Mathematics Option

Mathematics Education Option

See Mathematics Education Option

Introductory Mathematics: Subject Matter Authorization

Middle School Mathematics Option

High School Mathematics Option

Faculty

Frederic Brulois, Department Chair

Matthew Jones, MAT Graduate Program Coordinator

Jacqueline Barab, Frederic Brulois, George Jennings, Matthew Jones, Wai Yan Pong, Serban Raianu, Alexander Stanoyevitch

Department Office: NSM A-124, (310) 243-3378

Website: math.csudh.edu

Center for Science and Mathematics Education

NSM A-115, (310) 243-2203

Emeritus Faculty

Chi-lung Chang, William Gould, Garry Hart, Jackson Henry, Eunice Krinsky, Frank Miles, John Wilkins

Mathematics is about number operations and algebra, motion and change (calculus and differential equations), logical analysis, scientific visualization, structure and geometry, the prediction of random events (probability), the extraction of useful information from large sets of data (statistics), the discovery of the best ways to do things (optimization). It is abstract and theoretical, and intensely down-to-earth and practical, all at the same time.

The mathematics major and minor prepare students for exciting and rewarding work in industry, careers in teaching, and for advanced post-baccalaureate study. Our calculus, differential equations, analysis, and probability and statistics courses enable science students to analyze data and predict outcomes in static and dynamic situations. Our foundations, discrete math and algebra courses give students the tools they need for rigorous logical and structural analysis and a deep conceptual understanding of quantitative situations. Our mathematics education courses prepare students to be outstanding teacher leaders with a deep knowledge of mathematics and the best practices in teaching. Our general education courses give the general student the mathematical background she or he needs to function in life as an educated and informed citizen in an increasingly quantitative and data-driven world.

The Mathematics Department makes every effort to attempt to offer its courses at times that are convenient for students. Courses in the mathematics option of the major are generally offered in the morning. Courses in the mathematics education option of the major and Master of Arts in Teaching Mathematics are generally offered at night to accommodate the needs of working students.

For additional information, please visit our website math.csudh.edu.

Students are welcome to see a math advisor at any time when faculty are available. All full-time math faculty serve as advisors. To schedule an appointment with an advisor, please call the math department office (310) 243-3378 or drop by NSM A-124 during regular business hours. The math department requires majors to meet with an advisor at least once each semester.

High School students should complete Algebra II, a year of geometry and trigonometry. A mathematics course should be taken in the senior year. Transfer students should complete three semesters of calculus and one additional course if possible.

A degree in mathematics is a key that opens the door to a world of opportunity. Students who major in mathematics are able to pursue a diverse range of careers. They are sought out by profit and non-profit institutions for their ability to use reasoning and logic and for their ability to solve problems. Many are interested in passing their learning on to future generations through teaching. Others seek advanced degrees in mathematics or other sciences and pursue cutting-edge research. Some will pursue degrees in business or economics, where the ability to work with numbers can be a great advantage. Those with mathematical training have gone on to careers as business executives at major software companies, as analysts for stock trading companies, as actuaries and risk management experts for insurance companies and the healthcare industry, as scientists and data analysts in engineering and biotech firms, as software designers and programmers, and a whole host of other careers.

An undergraduate student may graduate with Honors in Mathematics provided that the following criteria are met:

- A minimum of 36 units in residence at CSU Dominguez Hills;
- A minimum grade point average of at least 3.5 in all courses used to satisfy the upper division requirements in the major;
- Recommendation by the faculty of the Mathematics Department.

See the "Requirements for the Bachelor's Degree" in the University Catalog for complete details on general degree requirements. A minimum of 40 units, including those required for the major, must be upper division.

Completion of elective courses (beyond the requirements listed below) to reach a total of a minimum of 120 or a maximum of 132 units.

See the "General Education" requirements in the University Catalog or the Class Schedule for the most current information on General Education requirements and course offerings.

See the "Graduation Writing Assessment Requirement" in the University Catalog.

No minor is required.

Students must select one of the options listed below. The following courses, or their approved transfer equivalents, are required of all candidates for this degree. All courses used to satisfy this major must be passed with a grade of "C" or better.

Single field major - no minor required

A. Lower Division Required Courses (32 units):

CSC 121. Introduction to Computer Science and Programming I (4)

MAT 191. Calculus I (5)

MAT 193. Calculus II (5)

MAT 211. Calculus III (5)

MAT 271. Foundations of Higher Mathematics (3)

PHY 130. General Physics I (5)

PHY 132. General Physics II (5)

B. Recommended Course - optional (0-4 units):

CSC 123. Introduction to Computer Science and Programming II (4)

C. Additional Required Courses (27 units):

MAT 281. Discrete Mathematics (3) or

MAT 367. Numerical Analysis (3)

MAT 311. Differential Equations (3) or

MAT 411. Mathematical Modeling (3) or

MAT 460. Graph Theory and Algorithms or

PHY 306. Mathematical Methods in Physics (3) or

PHY 310. Theoretical Mechanics (3) or

PHY 380. An Introduction to Nonlinear Phenomena (3)

MAT 321. Probability and Statistics (3)

MAT 331. Linear Algebra (3)

MAT 333. Abstract Algebra (3)

MAT 361. Finite Automata (3) or

MAT 347. Modern Geometry (3) or

MAT 447. Number Theory (3) or

MAT 448. Cryptography (3)

MAT 401. Advanced Analysis I (3)

MAT 403. Advanced Analysis II (3)

MAT 421. Complex Analysis (3)

Single field major - no minor required

This option will satisfy the subject matter preparation necessary for a secondary teaching credential in mathematics. Students do not get Subject Matter Preparation on their diploma; the diploma says Mathematics Education option.

