2007-2009 Catalog
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Mathematics Banner

Introduction | Bachelor of Arts in Mathematics
Minor in Mathematics
Minor in Mathematics for Teacher Education
Single Subject Teaching | Master of Arts in Mathematics
Mathematics Courses | Mathematics Education Courses
Dept Homepage

DEPARTMENT CHAIR
Paul De Land

VICE CHAIR
Martin Bonsangue

DEPARTMENT OFFICE
McCarthy Hall 154

DEPARTMENT WEBSITE
http://math.fullerton.edu

PROGRAMS OFFERED
Bachelor of Arts in Mathematics
   Pure Mathematics Concentration
   Applied Mathematics Concentration
   Probability and Statistics Concentration
   Teaching Mathematics Concentration
Minor in Mathematics
Minor in Mathematics for Teacher Education
Master of Arts in Mathematics
   Teaching Option
   Applied Mathematics Option
   Special Topics Program
Subject Matter Preparation Program for the Single Subject Credential

FACULTY
Alfonso Agnew, Gulhan Alpargu, Scott Annin, George Arthur, Martin Bonsangue, Alain Bourget, Cherlyn Converse, Paul De Land, Harriet Edwards, Nicole Engelke, James Friel, Gerald Gannon, William Gearhart, Stephen Goode, Mortaza Jamshidian, Margaret Kidd, Vuryl Klassen, Charles H. Lee, Gerald Legé, Kathy Lewis, HeeJeong Lim, Armando Martinez-Cruz, John Mathews, Tyler McMillen, A. Loc Nguyen, David Pagni, John Pierce, Angel Pineda, Maijian Qian, Nashat Saweris, Harris Shultz, Ernie Solheid, Bogdan Suceava, Yun-Cheng Zee

INTRODUCTION
The Department of Mathematics offers a standard undergraduate major program in mathematics with concentrations in pure mathematics, applied mathematics, probability and statistics, and teaching mathematics. Courses are provided to satisfy the needs of:

  • Students planning graduate study in mathematics;
  • Students planning to use mathematics in a career in business, industry or government;
  • Students planning to teach at the elementary or secondary level;
  • Students majoring in a discipline using mathematics as an analytic or descriptive tool.

All major programs are designed to give sufficient breadth and depth in the study of mathematics to prepare students for subsequent graduate study in mathematics or related areas.

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BACHELOR OF ARTS IN MATHEMATICS
The requirements for the Bachelor of Arts in Mathematics consist of:

  • The core mathematics courses for the major (28 units).
  • Courses in one of four possible concentrations: Pure Mathematics, Applied Mathematics, Probability and Statistics, or Teaching Mathematics (18-20 units). The Pure Mathematics concentration is designed for students planning on graduate study. The Applied and the Probability and Statistics concentrations provide the mathematics needed for certain careers in industry and government. For students interested in teaching in elementary or secondary schools, the Teaching concentration may be combined with programs leading to a teaching credential to meet both university degree requirements and California credential law.
  • A computer programming course selected from Mathematics 320 Introduction to Mathematical Computation, Comp Sci 120 Introduction to Programming or Comp Sci 121 Programming Concepts (3 units).
  • Courses in one of nine cognates selected from the disciplines of Actuarial Science, Chemistry, Civil Engineering, Computer Science, Economics, Information Systems and Decision Sciences, Mathematics, Physics or Research (9-12). Those students selecting the Computer Science cognate are required to take Comp Sci 120 or 121. Students may not double count Mathematics 320 for the Mathematics cognate and the programming requirement.
  • Math 380, the History of Mathematics, which fulfills the University’s upper division writing requirement (3 units).

Total units needed to complete the B.A. in Mathematics are 120, which include the 61–66 units required for the major, the 51 units required for general education, and units earned in elective courses (3-8 units). Each course required for the major must be completed with a grade of “C” (2.0) or better, and may not be taken on a credit/no credit basis. Courses required for the major may not be challenged by examination.

During their first year of study each student will develop an individual study plan in consultation with an academic adviser in the Mathematics Department. Normally mathematics majors take Math 150A and Math 150B in their first year. In the second year mathematics majors normally take Math 250A, Math 250B and Math 280. Mathematics 150A may also be used to satisfy the general education requirement in Disciplinary Learning.

Core Requirements (28 units)
All students are required to complete the following 28 units:
Math 150A,B Calculus (8)
Math 250A Multivariate Calculus (4)
Math 250B Introduction to Linear Algebra and Differential Equations (4)
Math 280 Strategies of Proof (3)
Math 307 Linear Algebra (3)
Math 335 Mathematical Probability (3)
Math 350 Advanced Calculus I (3)

Additional Requirements (18-20 units)
Each student is required to complete one of the following concentrations:

Pure Mathematics Concentration (18 units)
Math 302 Modern Algebra (3)
Math 414 Topology (3)
Math 450 Advanced Calculus II (3)

Three of the following courses:
Math 407 Abstract Algebra (3)
Math 412 Complex Analysis (3)
Math 425 Differential Geometry (3)
Math 430 Number Theory (3)
Math 471 Combinatorics (3)

Applied Mathematics Concentration (18 units)
Math 306 Vector and Tensor Analysis (3)
Math 310 Ordinary Differential Equations (3)
Math 340 Numerical Analysis (3)

