Science Building I, 114A
(661) 664-3151
(661) 664-2039 (fax)
email: bjacobs@csub.edu
http://www.cs.csub.edu/math/

Program Description

Mathematics is a unique and valuable science that can be exciting, enjoyable, and rewarding. The Department of Mathematics provides a collection of mathematics courses designed to challenge and stimulate all open-minded and thoughtful students regardless of individual backgrounds or major interest areas. This is done by combining flexibility, applicability, and historical perspective in the design of the mathematics curriculum. Furthermore, depth of understanding and appreciation are not sacrificed to quantity; the major emphasis is upon inquiry, creativity, methods, techniques, and thought processes rather than bulk of material.

The classroom goal is to discover both the importance and beauty of mathematics by combining lectures with discussions, problem solving laboratories, student presentations, writing assignments, and any other workable approaches to learning. A student is encouraged to interpret and communicate mathematically with others, to follow self-direction and in-depth study, and to investigate interrelatedness of mathematical concepts. A teacher acts as a resource person, stresses the spirit and point of view of mathematics, and provides for feedback of the relative value of classroom activities.

Upon completion of any mathematics course, students are better equipped to be participants in a highly technological, scientifically complex environment. From a subjective point of view, they should have an improved grasp of the art and beauty of rational reasoning and discourse both as an observer and a participant. From an objective point of view, they should have acquired new skills, which, alone or in combination with others, will enhance both an understanding of and performance in the scientific world.

With the completion of a mathematics major, a student, depending upon the choice of upper division courses, either will be prepared to pursue: (1) a career in the mathematical sciences (Applied Track); (2) a career in teaching (Teaching Track); or (3) a course of graduate study leading to an advanced degree (Theoretical Track). The Applied Track includes courses in differential equations, numerical analysis, complex analysis, statistics, and partial differential equations. The Teaching Track includes courses in geometry, algebra, probability and statistics; contacts with the teaching faculty; and experiences gained through student presentations in discussion and laboratory periods. The Theoretical Track for graduate school preparation includes advanced algebra, real analysis, probability, and statistics.
 

REQUIREMENTS FOR THE MAJOR IN MATHEMATICS

Students seeking a Bachelor of Science degree in Mathematics must complete the following:

1. MATH 211, 212, 213, 214, 222, 223, 300, 330, 331, 340, 363
2. CMPS 212
3. One of the following tracks:
1. Applied Mathematics Track
1. MATH 490
2. Four courses from MATH 302, 305, 312, 338, 339, 341, 350, 402, 420, 430, 431, 450, and 463. One of the four courses must be MATH 302 or 350, and a second must be one of MATH 338, 339, or 341.
3. Cognate area: One upper division course in a related discipline; must be approved by the department.

 
2. Teaching Mathematics Track
1. MATH 341, 420, 425, 430, 450, 491
2. EDSE 241 (2 units)
3. At least two five-unit courses in one of: Biology, or Chemistry, or Geology, or Physics

 
3. Theoretical Mathematics Track
1. MATH 490
2. Four courses from MATH 302, 305, 312, 338, 339, 341, 350, 402, 420, 430, 431, 450, and 463. One of the four courses must be MATH 431 or 463.
3. Cognate area: One upper division course in a related discipline; must be approved by the department.

TEACHING CREDENTIAL -- MATHEMATICS TEACHER PREPARATION PROGRAM

The California Commission on Teacher Credentialing has authorized CSUB to offer a single subject matter preparation program in Mathematics leading to a Bachelor of Science degree. Additional information may be obtained from the Mathematics Program Coordinator.

All of the following courses are required (19 courses, 93 units):

1. Lower Division
1. MATH 211, 212, 213, 214, 222, and 223
2. CMPS 212
3. EDSE 241 (2 units)

 
2. Upper Division
1. MATH 300, 330, 331, 340, 363, 420, 425, 450 and 491
2. One of MATH 338, 339, or 341
3. One of MATH 302, 305, 312, 350, or 430

 
3. Cognates
1. At least two five-unit courses in one of the following disciplines: Biology or Chemistry or Geology or Physics.

HONOURS OPTION

A student may, with the approval of the Chair of the Department of Mathematics, undertake the Honors Program in Mathematics by completing the following:

1. One of the tracks A, B, or C.

 
2. An additional ten hours of upper division courses to be chosen from the required and elective courses in A, B, and C.

 
3. Included in 1 and 2 above, at least one upper division sequence in Mathematics. (Currently the Upper Division sequences are MATH 331-431 Algebraic Structures I and II, MATH 363-463 Real Analysis I and II, and MATH 340 Probability Theory and MATH 341 Mathematical Statistics.)

