MATH 321 Introduction To Modern Geometry (5)
Introduction to the geometry of plane and solid shapes. Networks and
applications. Constructions,
congruence, and similarity. Concepts of measurement. Motion geometry and
tessellations. The use of
calculators and/or dynamical geometry software in discovery and problem solving.
This course involves
substantial use of 2- and 3-dimensional concrete materials in a cooperative
learning laboratory setting.
Required for entry into the CSUB Multiple Subjects Credential Program.
Prerequisites: A grade of C- or
better in Math 320. (4 units lecture & 1 unit lab)
MATH 330 Linear Algebra (5)
Matrices and systems of linear equations; vector spaces, dimensions, linear
independence; spaces
associated with matrices; bases, change of basis, orthogonal bases; linear
transformations , matrix
representation; eigenvalues and eigenvectors, diagonalization; selected
applications. Prerequisite:
MATH 203. Prerequisite or co-requisite: MATH 300 or CMPS 295. (3 units lecture &
2 unit lab)
MATH 331 Algebraic Structures I (5)
Introduction to binary operations and algebraic structures; groups, rings,
integral domains, and fields.
Prerequisite: (1) MATH 300, and (2) 330 (MATH 330 may be taken concurrently). (4
units lecture & 1
unit lab)
MATH 338 Analysis of Variance and Experimental Design (5)
Single-factor ANOVA; multiple comparisons; completely randomized design;
fixed and random effects;
two-factor ANOVA; randomized complete block design; factorial models; fixed,
random, and mixed
models; nested models. Use of statistical packages. Prerequisite; MATH 140. (4
units
lecture & 1 unit lab)
MATH 339 Regression Analysis (5)
Least squares; simple linear regression; correlation analysis; residual
analysis; multiple regression; model
selection techniques; logistic regression . Use of statistical packages.
Prerequisite: MATH 140. (4 units
lecture & 1 unit lab)
MATH 340 Probability Theory (5)
Sample spaces and events; counting problems, permutations and combinations ;
conditional probability;
independence; Bayes theorem; discrete and continuous random variables ; bivariate,
multivariate,
marginal, and conditional distributions; functions of random variables; expected
value, moments,
variance, covariance, and correlation; distribution theory including Bernoulli,
binomial, hypergeometric,
Poisson, uniform, normal, exponential, gamma, and beta distributions; central
limit theorem. Prerequisite:
MATH 203. Prerequisite or co-requisite: MATH 300 or CMPS 295. (3 units lecture &
2 unit lab)
MATH 350 Introduction to Mathematical Modeling (5)
Course designed to give the student an early introduction to the
construction and use of empirical and
analytic mathematical models from areas such as economics, game theory, integer
programming,
mathematical biology and mathematical physics (topics depend on instructor).
Course evaluation will
involve at least one extended project. Prerequisite: MATH 205 (4 units lecture &
1 unit lab)
MATH 360 Euclidean Geometry (5)
Elaboration of concepts in Euclidean geometry and 19th- and 20th-century
expansions of Euclid’s work.
Topics include concurrency of lines in a triangle, collinearity of some points
in a triangle, symmetric points
in a triangle, some properties of triangles and quadrilaterals, equicircles and
the nine- point circle .
Additional topics may be included. Ability to write formal synthetic and
analytic proofs is stressed.
Dynamical Geometry software is used for exploration and discovery. This course
provides a survey of
material needed to prepare students to teach high school geometry courses.
Prerequisites: (1) MATH
300, and (2) 330 (MATH 330 may be taken concurrently). (4 units lecture & 1 unit
lab)
MATH 363 Introduction to Analysis I (5)
Development of a rigorous foundation for analysis; axioms for the real
numbers; sequences and series;
continuity; introduction to differentiability and integration . Prerequisites:
(1) MATH 203, and (2) MATH
300. (4 units lecture & 1 unit lab)
MATH 402 Partial Differential Equations (5)
Fourier series; classical partial differential equations such as heat
equation, wave equation, and Laplace
equation; Sturm-Liouville problems; orthogonal functions; topics from Fourier
transform or calculus of
variation. Prerequisites: (1) MATH 204 and (2) MATH 205. (4 units lecture & 1
unit lab)
MATH 420 Foundations of Geometry (5)
Study of the classical axiomatization of Euclidean geometry. Hilbert’s
incidence, congruence, similarity,
separation, betweenness and continuity axioms are discussed. Special attention
is paid to the Parallel
Postulate and its alternative formulations , with an introduction to nonEuclidean
geometries. Prerequisite:
MATH 300. (4 units lecture & 1 unit lab)
MATH 425 Modern Mathematics for Teachers (5)
Course intended for prospective teachers of middle and high school
mathematics, and includes
investigations relevant to the California Mathematics Contents Standards from
the areas of number
theory, algebra, geometry, probability, and statistics. The course emphasizes
problem solving and
laboratory activities. Students are introduced to appropriate use of current
pedagogical technologies.
Prerequisite: Successful completion of 30 quarter units of college mathematics.