Three courses from the following list, with at least two at the 400 level:
Math 302 Modern Algebra (3)
Math 370 Mathematical Model Building (3)
Math 375 Discrete Dynamical Systems and Chaos (3)
Math 406 Introduction to Partial Differential Equations (3)
Math 412 Complex Analysis (3)
Math 425 Differential Geometry (3)
Math 435 Mathematical Statistics (3)
OR Math 438 Introduction to Stochastic Processes (3)
Math 440 Advanced Numerical Analysis (3)
Math 450 Advanced Calculus II (3)
Math 470 Advanced Mathematical Model Building (3)

Probability and Statistics Concentration (20 units)
Math 338 Statistics Applied to Natural Sciences (4)
Math 435 Mathematical Statistics (3)
Math 436 Advanced Applied Statistics (4)
Math 438 Introduction to Stochastic Processes (3)
Math 439 Intermediate Data Analysis (3)

And one of the following three courses:
Math 340 Numerical Analysis (3)
Math 370 Mathematical Model Building (3)
Math 390 Introduction to Actuarial Science (3)

Teaching Mathematics Concentration (18-19 units)
Math 302 Modern Algebra (3)
Math 338 Statistics Applied to Natural Sciences (4)
  OR Math 370 Mathematical Model Building (3)
  OR Math 375 Discrete Dynamical Systems and Chaos (3)
Math 401 Algebra and Probability for the Secondary Teacher (3)
Math 402 Logic and Geometry for the Secondary Teacher (3)

Two of the following courses:
Math 407 Abstract Algebra (3)
Math 414 Topology (3)
Math 417 Foundations of Geometry (3)
Math 430 Number Theory (3)
Math 471 Introduction to Combinatorics (3)

Cognates (9-11 units)
Each student is required to complete one of the following cognates:

Actuarial Cognate (9 units)
Finance 320 Business Finance (3) and One of the following options:

Two of the following courses:
Finance 332 Theory of Corporate Finance (3)
Finance 340 Introduction to Investments (3)
Finance 360 Principles of Insurance (3)
  OR InfoSys/DecSci 361B Quantitative Business Analysis: Statistics and Management Science (3) and
InfoSys/DecSci 440 Integrative Decision Tools for Business Operations (3)

Computer Science Cognate (10 units)
Comp Sci 131 Data Structures Concepts (3)
Any one of the Comp Sci 223 courses (3)
Comp Sci 240 Computer Organization and Assembly Language (3)
  OR Comp Sci 332 File Structures and Database Systems (3)
Comp Sci 253U Workshop in UNIX (1)

Economics Cognate (9 units)
Economics 201 Principles of Microeconomics (3)
Economics 202 Principles of Macroeconomics (3)

One of the following:
Economics 310 Intermediate Microeconomic Analysis (3)
Economics 320 Intermediate Macroeconomics Analysis (3)
Economics 440 Econometrics (3)
Economics 441 Mathematical Economics (3)

Information Systems and Decision Sciences Cognate (9 units)
Three courses from the following list:
InfoSys/DecSci 422 Surveys and Sampling Design and Applications (3)
InfoSys/DecSci 465 Linear Programming in Management Science (3)
InfoSys/DecSci 467 Statistical Quality Control (3)
InfoSys/DecSci 472 Design of Experiments (3)
InfoSys/DecSci 474 Data Mining (3)
InfoSys/DecSci 475 Multivariate Analysis (3)
InfoSys/DecSci 490 Queuing and Stochastic Models in
Management Science (3)

Physics Cognate (11 units)
Physics 225 Fundamental Physics: Mechanics (3)
Physics 225L Fundamental Physics: Laboratory (1)
Physics 226 Fundamental Physics: Electricity and Magnetism (3)
Physics 226L Fundamental Physics: Laboratory (1)
Physics 227 Fundamental Physics: Waves, Optics and
Modern Physics (3)

Chemistry Cognate (10 units)
Chemistry 120A General Chemistry (5)
Chemistry 120B General Chemistry (5)

Civil Engineering Cognate (9 units)
EGCE 201 Statics (3)
EGCE 301 Mechanics of Materials (3)
One of the following:
EGCE 302 Dynamics (3)
EGCE 325 Structural Analysis (3)

Mathematics Cognate (9 units)
Three upper-division courses in Mathematics from one of the four concentrations of the Mathematics major other than the student’s own concentration.

Research Cognate (9 units)
The research cognate is intended for students who would benefit more from research and a thesis than a standard cognate, for example, a student intending to enter graduate school in mathematics. The research student/adviser connection must be established by mutual consent, and prior to enrollment in cognate courses, the undergraduate research committee must approve a cognate plan. The student must pass a thesis defense at the end of the term in which the final cognate courses are completed. Although only one unit of seminar is formally required, it is strongly encouraged that the seminar course be taken during the entire research cognate process. Students should begin the cognate no later than their junior year.

Math 491 Research Seminar (1)
Math 497 Undergraduate Research (3,3)
Math 498 Senior Thesis (2)

Writing Requirement
Math 380 will satisfy the University’s upper-division writing requirement for mathematics majors.

Internships in Mathematics
Internships in applied mathematics provide work experience in advanced mathematics through positions in business, industry or government. Students should contact the Center for Internships and Cooperative Education, LH-209.