A. Lower Division Required Courses (40 units):

MAT 131. Elementary Statistics and Probability (3)

MAT 143. Problem Solving in Mathematics (3)

MAT 191. Calculus I (5)

MAT 193. Calculus II (5)

MAT 211. Calculus III (5)

MAT 241. Programming and Technology in Secondary School Mathematics Teaching (3)

MAT 271. Foundations of Higher Mathematics (3)

MAT 281. Discrete Mathematics (3)

PHY 130. General Physics I (5)

PHY 132. General Physics II (5)

B. Upper Division Required Courses (28 units):

MAT 331. Linear Algebra (3)

MAT 333. Abstract Algebra (3)

MAT 347. Modern Geometry (3)

MAT 401. Advanced Analysis I (3)

MAT 411. Mathematical Modeling (3)

MAT 443. History of Mathematics (3)

MAT 447. Number Theory (3)

MAT 489. Fundamental Mathematics and Teaching in Secondary School (4)

MAT 490. Seminar in Mathematics Education (3)

All courses used to satisfy this minor must be passed with a grade of "C" or better.

A. Required Courses (21 units):

MAT 191. Calculus I (5)

MAT 193. Calculus II (5)

MAT 211. Calculus III (5)

MAT 271. Foundations of Higher Mathematics (3)

MAT 331. Linear Algebra (3)

B. Electives: Select two courses from the following (6 units):

MAT 311. Differential Equations (3)

MAT 321. Probability and Statistics (3)

MAT 333. Abstract Algebra (3)

MAT 347. Modern Geometry (3)

MAT 361. Finite Automata (3)

MAT 367. Numerical Analysis I (3)

MAT 401. Advanced Analysis I (3)

MAT 403. Advanced Analysis II (3)

MAT 411. Mathematical Modeling (3)

MAT 413. Partial Differential Equations (3)

MAT 421. Complex Analysis (3)

MAT 447. Number Theory (3)

Holders of a Single Subject or Multiple Subject credential issued by the California Commission on Teacher Credentialing may secure an Introductory Mathematics Subject Matter Authorization that allows the holder to teach the subject matter content typically included in curriculum guidelines and textbooks approved for study in grades 9 and below. This allows an employer to assign a teacher with an introductory mathematics authorization to teach a class in which the curriculum is for grades 9 and below but the students in the class may be in grades K-12.

For other requirements governing issuance of this authorization, consult the Teacher Education section of this catalog or contact the School of Education Student Services Center.

A. A minimum of 32 units is required but must include at least one course in the content areas of algebra, advanced algebra, geometry, probability or statistics, and development of the real number system or introduction to mathematics.

B. The following is an extensive list of courses, and their specific content area, that can be used to satisfy the 32-unit requirement. A Mathematics Department advisor can assist you in preparing your 32-unit coursework plan.

MAT 153. Pre-calculus (4)

MAT 307. Foundations of Middle School Math I (3)

MAT 191. Calculus I (5)

MAT 193. Calculus II (5)

MAT 309. Foundations of Middle School Math III (3)

MAT 207. Mathematics for Elementary Teacher: Geometry (3)

MAT 308. Foundations of Middle School Math II (3)

MAT 131. Elementary Statistics and Probability (3)

MAT 107. Mathematics for Elementary Teachers: Real Numbers (3) or

MAT 105. Finite Mathematics (3)

MAT 143. Problem Solving in Mathematics (3) and

MAT 141. Computer for Mathematics Teaching (3) or

MAT 241. Programming and Technology in Secondary School Mathematics Teaching (3)

Can be used toward earning the required 32 units once each specific content area has been met.

Students must submit an application to the University for admission (or readmission) with graduate standing, and official transcripts of all previous college work in accordance with the procedures outlined in the Graduate Admissions section of the University Catalog. If the student is currently enrolled as a post-baccalaureate student, he/she must obtain a Request for Postbaccalaureate/Graduate Change of Objective form from the department office and submit it to the program's Graduate Coordinator.

