# Mathematics Major

Our mathematics program is intended to help mathematics majors gain knowledge and understanding of mathematics, its reasoning, its processes, its beauty, and its applications, at the undergraduate level. Some graduates of this program will go on to graduate study in mathematics or in other fields; some will get jobs in industry, business or government which require mathematical knowledge to a greater or lesser extent; some will teach mathematics at the secondary level; some may go on to professional study in other fields, such as medicine or law. The mathematics program is intended to give all these students a sound foundation in mathematics which will serve them well, whatever their future endeavor.

## Major Requirements

In order to obtain a major in mathematics, the student must satisfy the Core Curriculum requirements as set forth in this Bulletin and complete the following courses:

COMP 150 Computer Programming I | 3 units |

MATH 150 Calculus I | 4 units |

MATH 151 Calculus II | 4 units |

MATH 160 Logic for Mathematics and Computer Science | 3 units |

MATH 250 Calculus III | 4 units |

MATH 320 Linear Algebra | 3 units |

MATH 350 Probability, 361 Advanced Calculus, or 380 Geometry | 3 units |

MATH 360 Advanced Calculus | 3 units |

MATH 375 Algebraic Systems or 385 Topology | 3 units |

PHYS 270 Introduction to Mechanics and Wave Motion | 4 units |

PHYS 271 Introduction to Thermodynamics, Electricity, and Magnetism | 4 units |

Upper-division mathematics electives | 12 units |

Total | 50 units |
---|

Math 120, 370, 380, 375, 325W, and 305 are required for the Single Subject Credential in Mathematics. See the School of Leadership and Education Sciences for further requirements.

## Recommended Program of Study for the Mathematics Major

Semester I | Semester II | |
---|---|---|

Freshman Year |
Preceptorial (3), COMP 150 (3), MATH 150 (4), CC or Electives (6) | MATH 151 (4), MATH 160 (3), PHYS 270 (4), CC or Electives (3 or 6) |

Sophomore Year |
[MATH 160 (3)], MATH 250 (4), PHYS 271 (4), CC or Electives (6-9) | MATH 320 (3), CC or Electives (9) |

Junior Year |
Upper-division MATH (6), CC, Minor, or Electives (9) | Upper-division MATH (6), CC, Minor, or Electives (9) |

Senior Year |
Upper-division MATH (6), CC, Minor, or Electives (9) | Upper-division MATH (3), CC, Minor, or Electives (9) |

## Course Descriptions

**150 Calculus I / 4 UNITS**

Fundamental notions of analytic geometry, differential and integral calculus with elementary applications; historical references. Prerequisite: MATH 115 with a grade of C– or better, or pass Level 2 mathematics placement exam within the previous year. Students without a solid trigonometry background are strongly recommended to take MATH 118 prior to or concurrently with MATH 150. (every semester)

**151 Calculus II / 4 UNITS**

Continuation of Calculus I including integration, infinite series, differential equations, applications, and historical references. Prerequisite: MATH 150 or equivalent. (every semester)

**160 Logic for Mathematics and Computer Science / 3 UNITS**

Propositional calculus; first-order predicate calculus, mathematical proof, mathematical induction, fundamental set theory, relations and functions, and applications to problems in mathematics and computer science. Prerequisite: MATH 115, or pass Level 2 placement exam. This course satisfies the logic competency requirement. (every semester)

**250 Calculus III / 4 UNITS**

Calculus of several variables, partial derivatives, multiple integration, elements of vector calculus, elements of differential equations, applications, and historical references. Prerequisite: MATH 151 or equivalent. (every semester)

**310 Applied Mathematics for Science and Engineering I / 3 UNITS**

Matrix algebra, ordinary differential equations, and operational techniques. Prerequisite: MATH 151. Students may not take both MATH 310 and 330 for credit. (spring semester, every year)

**311 Applied Mathematics for Science and Engineering II / 3 UNITS**

Boundary value problems, partial differential equations, Fourier methods, and introduction to complex analysis. Prerequisites: MATH 250, 310. Students may not take both MATH 311 and 331 for credit. (fall semester, every year)

**315 Applied Probability and Statistics / 3 UNITS**

Introduction to probability; discrete and continuous random variables; conditional and joint distributions and densities; functions of random variables; expectation and estimation; central limit theorem; introduction to statistics; introduction to random sequences and random processes. Prerequisite: MATH 250. (spring semester, every year)

**320 Linear Algebra / 3 UNITS**

Systems of linear equations, matrix algebra and operations, vector spaces of three or more dimensions, linear independence, inner product spaces, linear transformations and their matrices, determinants, eigenvalues and eigenvectors, and brief introduction to canonical forms. Prerequisite: MATH 151 or consent of instructor. It is recommended that students take MATH 160 before taking MATH 320. (every semester) 325W History of Mathematics / 3 UNITS Selected topics from the history of mathematics. The course will include a variety of writing assignments. Emphasis will be on the history of mathematical ideas, rather than on personalities or social background. Prerequisite: MATH 250. (spring semester, even years)

**330 Ordinary Differential Equations / 3 UNITS**

Preliminary ideas, differential equations of the first and second order, linear equations with constant coefficients, operational techniques, simultaneous equations, series solutions, and applications. Prerequisite: MATH 250. (fall semester, everyyear)

**331 Partial Differential Equations / 3 UNITS**

Preliminary notions, techniques for solving well-known partial differential equations of physics, orthogonal functions, and applications. Prerequisite: MATH 330.