 
4. MATH 492 Senior Honors Thesis and presentation of an Honors thesis to the Department of Mathematics.

REQUIREMENTS FOR THE MINOR IN APPLIED STATISTICS

Although no minor is required for the BS degree, a minor in Applied Statistics is available, consisting of 20 quarter units chosen from MATH 140 or equivalent, MATH 210, MATH 338, MATH 339, MATH 340, and MATH 341.
 

REQUIREMENTS FOR MINOR IN MATHEMATICS

Although no minor is required for the BS degree, a minor in Mathematics is available. The requirements are 20 units, to include MATH 213, 214, 223, and 10 upper division units. These courses are to be chosen subject to the approval of a Department of Mathematics advisor. Note: MATH 320 and 321 together may count as 5 of the upper division units.
 

COURSE DESCRIPTIONS
 

Developmental Mathematics

MATH 70 Introduction to Algebra and Functions (5)

Introductory course in functions. Concepts of input/output, horizontal/vertical coordinates. Interpreting information from tables and graphs. Linear functions and their behavior; extrapolating values from tables and graphs. Solving linear equations algebraically and graphically. Solving linear inequalities graphically. Order of algebraic operations. Integration of basic geometric concepts. Course makes extensive use of Computer Algebra Systems. Course does not count toward graduation. Prerequisite: A score of 550 or higher on the ELM. [F, W, S]

MATH 80 Elementary Algebra and Functions (5)

Elementary course in functions. Solving linear inequalities and systems of linear equations both graphically and algebraically. Complete analysis of the quadratic function, predicting points from table, graph, or from the equation. Transformations of functions. Graphical interpretation of completing the square. Solutions to systems of non-linear equations by graphing. Concept of Domain and Range. Use of set notation and interval notation. Integration of basic geometric concepts. Course makes extensive use of Computer Algebra Systems. Course does not count toward graduation. Prerequisite: (1) Satisfactory completion of MATH 70 or (2) A score of 550 or higher on the ELM. [F, W, S]

MATH 90 Intermediate Algebra and Functions (5)

Intermediate course in functions. Graphical and algebraic analysis of polynomial functions; hand sketches, roots and their multiplicity. Graphical and algebraic analysis of rational functions. Exponential and Logarithmic functions. Inverse functions. Course makes extensive use of Computer Algebra Systems. Course does not count toward graduation. Prerequisite: (1) Satisfactory completion of MATH 80 or (2) A score of 550 or higher on the ELM. [F, W, S]

MATH 95 Intuitive Geometry (3)

Various topics will be selected from: descriptive geometry of the plane; classification and measurement of angles; notion of parallel and perpendicular; similarity; classification and properties of triangles and quadrilaterals; regular and convex polygons; circles; computations of perimeters and area. Introduction to transformational and coordinate geometry and the plane. Descriptive solid geometry: distance in three-dimensional space; lines and planes in three- dimensions, convex solids; volume and surface. Course uses computer geometric software. Course does not count toward graduation. Prerequisite: (1) Concurrent enrollment in MATH 90 or (2) A score of 550 or higher on the ELM. [F, W, S]
 

Lower Division

Note: To enroll in any course numbered 100 or above, a stud- ent must have satisfied the ELM requirement.

Mathematical topics for business, social, and life sciences selected from logic, set theory, combinatorics, statistics, matrix algebra, linear programming, Markov chains, analytic geometry, graph theory, and mathematics of finance. Prerequisite: (1) MATH 90; or (2) three years of college preparatory mathematics and a score of 550 or higher on the ELM. (CAN MATH 12) [S]

MATH 120 Introduction to Quantitative Methods in Business (5)

Matrix algebra and systems of equations, analytic geometry, basic concepts of differential calculus and introduction to integral calculus. Applications from the areas of business and economics. Students in this course are assumed to have retained mastery of their previous experiences in problem solving in the areas of algebra, geometry and probability. Course makes use of appropriate computing technology and graphing utilities. Prerequisite: (1) MATH 90; or (2) three years of college preparatory mathematics and a score of 550 or higher on the ELM. [F, W, S, SS]

MATH 140 Elementary Statistics (5)

Descriptions of sample data; exploratory data analysis; elementary probability; binomial, normal, "t", chi-square, F and other distributions; estimation and hypothesis testing techniques; non-parametric methods; linear regression and correlation; introduction to multiple regression and analysis of variance. Applications to fields including business, natural sciences, social sciences, and humanities. Course makes use of computer statistical packages. Prerequisite: (1) MATH 90; or (2) three years of college preparatory mathematics and a score of 550 or higher on the ELM. (Credit toward graduation cannot be earned for both MATH 140 and PSYC 200.) (CAN STAT 2) [F, W, S, SS]

