Mathematics

Departmental Affiliation: Physical Sciences and Mathematics

While offering students an opportunity to study mathematics as part of a liberal education, the mathematics major serves as excellent preparation for work in fields such as actuarial science, computer science, statistics, secondary teaching, business, or graduate study. Coupled with courses in chemistry and biology, a degree in mathematics also provides excellent preparation for entrance into schools of medicine, dentistry, or optometry.

Mathematics B.A. Degree

Required Courses

Lower Division:

MTH 5ABC

Calculus I/II/III

(4,4,4)

MTH 6

Sequences and Series

(1)

CIS 2

Introduction to Computer Programming

(3)

MTH 8

Transition to Higher Math

(3)

PHY 11AB

Mechanics/Electricity, Magnetism, and Optics

(4,3)

PHY 1BL

Physics Laboratory

(1)

Students who can demonstrate their proficiency in any of the above courses may enroll in the next course in the sequence. Students who need further preparation in algebra and elementary functions should take MTH 1, College Algebra, before MTH 5A.

Upper Division:

MTH 102

Advanced Calculus

(3)

MTH 103

Linear Algebra

(3)

MTH 111

Abstract Algebra

(3)

MTH 113

Probability and Statistics

(3)

MTH 119

Differential Equations

(3)

MTH 128A

Numerical Analysis

(3)

Twelve units from

MTH 101

Topics in Geometry

(3)

MTH 104

Number Theory

(3)

MTH 105

Complex Analysis

(3)

MTH 107

Topology

(3)

MTH 120

Discrete Mathematics

(3)

MTH 128B

Numerical Analysis

(3)

MTH 140

History of Mathematics

(1)

Total units in Mathematics: 57

Plus general studies requirements and electives totaling 124 semester units, including foreign language requirement. An overall GPA of 2.0 in major courses is required for the degree.

Mathematics Minor

A minimum of seven courses including the following:

MTH 5ABC

Calculus I/II/III

(4,4,4)

MTH 6

Sequence & Series

(1)

MTH 103

Linear Algebra

(3)

At least 3 additional upper-division courses (or MTH 8 plus two upper division courses) chosen in consultation with the student's advisor.

Computer Programming Minor

Lower Division:

MTH 5AB

Calculus I/II

(4,4)

CIS 2

Introduction to Computer Programming

(3)

Upper Division:

MTH 125

Programming

(3)

Two additional upper division courses chosen in consultation with the student's advisor from the following:

MTH 120

Discrete Mathematics

(3)

MTH 128AB

Numerical Analysis

(3,3)

MTH 135

Structure and Comparison of Programming Languages

(3)

Math Courses

MTH 0X Math Tutorial (1)

This class is for students who need a review in a limited number of mathematical topics. The topics may include the numbers of arithmetic, an introduction to algebra, linear equations in one variable, word problems, polynomials, graphing and straight lines, systems of equations, rational expressions, radicals, quadratic equations, absolute value and inequalities. Students will meet one hour per week with a tutor. Credit does not apply to the Baccalaureate degree.

MTH 1 Precalculus with Trigonometry (4)

MTH1 is a course aimed at preparing students for success in first semester calculus. The course material includes treatment and applications of Polynomial functions, Rational functions, Exponential functions, Logarithmic functions, and Trigonometric functions, including equations, inequalities, systems, graphs, identities and inverses. If time permits, additional topics may include Complex numbers, Conics, Sequences and Series, Binomial theorem, Induction, Matrices, Polar and Parametric equations. Prerequisite: Satisfactory score on the Mathematics Placement Examination or successful completion of MTH 2X or MTH 28. GS-IIIE, VIIB

MTH 2X Fundamentals of Algebra (3)

Real numbers and their properties, exponents and radicals, fundamental operations, polynomials, factoring, rational expressions, linear and quadratic equations and inequalities, systems of equations. Meets four hours per week. Successful completion of MTH 2X fulfills the AA Liberal Arts Math requirement. Credit does not apply to the Baccalaureate degree. In the Weekend College program it is offered as a one-unit course.

MTH 5A Calculus I (4)

Limits; continuity; derivatives of algebraic and transcendental functions with applications; antiderivatives; an introduction to the definite integral; the Fundamental Theorem of Calculus. Prerequisite: Three to four years of high school mathematics including trigonometry and satisfactory score on Mathematics Placement Examination or grade of C - or better in MTH 1. GS-IIIE, VIIB

MTH 5B Calculus II (4)

Techniques of integration (including substitution and parts); numerical methods of integration; applications of the integral (including areas, and volumes); improper integrals; differential equations, an introduction to parametric equations and polar coordinates. Prerequisite: Grade of C - or better in MTH 5A. GS-IIIE, VIIB

MTH 5C Calculus III (4)

Partial derivatives; multiple integrals; three-dimensional space; vectors in two- and three-dimensional space; vector calculus. Prerequisite: Grade of C or higher in MTH 5B or consent of instructor. GS-VIIB

MTH 6 Sequences and Series (1)

Sequences, infinite series, Taylor and Maclaurin series. Prerequisite:  concurrent enrollment in MTH 5B.