**340 Numerical Analysis / 3 UNITS**

Approximate computations and round-off errors, Taylor expansions, numerical solution of equations and systems of equations, numerical integration, numerical solution of differential equations, interpolation, and problem solving on the computer. Prerequisites: MATH 151 and COMP 150. Cross-listed as COMP 340. (spring semester, every year)

**341 Numerical Analysis II / 3 UNITS**

Estimation of eigenvalues and eigenvectors of matrices; numerical solutions of differential equations, existence, and stability theory; and computer lab assignments. Prerequisites: MATH 250, 320, 330 (may be taken concurrently), and 340.

**350 Probability / 3 UNITS**

Probability axioms, conditional probability, discrete and continuous sample spaces, random variables and common distributions, jointly distributed random variables, and central limit theorem. Prerequisite: MATH 250 or consent of instructor. (fall semester, every year)

**351 Mathematical Statistics / 3 UNITS**

Statistical models, estimation, hypothesis testing, optimality, linear models, analysis of discrete data, and nonparametric methods. Prerequisite: MATH 350.

**355 Combinatorics / 3 UNITS**

Principles of enumeration, finite difference calculus, generating functions, finite difference equations, principle of Inclusion and Exclusion, introduction to the theory of combinatorial graphs, and applications to computer science. Prerequisites: MATH 151 and 160, or consent of instructor.

**360-361 Advanced Calculus / 3-3 UNITS**

A study of the foundations of real analysis, including the calculus of functions of one and several variables, infinite processes, convergence theory, and selected topics of advanced undergraduate analysis. Prerequisites: MATH 160 and 250. (360: fall semester, every year; 361: spring semester, odd years)

**365 Complex Function Theory / 3 UNITS**

Analytic function theory; power series, analytic continuation, conformal mapping, and applications. Prerequisite: MATH 160 and 250, or consent of instructor.

**370 Theory of Numbers / 3 UNITS**

Divisibility, Euclidean algorithm, fundamental theorem of arithmetic, congruences, Fermat’s theorem, Euler’s function, Chinese Remainder Theorem, Diophantine equations, primitive roots, quadratic residues, reciprocity law, and continued fractions. Prerequisites: MATH 160 and 250, or consent of instructor. (spring semester, even years)

**375 Algebraic Systems / 3 UNITS**

An introduction to groups, rings, integral domains, divisionrings, fields, vector spaces, and algebras, and applications ofthese systems to other branches of mathematics. Prerequisites:MATH 160 and 250, or consent of instructor. (spring semester,odd years)

**380 Geometry / 3 UNITS**

An introduction to an area of modern geometry. The specific topic will be chosen from the following: non-Euclidean geometry, differential geometry, projective geometry, or metric geometry, and historical references. Prerequisites: MATH 160 and 250, or consent of instructor. (fall semester, odd years)

**385 Topology / 3 UNITS**

Metric spaces, topologies, subspaces, continuity, separation axioms, compactness, and connectedness. Prerequisites: MATH 160 and 250, or consent of instructor. (spring semester, even years)

**388 Mathematical Logic / 3 UNITS**

Abstract structure of logical arguments, theory of the propositional and predicate calculus, and selected topics in modern logic. Prerequisites: MATH 160 and 250, or consent of iinstructor.

**395 Mathematical Problem Solving Seminar / 1 UNIT**

This course is intended for students who enjoy the challenge of mathematical problems. This course differs from other mathematics courses which are focused on the theory and applications of a single branch of mathematics. It emphasizes problem-solving techniques, creative thinking, and exposition of skills in different areas of mathematics such as algebra, calculus, geometry, and number theory. Prerequisite: MATH 151. (fall semester, every year)

**405 Advanced Perspective on High School** **Mathematics / 3 UNITS**

This course is a required course in the Mathematics Single Subject credential program. It provides a capstone experience for students in which they will look at topics in high school mathematics from an advanced viewpoint. Connections between mathematics topics and between basic and more advanced mathematics will be emphasized. This course will not apply toward the major or minor in mathematics.

**445 Mathematical Modeling / 3 UNITS**

The construction and analysis of mathematical models, simplifying assumptions and testing strategies; topics chosen by the instructor in dimensional analysis, discrete and continuous dynamical systems, stochastic models, linear systems, optimization models, statistical methods, and graph theory. Prerequisites: MATH 250, 320, or consent of the instructor, and 330. (fall semester, every year)

**494 Special Topics / 3 UNITS**

Topics of special interest chosen by the instructor. May be repeated for credit with the consent of the instructor. Prerequisite: MATH 250 or consent of instructor.

**495W Senior Project in Applied Mathematics A / 1 UNIT**

Capstone senior project involving the application of mathematics to the solution of a problem or problems. Meets once per week: prepare a written research proposal for work to be carried out in MATH 496W; ongoing written and oral progress reports and regular consultation with the faculty supervisor. Prerequisites: MATH 445 (can be taken concurrently) and consent of the instructor. (fall semester, every year)

**496W Senior Project in Applied Mathematics B / 2 UNITS**

Capstone senior project involving the application of mathematics to the solution of a problem or problems. Meets twice per week: carry out the project defined in MATH 495W; ongoing written and oral progress reports and regular consultation with the faculty supervisor; final written and oral presentation in the presence of other students and faculty. Prerequisite: MATH 495W with a C– or better. (spring semester, every year)

**498 Internship / 1-3 UNITS**

Practical experience in the application of mathematics. Students will be involved in projects conducted by businesses, agencies, and institutions. Enrollment is arranged on an individual basis according to the student’s interest and background, and the availability of positions. A written report is required. Units may not normally be applied toward the major or minor in mathematics. MATH 498 may be repeated for a total of 3 units.

**499 Independent Study / 3 UNITS**

Student reading and research in selected special topics; student presentations. May be repeated for credit once with a different topic. Prerequisite: Consent of instructor.