MATH 191 Precalculus Mathematics I: College Algebra (5)

The algebraic and geometric analysis of polynomial and rational equations, inequalities, and conic sections. The concept of function is used as the unifying theme. This course makes use of graphing utilities. Prerequisite: (1) MATH 90 or (2) A score of 550 or higher on the ELM. [F, W, S, SS]

MATH 192 Precalculus Mathematics II: Elementary Functions (5)

Introduction to trigonometry. The algebraic and geometric analysis of exponential, logarithmic, trigonometric and inverse trigonometric equations and inequalities. The concept of function is used as the unifying theme. This course makes use of graphing utilities. Students having no prior experience with graphing utilities are encouraged to enroll concurrently in GST 222. Prerequisite: MATH 191. [F, W, S, SS]

Note: Concurrent enrollment in MATH 191 and 192 is possible for students with unusually strong high school math-ematics backgrounds. Approval by the Chair of the De-partment of Mathematics is required.

Expected values and variances, properties of estimators, basic concepts of sampling theory; simple random sampling; stratified random sampling; systematic sampling; cluster sampling. Sources of errors in surveys. Ratio estimators. Prerequisite: MATH 140. [W]

MATH 211 Calculus I (5)
(Formerly numbered MATH 201)

Introduction to the differential calculus of elementary functions (including logarithmic, exponential, and trigonometric functions). Emphasis on limits, continuity, and differentiation. Applications of differentiation (including curve sketching, optimization, and related rates). Light introduction to integration and the Fundamental Theorem of Calculus. This course makes use of graphing calculators, but not of computer algebra systems. Prerequisite: (1) A mark of C- or better in MATH 192 or (2) A score of 550 or higher on the ELM and an appropriate score on the UC/CSU MDTP Calculus Readiness Test. [F, W, S]

Note: In order to take Math 211, students without credit in Math 192 must satisfy the ELM requirement and take the MDTP Calculus Readiness Test and score at a satisfactory level. Please contact the Mathematics Department for the appropriate test date.

Introduction to the integral calculus of elementary functions. The Fundamental Theorem of Calculus; techniques of integration; applications of integration; improper integrals; introduction to differential equations. This course makes use of graphing calculators, but not of computer algebra systems. Corequisite: MATH 222. Prerequisite: A mark of C- or better in MATH 211. [F, W, S]

MATH 213 Calculus III (4)
(Formerly numbered Math 203)

Three-dimensional analytic geometry; parametric curves; functions of several variables; partial and directional derivatives; the chain rule; gradients; optimization; double integrals. This course may make use of computer algebra systems. Prerequisite: Marks of C- or better in MATH 212 and MATH 222. [W, S]

MATH 214 Calculus IV (4)
(Formerly numbered Math 204)

Cylindrical and spherical coordinates; triple integrals; Vector Calculus (including line and surface integrals and the theorems of Gauss, Stokes and Green and the Fundamental Theorem of Line Integrals); sequences and series. This course may make use of computer algebra systems. Prerequisite or corequisite: MATH 223. Prerequisite: A mark of C- or better in MATH 213. [F, S]

MATH 220 Introduction to Problem Solving (5)

Introduction to problem solving in algebra and geometry. Requires substantial use of a scientific calculator. Recommended for Liberal Studies students who lack a previous college-level mathematics course that includes topics listed above and/or those having a weak or distant background in mathematics. Prerequisites: (1) A score of 550 or higher on the ELM and (2) two years of high school algebra and one year of high school geometry, or equivalent. [F, W, S, SS]

MATH 222 Laboratory Experience I (3)

Newton’s Method; derivative and integral estimation; applications of the integral; average value of a function; elementary differential equations; modeling with derivatives; polar coordinates; Taylor polynomials; additional topics as time permits. This course makes extensive use of computer algebra systems. Corequisite: MATH 212. Prerequisite: A mark of C- or better in MATH 211. [F, W, S]

MATH 223 Laboratory Experience II (3)

Matrices and systems of ordinary differential equations; parametrizations; projectile motion; quadric surfaces; applications of Taylor and Maclaurin series; vector fields; Lagrange multipliers and linear programming; topics from the applied sciences. This course makes extensive use of computer algebra systems. Prerequisite: Marks of C- or better in MATH 212 and MATH 222. [F, W, S]

MATH 277 Special Topics in Mathematics (1-5)

Analysis of contemporary and interdisciplinary problems. Topics and prerequisites to be announced.