The student will qualify for admission to the program if he/she:

1. has a baccalaureate degree from an accredited university. (See the University Catalog for requirements of graduates of non-accredited institutions.);

2. has completed two years of teaching and is currently teaching mathematics in a California school;

3. a) has a California Single Subject Credential in Mathematics or

b) is eligible for a California Single Subject Credential in Mathematics or

c) has completed a major in mathematics or

d) has completed, with an average grade of "B" or better, 20 semester units in college level mathematics and passed a department administered entrance examination;

4. has submitted three letters of recommendation, including one from the principal at the applicant's school;

5. has completed a successful interview with the program's Graduate Coordinator and representatives from the department's mathematics education faculty;

6. has achieved a TOEFL score of 550 (for those applicants who do not possess a bachelor's degree from a postsecondary institution where English is the principal language of instruction);

7. has a grade point average of at least 2.5 (on a 4.0 scale) in his/her last 60 semester units of upper division course work; lower division courses taken after obtaining the bachelor's degree and extension courses, (except CSU Dominguez Hills upper division resident extension courses or the equivalent on other campuses), will be excluded from the calculation; and

8. is in good standing at the last college attended.

To qualify for admission with a graduate degree objective, students must meet the admission requirements for postbaccalaureate unclassified standing as well as any additional requirements of the particular program. Students who apply to a graduate degree program but who do not satisfy all program requirements may be admitted to conditionally classified status. Program coordinators will outline all conditions for attainment of classified status.

Students applying for master's degree programs will be admitted in classified status if they meet all program admission requirements.

Classified standing as a graduate student is granted by the academic unit to which the student is applying. Classified standing is normally granted when all prerequisites have been satisfactorily completed for admission to a master's degree program. Students must have classified standing to qualify for Advancement to Candidacy.

All graduate students entering the University in the Fall of 1983 or thereafter are required to satisfy the Graduation Writing Assessment requirement (GWAR) in accordance with the established policies of the university. Students must satisfy the requirements before being Advanced to Candidacy. (See "Graduation Writing Assessment requirement" section of the University Catalog.

Advancement to candidacy recognizes that the student has demonstrated the ability to sustain a level of scholarly competency commensurate with successful completion of degree requirements. Upon advancement to candidacy, the student is cleared for the final stages of the graduate program which, in addition to any remaining course work, will include the thesis, project, or comprehensive examination.

Following are the requirements for Advancement to Candidacy:

1. A minimum of 15 resident units

2. Classified standing

3. An approved Program of Study

4. Successful completion of the GWAR

5. A cumulative GPA of 3.0 in all courses taken as a graduate student

6. No grade lower than a "C" in the degree program

Advancement to Candidacy must be certified on the appropriate form to the Graduate Dean by the department prior to the final semester, prior to the semester of the comprehensive exams, and prior to enrolling in thesis or project.

The following are specific graduation requirements which must be met to earn this graduate degree:

1. Completion of a minimum of 30 semester units of approved graduate work within five years. An extension of time may be granted if warranted by individual circumstances and if the outdated work is validated by such means as examination, independent study, continuing education, relevant additional course work, or by such other demonstration of competence and/or currency as deemed acceptable by the Graduate Coordinator and mathematics education faculty.

Distribution pattern of the 30 units:

a. at least 16 semester units will be completed in residence after admission to graduate standing in the program;

b. not more than 4 semester units of Graduate Seminar in Mathematics Education (MAT 590) can be used to meet graduation requirements;

c. not more than 9 semester units may have been earned from approved extension and/or transfer course credit; and

d. upon approval by the Graduate coordinator and representatives from the mathematics education faculty, courses taken previously may be used to meet the course content requirements if they have been completed within the five years immediately preceding the completion of the requirements of the degree. However, no courses (with the exception of GED 500 - Research Methods in Education) previously used to meet their requirements of another degree may apply toward the required number of 30 semester units of approved graduate work.

2. achievement of a grade point average of 3.0 or better in all courses taken to satisfy the requirements for the degree, except that an approved course in which no letter grade is assigned shall not be used in computing the grade point average;

3. satisfactory completion of the research project, or passing all parts of the comprehensive exam The subject of the research project will depend upon that which is educationally most appropriate to the student and mathematics education. The research project is equivalent in rigor to the thesis, will be supervised by a committee of three faculty, and may include an oral defense or presentation as part of the culminating experience;

4. satisfactory completion of the Graduation Writing Assessment Requirement (GWAR); and

5. filing of an application for the award of the Master's degree.

Upon completion of the CSU Dominguez Hills' graduation requirements, award of the graduate degree must be approved by

the program, the school dean, and the faculty of the University.

The Master of Arts Degree in Mathematics requires completion of 30 units of course work and one of the following:

a. Passing score on a comprehensive written examination. After completion of all course work or during the last semester of course work, the MAT degree candidate may apply to take the comprehensive examination. There is only one retake opportunity.

b. Completion of an approved thesis or creative project (MAT 599 - 6 units). Students must have the approval of a faculty thesis advisor prior to enrolling for thesis credit.

A. Core Courses (21 units):

MAT 500. Mathematics Education Research and Design Statistics (3)

MAT 515. Topics in Advanced Finite Mathematics (3)

MAT 522. Foundations of Algebraic Thinking (3)

MAT 543. Advanced Problem Solving for Teachers (3)

MAT 545. History of Mathematics Education (3)

MAT 557. Research in Mathematics Education I (3)

MAT 559. Research in Mathematics Education II (3)

B. Each student must select one of the options below.

MAT 501. Foundations of Geometric Thinking (3)

MAT 505. Foundations of Mathematical Structures (3)

MAT 506. Foundations of Rational Numbers (3)

MAT 521. Geometry for Teachers (3)

MAT 523. Theory of Functions for Teachers (3)

MAT 525. Algebraic Structures for Teachers (3)

C. Culminating Activity (0-6 units):

MAT 599. Masters Project (6) or

Comprehensive Exam (0)

The credit value for each course in semester units is indicated for each term by a number in parentheses following the title. For course availability, please see the list of tentative course offerings in the current Class Schedule.