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MINOR IN MATHEMATICS
The mathematics minor consists of 25 units of course work which must include Math 150A,B, 250A,B and at least nine units of upper-division mathematics. Math 303A,B, 380, 401, 402, 403A,B, 495, 496 or 499 may not be used to fulfill the requirements for the minor in mathematics. All courses must be completed with a grade of “C” (2.0) or better.

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MINOR IN MATHEMATICS FOR TEACHER EDUCATION

A. For elementary education the minor consists of 20 units of course work selected from the courses offered by the Department of Mathematics. The courses must include Mathematics 150B or 338, and Mathematics 303A,B. All courses must be completed with a grade of “C” (2.0) or better.

B. For secondary education the minor consists of 22 units of course work selected from the courses offered by the Department of Mathematics. The courses must include Mathematics 250B and six units of upper-division courses in mathematics. All courses must be completed with a grade of “C” (2.0) or better.

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SINGLE SUBJECT TEACHING REQUIREMENT IN MATHEMATICS
The Department of Mathematics offers coursework meeting the requirements for California single subject credential in mathematics. For CSUF to recommend this credential, an individual must have completed the department’s state-approved Single Subject Matter Preparation Program or equivalent, and have completed the two-semester math education and teacher education program, which includes methodology coursework and the student teaching experience. Students may enter this program in either the fall or spring semester. Students should contact the Department of Secondary Education for information on the application process and orientation meetings.

MASTER OF ARTS IN MATHEMATICS

The M.A. in Mathematics provides advanced study for students with one or more of the following interests: a Ph.D. program in mathematics or mathematics education, teaching in high school or community college, or using mathematical analysis in government, business or industry. Two options are offered under the M.A. program: Teaching and Applied Mathematics, as well as a Special Topics program.

The Teaching option is designed for those individuals who are presently teaching mathematics at the secondary or community college level. Students must have completed courses in linear algebra, modern algebra and advanced calculus with at least a “B” (3.0) average. In addition, students should have completed a minimum of one year of full-time teaching.

The Applied Mathematics option is designed specifically for individuals who are seeking, or who currently hold positions that involve mathematics or quantitative applications. Students must have completed one semester of mathematical probability and one semester of advanced calculus with grades of “B” (3.0) or better in each course.

The Special Topics program allows the student under certain circumstances to develop a personalized study plan in order to pursue advanced work in mathematics. The courses must be selected from our regular offerings at the undergraduate and graduate level.

Admission Requirements
Students are admitted in conditionally classified standing when the following requirements have been met:

  • A bachelor’s degree from an accredited institution
  • A grade-point average of at least 2.5 in the last 60 semester units attempted
  • Good standing at the last college attended
  • An undergraduate major in mathematics with a 3.0 in all upper-division mathematics courses or a combination of previous course work and work experience approved as equivalent by the graduate committee of the Mathematics Department.

Classified Standing
A student’s status is changed to classified standing when the following requirements have been met:

  • Completion of all prerequisites and/or deficiencies including the University Writing Requirement.
  • Development of a study plan approved by the Mathematics Department and Academic Programs. The study plan should be developed prior to the completion of 9 units.

Teaching Option
This option, designed for mathematics teachers, requires 30 units of graduate study approved by the graduate committee. At least sixteen of these units must be 500-level mathematics courses. The following course work must be included:

Math 581 Studies in Geometry (3)
Math 582 Studies in Algebra (3)
Math 584 Studies in Analysis (3)
Math 586 Studies in Discrete Mathematics (3)
Math 587 Studies in Mathematical Problem Solving (3)
Math 599 Independent Graduate Research (3-6)

Each student will be required to take adviser-approved mathematics electives to meet the 30-unit requirement, and pass a set of four comprehensive exams. Comprehensive exams may be taken no more than twice.

Applied Mathematics Option

The courses for this option have been developed in consultation with mathematicians and scientists in the local industrial community and are specifically intended for individuals who are seeking positions, or who currently hold positions, that involve mathematics or quantitative applications. The subject matter emphasizes modern practical applied mathematics, modeling, problem solving and computation. The culminating experience is a project in which students have the opportunity of working in teams on a real world problem, contracted and paid for by a local industrial firm. Students normally begin this program in the fall semester. All classes are scheduled in the evening and can be taken in sequence in two calendar years, summers included.

Math 489A,B Applicable Analysis and Linear Algebra (3,3)
Math 501A,B Numerical Analysis and Computation I and II (3,3)
Math 502A,B Probability and Statistics I and II (3,3)
Math 503A,B Mathematical Modeling I and II (3,3)
Math 504A,B Simulation Modeling and Analysis (3,3)
Math 597 Project (6)

Special Topics Program
The Special Topics program requires a study plan with a minimum of 30 units of course work, planned by the student and the student’s adviser, and approved by the graduate committee of the Mathematics Department. At least 16 of these units must be 500-level mathematics courses. Some of the 500-level courses may be accompanied by one unit of Mathematics 599 Independent Graduate Research. Students will also be required to pass a set of comprehensive exams or complete a six-unit project.