MATH 289 Experiential Prior Learning (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.
 

Upper Division

MATH 300 Sets and Logic (5)

An investigation of the fundamental tools used in writing mathematical proofs, including sentential and predicate calculus, topics from naive set theory, Cartesian products, partitions, equivalence relations, functions, countability, and mathematical induction. This course relies heavily on problem solving and writing complete, logically consistent arguments in the context of an axiomatic system to illustrate the correct use of the logical tools and methods discussed. Prerequisite: MATH 213 (formerly numbered MATH 203). [F, S]

MATH 302 Ordinary Differential Equations (5)

First-order differential equations; linear differential equations; linear systems; Laplace transforms and their application to solutions of linear differential equations and systems; series solutions of second-order linear equations and/or numerical solutions of differential equations; topics in nonlinear differential equations and systems; applications. Prerequisite: MATH 213 (formerly numbered MATH 203). [S]

MATH 305 Numerical Analysis (5)

Number representation and basic concepts of error; numerical solutions of nonlinear equations and systems of equations; interpolation and extrapolation; numerical differentiation and integration; numerical solutions of ordinary differential equations; approximation by spline functions. Cross-listed as CMPS 305. Prerequisites: (1) MATH 213 (formerly numbered MATH 203); and (2) CMPS 140 or CMPS 212. [F-odd yrs.]

MATH 312 Complex Variables (5)

Complex numbers; analytic functions; conformal mapping; integrals; Cauchy’s Theorem and the calculus of residues; power series. Prerequisite: MATH 214 (formerly numbered MATH 204) and MATH 223. [W-even yrs.]

MATH 320 Introduction to Number Systems (5)

Introduction to set theory, numeration systems, number theory, probability, computational algorithms, and applications involving calculators and/or computers in problem solving. This course involves substantial use of concrete materials in a laboratory setting. Students in this course are assumed to have retained mastery of their previous experiences in problem solving in the areas of algebra and geometry. Required for entry into the Multiple Subjects Credential Program. Prerequisite: (1) MATH 220 (or a passing score on the MATH 220 Waiver Exam) or (2) A score of 550 or higher on the ELM. [F, W, S, SS]

MATH 321 Introduction to Modern Geometry (5)

Introduction to principles of measurement, the metric system, intuitive geometry of plane and solid shapes, constructions, networks, data collection and display (statistics), and applications involving calculators and computers in problem solving. This course involves substantial use of concrete materials in a laboratory setting. Students in this course are assumed to have retained mastery of their previous experiences in problem solving in the areas of algebra, geometry and probability. Requirement for entry into the Multiple Subjects Credential Program. Prerequisite: A mark of C- or better in MATH 320. (Or permission of the Coordinator of Mathematics Education.) [F, W, S, SS]

MATH 330 Linear Algebra (5)

Matrices; 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; quadratic forms. Prerequisite: MATH 213 (formerly numbered MATH 203). Recommended: MATH 300 or CMPS 300. [W, S]

MATH 331 Algebraic Structures I (5)

Mappings, relations, binary operations; groups; rings; integral domains and fields. Prerequisite: MATH 300. [W]

MATH 338 Analysis of Variance and Experimental Design (5)

One-way ANOVA: completely randomized design, multiple comparisons and contrasts; Two-way ANOVA: randomized complete block design, fixed and random effects; Multi-way factorial models, analysis of nonorthogonal factorial designs; Analysis of covariance. Use of statistical packages. Prerequisite: MATH 140. [F]

MATH 339 Regression Analysis (5)

Least squares and simple linear regression; correlation analysis; multiple regression; residual analysis. Model selection techniques. Log-linear and Logit models. Time series analysis. Use of statistical packages. Prerequisite: MATH 140. [W]

MATH 340 Probability Theory (5)

Mathematical models; sample spaces and events; combinatorial and occupancy problems; axiomatic probability; conditional probability and Bayes’ Theorem; random variables, expected value, and functions of random variables; probability mass and density functions and distribution functions for both discrete and continuous variables; waiting times and queues; joint distribution for discrete variables. Prerequisite: MATH 213 (formerly numbered MATH 203). Recommended: MATH 300 or CMPS 300. [S]

MATH 341 Mathematical Statistics (5)

Derivation of sampling distributions and their properties: estimation of parameters; theory of confidence intervals and hypothesis testing; properties of estimators and tests; likelihood ratio tests; power and most powerful tests. Prerequisites: (1) MATH 340; and (2) MATH 214 (formerly numbered MATH 204) and MATH 223. [F-odd yrs.]

