# Mathematics Course Descriptions and Sample Syllabi

Updated Tue Dec 29 20:21:48 PST 2015

• Course Descriptions and Sample Syllabi
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Below are official course descriptions and links to sample syllabi that provide more detailed information than the official course descriptions. The sample syllabi are only included for illustration. Instructors will provide their own official course syllabi. For more complete information about the math program including requirements for the undergraduate major and minor, the masters degree in mathematics education, etc., please visit our official online University catalog.

Note for Faculty: The official university requirements for course syllabi have changed. You can find them here http://www5.csudh.edu/aapm/pdf/aa-2015-03.pdf

### Developmental Math Courses

#### MAT 003 Beginning Algebra (3 units) FS.

Sample Syllabus

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 units) FS.

Sample Syllabus

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.

### Lower Division Courses

#### MAT 105 Finite Mathematics (3 units) FS.

Sample Syllabus

Prerequisite: Fulfillment of ELM requirement. Satisfies Quantitative Reasoning Requirement in General Education Program. Mathematics of finance, combinatorics, probability, statistical measures of central tendency and dispersion, problem solving and mathematical reasoning, and additional topics selected by instructor e.g. linear programming, statistics, graph theory, game theory.

#### MAT 107 Math for Elementary School Teachers: Real Numbers (3 units) FS.

Sample Syllabus

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. Three hours of lecture per week.

#### MAT 131 Elementary Statistics and Probability (3 units) FS.

Sample Syllabus

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.

#### MAT 143 Problem Solving in Mathematics (3 units) EOY.

Sample Syllabus

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.

#### MAT 153 Precalculus (4 units) FS.

Sample Syllabus

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.

#### MAT 171 Survey of Calculus for Management and Life Sciences (4 units) FS.

Sample Syllabus

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.

#### MAT 191 Calculus I (5 units) FS.

Sample Syllabus

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, inverse functions. Five hours of lecture per week.

#### MAT 193 Calculus II (5 units) FS.

Sample Syllabus

Prerequisite: MAT 191 or equivalent with a grade of "C" or better. Techniques and applications of integration. Polar coordinates. Infinite sequences and series, power series, convergence.

#### MAT 195 Special Topics in Mathematics (4 units)

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

We offer two topics, statistics ("stats"), and finite math. Please see the sample syllabi for details on each version.

#### MAT 207 Mathematics for Elementary School Teachers: Geometry & Statistics (4 units) FS.

Sample Syllabus

Prerequisite: Satisfaction of the ELM requirement. 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.

(MAT 207 also covers some topics from probability and statistics that are not mentioned in the official course description quoted above. See the sample syllabus.)

#### MAT 211 Calculus III (5 units) FS.

Sample Syllabus

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 units) EOY

Sample Syllabus

Prerequisite: MAT 193 with grade 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 units) FS.

Sample Syllabus

Prerequisite: MAT 193 with grade 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 units) FS.

Sample Syllabus

Prerequisite: MAT 153, and CSC 121 or MAT 241 or CSC 111 or equivalent with grades C or better. Matrix algebra, graph theory, trees, combinatorics, Boolean algebra; with applications to computers and computer programming. (See sample syllabus for an updated course description).

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

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.

#### MAT 297 Independent Study (1-4 units) FS.

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.

### Upper Division Courses

#### MAT 311 Differential Equations (3 units) F.

Sample Syllabus

Prerequisite: MAT 211 and MAT 271 with grade 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 units) F.

Sample Syllabus

Prerequisite: MAT 193 and MAT 271 with grade C or better. A calculus based survey of topics in probability and statistics emphasizing applications.

#### MAT 331 Linear Algebra (3 units) F.

Sample Syllabus

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 units) S.

Sample Syllabus

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 units) EOY.

Sample Syllabus

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 units) F.

Sample Syllabus

Prerequisite: MAT 281 or equivalent with grade C or better. Study of the abstract formalization of digital computers. Applications to computation theory and formal linguistics.

#### MAT 367 Numerical Analysis I (3 units) EOY.

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.

(Note: the list of computer languages in the official prerequisite description is out of date. Modern computer languages are also allowed; ask your instructor.)

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

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 units) F.

Sample Syllabus

Prerequisites: MAT 211 and MAT 271 with grade 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 units) S.

