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The Bachelor of Science in Mathematics

Total Course Requirements for the Bachelor's Degree: 120 units

See Bachelor's Degree Requirements in the University Catalog for complete details on general degree requirements. A minimum of 39 units, including those required for the major, must be upper division.

A suggested Major Academic Plan (MAP) has been prepared to help students meet all graduation requirements within four years. You can view MAPs on the Degree MAPs page in the University Catalog or you can request a plan from your major advisor.

General Education Pathway Requirements: 48 units

See General Education in the University Catalog and the Class Schedule for the most current information on General Education Pathway Requirements and course offerings.

This major has approved GE modification(s). See below for information on how to apply these modification(s).

  • MATH 217 is an approved major course substitution for Critical Thinking (A3).
  • MATH 330W is an approved major course substitution for Upper-Division Natural Sciences.

These modifications apply to The Option in Mathematics Education - Credential Path only

  • EDTE 451 fulfills Learning for Life (E)
  • EDTE 302, ENGL 471, and MATH 333 fulfill the Upper-Division Pathway requirement.

Diversity Course Requirements: 6 units

See Diversity Requirements in the University Catalog. Most courses taken to satisfy these requirements may also apply to General Education .

Upper-Division Writing Requirement:

Writing Across the Curriculum (Executive Memorandum 17-009) is a graduation requirement and may be demonstrated through satisfactory completion of four Writing (W) courses, two of which are designated by the major department. See Mathematics/Quantitative Reasoning and Writing Requirements in the University Catalog for more details on the four courses.  The first of the major designated Writing (W) courses is listed below.

SUBJ NUM Title Sustainable Units Semester Offered Course Flags
MATH 330W Methods of Proof (W)   3.0 FS  W
Prerequisites: GE Written Communication (A2) requirement and MATH 121.
A survey of elementary principles of logic, emphasizing the nature of proof. Standard methods of proof will be illustrated with examples from various branches of mathematics, including set theory and the theory of functions and relations. Other possible sources of examples include the calculus, number theory, theory of equations, topology of the real line. 3 hours seminar. This is an approved Writing Course. (005530)

The second major-designated Writing course is the Graduation Writing Assessment Requirement (GW) (Executive Order 665). Students must earn a C- or higher to receive GW credit. The GE Written Communication (A2) requirement must be completed before a student is permitted to register for a GW course.

Grading Requirement:

All courses taken to fulfill major course requirements must be taken for a letter grade except those courses specified by the department as Credit/No Credit grading only.

Enrollment in any mathematics course requires a grade of C- or higher in all prerequisite courses or their transfer equivalents.

Course Requirements for the Major: 48-56 units

Completion of the following courses, or their approved transfer equivalents, is required of all candidates for this degree. Additional required courses, depending upon the selected option are outlined following the major core program requirements.

Major Core Program: 26-29 units

5 courses required:

SUBJ NUM Title Sustainable Units Semester Offered Course Flags
MATH 120 Analytic Geometry and Calculus   4.0 FS  GE
Prerequisites: GE Mathematics/Quantitative Reasoning Ready; both MATH 118 and MATH 119 (or college equivalent); first-year freshmen who successfully completed trigonometry and precalculus in high school can meet this prerequisite by achieving a score that meets department guidelines on a department administered calculus readiness exam.
Limits and continuity. The derivative and applications to related rates, maxma and minima, and curve sketching. Transcendental functions. An introduction to the definite integral and area. 4 hours discussion. This is an approved General Education course. (005506)
MATH 121 Analytic Geometry and Calculus   4.0 FS  
Prerequisite: MATH 120.
The definite integral and applications to area, volume, work, differential equations, etc. Sequences and series, vectors and analytic geometry in 2 and 3-space, polar coordinates, and parametric equations. 4 hours discussion. (005507)
MATH 235 Elementary Linear Algebra   3.0 FS  
Prerequisites: MATH 121.
Matrices, determinants, cartesian n-space (basis and dimension of a subspace, rank, change of basis), linear transformations, eigenvalues. Numerical problems will be emphasized. 3 hours discussion. (005553)
MATH 300 Undergraduate Mathematics Seminar   2.0 FS  
Prerequisite: GE Mathematics/Quantitative Reasoning Ready.
This course is designed to expose you to mathematics not normally covered in your regular curriculum. Guest speakers are drawn from the ranks of our faculty, including other disciplines, our students, and industry. Talks are interactive, participatory, and fun. There is no prerequisite, except an interest in interesting mathematics. Topics typically include selections from number theory, math education, statistics, problem solving, undergraduate research, calculus, differential equations, spatial and planar geometry, probability, computer applications, mathematical operations, modeling, topology, trigonometry, metric measurements, elliptical curves, and bubbles, among others. This exposure broadens your horizons and expands your curiosity in hopes that you will explore mathematics beyond your required courses. 2 hours lecture. You may take this course more than once for a maximum of 8.0 units. Credit/no credit grading. (021647)
MATH 330W Methods of Proof (W)   3.0 FS  W
Prerequisites: GE Written Communication (A2) requirement and MATH 121.
A survey of elementary principles of logic, emphasizing the nature of proof. Standard methods of proof will be illustrated with examples from various branches of mathematics, including set theory and the theory of functions and relations. Other possible sources of examples include the calculus, number theory, theory of equations, topology of the real line. 3 hours seminar. This is an approved Writing Course. (005530)

4-6 units selected from:

SUBJ NUM Title Sustainable Units Semester Offered Course Flags
MATH 220 Analytic Geometry and Calculus   4.0 FS  
Prerequisites: MATH 121.
Vector functions and space curves. Functions of several variables, partial derivatives, and multiple integrals. Vector calculus line integrals, surface integrals, divergence/curl, Green's Theorem, Divergence Theorem, and Stokes' Theorem. 4 hours discussion. (005508)

Or the following group of courses may be selected:

SUBJ NUM Title Sustainable Units Semester Offered Course Flags
MATH 125 Advanced Number and Operation   3.0 FA  
Prerequisite: Successful completion of high school precalculus, concurrent enrollment in MATH 118 or 119, or faculty permission.
Investigate number and operation through calculation and abstraction, find patterns and relationships through computation, develop and test mathematical conjectures, and develop an appreciation of proof and an ability to make mathematical arguments. Basic concepts from Number Theory are explored, culminating in proof of the Fundamental Theorem of Arithmetic and related theorems in other number sets. 3 hours discussion. (021846)
MATH 225 Algebra Functions, Real and Complex Number Systems   3.0 SP  
Prerequisite: MATH 125.
This course focuses on developing your abilities in making sense of algebraic manipulation in the context of functions, polynomial rings, and matrices. The course and the classroom are structured as a supportive, collaborative learning environment in which mathematical discourse is valued and exploration encouraged. You will investigate algebra and polynomials through calculation and abstraction, find patterns and relationships through computation, develop and test mathematical conjectures, and develop an appreciation of proof and an ability to construct mathematical arguments. More advanced concepts from Number Theory are explored, culminating in proofs of the Unique Prime Factorization Theorem and the Division Algorithm for different rings. 3 hours discussion. (021953)

1 course selected from:

SUBJ NUM Title Sustainable Units Semester Offered Course Flags
MATH 420W Advanced Calculus (W)   3.0 FS  GW  W
Prerequisites: Completion of GE Written Communication (A2) requirement, MATH 220, MATH 330, upper-division standing.
Limits, continuity, uniform continuity, the definite integral, series, convergence, uniform convergence, and metric spaces. Differentiation and integration of functions of several variables. Transformation of multiple integrals. 3 hours discussion. This is an approved Graduation Writing Assessment Requirement course; a grade of C- or higher certifies writing proficiency for majors. This is an approved Writing Course. (005575)
MATH 425W Computational and Communication in Mathematical Modeling (W)   3.0 FA  GW  W
Prerequisites: GE Written Communication (A2) requirement, completion of computer literacy requirement, MATH 225, MATH 235, MATH 330W, and upper division standing.
In this course, intended for pre-service teachers, student experience mathematical modeling with content common in the secondary setting (algebra through calculus) as well as from their undergraduate coursework and develop and produce formal modeling reports. Students use technology to aid in exploring real-world circumstances, make sense of and analyze existing models, and develop their own mathematical models. 3 hours discussion. This is an approved Graduation Writing Assessment Requirement course; a grade of C- or higher certifies writing proficiency for majors. This is an approved Writing Course. (021977)

The MATH 120, MATH 121, MATH 220 sequence should be started as early as possible, provided the student has the necessary background. MATH 118 and MATH 119 (or their equivalents) are required pre-calculus courses for MATH 120.

Some upper-division courses require only MATH 120 or MATH 121 as a prerequisite. Refer to catalog course listings when choosing courses.

Computer Literacy Requirement

A passing grade in one of the following classes or its transfer equivalent.

1 course selected from:

SUBJ NUM Title Sustainable Units Semester Offered Course Flags
CINS 110 Introductory Web Programming   3.0 FS  
This course introduces students to programming in the context of dynamic web page development. The operation of the web browser and its interaction with web servers is explored. Structure and style of web page content using HTML and CSS is introduced. The main focus of the course is programming in JavaScript to add dynamic content to a web page. Topics include all language constructs, interaction with the DOM, event-driven programming, debugging using an integrated debugger in the browser, and the use of existing APIs. 2 hours discussion, 2 hours activity. (002298)
CSCI 111 Programming and Algorithms I   4.0 FS  
Prerequisite: MATH 109, MATH 119 (or high school equivalent), or MATH 120; or a passing score on the Math department administered calculus readiness exam.
A first-semester programming course, providing an overview of computer systems and an introduction to problem solving and software design using procedural object-oriented programming languages. Coverage includes the software life cycle, as well as algorithms and their role in software design. Students are expected to design, implement, and test a number of programs. 3 hours lecture, 2 hours activity. (002281)
MATH 230 An Introduction to Computational Mathematics   3.0 FA  
Prerequisites: MATH 121, no previous computer experience required.
An introduction to the use of mathematical computer software. This course provides an introduction to a programming environment, preparing math majors to use computers to explore and solve varied math problems. The software used in this class depends on the instructor and may be chosen from Mathematica, GP/PARI, GAP, SAS, R, etc. This course satisfies the computer literacy requirement for mathematics majors. 3 hours discussion. You may take this course more than once for a maximum of 9.0 units. (005526)

Major Option Course Requirements: 22-27 units

The following courses, or their approved transfer equivalents, are required dependent upon the option chosen. Students must select one of the following options for completion of the major course requirements.  Use the links below to jump to your chosen option.

The Option in General Mathematics: 24-26 units

3 courses required:

SUBJ NUM Title Sustainable Units Semester Offered Course Flags
MATH 421 Advanced Calculus   3.0 SP  
Prerequisite: MATH 420W.
Continuation of MATH 420W. 3 hours discussion. (005576)
MATH 449 Modern Algebra   3.0 FA  
Prerequisites: MATH 220, MATH 235, MATH 330.
Introduction to basic algebraic structures such as groups, ring, and fields. The fundamental concepts of homomorphism, subgroup, normal subgroup and factor group of a group as well as subring, ideal and factor ring of a ring; permutation groups and matrix groups. 3 hours discussion. (005582)
MATH 465 Introduction to Complex Variables   3.0 FA  
Prerequisites: MATH 220.
Algebra of Complex Numbers, Cauchy-Riemann Equations, the exponential, trigonometric, and logarithmic functions, complex integration and Cauchy integral formula, Taylor and Laurent series, the residue theorem, conformal mapping, and applications. 3 hours discussion. (005577)

1 course selected from:

SUBJ NUM Title Sustainable Units Semester Offered Course Flags
MATH 260 Elementary Differential Equations   4.0 FS  
Prerequisites: MATH 121.
First order separable, linear, and exact equations; second order linear equations, Laplace transforms, series solutions at an ordinary point, systems of first order linear equations, and applications. 4 hours discussion. (005509)
MATH 350 Introduction to Probability and Statistics   3.0 FA  
Prerequisites: MATH 121.
Basic concepts of probability theory, random variables and their distributions, limit theorems, sampling theory, topics in statistical inference, regression, and correlation. 3 hours discussion. (005534)