Application Deadline
The deadlines for completing online applications are March 1st for the fall semester and October 1st for the spring semester (see http://www.csumentor.edu). Mailed applications need to be postmarked by the same deadlines. However, deadlines may be changed based upon enrollment projections. Check the university graduate studies website for current information at http://www.fullerton.edu/graduate.

Additional Information
Part-time teaching opportunities and research assistantships are available for selected graduate students. For more information, contact the Department of Mathematics.

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MATHEMATICS COURSES
Courses are designated as MATH in the class schedule.

MATH 030A    Intermediate Algebra-ILE

Description: Prerequisite: A score of 30 or below on the ELM exam. An intermediate algebra course designed specifically for students who have taken but not passed the ELM exam. Equations and inequalities, algebraic expressions, functions, and sequences and series. Degree credit is not awarded for these courses. Successful completion of Math 30A and 30B satisfies the ELM requirement.
Units: (3)

MATH 030B    Intermediate Algebra-ILE

Description: Prerequisite: Math 30A and a score of 30 or below on the ELM exam. An intermediate algebra course designed specifically for students who have taken but not passed the ELM exam. Equations and inequalities, algebraic expressions, functions, and sequences and series. Degree credit is not awarded for these courses. Successful completion of Math 30A and 30B satisfies the ELM requirement.
Units: (3)

MATH 040    Intermediate Algebra

Description: Prerequisite: a score of 32-48 on the ELM exam. An intermediate algebra course designed specifically for students who have taken but not passed the ELM exam. Linear equations and inequalities, polynomial, rational, and radical expressions, quadratic functions, exponential and logarithmic functions, and sequences and series. Degree credit is not awarded for this course. Successful completion satisfies the ELM requirement.
Units: (3)

MATH 045    Intermediate Algebra Minicourse

Description: Prerequisite: a score between 36 and 48 on the ELM exam. An intermediate algebra course designed specifically for students who have taken but not passed the ELM exam. Linear equations, polynomials, rational expressions, radical expressions, quadratic formulas, exponential functions and logarithmic functions. Degree credit is not awarded for this course. Successful completion satisfies the ELM requirement. Offered via Internet only.
Units: (1)

MATH 110    Mathematics for Liberal Arts Students

Description: Prerequisites: passing score on the ELM or exemption and three years of high school mathematics, including two years of algebra and one year of geometry. Survey of traditional and contemporary topics in mathematics, such as elementary logic, counting techniques, probability, graph theory, codes and coding, and the mathematics of the social sciences. For non-science majors. (CAN MATH 2)
Units: (3)

MATH 115    College Algebra

Description: Prerequisites: passing score on the ELM or exemption and three years of high school mathematics, including two years of algebra and one year of geometry. For students planning to take Math 130 or 135. Equations, inequalities, and systems of equations. Properties of functions and their graphs, including polynomial functions, rational functions, exponential and logarithmic functions, with applications. Sequences and series. If both Math 115 and Math 125 are taken, credit is given for second course only. (CAN MATH 10)
Units: (4)

MATH 120    Introduction to Probability and Statistics

Description: Prerequisites: passing score on the ELM or exemption and three years of high school mathematics, including two years of algebra and one year of geometry. Set algebra, finite probability models, sampling, binomial trials, conditional probability and expectation. Recommended for students of economics, business, the biological, geological and social sciences.
Units: (3)

MATH 125    Precalculus

Description: Prerequisites: passing score on the ELM or exemption and three years of high school mathematics, including two years of algebra and one year of geometry. For students planning to take Math 150A. Functions and their use in mathematical models, including linear functions, polynomial and rational functions, exponential and logarithmic functions, and trigonometric functions. If both Math 115 and Math 125 are taken, credit is given for second course only. (CAN MATH 16)
Units: (5)

MATH 125W    Precalculus Workshop

Description: Corequisites: Math 125 and consent of instructor. Supplementary problem-solving workshop in a collegial setting.
Units: (1)

MATH 130    A Short Course in Calculus

Description: Prerequisites: three years of high school mathematics, including two years of algebra and one year of geometry; a passing score on the ELM or exemption; and a passing score on the MQE or exemption. Math 115 or Math 125 (with a grade of “C” (2.0) or better) is an MQE exemption. A survey of differential and integral calculus and applications. For students of biological and social sciences, business and economics. If both Math 130 and Math 135 are taken, credit is given for second course only. Six units of credit are given if both Math 130 and Math 150A are taken. (CAN MATH 30)
Units: (4)

MATH 135    Business Calculus

Description: Prerequisites: three years of high school mathematics, including two years of algebra and one year of geometry; a passing score on the ELM or exemption; and a passing score on the MQE or exemption. Math 115 or Math 125 (with a grade of “C” (2.0) or better) is an MQE exemption. A survey of differential and integral calculus with applications, including derivatives, integrals and max-min problems. For students of business and economics. If both Math 130 and Math 135 are taken, credit is given for the second course only. Six units of credit are given if both Math 135 and 150A are taken. (CAN MATH 34)
Units: (3)

MATH 150A    Calculus

Description: Prerequisites: four years of high school mathematics, including geometry, two years of algebra and trigonometry; a passing score on the ELM or exemption; and a passing score on the MQE or exemption. Math 125 (with a grade of “C” (2.0) or better) is an MQE exemption. Properties of functions. The limit, derivative, and definite integral concepts; applications of the derivative, techniques and applications of integration. Six units of credit are given for both Math 150A and Math 130 or for both Math 150A and Math 135. (150A = CAN MATH 18, 150B = CAN MATH 20; 150A + 150B = CAN MATH SEQ B; 150A, 150B, + 250A = CAN MATH SEQ C)
Units: (4)