Students need to take the ELM test, or to have an exception from the ELM test prior to enrolling in any mathematics course. The ELM test score will be used to place the students into the proper mathematics course.

**ESM 3 Early Start Beginning Algebra (3).**

Integers, rational and real numbers, basic algebraic expressions, ratio, percent, solutions and graphs of linear equations, inequalities, polynomials, applications. Does not count for Bachelor's degree. CR/NC grading.

**ESM 9 Early Start Intermediate Algebra (3).**

Prerequisite: MAT 003 or satisfactory score on ELM test.

Polynomials, factoring, rational expressions, quadratic equations, roots, radicals, radical expressions, exponents, logarithms, graphs, applications. Does not count for the Bachelor's degree. CR/NC grading.

**ESM 11 Early Start Algebra Review Part 1 (1).**

Units of measurement, arithmetic with signed numbers and fractions, word problems, linear equations, applications. Does not count for Bachelor's degree. CR/NC grading.

*NOTE: Early Start Math (ESM) courses are offered summer term only for incoming freshmen. Contact the Office of Admissions and Records for more information.

**MAT 003 Beginning Algebra (3).**

Integers, rational and real numbers, basic algebraic expressions, ratio, percent, solutions and graphs of linear equations, inequalities, polynomials, applications. Does not count for Bachelor's degree. CR/NC grading.

**MAT 009 Intermediate Algebra (3).**

Prerequisite: MAT 003 or satisfactory score on

ELM test.

Polynomials, factoring, rational expressions, quadratic equations, roots, radicals, radical expressions, exponents, logarithms, graphs, applications. Does not count for the Bachelor's degree. CR/NC grading.

**MAT 095 Special Topics in Mathematics (3).**

A course in a topic of special interest to both faculty and students for which no current course exists. Topic will be announced in schedule of classes. Repeatable for credit. CR/NC grading

**MAT 105 Finite Mathematics (3).**

Prerequisite: Fulfillment of ELM requirement.

Mathematics of finance, combinatorics, probability, statistical measures of central tendency and dispersion, problem solving and mathematical reasoning, and additional topical selected by instructor e.g. linear programming, statistics, graph theory, game theory. A-C/NC grading. Satisfies the General Education Quantitative Reasoning Requirement.

**MAT 107 Mathematics for Elementary School Teachers: Real Numbers (3).**

Prerequisite: Fulfillment of ELM requirement.

Sets and set theoretic operations as related to counting numbers and rational numbers and arithmetic operations. Real number system and its origins, development, structure and use. Special emphasis on problem solving, and the development and application of algorithms. Does not satisfy General Education Quantitative Reasoning Requirement.

**MAT 131 Elementary Statistics and Probability (3).**

Prerequisite: Fulfillment of ELM requirement.

A practical course in probability and statistics including such topics as the binomial and normal distributions, confidence intervals, t, F, and chi-square tests, linear regression and correlation, and conditional probability. Satisfies the General Education Quantitative Reasoning Requirement.

**MAT 143 Problem Solving in Mathematics (3).**

Prerequisite: Fulfillment of the ELM requirement.

Objective is to increase students abilities to use knowledge and experience when encountering new and unexpected situations. Develop higher level thinking skills, learn to formulate, analyze, and model problems. Choosing relevant information, making conjectures, devising plans and testing solutions. A-C/NC grading. Does not satisfy General Education Quantitative Reasoning Requirement.

**MAT 153 Pre-calculus (4).**

Prerequisites: MAT 009 or equivalent.

Topics include functions and their graphs; systems of linear and quadratic equations; ratios, proportion, variation; sequences; mathematical induction; the binomial theorem; complex numbers; theory of equations and trigonometry. Satisfies the General Education Quantitative Reasoning Requirement.

**MAT 171 Survey of Calculus for Management and Life Sciences (4).**

Prerequisite: Fulfillment of ELM requirement.

Not available for credit to students who have credit in MAT 191 or its equivalent or courses which have MAT 191 as a prerequisite. Functions, linear equations, the derivative and its applications, the integral and its applications, and partial derivatives. Satisfies the General Education Quantitative Reasoning Requirement.

**MAT 191 Calculus I (5).**

Prerequisite: MAT 153 or equivalent with a grade of "C" or better and fulfillment of ELM requirement.

Limits, continuity, derivatives, differentiation formulas, applications of derivatives, introduction to integration, Fundamental Theorem of Calculus, application of integration. Satisfies the General Education Quantitative Reasoning Requirement.

**MAT 193 Calculus II (5).**

Prerequisite: MAT 191 or equivalent with a grade of "C" or better.