MATH 350 Introduction to Mathematical Modeling (5)

Course to meet in two lectures and two laboratory sessions. The course is designed to give the student an early introduction to the construction and use of empirical and analytic mathematical models. Course evaluation will involve at least one extended project. Prerequisites: (1) MATH 213 (formerly numbered MATH 203); and (2) MATH 302 or MATH 330. [F-even yrs.]

MATH 363 Real Analysis I (5)

Development of a rigorous foundation for analysis; open and closed sets; sequences and series; continuity; differentiability and an introduction to integration. Prerequisites: MATH 214 (formerly numbered MATH 204) and MATH 223; and MATH 300. [F]

MATH 402 Partial Differential Equations (5)

Classical partial differential equations; orthogonal sets of functions; Fourier series and integrals; Bessell functions and applications, Legendre polynomials and applications. Prerequisites: (1) MATH 214 (formerly numbered MATH 204) and MATH 223; and (2) MATH 302. [F-even yrs.]

MATH 420 Foundations of Geometry (5)

Axiomatic approach to Euclidean geometry and topics selected from distance, congruence, similarity, separation, betweeness, inequalities, parallel postulate coordinate systems, constructions, area, length, and volume; introduction to non-Euclidean geometries. Prerequisite: MATH 300. [F]

MATH 425 Modern Mathematics for Teachers (5)

This course is designed for both preservice and inservice middle and high school mathematics teachers. It will involve investigations, problem solving, and laboratory activities in number theory, algebra, geometry, probability, and statistics. Prerequisite: Successful completion of 30 quarter units of college mathematics. Credit cannot be earned for both MATH 425 and MATH 320/321. [W-even yrs.]

MATH 426 Mathematics Curriculum and Instruction for Secondary Teachers (3)

Instructional strategies, resources, and methods for prospective junior high and high school mathematics teachers. This course does not count toward a major or a minor in mathematics. Cross-listed as EDSE 421 [F]

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. [S-odd yrs.]

MATH 431 Algebraic Structures II (5)

A continuation of MATH 331. Group structure theorems, structure of finite fields, Galois Theory, and selected topics and applications. Prerequisite: MATH 331. [S-even yrs.]

MATH 450 Introduction to the History of Mathematics (5)

Development of mathematics from its empirical origins to its present form. Emphasis may vary with the instructor. Evaluation will include at least one substantial student paper. Prerequisites: (1) MATH 300; AND (2) At least two other upper division mathematics courses; AND (3) Completion of CSUB’s Graduation Writing Assessment Requirement. [W-odd yrs.]

MATH 463 Real Analysis II (5)

A continuation of MATH 363, Riemann integration; the fundamental theorem of calculus; Taylor’s theorem with remainder; uniform convergence and Taylor series; spaces of functions and applications; e.g., Fourier series and existence theorems for differential equations. Prerequisite: MATH 363. [W-odd yrs.]

MATH 477 Special Topics in Mathematics (1-5)

Topics and prerequisites to be announced.

MATH 480 Research Participation (1-5)

Supervised mathematical investigation. May be repeated. Offered on a credit, no-credit basis only. Prerequisite: Permission of instructor.

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.

MATH 490 Senior Seminar (5)

Preparation of papers and discussion by faculty and students. Prerequisites: (1) At least four upper division courses from either the Applied or Theoretical Tracks; and (2) Completion of CSUB’s Graduation Writing Assessment Requirement. [S]

MATH 491 Senior Seminar in Mathematics for Prospective Teachers (5)

Preparation of papers and discussion by faculty and students. Mathematics relevant to secondary education. Prerequisites: (1) At least four upper division courses from the Teaching Track; and (2) Completion of CSUB’s Graduation Writing Assessment Requirement. [S]

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.

MATH 494 Senior Seminar for Elementary/Middle School Mathematics Teachers (6)

Preparation of papers and discussion by faculty and students. Mathematics relevant to elementary and middle school education. 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. [W]

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, no-credit basis only.

MATH 497 Cooperative Education (1-5)

The Cooperative Education program 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, no-credit basis only.
 

Graduate Courses

MATH 577 Advanced Topics in Mathematics (1-5)

Topics and prerequisites to be announced. May be repeated for different topics. General prerequisite: Major or minor in Mathematics.

MATH 580 Advanced Research Participation (1-5)

Individual mathematical investigation, under supervision. (Experience as a research assistant does not count for credit.) Offered on a credit, no-credit basis only. Prerequisite: Permission of instructor.