MATH 150B    Calculus

Description: Prerequisite: Math 150A or equivalent. Techniques of integration, improper integrals and applications of integration.
Units: (4)

MATH 151A    Calculus I Workshop

Description: Corequisites: Math 150A and consent of instructor. Supplementary problem-solving in a collegial setting. (3 hours workshop)
Units: (1)

MATH 151B    Calculus II Workshop

Description: Corequisites: Math 150B and consent of instructor.  Supplementary problem-solving in a collegial setting. (3 hours workshop)
Units: (1)

MATH 196    Student-to-Student Tutorials

Description: Consult “Student-to-Student Tutorials” in this catalog for more complete course description. May be taken Credit/No Credit only.
Units: (1-3)

MATH 250A    Multivariate Calculus

Description: Prerequisites: Math 150A,B or equivalent. Calculus of functions of several variables. Partial derivatives and multiple integrals with applications. Parametric curves, vector-valued functions, vector fields, line integrals, Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem. (CAN MATH 22; 150A + 150B + 250A = CAN MATH SEQ C).
Units: (4)

MATH 250B    Introduction to Linear Algebra and Differential Equations

Description: Prerequisite: Math 250A. An introduction to the solutions of ordinary differential equations and their relationship to linear algebra. Topics include matrix algebra, systems of linear equations, vector spaces, linear independence, linear transformations and eigenvalues.
Units: (4)

MATH 270A    Mathematical Structures I

Description: Prerequisite: four years of high school mathematics. First of two semesters of fundamental discrete mathematical concepts and techniques needed in computer-related disciplines. Logic, truth tables, elementary set theory, proof techniques, combinatorics and Boolean algebra.
Units: (3)

MATH 270B    Mathematical Structures II

Description: Prerequisite: Math 270A. Second of two semesters of fundamental discrete mathematical concepts and techniques needed in computer-related disciplines. Graph theory, algebraic structures and linear algebra.
Units: (3)

MATH 280    Strategies of Proof

Description: Prerequisite: Math 150B. Logic, set theory, and methods for constructing proofs of mathematical statements. A bridge to the rigors of upper-division mathematics courses containing significant abstract content.
Units: (3)

MATH 302    Modern Algebra

Description: Prerequisites: Math 250B and Math 280. The integers, rational numbers, real and complex numbers, polynomial domains, introduction to groups, rings, integral domains and fields.
Units: (3)

MATH 303A    Fundamental Concepts of Elementary Mathematics

Description: Prerequisite: Completion of a mathematics course that satisfies the General Education requirement. Structure and form of the mathematics that constitutes the core of the K-8 mathematics curriculum, including the real number system, number theory and equations.
Units: (3)

MATH 303B    Fundamental Concepts of Elementary Mathematics

Description: Prerequisites: Completion of a mathematics course that satisfies the General Education requirement and a grade of “C” (2.0) or better in Math 303A. Structure and form of the mathematics that constitutes the core of the K-8 mathematics curriculum, including the real number system, number theory and equations.
Units: (3)

MATH 306    Vector and Tensor Analysis

Description: Prerequisite: Math 250B. Vector analysis, including coordinate bases, gradient, divergence, and curl, Green’s, Gauss’ and Stokes’ theorems. Tensor analysis, including the metric tensor, Christoffel symbols and Riemann curvature tensor. Applications will be drawn from differential geometry, continuum mechanics, electromagnetism, general relativity theory.
Units: (3)

MATH 307    Linear Algebra

Description: Prerequisite: Math 250B. Corequisite: Math 280. Introduction to the theory of vector spaces. Linear equations and matrices, determinants, linear transformations and eigenvalues, norms and inner products.
Units: (3)

MATH 310    Ordinary Differential Equations

Description: Prerequisite: Math 250B. Theory and methods of solutions for ordinary differential equations, including Laplace transform methods and power series methods. Oscillation theory for second order linear differential equations and/or theory for systems of linear and nonlinear differential equations.
Units: (3)

MATH 320    Introduction to Mathematical Computation

Description: Corequisite: Math 250B. Introduction to problem-solving on the computer using modern interactive software. Numerical and symbolic computation. A variety of problems arising in mathematics, science, and engineering will be explored. Also serves as preparation for subsequent computer-based courses in mathematical modeling.
Units: (3)

MATH 335    Mathematical Probability

Description: Prerequisite: Math 250A. Probability theory; discrete, continuous, and multivariate probability distributions, independence, conditional probability distribution, expectation, moment generating functions, functions of random variables, and the central limit theorem.
Units: (3)

MATH 337    Introduction to Experimental Design and Statistics in the Laboratory Sciences

Description: Prerequisite: passing score on the ELM or exemption; completion of one of the following courses: Biology 241, 261; Chemistry 120; or Physics 211, 225. Graphical and numerical descriptive statistics; experimental design, randomization, replication, block designs, stratified samples, controlled experiments versus observational studies. Fundamental inference for proportions, means, variances. Analysis of variance, regression. Computer analysis of data from the laboratory sciences, e.g., biology, chemistry, geology.
Units: (3)