1 course selected from:

SUBJ NUM Title Sustainable Units Semester Offered Course Flags
MATH 337 Introduction to the Theory of Numbers   3.0 FA  
Prerequisites: MATH 121, MATH 330.
Basic properties of the integers, division algorithm, fundamental theorem of arithmetic, number-theoretic functions, Diophantine equations, congruences, quadratic residues, continued fractions. 3 hours discussion. (005585)
MATH 344 Combinatorial Mathematics and Graph Theory   3.0 FA  
Prerequisites: MATH 121, MATH 330.
The analysis of mathematical and applied problems through the use of permutations and combinations, generating functions and recurrence relations. Directed graphs, trees, connectivity, and duality. 3 hours discussion. (005591)

1 course selected from:

SUBJ NUM Title Sustainable Units Semester Offered Course Flags
MATH 428 Differential Geometry   3.0 F1  
Prerequisites: MATH 220, MATH 330.
The geometry of curves and surfaces in Euclidean 3-space. 3 hours lecture. (005566)
MATH 437 Topology   3.0 F2  
Prerequisites: MATH 220, MATH 330.
Metric spaces, continuous functions, homeomorphisms, separation, and covering axioms, connectedness. 3 hours discussion. (005563)

1 course selected from:

SUBJ NUM Title Sustainable Units Semester Offered Course Flags
MATH 435 Linear Algebra   3.0 S2  
Prerequisites: MATH 220, MATH 235, MATH 330.
Vector spaces, linear operators, bilinear forms and scalar products, unitary spaces; matrix polynomials, eigenvalues, and Jordan normal form. 3 hours discussion. (005581)
MATH 451 Modern Algebra II   3.0 S1  
Prerequisite: MATH 449.
Continuation of MATH 449, topics may include group actions, the Sylow theorems, number fields, finite fields, algebraic extensions, field automorphisms, splitting fields of polynomials, Galois groups, and solvable groups. 3 hours discussion. (021971)

3-4 units selected from:

Any upper-division Mathematics (MATH) courses except MATH 305, MATH 310, MATH 311, MATH 341, MATH 342, and MATH 441.

The Option in Applied Mathematics: 25 units

7 courses required:

SUBJ NUM Title Sustainable Units Semester Offered Course Flags
MATH 260 Elementary Differential Equations   4.0 FS  
Prerequisites: MATH 121.
First order separable, linear, and exact equations; second order linear equations, Laplace transforms, series solutions at an ordinary point, systems of first order linear equations, and applications. 4 hours discussion. (005509)
MATH 350 Introduction to Probability and Statistics   3.0 FA  
Prerequisites: MATH 121.
Basic concepts of probability theory, random variables and their distributions, limit theorems, sampling theory, topics in statistical inference, regression, and correlation. 3 hours discussion. (005534)
MATH 360 Ordinary Differential Equations   3.0 SP  
Prerequisites: MATH 260.
Systems of first order linear equations, existence and uniqueness theorems, stability, Sturm separation theorems, power series methods. 3 hours discussion. (005538)
MATH 361 Boundary Value Problems and Partial Differential Equations   3.0 FA  
Prerequisites: MATH 260.
Partial differential equations, separation of variables, orthogonal sets of functions, Sturm-Liouville problems, Fourier series, boundary value problems for the wave equation, heat equation, and Laplace equation; Bessel functions, Legendre polynomials. 3 hours discussion. (005540)
MATH 461 Numerical Analysis   3.0 SP  
Prerequisites: MATH 220 or MATH 260; completion of computer literacy requirement.
Approximation; numerical integration; numerical solution of ordinary and partial differential equations; interpolation and extrapolation. 3 hours discussion. (005584)
MATH 465 Introduction to Complex Variables   3.0 FA  
Prerequisites: MATH 220.
Algebra of Complex Numbers, Cauchy-Riemann Equations, the exponential, trigonometric, and logarithmic functions, complex integration and Cauchy integral formula, Taylor and Laurent series, the residue theorem, conformal mapping, and applications. 3 hours discussion. (005577)
MATH 480 Mathematical Modeling   3.0 SP  
Prerequisites: MATH 235, MATH 260.
The translation of real world phenomena into mathematical language. Possible applications include population and competing species models, mathematical theories of war, traffic flow, river pollution, water waves and tidal dynamics, probabilistic and simulation models. 3 hours discussion. (005592)

1 course selected from:

SUBJ NUM Title Sustainable Units Semester Offered Course Flags
MATH 472 Introduction to Chaotic Dynamical Systems   3.0 F1  
Prerequisites: MATH 260. Recommended: MATH 235, MATH 360.
An introduction to the study of non-linear dynamical systems. Both discrete and continuous systems will be studied using classical analysis combined with geometric techniques and computer simulation. Areas of application include fractal geometry, coding theory, fluid turbulence, population fluctuation, and chaotic vibrations of structures and circuits. 3 hours discussion. (005588)
MATH 475 Calculus of Variations   3.0 F2  
Prerequisites: MATH 260; MATH 361 is recommended.
Classical problems in the calculus of variations. Euler-Lagrange equations. Isoperimetric problems, Fermat's principle. Lagrangian and Hamiltonian mechanics of particles. Two independent variables. Applications to physics and engineering. 3 hours discussion. (005590)

The Option in Mathematics Education: 25-27 units

The following program, together with the major core program, fulfills all requirements for the Single Subject Matter Preparation Program in Mathematics.