Differentiation and integration of transcendental function. Techniques and applications of integration. Polar coordinates. Infinite sequences and series, power series, convergence. Satisfies the General Education Quantitative Reasoning Requirement.

**MAT 195 Selected Topics in Mathematics (1-4).**

Introductory course of special interest in Mathematics for entry level students. Topic and content will vary. See class schedule for current topic.

**MAT 207 Mathematics for Elementary School Teachers: Geometry & Statistics (4).**

Prerequisite: Satisfaction of ELM required.

Primarily for prospective elementary school teachers. Geometry from an intuitive problem solving standpoint. Constructions, symmetry, translations, rotations, patterns, area, volume, and the metric system. Topics from graph theory and topology. Two hours of lecture and two hours of activity per week. Does not satisfy General Education Quantitative Reasoning Requirement.

**MAT 211 Calculus III (5).**

Prerequisite: MAT 193 or equivalent with a grade of "C" or better.

Multivariable calculus: analytic geometry, scalar and vector products, partial differentiation, multiple integration, change of coordinates, gradient, optimization, line integrals, Green's Theorem, elements of vector calculus.

**MAT 241 Programming and Technology for Teaching Secondary School** **Mathematics (3).**

Prerequisite: MAT 193 or equivalent with a grade of "C" or better.

Introduction to application software appropriate for the teaching of secondary school mathematics. The programs include spreadsheet, geometric modeling, and statistics modeling. Writing simple programs for graphing calculators to demonstrate and solve mathematical problems.

**MAT 271 Foundations of Higher Mathematics (3).**

Prerequisite: MAT 191 with grade of "C" or better.

Topics include logic, methods of mathematical proof, set theory, relations and functions. Introduction to complex numbers and proof strategies using ideas of vector algebra. Meant to prepare students for mathematics program as well as concepts of computer science.

**MAT 281 Discrete Mathematics (3).**

Prerequisite: MAT 153, and CSC 121 or MAT 241 or CSC 111 or equivalent with grade of "C" or better.

Matrix algebra, graph theory, trees, combinatorics, Boolean algebra; with applications to computers and computer programming.

**MAT 295 Selected Topics in Mathematics (1-4).**

Prerequisites: MAT 193 and consent of instructor.

A course in a topic of special interest to both faculty and students for which no current course exists. Topic will be announced in schedule of classes. Repeatable for credit. One to four hours of lecture per week.

**MAT 297 Independent Study (1-4).**

Prerequisites: MAT 193, consent of instructor and consent of department chair.

A reading program of selected topics not covered by regularly offered courses conducted under the supervision of a faculty member.

**MAT 307 Foundations of Middle School Mathematics I (3).**

Prerequisites: MAT 143 and MAT 153 with a grade of C or better.

Foundations of Mathematics related to the middle school curriculum. Course 1 includes the following topics: reasoning with numbers, basic number proofs, understanding exponents, proportional reasoning, rates, linear functions, method of finite differences, and the theory and application of these topics.

**MAT 308 Foundations of Middle School Mathematics II (3).**

Prerequisites: MAT 143 and MAT 153 and grade of C or better

Foundations of Mathematics related to the middle school curriculum. Course 2 includes the following topics: basic Euclidean facts, algebra-geometry connections, volume and surface area formulas, similarity, congruence, and scale factors, and the theory and application underlying these topics.

**MAT 309 Foundations of Middle School Mathematics III (3).**

Prerequisites: MAT 143, MAT 153, MAT 307 with grade of C or better.

Foundations of Mathematics related to the middle school curriculum. Course 3 includes the following topics: concepts of functions, inverse functions, properties of rational, trigonometric and exponential functions and fundamental concepts in Calculus.

**MAT 311 Differential Equations (3).**

Prerequisite: MAT 211 and MAT 271 with a grades of "C" or better.

Topics covered include first and second order linear equations including existence and uniqueness theorems, series solutions; nonlinear equations; systems of linear equations. Other topics may include the Laplace transform, qualitative theory.

**MAT 321 Probability and Statistics (3).**

Prerequisite: MAT 193 and MAT 271 or equivalent with grade "C" or better.

A calculus based survey of topics in probability and statistics emphasizing applications.

**MAT 331 Linear Algebra (3).**

Prerequisite: MAT 271 or equivalent with a grade of "C" or better.

Linear equations, vector spaces, matrices, linear transformations, determinants, eigenvalues, eigenvectors, etc.

**MAT 333 Abstract Algebra (3).**

Prerequisite: MAT 271 or equivalent with a grade of "C" or better.

The theory of groups, rings, ideals, integral domains, fields and related results.

**MAT 347 Modern Geometry (3).**

Prerequisite: MAT 271 or equivalent with a grade of "C" or better.

Topics in synthetic and analytic geometry; transformations, similarity, congruence, distance, angles, constructions; introduction to projective and/or non-Euclidean geometry.

**MAT 361 Finite Automata (3).**

Prerequisite: MAT 281 or equivalent with a grade of "C" or better.

Study of the abstract formalization of digital computers. Applications to computation theory and formal linguistics.