MATH 338    Statistics Applied to Natural Sciences

Description: Prerequisite: Math 130 or 150B or consent of instructor. Introduction to the theory and application of statistics. Elementary probability, estimation, hypothesis testing, regression, analysis of
Units: (4)

MATH 340    Numerical Analysis

Description: Prerequisites: Math 250B and one of the following: Math 320, Comp Sci 120, Comp Sci 121 or equivalent. Approximate numerical solutions of systems of linear and nonlinear equations, interpolation theory, numerical differentiation and integration, numerical solution of ordinary differential equations. Computer coding of numerical methods.
Units: (3)

MATH 350    Advanced Calculus I

Description: Prerequisite: Math 250B. Corequisite: Math 280. Development of the theoretical foundations of calculus with an emphasis on mathematical rigor and formal proof. Algebraic and topological properties of the real numbers; limits of sequences and functions; continuity, differentiation, and integration of functions of one variable; infinite series.
Units: (3)

MATH 368    First Course in Symbolic Logic

Description: (Same as Philosophy 368)
Units: (3)

MATH 370    Mathematical Model Building

Description: Prerequisite: Math 250B or consent of instructor and one of the following: Math 320, Comp Sci 120, Comp Sci 121 or equivalent. Introduction to mathematical models in science and engineering: dimensional analysis, discrete and continuous dynamical systems, flow and diffusion models.
Units: (3)

MATH 375    Discrete Dynamical Systems and Chaos

Description: Prerequisite: Math 250B or consent of instructor. Analysis of the evolution of linear and nonlinear deterministic discrete systems with emphasis on long range behavior, stability and instability of stationary states and periodic orbits, chaotic orbits, strange attractors, fractional dimension and Lyapunov exponents; examples from current research literature.
Units: (3)

MATH 380    History of Mathematics

Description: Prerequisite: Math 250B. The history of mathematics through its methods and concepts. Designed to help the student become proficient in writing and reading mathematical literature. Satisfies the upper-division writing requirement for mathematics majors.
Units: (3)

MATH 390    Introduction to Actuarial Science

Description: Prerequisite: Math 150B. Corequisites: Math 335 or 338 or InfoSys/DecSci 361A. Fundamentals of actuarial science, including risk theory, interest theory, rate making, loss reserve, and actuarial modeling. Selective corporate finance, investment and insurance topics, such as amortization, bonds, sinking funds, securities, annuities, and pensions.
Units: (3)

MATH 401    Algebra and Probability for the Secondary Teacher

Description: Prerequisites: 12 units of upper-division mathematics exclusive of Math 303A,B and Math 403A,B. Overview of mathematical topics relevant to the teacher of secondary mathematics. Problem-solving approach to areas including algebra, number theory, combinatorics and probability while maintaining an historical perspective.
Units: (3)

MATH 402    Logic and Geometry for the Secondary Teacher

Description: Prerequisites: 12 units of upper-division mathematics exclusive of Math 303A,B and Math 403A,B. A course parallel to Math 401 but with emphasis on geometry, trigonometry and the theory of equations.
Units: (3)

MATH 403A    Fundamental Concepts of Middle School Mathematics I

Description: Prerequisite: Math 303B. Designed to provide content background in mathematics to help satisfy credentialing requirements for teaching mathematics at the middle school level. Focuses on gaining a thorough understanding of algebra, including patterns, functions and the use of technology.
Units: (3)

MATH 403B    Fundamental Concepts of Middle School Mathematics II

Description: Prerequisite: Math 403A. Designed to provide content background in mathematics to help satisfy credentialing requirements for teaching mathematics at the middle school level. Focuses on gaining a thorough understanding of advanced algebra, geometry, probability and statistics, and the use of technology.
Units: (3)

MATH 406    Introduction to Partial Differential Equations

Description: Prerequisite: Math 306. First order linear and quasi-linear partial differential equations. Classification of second order linear partial differential equations. Fourier analysis, Sturm-Liouville theory, integral transforms, and their application to boundary-value problems for the potential, wave, and diffusion equations.
Units: (3)

MATH 407    Abstract Algebra

Description: Prerequisite: Math 302. Sets, mappings, groups, rings, modules, fields, homomorphisms, advanced topics in vector spaces and theory of linear transformations, matrices, algebras, ideals, field theory, Galois theory.
Units: (3)

MATH 412    Complex Analysis

Description: Prerequisite: Math 350. Complex differentiation and integration, Cauchy’s theorem and integral formulas, maximum modulus theorem, harmonic functions, Laurent series, analytic continuation, entire and meromorphic functions, conformal transformations and special functions.
Units: (3)

MATH 414    Topology

Description: Prerequisite: Math 350. Topological spaces and continuous functions, connectedness and compactness, metric spaces and function spaces.
Units: (3)

MATH 417    Foundations of Geometry

Description: Prerequisite: Math 307. A study of the foundations of Euclidean and non-Euclidean geometries through transformations and formal axiomatics.
Units: (3)

MATH 425    Differential Geometry

Description: Prerequisite: Math 307. The differential geometry of curves and surfaces. Frenet-Seret formulas, the Gauss-Weingarten equations, the Gauss-Bonnet theorem.
Units: (3)