7 courses required:

SUBJ NUM Title Sustainable Units Semester Offered Course Flags
MATH 305 Conceptual and Practical Statistics   3.0 SP  
Prerequisites: MATH 120 or MATH 109 (may be taken concurrently).
Design of statistical experiments, graphing, sampling techniques, probability, and common probability distributions will be discussed, with an emphasis on practical applications. Uses and misuses of statistics, misrepresentation of data, and proper and improper statistical analyses will be discussed. 3 hours discussion. (005532)
MATH 333 History of Mathematics   3.0 SP  
Prerequisites: MATH 121; MATH 220 or MATH 225; and at least one upper division mathematics course. MATH 330 is recommended.
Study of the historical development of mathematics, with particular emphasis on the relationship between mathematics and society. 3 hours discussion. (005531)
MATH 337 Introduction to the Theory of Numbers   3.0 FA  
Prerequisites: MATH 121, MATH 330.
Basic properties of the integers, division algorithm, fundamental theorem of arithmetic, number-theoretic functions, Diophantine equations, congruences, quadratic residues, continued fractions. 3 hours discussion. (005585)
MATH 341 Mathematical Topics for the Credential   3.0 FA  
Prerequisites: MATH 121 or MATH 225.
This course is designed to supplement the mathematical background of the candidate for the single subject credential in mathematics. The mathematical topics will be discussed from the student's and the teacher's points of view to aid the candidate in making the transition to secondary school mathematics. Topics include mathematical problem-solving, conceptual ideas using algebra, geometry, and functions, incorporating technology into the mathematics curriculum, and finite systems. 3 hours seminar. (005544)
MATH 342 Math Topics for the Credential   3.0 SP  
Prerequisites: MATH 341.
This course focuses on having students examine mathematical pedagogy and the understanding and evaluations of students as mathematical learners as it analyzes secondary mathematics curriculum from an advanced standpoint. Students will have opportunities to be involved in the facilitation of mathematical learning. Topics include: history of mathematics education, contemporary mathematics curricula, problem solving, mathematical reasoning and methods of proof, mathematical learning theories, communication, assessment and collaborative learning communities. 3 hours discussion. (005545)
MATH 346 College Geometry   3.0 SP  
Prerequisites: MATH 220 or MATH 225; MATH 330.
An exploration of axioms and models for Euclidean and non-Euclidean geometries focusing on the independence of the Parallel Postulate. Additional topics will be chosen from Euclidean plane geometry, transformation geometry, and the geometry of polyhedra. 3 hours discussion. (005561)
MATH 449 Modern Algebra   3.0 FA  
Prerequisites: MATH 220, MATH 235, MATH 330.
Introduction to basic algebraic structures such as groups, ring, and fields. The fundamental concepts of homomorphism, subgroup, normal subgroup and factor group of a group as well as subring, ideal and factor ring of a ring; permutation groups and matrix groups. 3 hours discussion. (005582)

1 course selected from:

SUBJ NUM Title Sustainable Units Semester Offered Course Flags
MATH 195 Project MATH Seminar Year 1   1.0 FS  
The Project M.A.T.H. Seminar - Year 1 is a biweekly seminar for students in their first year of Project M.A.T.H., an innovative program for students interested in becoming secondary mathematics teachers. Students work with mentor teachers, prepare and present lessons, and participate in a structured early field experience. Completion of the seminar series satisfies the Credential Program's Early Field Experience requirement. 1 hour seminar. You may take this course more than once for a maximum of 2.0 units. Credit/no credit grading. (020431)
MATH 241 Secondary Math Early Field Experience   1.0 FS  
This seminar and the associated CAVE field experience give prospective teachers early exposure to issues relevant to the profession of teaching secondary mathematics. In particular, the experience helps these future teachers develop a deeper understanding of the K-12 mathematics curriculum, understand connections between their university subject matter preparation and K-12 academic content, and reflect on developmental and social factors that affect K-12 students' learning of mathematics. 1 hour seminar. You may take this course more than once for a maximum of 4.0 units. Credit/no credit grading. (020432)

3-5 units selected from:

Note: If MATH 441 is chosen, an additional unit of MATH 241 or MATH 295 must be taken.

SUBJ NUM Title Sustainable Units Semester Offered Course Flags
MATH 442 Mathematics and the Teaching of Mathematics   3.0 FA  
Prerequisites: MATH 342.
Completes a three course series, started with two semesters of Mathematics for the Credential, MATH 341 and MATH 342. Students compare instructional strategies and explore the role content and pedagogical content knowledge has in these strategies. Central to the class is a lesson study project which entails a cycle of lesson development, implementation, reflection and revision, and implementation again. Students concurrently enrolled in EDTE 535A, Teaching Practicum I for Blended Math Candidates, are able to implement their lesson as part of the practicum, and have a real context for the full content of the course. 3 hours lecture. (020978)

Or the following group of courses may be selected:

SUBJ NUM Title Sustainable Units Semester Offered Course Flags
MATH 295 Project MATH Seminar Year 2   1.0 FS  
Prerequisite: MATH 195.
The Project M.A.T.H. Seminar - Year 2 is the continuation of a biweekly seminar for students in Project M.A.T.H., an innovative program for students interested in becoming secondary mathematics teachers. Students work with mentor teachers, prepare and present lessons, and participate in a structured early field experience. They also take on a leadership role in the seminar. Completion of the seminar series satisfies the Credential Program's Early Field Experience requirement. 1 hour seminar. You may take this course more than once for a maximum of 2.0 units. Credit/no credit grading. (020433)
MATH 441 Math Topics for the Credential   4.0 FS  
Prerequisites: MATH 342.
 Corequisites: Assignment as a Mathematics Department intern.
Supervised internship in teaching mathematics with accompanying seminar. Guidance in facilitation of mathematical learning. Topics include contemporary mathematics curriculum topics, mathematical learning theories, communication, and assessment. 3 hours seminar, 3 hours supervision. You may take this course more than once for a maximum of 8.0 units. Credit/no credit grading. (005546)

Or the following group of courses may be selected:

SUBJ NUM Title Sustainable Units Semester Offered Course Flags
MATH 241 Secondary Math Early Field Experience   1.0 FS  
This seminar and the associated CAVE field experience give prospective teachers early exposure to issues relevant to the profession of teaching secondary mathematics. In particular, the experience helps these future teachers develop a deeper understanding of the K-12 mathematics curriculum, understand connections between their university subject matter preparation and K-12 academic content, and reflect on developmental and social factors that affect K-12 students' learning of mathematics. 1 hour seminar. You may take this course more than once for a maximum of 4.0 units. Credit/no credit grading. (020432)
MATH 441 Math Topics for the Credential   4.0 FS  
Prerequisites: MATH 342.
 Corequisites: Assignment as a Mathematics Department intern.
Supervised internship in teaching mathematics with accompanying seminar. Guidance in facilitation of mathematical learning. Topics include contemporary mathematics curriculum topics, mathematical learning theories, communication, and assessment. 3 hours seminar, 3 hours supervision. You may take this course more than once for a maximum of 8.0 units. Credit/no credit grading. (005546)

Subject matter preparation requirements are governed by federal and state legislative action and approval of the California Commission on Teacher Credentialing. Requirements may change between catalogs. Please consult with your departmental credential advisor for current information.