**MAT 367 Numerical Analysis I (3).**

Prerequisites: Experience in BASIC, FORTRAN or Pascal and MAT 211 or equivalent with a grade of "C" or better.

Approximation of roots of functions, interpolation formulas, numerical solutions of systems of equations, numerical differentiation and integration, numerical solutions to ordinary differential equations.

**MAT 395 Selected Topics in Mathematics (1-4).**

Prerequisites: MAT 211 and consent of instructor.

A course in a topic of special interest to both faculty and students for which no current course exists. Topic will be announced in schedule of classes. Repeatable for credit. One to four hours of lecture per week.

**MAT 401 Advanced Analysis I (3).**

Prerequisites: MAT 211 and MAT 271, or equivalent with a grade of "C" or better.

Elements of set theory, numerical sequences and series, continuity and differentiability of functions of one and several variables.

**MAT 403 Advanced Analysis II (3).**

Prerequisite: MAT 401 or equivalent with a grade of "C" or better.

Integration of functions of one and several variables, sequences and series of functions, uniform convergence, power series, differentiation of functions of several variables.

**MAT 411 Mathematical Modeling (3).**

Prerequisite: MAT 211, MAT 241, and MAT 271 or CSC 121 or CSC 111.

Flexible course content depending on interest of instructor and students. Possible topics are: epidemic and predator-prey models from differential equations; linear programming models; Arrow's theorem; and probability models.

**MAT 413 An Introduction to Partial Differential Equations (3).**

Prerequisites: MAT 311 with a grade of "C" or better is required; MAT 213 is recommended.

Solutions to partial differential equations by separation of variables and Fourier series. Applications to heat flow and diffusion, wave motion, and potentials. Some discussion of existence and uniqueness of solutions.

**MAT 421 Complex Analysis (3).**

Prerequisites: MAT 211 and MAT 271 with a grade of "C" or better. MAT 331 and MAT 401 (may be taken concurrently) are recommended.

Complex numbers; point sets, sequences and mappings; analytic functions; elementary functions; integration; power series; the calculus of residues; and applications.

**MAT 443 History of Mathematics (3).**

Prerequisite: MAT 193 with a grade of "C" or better.

Traces the growth and development of mathematics from primitive origins to present, uses methods and concepts of mathematics to present the topics.

**MAT 447 Number Theory (3).**

Prerequisite: MAT 271 with a grade of "C" or better.

Divisibility, congruencies, prime number theory, Diophantine Equations, and other topics from elementary number theory.

**MAT 448 Cryptography (3).**

Prerequisites: MAT 271 with a grade of "C" or better. CSC 115 or CSC 121 with a grade of "C" or better are recommended.

Congruencies and number theory, history and early cryptosystems, cryptographic data structures, public key cryptography, additional cryptosystems such as DES, AES, and elliptic curve cryptography. Computer implementations will also be covered, as will any needed additional mathematical topics (e.g., finite fields).

**MAT 460 Graph Theory and Algorithms (3).**

Prerequisites: MAT 211, MAT 271, and MAT 241 or CSC 121 or CSC 115, or equivalent with a grade of "C" or better. MAT 281 with a grade of "C" or better is recommended.

Graphs, digraphs, multigraphs, graph modeling, degrees and degree sequences, subgraphs, isomorphisms of graphs, and digraphs, distance concepts and applications, trees, and tree algorithms, Hamiltonian and Eulerean graphs. The viewpoints will be conceptual, theoretical, and algorithmic.

**MAT 489 Fundamental Mathematics and Teaching in Secondary Schools (4).**

Prerequisite: 9 units of 300/400-level mathematics with a grade of "C" or better; In order to begin the hours for fieldwork in this course, you will need a valid Certificate of Clearance (fingerprints) and proof of a negative TB (within 4 months of the fieldwork course beginning). For information on submitting these documents, contact the Center for Teaching Careers.

Synthesis and analysis of secondary mathematics and its teaching. Emphasis will be placed on algebraic thinking and its teaching in high school. Forty hours of secondary classroom observations will be a required activity in this course. A Certificate of Clearance is required.

**MAT 490 Seminar in Mathematics Education (3).**

Prerequisite: 9 units of 300/400 mathematics courses with a grade of "C" or better.

The synthesis and analysis of the secondary mathematics curriculum from an advanced standpoint. Emphasis will be on the integration of problem solving, investigations, reasoning, and communication as recommended in state and national standards.

**MAT 495 Selected Topics in Mathematics (1-4).**

Prerequisites: Consent of instructor and MAT 271.

A course in a topic of special interest to both faculty and students for which no current course exists. Topic will be announced in schedule of classes. Repeatable for credit. One to four hours of lecture per week.

**MAT 497 Independent Study (1-4).**

Prerequisites: MAT 211, consent of instructor and consent of department chair.

A reading program of selected topics not covered by regularly offered courses conducted under the supervision of a faculty member.

Graduate standing and consent of the graduate program coordinator is prerequisite to enrollment in graduate (500 level) courses.

**MAT 500 Mathematics Education Research Design and Statistics (3).**

Prerequisites: Students must have graduate standing and must have completed one year of full time secondary mathematics teaching.

