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# Description of Mathematics

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)