The Option in Mathematics Education - Credential Path: 73-75 units

The following program, together with the major core program, fulfills all requirements for both a degree in Mathematics (Mathematics Education Option) and the Single Subject Credential in Mathematics.

Mathematics

7 courses required:

SUBJ NUM Title Sustainable Units Semester Offered Course Flags
MATH 305 Conceptual and Practical Statistics   3.0 SP  
Prerequisites: MATH 120 or MATH 109 (may be taken concurrently).
Design of statistical experiments, graphing, sampling techniques, probability, and common probability distributions will be discussed, with an emphasis on practical applications. Uses and misuses of statistics, misrepresentation of data, and proper and improper statistical analyses will be discussed. 3 hours discussion. (005532)
MATH 333 History of Mathematics   3.0 SP  
Prerequisites: MATH 121; MATH 220 or MATH 225; and at least one upper division mathematics course. MATH 330 is recommended.
Study of the historical development of mathematics, with particular emphasis on the relationship between mathematics and society. 3 hours discussion. (005531)
MATH 337 Introduction to the Theory of Numbers   3.0 FA  
Prerequisites: MATH 121, MATH 330.
Basic properties of the integers, division algorithm, fundamental theorem of arithmetic, number-theoretic functions, Diophantine equations, congruences, quadratic residues, continued fractions. 3 hours discussion. (005585)
MATH 341 Mathematical Topics for the Credential   3.0 FA  
Prerequisites: MATH 121 or MATH 225.
This course is designed to supplement the mathematical background of the candidate for the single subject credential in mathematics. The mathematical topics will be discussed from the student's and the teacher's points of view to aid the candidate in making the transition to secondary school mathematics. Topics include mathematical problem-solving, conceptual ideas using algebra, geometry, and functions, incorporating technology into the mathematics curriculum, and finite systems. 3 hours seminar. (005544)
MATH 342 Math Topics for the Credential   3.0 SP  
Prerequisites: MATH 341.
This course focuses on having students examine mathematical pedagogy and the understanding and evaluations of students as mathematical learners as it analyzes secondary mathematics curriculum from an advanced standpoint. Students will have opportunities to be involved in the facilitation of mathematical learning. Topics include: history of mathematics education, contemporary mathematics curricula, problem solving, mathematical reasoning and methods of proof, mathematical learning theories, communication, assessment and collaborative learning communities. 3 hours discussion. (005545)
MATH 346 College Geometry   3.0 SP  
Prerequisites: MATH 220 or MATH 225; MATH 330.
An exploration of axioms and models for Euclidean and non-Euclidean geometries focusing on the independence of the Parallel Postulate. Additional topics will be chosen from Euclidean plane geometry, transformation geometry, and the geometry of polyhedra. 3 hours discussion. (005561)
MATH 449 Modern Algebra   3.0 FA  
Prerequisites: MATH 220, MATH 235, MATH 330.
Introduction to basic algebraic structures such as groups, ring, and fields. The fundamental concepts of homomorphism, subgroup, normal subgroup and factor group of a group as well as subring, ideal and factor ring of a ring; permutation groups and matrix groups. 3 hours discussion. (005582)

2 units selected from:

SUBJ NUM Title Sustainable Units Semester Offered Course Flags
MATH 195 Project MATH Seminar Year 1   1.0 FS  
The Project M.A.T.H. Seminar - Year 1 is a biweekly seminar for students in their first year of Project M.A.T.H., an innovative program for students interested in becoming secondary mathematics teachers. Students work with mentor teachers, prepare and present lessons, and participate in a structured early field experience. Completion of the seminar series satisfies the Credential Program's Early Field Experience requirement. 1 hour seminar. You may take this course more than once for a maximum of 2.0 units. Credit/no credit grading. (020431)
MATH 241 Secondary Math Early Field Experience   1.0 FS  
This seminar and the associated CAVE field experience give prospective teachers early exposure to issues relevant to the profession of teaching secondary mathematics. In particular, the experience helps these future teachers develop a deeper understanding of the K-12 mathematics curriculum, understand connections between their university subject matter preparation and K-12 academic content, and reflect on developmental and social factors that affect K-12 students' learning of mathematics. 1 hour seminar. You may take this course more than once for a maximum of 4.0 units. Credit/no credit grading. (020432)

Education

9 courses required:

SUBJ NUM Title Sustainable Units Semester Offered Course Flags
EDTE 302 Access and Equity in Education   3.0 FS  
Prospective teachers examine socio-political issues of education relative to current demographics of California schools, integration of multicultural education, and promotion of social justice. Candidates identify, analyze, and minimize personal and institutional bias and explore the complexities of living and teaching in a pluralistic, multicultural society. Candidates identify barriers English Learners experience in becoming full participants in the school program and strategies for assisting students in overcoming these barriers. 3 hours lecture. (002977)
EDTE 530 Fundamentals of Teaching Practice for Secondary Teachers   3.0 FS  
Teaching is an intellectual challenge that involves planning, facilitating, and reflecting on the process of student learning. Teacher candidates develop strategies necessary to create safe and structured learning environments and explore relationships among curriculum, instruction, assessment, and classroom climate to meet the needs of a diverse student population within a democratic society. This is a Single Subject Program course and is not applicable to a master's degree. 3 hours seminar. ABC/no credit grading. (002935)
EDTE 532 Literacy Development   3.0 FS  
This course examines issues of language and literacy development for first and second language learners with an emphasis on the adolescent learner. Theory and research on the effects of prior knowledge, motivation, and culture on reading and writing are addressed. Specific reading, writing, speaking, and listening strategies to support comprehension of academic content by diverse student populations are emphasized. Assessment techniques specific to literacy development are explored. The central theme of the course is helping students (grades 7-12) become strategic readers and critical consumers of information in a democratic society. 3 hours seminar. (002902)
EDTE 534 Teaching Special Populations   2.0 FS  
This course focuses on legal mandates and practical instructional strategies for general education instructors working with the exceptional student. Content includes the general education teachers' obligations under IDEA and ADA, the nature and range of exceptional students, models within schools for supporting special populations and selection of appropriate instructional materials and teaching strategies. The course addresses teachers' attitudes toward inclusion and emphasizes the development of a positive climate of instruction for all special populations in the general classroom. This is a Single Subject Program course and is not applicable to a master's degree. 2 hours lecture. ABC/no credit grading. (002938)
EDTE 535A Teaching Practicum I for Blended Mathematics Candidates   3.0 FS  
This is the first of two teaching practica designed for mathematics teachers. It provides a developmental sequence of carefully planned substantive, supervised field experiences in the 7-12 classroom, including opportunities to observe and apply mathematics-specific pedagogy and democratic practices. This course is a Single Subject Program course and is not applicable to a master's degree program. 9 hours supervision. Credit/no credit grading. (020985)
EDTE 536 Subject Area Pedagogy II   3.0 FS  
This course increases the candidates' awareness and understanding of issues, trends, challenges, and democratic practices of their selected areas of specialization. Teacher candidates advance their knowledge and skills in teaching academic content standards-based curriculum in the subject area guided by multiple measures of assessing student learning. They make and reflect on instructional decisions informed by educational theories and research, state-adopted materials and frameworks, and consultations with other professionals. 3 hours lecture. You may take this course more than once for a maximum of 12.0 units. (002940)
EDTE 537 Applications for Democratic Education   3.0 FS  
Prerequisites: Capstone course to be taken in the final semester of the program.
To meet the needs of students in a democratic and diverse society, teachers must be change agents in their school and community. This capstone course advances candidates' knowledge and skills in developing applications for authentic democratic classroom and school practice. 3 hours lecture. You may take this course more than once for a maximum of 6.0 units. (002941)
EDTE 538 Teaching Practicum II   9.0 FS  
Prerequisites: Successful completion of Practicum I (EDTE 535).
This second course in teaching practica continues the sequence of carefully planned substantive, supervised field experiences in the 7-12 grade classroom. Teacher candidate placements are determined through a collaborative effort of the University and colleagues in cooperating 7-12 grade schools. This is a Single Subject Program course and is not appplicable to a master's degree. 27 hours supervision. Credit/no credit grading. (002942)
EDTE 580 Educational Psychology   3.0 FS  
Prerequisites: Conditional admission to a Professional Education Program.
This course is designed to help candidates understand how students' cognitive, personal-social, and physical development, and cultural and linguistic backgrounds are related to effective teaching and interpersonal relations in secondary schools. Major segments of instruction include the study of how students learn, remember, and make use of the knowledge they have acquired and how students' educational growth is assessed in schools. Each candidate begins to use this knowledge to organize and manage a learning environment that supports student development, motivation, and learning. 3 hours seminar. (015899)

Additional Requirements

5 courses required:

SUBJ NUM Title Sustainable Units Semester Offered Course Flags
CMST 131 Speech Communication Fundamentals   3.0 FS  GE
Effective oral communication. Introduction to human communication theory. Practice in gathering, organizing, and presenting material in speeches to persuade, inform, and interest. 1 hour lecture, 2 hours discussion. This is an approved General Education course. (002206)
EDTE 451 Health Education for Secondary School Teachers   3.0 FS  
Addresses major health issues affecting the adolescent, including, but not limited to, health promotion and disease prevention, nutrition, substance use and abuse, and sexuality. Fulfills the state health education requirement for a preliminary teaching credential. 3 hours discussion. (004394)
ENGL 471 Intensive Theory and Practice of Second Language Acquisition   3.0 FS  
An intensive introduction to the theory and practice of second language acquisition and teaching. 3 hours lecture. (020485)
POLS 155 American Government: National, State, and Local   3.0 SMF  GE
An investigation of Who gets What, When, and How in national, state, and local politics. Also includes principles of American governmental institutions, federal systems, congress, president, and courts. Fulfills California state graduation and credential requirements for the American Constitution. (Satisfies requirement in California Administrative Code, Title 5, Section 40404.) 3 hours lecture. This is an approved General Education course. (007475)
HIST 130 United States History   3.0 SMF  GE
Survey of American history. Development of the United States and its political, economic, social, and cultural institutions. From colonial times to the present. Satisfies requirement in California Administrative Code, Title 5, Education, Sec. 40404. 3 hours lecture. This is an approved General Education course. (004500)

3-5 units selected from:

Note: If MATH 441 is chosen, an additional unit of MATH 241 or MATH 295 must be taken.

SUBJ NUM Title Sustainable Units Semester Offered Course Flags
MATH 442 Mathematics and the Teaching of Mathematics   3.0 FA  
Prerequisites: MATH 342.
Completes a three course series, started with two semesters of Mathematics for the Credential, MATH 341 and MATH 342. Students compare instructional strategies and explore the role content and pedagogical content knowledge has in these strategies. Central to the class is a lesson study project which entails a cycle of lesson development, implementation, reflection and revision, and implementation again. Students concurrently enrolled in EDTE 535A, Teaching Practicum I for Blended Math Candidates, are able to implement their lesson as part of the practicum, and have a real context for the full content of the course. 3 hours lecture. (020978)

Or the following group of courses may be selected:

SUBJ NUM Title Sustainable Units Semester Offered Course Flags
MATH 295 Project MATH Seminar Year 2   1.0 FS  
Prerequisite: MATH 195.
The Project M.A.T.H. Seminar - Year 2 is the continuation of a biweekly seminar for students in Project M.A.T.H., an innovative program for students interested in becoming secondary mathematics teachers. Students work with mentor teachers, prepare and present lessons, and participate in a structured early field experience. They also take on a leadership role in the seminar. Completion of the seminar series satisfies the Credential Program's Early Field Experience requirement. 1 hour seminar. You may take this course more than once for a maximum of 2.0 units. Credit/no credit grading. (020433)
MATH 441 Math Topics for the Credential   4.0 FS  
Prerequisites: MATH 342.
 Corequisites: Assignment as a Mathematics Department intern.
Supervised internship in teaching mathematics with accompanying seminar. Guidance in facilitation of mathematical learning. Topics include contemporary mathematics curriculum topics, mathematical learning theories, communication, and assessment. 3 hours seminar, 3 hours supervision. You may take this course more than once for a maximum of 8.0 units. Credit/no credit grading. (005546)

Or the following group of courses may be selected:

SUBJ NUM Title Sustainable Units Semester Offered Course Flags
MATH 241 Secondary Math Early Field Experience   1.0 FS  
This seminar and the associated CAVE field experience give prospective teachers early exposure to issues relevant to the profession of teaching secondary mathematics. In particular, the experience helps these future teachers develop a deeper understanding of the K-12 mathematics curriculum, understand connections between their university subject matter preparation and K-12 academic content, and reflect on developmental and social factors that affect K-12 students' learning of mathematics. 1 hour seminar. You may take this course more than once for a maximum of 4.0 units. Credit/no credit grading. (020432)
MATH 441 Math Topics for the Credential   4.0 FS  
Prerequisites: MATH 342.
 Corequisites: Assignment as a Mathematics Department intern.
Supervised internship in teaching mathematics with accompanying seminar. Guidance in facilitation of mathematical learning. Topics include contemporary mathematics curriculum topics, mathematical learning theories, communication, and assessment. 3 hours seminar, 3 hours supervision. You may take this course more than once for a maximum of 8.0 units. Credit/no credit grading. (005546)

Note: A Major Academic Plan (MAP) is available for this option so students can complete it in four years. Please request a plan from your major advisor or view it at Degree MAPs . It is important to follow this plan carefully as there are several GE substitutions that apply only if the entire program is completed.

The Option in Statistics: 25-26 units

6 courses required:

SUBJ NUM Title Sustainable Units Semester Offered Course Flags
MATH 260 Elementary Differential Equations   4.0 FS  
Prerequisites: MATH 121.
First order separable, linear, and exact equations; second order linear equations, Laplace transforms, series solutions at an ordinary point, systems of first order linear equations, and applications. 4 hours discussion. (005509)
MATH 350 Introduction to Probability and Statistics   3.0 FA  
Prerequisites: MATH 121.
Basic concepts of probability theory, random variables and their distributions, limit theorems, sampling theory, topics in statistical inference, regression, and correlation. 3 hours discussion. (005534)
MATH 351 Introduction to Probability and Statistics   3.0 SP  
Prerequisites: MATH 350.
Continuation of MATH 350. 3 hours discussion. (005535)
MATH 450 Mathematical Statistics   3.0 FA  
Prerequisites: MATH 220, MATH 330, MATH 351.
A rigorous theoretical treatment of the following topics: transformations of random variables, estimation, Neyman-Pearson hypothesis testing, likelihood ratio tests, and Bayesian statistics. 3 hours discussion. (005562)
MATH 456 Applied Statistical Methods II   3.0 S2  
Prerequisites: MATH 314 or MATH 315.
Advanced topics in applied statistics including multiple and logistic regression, multivariate methods, multi-level modeling, repeated measures, and others as appropriate. The statistical programming language R is used. Appropriate for biology, agriculture, nutrition, business, psychology, social science and other majors. 3 hours discussion. (005570)
MATH 458 Sampling Methods   3.0 S1  
Prerequisite: MATH 314, MATH 315, or MATH 351 (may be taken concurrently).
The theory and application of survey sampling techniques. Topics include simple random sampling, stratified sampling, systematic sampling, and cluster sampling. Appropriate for mathematics, computer science, psychology, social science, agriculture, biology, and other majors. 3 hours discussion. (005573)

1 course selected from:

SUBJ NUM Title Sustainable Units Semester Offered Course Flags
MATH 314 Probability and Statistics for Science and Technology   4.0 FS  
Prerequisite: MATH 121; and one of the following: CINS 110, CSCI 111, MATH 130 (may be taken concurrently), or MATH 230.
Basic concepts of probability and statistics with emphasis on models used in science and technology. Probability models for statistical estimation and hypothesis testing. Confidence limits. One- and two-sample inference, simple regression, one- and two-way analysis of variance. Credit cannot be received for both MATH 314 and MATH 315. 4 hours discussion. (005533)
MATH 315 Applied Statistical Methods I   3.0 FS  
Prerequisite: MATH 105, MATH 109, or MATH 120, or faculty permission.
Single and two sample inference, analysis of variance, multiple regression, analysis of co-variance, experimental design, repeated measures, nonparametric procedures, and categorical data analysis. Examples are drawn from biology and related disciplines. The statistical programming language R is used. Appropriate for biology, agriculture, nutrition, psychology, social science and other majors. 3 hours discussion. (005568)

3 units selected from:

Any upper-division mathematics (MATH) courses except MATH 310, MATH 311, MATH 341, MATH 342, and MATH 441.

The Option in Foundational Mathematics Education: 22 units

The following program, together with the major core program, fulfills all requirements for the Foundational Subject Matter Preparation Program in Mathematics.