MATH 430    Number Theory

Description: Prerequisite: Math 302. Basic concepts of classical number theory with modern applications. Divisibility, congruences. Diophantine approximations and equations, primitive roots, continued fractions. Applications to public key cyprotography, primality testing, factoring methods, and check digits.
Units: (3)

MATH 435    Mathematical Statistics

Description: Prerequisite: Math 335 or equivalent. Statistical theory and its applications, based on the use of calculus.
Units: (3)

MATH 436    Advanced Applied Statistics

Description: (Same as Biology 436)
Units: (4)

MATH 438    Introduction to Stochastic Processes

Description: Prerequisite: Math 335. Stochastic processes including Markov chains, the Poisson Process, the Wiener Process. Applications to birth and death processes and queuing theory.
Units: (3)

MATH 439    Intermediate Data Analysis

Description: Prerequisite: Math 250B or 270B, and 338. Simple and multiple linear regression, testing hypotheses, dummy variables, ANOVA, ANCOVA, confounding and interaction, diagnostics, influence and outliers, transformation and weighting, and model selection. Introductory nonlinear and logistic regression. SAS statistical software will be used.
Units: (3)

MATH 440    Advanced Numerical Analysis

Description: Prerequisite: Math 340. Advanced topics in numerical analysis selected from iterative methods for linear systems, approximation of eigenvalues and eigenvectors, numerical methods for ordinary and partial differential equations, optimization methods and approximation theory. Error and convergence analysis and computer coding.
Units: (3)

MATH 450    Advanced Calculus II

Description: Prerequisite: Math 350. Sequences and series of functions. Continuity, differentiation, and integration of functions of several variables. Advanced topics in analysis, such as Lebesgue integration or the theory of metric spaces.
Units: (3)

MATH 470    Advanced Mathematical Model Building

Description: Prerequisites: Math 307, 335, and 370. A capstone course for students with strong mathematical preparation. Topics may include stochastic models, Monte Carlo integration, simulation of discrete event systems, simulation software, and further studies in dynamic systems and flow and diffusion models.
Units: (3)

MATH 471    Combinatorics

Description: Prerequisite: Math 302 or 307. Analysis of discrete structures, including existence, enumeration, and optimization. Permutations and combinations, combinatorial identities, the inclusion-exclusion principle, recurrence relations, Polya counting. Basic definitions and properties of graphs, Eulerian and Hamiltonian graphs, trees, graph colorings and chromatic number, planar graphs.
Units: (3)

MATH 489A    Applicable Linear Algebra

Description: Prerequisites: undergraduate calculus, linear algebra, advanced calculus and consent of instructor. Corequisite: Math 489B. Topics from linear algebra useful in graduate studies in applied mathematics. Finite and infinite dimensional vector spaces, linear transformations and matrices. An introduction to Hilbert spaces. The projection theorem and some of its applications.
Units: (3)

MATH 489B    Applicable Analysis

Description: Prerequisites: undergraduate calculus, linear algebra, advanced calculus and consent of instructor. Corequisite: Math 489A. Topics from analysis useful in graduate studies in applied mathematics. Topics may include initial and boundary value problems, including series solutions, eigenvalues and eigenfunctions, Fourier analysis, generalized functions, an introduction to the calculus of variations, and transform methods.
Units: (3)

MATH 491    Research Seminar

Description: Prerequisite: consent of instructor. Corequisite: Math 497 or 498. Students are required to attend the weekly undergraduate research seminars and give at least one seminar presentation as determined by the faculty adviser. May be repeated for credit.
Units: (1)

MATH 495    Internship in Applied Mathematics

Description: Prerequisites: 15 units of upper-division mathematics and consent of instructor. Work experience in advanced mathematics through positions in business, industry or government.
Units: (1-3)

MATH 496    Student-to-Student Tutorials

Description: Consult “Student-to-Student Tutorials” in this catalog for more complete course description. May be taken Credit/No Credit only.
Units: (1-3)

MATH 497    Undergraduate Research

Description: Prerequisites: nine units of upper-division math and consent of instructor. Methods of research in the mathematical sciences through a research project supervised by a departmental faculty. May be repeated for up to 6 units credit towards major.
Units: (1-3)

MATH 498    Senior Thesis

Description: Prerequisites: six units Math 497 (up to 2 units concurrently) and consent of instructor. Preparation, presentation, and defense of thesis. Topic approved by the undergraduate research committee. Thesis formatted in accordance with journal in field. May not be repeated for credit.
Units: (2)

MATH 499    Independent Study

Description: Prerequisite: consent of instructor. Special topic in mathematics, selected in consultation with and completed under supervision of instructor.
Units: (1-3)

MATH 501A    Numerical Analysis and Computation I

Description: Prerequisites: Math 489A,B. Corequisite: Math 501B. Numerical methods for linear and nonlinear systems of equations, eigenvalue problems. Interpolation and approximation, spline functions, numerical differentiation, integration and function evaluation. Error analysis, comparison, limitations of algorithms.
Units: (3)

MATH 501B    Numerical Analysis and Computation II

Description: Prerequisites: Math 489A,B. Corequisite: Math 501A. Numerical methods for initial and boundary-value problems for ordinary and partial differential equations. The finite element method. Error analysis, comparison, limitations of algorithms.
Units: (3)