Sample Syllabus

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 units) S.

Sample Syllabus

Required prerequisites: MAT 211, MAT 271, and MAT 241 or CSC 121 or CSC 111, or equivalent with grade C or better. Recommended prerequisites: MAT 311 and MAT 331. 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 units) EOY.

Sample Syllabus

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 units) EOY.

Sample Syllabus

Prerequisites: MAT 213 and MAT 271, or equivalent with a grade of "C" or better. 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 units) EOY.

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 units) EOY.

Sample Syllabus

Prerequisite: MAT 271 with a grade of "C" or better. Divisibility, congruences, prime number theory, Diophantine Equations, and other topics from elementary number theory.

#### MAT 448 Cryptography (3 units)

Sample Syllabus

Prerequisite: Required: MAT 271 with a grade C or better. Recommended: CSC 115 or 121 with a grade of "C" or better. Recommended: CSC 115 or 121 with a grade of "C" or better. 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 (3 units)

Sample syllabus

Prerequisites: Required: MAT 211, MAT 271, and MAT 241 or CSC 121 or CSC 115, or equivalent with grade of "C" or better. Recommended: MAT 281 with a grade of "C" or better. 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 (3 units) F.

Sample syllabus

Prerequisite: 9 units of 300/400 level mathematics courses with grades C or better. Synthesis and analysis of secondary mathematics and its teaching. Emphais on algebraic thinking and its teaching in high school. Observation and discussion of teaching is an important activity in this course.

#### MAT 490 Seminar in Mathematics Education (3 units) S.

Sample Syllabus

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, investigation, reasoning, and communication as recommended in state and national standards. Three hours of lecture per week.

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

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.

#### MAT 497 Independent Study (1-4 units) FS.

Prerequisites: MAT 213, 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 500 Mathematics Education Research Design and Statistics (3 units)

Sample Syllabus

Prerequisites: Graduate standing, must have completed one year of mathematics teaching. Mathematics Education Research Design and Statistics includes such topics as the 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 units)

Sample Syllabus

Prerequisites: MAT 543 or concurrent enrollment, graduate standing, and must have completed one year of mathematics teaching. Students will read and discuss research and work on various topics in geometry. Focus will be 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 units)

Sample Syllabus

Prerequisites: MAT 543 or concurrent enrollment, 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 the Rational Numbers (3 units)

Sample Syllabus

Prerequisites: MAT 543 or concurrent enrollment, graduate standing, and must have completed one year of full time secondary mathematics teaching. Course 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 units) EOY.

(This course previously was called "Combinatorics for Teachers".)

Sample Syllabus

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 units) EOY.

Sample Syllabus

Prerequisites: MAT 543, graduate standing and one year of full time secondary teaching. Topics from Geometry including: points and lines in a triangle, properties of circles, collinearity, concurrence, transformations, arithimetic and geometric means, isoperimetric theorems, reflection principle.

#### MAT 522 Foundations of Algebraic Thinking (3 units)

Sample Syllabus

Prerequisites: graduate standing, must have completed one year of full time secondary mathematics teaching. Topics include patterns and 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. current research on the understanding and learning of these topics.

#### MAT 523 Theory of Functions for Teachers (3 units) EOY.

Sample Syllabus

Prerequisites: MAT 543, graduate standing and one year of full time secondary 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 units)

Sample Syllabus

Prerequisite: MAT 543, graduate standing and one year of full time secondary 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 units).

Sample Syllabus

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

#### MAT 545 History of Mathematics Education (3 units) EOY.

Sample Syllabus

Prerequisite: 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 units).

Sample Syllabus

Prerequisite: MAT 500. Research in Mathematics Education I provides an overview of the current research literature pertaining to mathematics education in elementary and secondary schools. The research topics such as mathematical reasoning, communication, problem solving, algebra and geometry will be discussed and analyzed.

#### MAT 559 Research in Mathematics Education II (3 units).

Sample Syllabus

Prerequisite: MAT 557. Research in Mathematics Education II provides an overview of the current research literature pertaining to mathematics education in elementary and secondary schools. The research 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 units) FS.

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 units).

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 units).

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

#### MAT 597 Directed Reading (1-4 units).

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 units).

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 units).

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 units).

Graduate students who have completed their coursework 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.