(4 units lecture & 1 unit
lab)
MATH 427 Mathematics Curriculum and Instruction for Secondary Teachers (5)
Required during Stage III of the program of all candidates for a Single
Subject Secondary Teaching
Credential in Mathematics. The content is designed to acquaint the candidates
with the pedagogical
techniques, philosophies, and practices utilized by successful secondary
mathematics teachers and
required by the Teaching Performance Expectations as delineated in the Standards
of Quality and
Effectiveness for Teacher Preparation Programs. The course includes at least ten
hours of field
experience in a high school or middle school mathematics classroom. This course
does not count
toward a major or a minor in mathematics. Cross-listed as EDSE 405. (5 units
lecture)
MATH 430 Number Theory (5)
Elementary theory of the natural numbers, including prime numbers and
divisibility, congruences,
number theoretic functions, Diophantine equations, and selected topics.
Prerequisite: MATH 300. (4
units lecture & 1 unit lab)
MATH 431 Algebraic Structures II (5)
Continuation of MATH 331. Galois Theory and selected topics. Prerequisite:
MATH 331. (4 units lecture
& 1 unit lab)
MATH 440 Mathematical Statistics (5)
Statistical inference; prior and posterior distributions, Bayes estimation,
maximum likelihood estimation,
method of moments ; derivation of sampling distributions and their properties;
unbiased estimators, Fisher
information; theory of confidence intervals and hypothesis testing; power,
t-test and F-test; analysis of
categorical data, goodness of fit and contingency tables; inference for linear
statistical models, regression
and ANOVA Prerequisites: MATH 340. (4 units lecture & 1 unit lab)
MATH 450 Introduction to the History of Mathematics (5)
Development of mathematics from its empirical origins to its present form.
Prerequisites: (1) MATH 300;
(2) At least two mathematics courses numbered above 300; and (3) Completion of
CSUB’s Graduation
Writing Assessment Requirement (GWAR). (4 units lecture & 1 unit lab)
MATH 463 Introduction to Analysis II (5)
Continuation of MATH 363; the fundamental theorem of calculus; further
topics of Riemann integration;
Taylor’s theorem with remainder; uniform convergence and Taylor series; the
topology of the real line;
other selected topics if time allows. Prerequisite: MATH 363. (4 units lecture &
1 unit lab)
MATH 477 Special Topics in Mathematics (1-5)
Topics and prerequisites to be announced. Permission of instructor. (4 units
lecture & 1 unit lab)
MATH 480 Research Participation (1-5)
Supervised mathematical investigation. May be repeated. Offered on a credit,
no credit basis only.
Prerequisite: Permission of instructor. (5 units lecture)
MATH 489 Experiential Prior Learning (1-5)
Evaluation and assessment of learning which has occurred as a result of
prior off-campus experience
relevant to the curriculum of the department. Requires complementary academic
study and/or
documentation. Available by petition only, on a credit, no-credit basis. Not
open to post-graduate
students. Interested students should contact the Department of Mathematics. (5
units lecture)
MATH 490 Senior Seminar (5)
Preparation of papers and discussion by faculty and students. Prerequisites:
(1) At least four upper-
division courses from the Applied, Statistics or Theoretical Tracks; and (2)
Completion of CSUB’s
Graduation Writing Assessment Requirement (GWAR). (5 units lecture)
MATH 491 Senior Seminar in Mathematics for Prospective Teachers (5)
Students will make presentations on, write papers about, and discuss
solutions of mathematical problems
grounded in secondary school mathematics education. The focus is mathematics
with appropriate
inclusion of pedagogical ideas. For students in the Blended Program there is a
requirement of 25 hours of
supervised field experience in middle or high school mathematics classrooms.
Prerequisites: (1) At least
four upper division courses from the Teaching Track; and (2) Completion of
CSUB’s Graduation Writing
Assessment Requirement (GWAR). (5 units lecture)
MATH 492 Senior Honors Thesis (5)
Individual study with a faculty sponsor leading to a formal written report
on a specific topic or problem.
Prerequisites: (1) Senior standing; and (2) consent of faculty sponsor; and (3)
approval of the Chair of
the Department of Mathematics. (5 units lecture)
MATH 494 Senior Seminar for Elementary/Middle School Mathematics Teachers (5)
Students will make presentations on, write papers about, and discuss
solutions of mathematical problems
grounded in elementary and middle school mathematics education with special
emphasis on middle
school. The focus is mathematics with appropriate inclusion of pedagogical
ideas. Appropriate uses of
current pedagogical technologies are discussed. Prerequisites: (1) MATH 321 ( or
the equivalent ), (2)
MATH 192 (or a course which has MATH 192 as a prerequisite) may be taken
concurrently, and (3)
Completion of CSUB’s Graduation Writing Assessment Requirement (GWAR). (5 units
lecture)
MATH 496 Internship in Mathematics (1-5)
Internships may be arranged by the department with various agencies,
businesses, or industries. The
assignments and coordination of work projects with conferences and readings, as
well as course credits,
evaluation, and grading, are the responsibility of the faculty liaison (or
course instructor) working with the
field supervisor. Offered on a credit, nocredit basis only. (5 units lecture)
MATH 497 Cooperative Education (1-5)
Class offers a sponsored learning experience in a work setting, integrated
with a field analysis seminar.
The field experience is contracted by the Cooperative Education office on an
individual basis, subject to
approval by the department. The field experience, including the seminar and
reading assignments, is
supervised by the cooperative education coordinator and the faculty liaison (or
course instructor), working
with the field supervisor. Students are expected to enroll in the course for at
least two quarters. The
determination of course credits evaluation and grading are the responsibility of
the departmental faculty.
Offered on a credit, nocredit basis only. (1-5 units lecture)
GRADUATE COURSES
Graduate courses are listed in the “Graduate Studies” section of the catalog.