MATH 502A    Probability and Statistics I

Description: Prerequisites: Math 335, 489A,B. Corequisite: Math 502B. Theory and applications of probability models including univariate and multivariate distributions; expectations and transformations of random variables. Must be taken prior to or concurrently with Math 502B.
Units: (3)

MATH 502B    Probability and Statistics II

Description: Prerequisite: Math 335, 489A,B. Corequisite: Math 502A. Theory and applications of sampling theory, statistical estimation, and hypothesis testing. Must be taken after or concurrently with Math 502A.
Units: (3)

MATH 503A    Mathematical Modeling I

Description: Prerequisites: Math 489A,B and 501A,B. Mathematical modeling concepts. Topics may include: dimensional analysis, scaling, and sensitivity; system concepts, state space, observability, controllability, and feedback; dynamical systems, models and stability analysis; optimization models.
Units: (3)

MATH 503B    Mathematical Modeling II

Description: Prerequisite: Math 503A. Development and analysis of mathematical models in such areas as mechanics, economic planning, operations management, environmental and ecological sciences, biology and medicine.
Units: (3)

MATH 504A    Simulation Modeling and Analysis

Description: Prerequisites: Math 501A,B; 502A,B; 503A,B. Corequisite: Math 504B. Advanced techniques of simulation modeling, including the design of Monte Carlo, discrete event, and continuous simulations. Topics may include output data analysis, comparing alternative system configurations, variance-reduction techniques, and experimental design and optimization.
Units: (3)

MATH 504B    Applications of Simulation Modeling Techniques

Description: Prerequisites: Math 501A,B; 502A,B; 503A,B. Corequisite: Math 504A. Introduction to a modern simulation language, and its application to simulation modeling. Topics will include development of computer models to demonstrate the techniques of simulation modeling, model verification, model validation, and methods of error analysis.
Units: (3)

MATH 581    Studies in Geometry

Description: Prerequisites: Math 307, graduate standing, plus one year of full-time teaching in secondary school mathematics. Topics relating to the high school curriculum from an advanced standpoint including the axiomatic method and non-Euclidean geometry.
Units: (3)

MATH 582    Studies in Algebra

Description: Prerequisites: Math 302, graduate standing, plus one year of full-time teaching in secondary school mathematics. Topics relating to the high school curriculum from an advanced standpoint including algorithms, fields and polynomials.
Units: (3)

MATH 583    Topics in Statistics

Description: Prerequisite: Math 338, graduate standing, plus one year of full-time teaching in secondary school mathematics. Calculus based course is designed to teach appropriate strategies and tools to effectively address problems in statistics. Includes project design, exploratory data analysis and interpretation, and effective communication of results.
Units: (3)

MATH 584    Studies in Analysis

Description: Prerequisites: Math 350, graduate standing, plus one year of full-time teaching in secondary school mathematics. Topics relating to the high school curriculum from an advanced standpoint including limits, continuity, differentiation and integration.
Units: (3)

MATH 586    Studies in Discrete Mathematics

Description: Prerequisites: Math 335 and one of the following: Math 320, Comp Sci 120, Comp Sci 121 or equivalent; graduate standing and one year of full time teaching in secondary school mathematics. Topics relating to the high school curriculum from an advanced standpoint including combinatorics, probability, matrices, and linear programming.
Units: (3)

MATH 587    Studies in Mathematical Problem Solving

Description: Prerequisites: Math 302, graduate standing, plus one year of full-time teaching in secondary school mathematics. Problem solving via non-routine and enrichment-type problems from several branches of mathematics.
Units: (3)

MATH 597    Project

Description: Prerequisite: consent of instructor. May be repeated for credit. Students in the Applied Master’s Program earn a total of 6 units
Units: (3)

MATH 599    Independent Graduate Research

Description: Prerequisites: graduate standing and consent of instructor. One unit required for each regular graduate course. Also offered without being attached to any course. May be repeated for credit.
Units: (1-3)

MATHEMATICS EDUCATION COURSES
Courses are designated as MAED in the class schedule

MAED 442    Teaching Mathematics in Secondary School

Description: Prerequisite: admission to Teacher Education Program in Mathematics or consent of instructor. Objectives, methods, and materials and technology for teaching mathematics. Required before student teaching, of mathematics majors for the general single subject credential. (2 hours lecture, 2 hours activity)
Units: (3)

MAED 449E    Externship in Secondary Teaching

Description: See description under Department of Secondary Education.
Units: (3)

MAED 449I    Internship in Secondary Teaching

Description: See description under Department of Secondary Education.
Units: (10)

MAED 449S    Seminar in Secondary Teaching

Description: See description under Department of Secondary Education.
Units: (3)

MAED 499    Independent Study

Description: Prerequisite: consent of instructor. Special topic in mathematics education, selected in consultation with and completed under supervision of the instructor. May be repeated for credit.
Units: (1-3)

MAED 530    Teaching Problem Solving in Middle School

Description: Prerequisite: Math 403B. Seminar to explore techniques of problem solving for mathematics teachers of grades 5-9. Review of research on problem solving at the middle school level. Review of state and national documents on middle school mathematics education. Emphasis on problem solving in algebra, geometry and probability.
Units: (3)

 

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