Mathematics

7 courses required:

SUBJ NUM Title Sustainable Units Semester Offered Course Flags
MATH 305 Conceptual and Practical Statistics   3.0 SP  
Prerequisites: MATH 120 or MATH 109 (may be taken concurrently).
Design of statistical experiments, graphing, sampling techniques, probability, and common probability distributions will be discussed, with an emphasis on practical applications. Uses and misuses of statistics, misrepresentation of data, and proper and improper statistical analyses will be discussed. 3 hours discussion. (005532)
MATH 310 Patterns and Structures in Mathematics   3.0 FS  
Prerequisites: MATH 110; MATH 210 or MATH 225.
Builds upon student's understanding of numbers and operations to develop their algebraic and proportional reasoning. Probability viewed as an application of proportional reasoning. Foundational statistics is also covered. Overall focus on developing a deep understanding of mathematics that is relevant to the teaching of Kindergarten-8th grade. Not acceptable for a mathematics major or minor except the Foundational Math Education option and Math Education minor. 3 hours discussion. (005542)
MATH 333 History of Mathematics   3.0 SP  
Prerequisites: MATH 121; MATH 220 or MATH 225; and at least one upper division mathematics course. MATH 330 is recommended.
Study of the historical development of mathematics, with particular emphasis on the relationship between mathematics and society. 3 hours discussion. (005531)
MATH 341 Mathematical Topics for the Credential   3.0 FA  
Prerequisites: MATH 121 or MATH 225.
This course is designed to supplement the mathematical background of the candidate for the single subject credential in mathematics. The mathematical topics will be discussed from the student's and the teacher's points of view to aid the candidate in making the transition to secondary school mathematics. Topics include mathematical problem-solving, conceptual ideas using algebra, geometry, and functions, incorporating technology into the mathematics curriculum, and finite systems. 3 hours seminar. (005544)
MATH 342 Math Topics for the Credential   3.0 SP  
Prerequisites: MATH 341.
This course focuses on having students examine mathematical pedagogy and the understanding and evaluations of students as mathematical learners as it analyzes secondary mathematics curriculum from an advanced standpoint. Students will have opportunities to be involved in the facilitation of mathematical learning. Topics include: history of mathematics education, contemporary mathematics curricula, problem solving, mathematical reasoning and methods of proof, mathematical learning theories, communication, assessment and collaborative learning communities. 3 hours discussion. (005545)
MATH 346 College Geometry   3.0 SP  
Prerequisites: MATH 220 or MATH 225; MATH 330.
An exploration of axioms and models for Euclidean and non-Euclidean geometries focusing on the independence of the Parallel Postulate. Additional topics will be chosen from Euclidean plane geometry, transformation geometry, and the geometry of polyhedra. 3 hours discussion. (005561)
MATH 442 Mathematics and the Teaching of Mathematics   3.0 FA  
Prerequisites: MATH 342.
Completes a three course series, started with two semesters of Mathematics for the Credential, MATH 341 and MATH 342. Students compare instructional strategies and explore the role content and pedagogical content knowledge has in these strategies. Central to the class is a lesson study project which entails a cycle of lesson development, implementation, reflection and revision, and implementation again. Students concurrently enrolled in EDTE 535A, Teaching Practicum I for Blended Math Candidates, are able to implement their lesson as part of the practicum, and have a real context for the full content of the course. 3 hours lecture. (020978)

1 course selected from:

SUBJ NUM Title Sustainable Units Semester Offered Course Flags
MATH 195 Project MATH Seminar Year 1   1.0 FS  
The Project M.A.T.H. Seminar - Year 1 is a biweekly seminar for students in their first year of Project M.A.T.H., an innovative program for students interested in becoming secondary mathematics teachers. Students work with mentor teachers, prepare and present lessons, and participate in a structured early field experience. Completion of the seminar series satisfies the Credential Program's Early Field Experience requirement. 1 hour seminar. You may take this course more than once for a maximum of 2.0 units. Credit/no credit grading. (020431)
MATH 241 Secondary Math Early Field Experience   1.0 FS  
This seminar and the associated CAVE field experience give prospective teachers early exposure to issues relevant to the profession of teaching secondary mathematics. In particular, the experience helps these future teachers develop a deeper understanding of the K-12 mathematics curriculum, understand connections between their university subject matter preparation and K-12 academic content, and reflect on developmental and social factors that affect K-12 students' learning of mathematics. 1 hour seminar. You may take this course more than once for a maximum of 4.0 units. Credit/no credit grading. (020432)

Electives Requirement:

To complete the total units required for the bachelor's degree, select additional elective courses from the total University offerings. You should consult with an advisor regarding the selection of courses which will provide breadth to your University experience and possibly apply to a supportive second major or minor.

Advising Requirement:

Advising is mandatory for all majors in this degree program. Consult your undergraduate advisor for specific information.

A student may complete more than one option in the major. Only courses specifically required by both options may be double counted.

Honors in the Major:

Honors in the Major is a program of independent work in your major. It requires 6 units of honors course work completed over two semesters.

The Honors in the Major program allows you to work closely with a faculty mentor in your area of interest on an original performance or research project. This year-long collaboration allows you to work in your field at a professional level and culminates in a public presentation of your work. Students sometimes take their projects beyond the University for submission in professional journals, presentation at conferences, or academic competition. Such experience is valuable for graduate school and professional life. Your honors work will be recognized at your graduation, on your permanent transcripts, and on your diploma. It is often accompanied by letters of commendation from your mentor in the department or the department chair.

Some common features of Honors in the Major program are:

  • You must take 6 units of Honors in the Major course work. All 6 units are honors classes (marked by a suffix of H), and at least 3 of these units are independent study (399H, 499H, 599H) as specified by your department. You must complete each class with a minimum grade of B.
  • You must have completed 9 units of upper-division course work or 21 overall units in your major before you can be admitted to Honors in the Major. Check the requirements for your major carefully, as there may be specific courses that must be included in these units.
  • Your cumulative GPA should be at least 3.5 or within the top 5% of majors in your department.
  • Your GPA in your major should be at least 3.5 or within the top 5% of majors in your department.
  • Most students apply for or are invited to participate in Honors in the Major during the second semester of their junior year. Then they complete the 6 units of course work over the two semesters of their senior year.
  • Your honors work culminates with a public presentation of your honors project.

While Honors in the Major is part of the Honors Program, each department administers its own program. Please contact your major department or major advisor to apply.

Honors in Mathematics

Well-qualified Mathematics majors are encouraged to apply for Honors in Mathematics. The program is open to junior and senior Mathematics majors who have completed 9 upper-division units (or a total of 24 units) in mathematics, including MATH 420W with a grade of B or better, and have a grade point average among the top 5% of junior-senior mathematics majors. Please visit the department office in HOLT 181 for further information.

Catalog Cycle:19