Includes topics such as normal distribution, confidence intervals, t, F, chi-squared tests, linear regression, and correlation. These topics are presented in the context of mathematics education research in typical classrooms.

**MAT 501 Foundations of Geometric Thinking (3).**

Prerequisites: MAT 543 or concurrent enrollment. Students must have graduate standing and must have completed one year of full time secondary mathematics teaching.

Research on Various topics in geometry. Focus on developing notions of rigorous proof and grade-appropriate explanations. Topics are chosen from the Geometry areas and standards emphasized in K-12.

**MAT 505 Foundations of Mathematical Structures (3).**

Prerequisites: MAT 543 or concurrent enrollment. Students must have graduate standing and must have completed one year of full time secondary mathematics teaching.

Topics include the algebraic properties of sets and operations applied to classical number systems, equivalence, modular arithmetic, Diophantine equations, decomposition of natural numbers, special families of natural numbers, current research on understanding and learning these topics.

**MAT 506 Foundations of Rational Numbers (3).**

Prerequisites: MAT 543 or concurrent enrollment. Students must have graduate standing and must have completed one year of full time secondary mathematics teaching.

Covers theory and applications of Rational numbers. Focus on number systems, representation of numbers, equivalence classes, rationality and irrationality, properties of the rational numbers system, central ideas of proportional reasoning, and developing intuitive models of standard rules and algorithms.

**MAT 515 Topics in Advanced Finite Mathematics (3).**

Prerequisites: Possession of a baccalaureate degree and one year of full-time secondary mathematics teaching.

Topics from areas of Modern Mathematics which relate to the high school mathematics curriculum such as: algorithms, graph theory, coding theory, game theory, finite probability theory, difference equations, voting, recursion.

**MAT 521 Geometry for Teachers (3).**

Prerequisites: MAT 543, graduate standing and one year of full time secondary mathematics teaching.

Topics from Geometry including: points and lines in a triangle, properties of circles, collinearity, concurrence, transformations, arithmetic and geometric means, isoperimetric theorems, reflection principle.

**MAT 522 Foundations of Algebraic Thinking (3).**

Prerequisites: Students must have graduate standing and must have completed one year of full time secondary mathematics teaching.

Patterns, functions, and multiple representations; independent and dependent variables; discrete and continuous functions; linear and nonlinear relationships in context; connections to arithmetic operations; algebraic expressions and equations. Examines current research on the understanding and learning of these topics.

**MAT 523 Theory of Functions for Teachers (3).**

Prerequisites: MAT 543, graduate standing and one year of full time secondary mathematics teaching.

Topics from Function Theory including: mathematical models, linear functions, non-linear functions, transformations, limits, continuity, functions of several variables.

**MAT 525 Algebraic Structures for Teachers (3).**

Prerequisites: MAT 543, graduate standing and one year of full time secondary mathematics teaching.

Topics relating to the high school Algebra curriculum from an advanced standpoint including algorithms, fields, polynomials, groups, fields, and rings.

**MAT 543 Advanced Problem Solving for Teachers (3).**

Problem solving using non-routine strategies. Problems to be representative of several branches of mathematics and mathematically based disciplines.

**MAT 545 History of Mathematics Education (3).**

Prerequisites: Graduate standing and one year of full time secondary teaching.

Traces the development of the mathematics curriculum K-12 in the United States and internationally, concentrating both on content taught at different stages and the teaching methods employed. Reviews the various mathematics reform efforts over the past 170 years.

**MAT 557 Research in Mathematics Education I (3).**

Prerequisites: MAT 500 and 15 units of program.

Overview of the current research literature pertaining to mathematics education in elementary and secondary schools. Topics such as mathematical reasoning, communication, problem solving, algebra, and geometry will be discussed and analyzed.

**MAT 559 Research in Mathematics Education II (3).**

Prerequisite: MAT 557.

Overview of the current research literature pertaining to mathematics education in elementary and secondary schools. Topics such as mathematical reasoning, communication, problem solving, algebra, and geometry will be discussed and analyzed.

**MAT 590 Graduate Seminar in Mathematics Education (1-4).**

Prerequisites: Possession of a baccalaureate degree and one year of full-time secondary mathematics teaching.

Presentation and discussion of selected topics in Mathematics Education. Repeatable course.

**MAT 594 Independent Study (1-4).**

Prerequisites: Consent of instructor and department chair.

In consultation with a faculty member, the student will investigate in detail current scholarship in some area. Repeatable course.

**MAT 595 Selected Topics (1-4).**

An intensive study of selected issues in mathematics education. Repeatable course.

**MAT 597 Directed Reading (1-4).**

Prerequisites: Consent of instructor and department chair.

Extensive reading in selected areas under the guidance of faculty mentor. Repeatable course.

**MAT 598 Directed Research (1-4).**

Prerequisite: Classified graduate standing.

Students will design and conduct research projects under the direct supervision of the instructor. Repeatable course.

**MAT 599 Masters Project (6).**

Prerequisite: Advancement to Candidacy.

