publication | 2009-05 |
| Subjects | California State University, Fresno. Curricula. Catalogs |
| Object type | Document |
| Location | Fresno, California |
| Language | eng |
Description
| Title | Page 416 |
| Full Text Search | Mathematics 416 2009-2010 California State University, Fresno General Catalog 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) Prerequisites: MATH 111; EHD 50 (may be enrolled concurrently). A study of for-mulation of problems into mathematical form; analysis of methods of attack such as specialization, generalization, analogy, induction, recursion, etc. applied to a vari-ety of non-routine problems. Topics will be handled through student presentation. F MATH 149. Capstone Mathematics for Teachers (4) Prerequisites: MATH 151, 161, and 171. (MATH 161 and MATH 171 may be taken concurrently.) Secondary school mathematics from an advanced viewpoint. Builds on students’ work in upper-division mathematics to deepen their understand-ing of the mathematics taught in second-ary school. Students will actively explore topics in number theory, algebra, analysis, geometry. MATH 151. Principles of Algebra (4) Prerequisite: MATH 111. Equivalence relations; groups, cyclic groups, normal sub-groups, and factor groups; rings, ide-als, and factor rings; integral domains and polynomial rings; fields and field exten-sions. FS MATH 152. Linear Algebra (4) Prerequisite: MATH 77. Vector spaces, lin-ear transformations, matrices, determinants, eigenvalues and eigenvectors, linear func-tions, 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 el-liptic, parabolic, and hyperbolic geometries developed on a framework of incidence, order and separation, congruence; coor-dinatization. Theory of parallels for par-abolic 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 sur-face. F MATH 171. Intermediate Mathematical Analysis I (4) Prerequisite: MATH 111. Natural and ra-tional numbers, real numbers as a complete ordered field, its usual topology, sequences and series of real numbers, functions of a real variable, limits, continuity, uniform continu-ity, differentiability, generalized mean value theorem, Riemann integrals, and power series. FS MATH 172. Intermediate Mathematical Analysis II (4) Prerequisite: MATH 77 and 171. Pointwise and uniform convergence of sequences and series of functions, convergence of sequences in higher dimensions, continuity and differentiability of functions of several variables. Inverse and implicit function theorems; topics in integration theory in higher dimensions. 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; appli-cations 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. Pre-sentation 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 presenta-tion of an advanced topic in mathematics. Satisfies the senior major requirement for the B.A. in Mathematics. GRADUATE COURSES (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. |