Completion of classroom based project under the guidance of faculty advisor. The culminating learning experience of the program which emphasizes the application of the mathematics education curriculum in the classroom.

**MAT 600 Graduate Continuation Course (0).**

Graduate students who have completed their course work but not their thesis, project, or comprehensive examination, or who have other requirements remaining for the completion of their degree, may maintain continuous attendance by enrolling in this course. Signature of graduate program coordinator required.

The following courses are scheduled on a "demand" basis. Students should consult the department office for information about the next schedule offering.

**MAT 011 Algebra Review Part 1 (1).**

Units of measurement, arithmetic with signed numbers and fractions, word problems, linear equations, and applications. Does not count for Bachelor's degree. CR/NC grading.

**MAT 012 Algebra Review Part 2 (1).**

Prerequisite: MAT 011.

Percent, ratio and proportion, equations of lines, inequalities, graphs, word problems, applications. Does not count for Bachelor's degree. CR/NC grading.

**MAT 013 Algebra Review Part 3 (1).**

Prerequisite: MAT 012.

Systems of linear equations, multiplying and dividing polynomials, solving simple polynomial and rational equations, rate, direct and indirect variation, word problems, applications. Does not count for Bachelor's degree. CR/NC grading.

**MAT 014 Algebra Review Part 4 (1).**

Prerequisite: MAT 013.

Quadratic formula, solving quadratic equations, graphs, brief and practical introduction to logarithms and exponential functions, word problems, applications. Satisfies ELM requirement. Does not count for Bachelor's degree. CR/NC grading.

**MAT 015 Algebra and Geometry Review Part 5 (1).**

Prerequisite: MAT 014.

Flexible course covering topics in intermediate algebra and geometry beyond those that are covered in the basic remedial MAT 011-014 sequence. Aimed at preparing students for more technical university level math and science courses (e.g. Pre-calculus). Does not count for the Bachelor's degree. CR/NC grading.

**MAT 016 Algebra and Geometry Review Part 6 (1).**

Prerequisite: MAT 015.

Sequel to Mat 015. Flexible course covering topics in intermediate algebra and geometry beyond those that are covered in the basic remedial MAT 011-014 sequence. Aimed at preparing students for more technical university level math and science courses (e.g. Pre-calculus). Does not count for the Bachelor's degree. CR/NC grading.

**MAT 141 Computers for Mathematics Teaching (3).**

Prerequisite: Fulfillment of the ELM requirement.

Introduction to computers for teachers of mathematics. Topics include flowcharting, programming in LOGO on microcomputers. Applications of computers to problem solving, statistics, and other areas of mathematics relevant to teachers of mathematics. Applications packages, CAI and social issues are studied. A-C/NC grading. Does not satisfy General Education Quantitative Reasoning Requirement.

**MAT 213 Calculus IV (4).**

Prerequisite: MAT 211 or equivalent with a grade of "C" or better.

Topics covered include vector calculus, line and surface integrals, and the theorems of Green, Gauss, and Stokes.

**MAT 337 Mathematical Logic (3).**

Prerequisite: MAT 191 or equivalent with a grade of "C" or better.

Topics covered include propositional calculus, classical and intuitionistic; completeness and consistency theorems; first order predicate calculus with equality; axiomatic arithmetic; Godel's Incompleteness Theorem.

**MAT 351 Probability Theory (3).**

Prerequisite: MAT 193 or equivalent with a grade of "C" or better.

Probability as a mathematical system, set theory, conditional probability and independent events, random variables, distribution and density functions, covariance and correlation, limit theorems, convolutions, computer generation of random numbers.

**MAT 353 Stochastic Processes (3).**

Prerequisite: MAT 351 or equivalent with a grade of "C" or better.

A selection from among several topics, including Markov chains; Markov processes; queuing, branching, Poisson, and Gaussian processes; stationary processes.

**MAT 369 Numerical Analysis II (3).**

Prerequisite: MAT 367 or equivalent with a grade of "C" or better.

A continuation of MAT 367, including approximation of eigenvalues and eigenvectors, approximation by splines, numerical solutions of parabolic, elliptic, and hyperbolic partial differential equations.

**MAT 451 Mathematical Statistics (3).**

Prerequisite: MAT 351 or equivalent with a grade of "C" or better.

Sums of independent random variables; functions of random variables; chi-square, F, and t distributions; estimation of parameters; maximum-likelihood, unbiased, consistent, minimum-variance, and minimum-mean- square error estimators; confidence intervals; central limit theorem.

**MAT 517 Fractals for Teachers (3).**

Prerequisites: Possession of a baccalaureate degree and one year of full-time secondary mathematics teaching.

Topics from Fractal and Chaos Theory including: the Cantor Set, Koch Curve, Julia Sets, space filing curves, Brownian motion and Chaotic behavior. Selections to relate to the high school mathematics curriculum.

**MAT 555 Research in Mathematics Education (3).**

Prerequisites: GED 500 and consent of program.

Integrates previous work and experience by emphasizing the application of theoretical models and research designs to the field of mathematics education. Special emphasis will be given to analyzing, organizing, and evaluating findings, and communicating the results.

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