MTH 8 Transition to Higher Math (3)

The goal of this course is to ease the transition from lower-division mathematics courses to upper-division mathematics courses. In this course students will gain experience working with abstract ideas at a nontrivial level and understanding and writing proofs, in order to achieve the sophisticated blend of knowledge, discipline, and creativity that we call "mathematical maturity." Topics include logic, finite and infinite sets, functions, and problem solving. Prerequisite: MTH 5A

MTH 10 Quantitative Reasoning and Mathematical Ideas (3)

Ideas in mathematics chosen to emphasize problem-solving, decision-making, economic productivity and real-world applications. Recommended to fulfill GS IIIE requirement absent other major requirements. Topics include critical thinking, inductive reasoning, problem solving, numbers, finances, statistics, probability, geometry, algebra and exponential functions. Prerequisite: Satisfactory score on Mathematics Placement Examination or completion of MTH 2X. GS-IIIE, VIIB

MTH 25 The LINUX/UNIX Environment (3)

Basic LINUX and UNIX commands, the file systems, pipes, filters, shell procedures, reading of binary files and programming debugging aids. Prerequisite: CIS 2 and familiarity with a compiled programming language; MTH 5A is highly recommended.

MTH 28 Mathematical Analysis for Business (3)

Topics in Algebra including solutions of systems of equations and inequalities; exponential and logarithmic functions; linear programming and mathematics of finance. Emphasis is placed on the application of mathematics to problems in business. Prerequisites: Satisfactory score on the Mathematics Placement Examination or completion of MTH 2X. GS-IIIE, VIIB

MTH 38 Elements of Probability and Statistics (3)

Elementary probability theory, properties of distributions, sampling, estimation, hypothesis testing, correlation. Prerequisite: Satisfactory score on the Mathematics Placement Examination or completion of MTH 2X. GS-IIIE, VIIB

MTH 38H Elements of Probability and Statistics (3)

Topics in probability and statistics including measures of central tendency and spread, elementary probability theory, properties of distributions, estimation, confidence intervals, hypothesis testing, linear correlations and regression. An algebra-based course intended primarily for nonmathematics majors. Prerequisite: Satisfactory score on the Mathematics Placement Examination or completion of MTH 2X. Open only to students admitted to the Honors Program. GS-IIIE

MTH 50 Elementary Number Systems (3)

Sets, numeration systems, properties of integers, rational and real numbers, elementary number theory, modular systems, problem-solving processes, ratio, proportion, percentage. This course receives General Studies credit and is required for Liberal Studies majors. Can be taken for professional credit. Prerequisite: Satisfactory score on the Mathematics Placement Examination. GS-IIIE, VIIA

MTH 51 Elements of Geometry and Statistics (3)

Intuitive geometry of lines, planes, and space; congruence, similarity, measurement, geometric constructions, elements of probability and statistics. This course is intended primarily for Liberal Studies majors. Can be taken for professional credit. Prerequisite: Satisfactory score on the Mathematics Placement Examination. GS-IIIE, VIIB

MTH 99/199 Special Studies in Mathematics (1-3)

Independent or group studies in mathematics. Course may be repeated for credit. Prerequisite: Approval of the department and consent of the instructor.

Any upper division mathematics course will require a minimum grade of C in prerequisite courses.

MTH 101 Topics in Geometry (3)

A brief treatment of the axiomatic foundations of Euclidean and non-Euclidean geometry. An introduction to differential geometry. Prerequisite: MTH 5C, 103 concurrent.

MTH 102 Advanced Calculus (3)

Set theory, real numbers and their topology, limits, continuity, differentiation and integration theory. Prerequisite: MTH 5C.

MTH 103 Linear Algebra (3)

Vectors and vector spaces, linear transformations and matrices, determinants, eigenvalues and eigenvectors. Prerequisite: MTH 5B.

MTH 104 Number Theory (3)

The division algorithm, different bases, g.c.d. and 1.c.m., the equation ax + by = n, the fundamental theorem of arithmetic; properties of congruence, reduced residue systems, Euler phi-function, simultaneous congruences; polynomial congruences, primitive roots, indices, the law of quadratic reciprocity, finite and infinite continued fractions, some computer applications in elementary number theory. Prerequisite: MTH 5C or consent of instructor.

MTH 105 Complex Analysis (3)

Complex numbers and functions, analytic functions, integration, conformal mapping. Prerequisite: MTH 5C.

MTH 107 Topology (3)

Topological spaces and continuous functions, connectedness, compactness, countability and separation axioms. Prerequisite: MTH 5C or consent of instructor; MTH 8 or MTH 120 recommended.

MTH 111 Abstract Algebra (3)

Numbers and number systems, groups, rings; fields; homomorphism and isomorphism theorems. Prerequisite: MTH 5C; MTH 120 strongly recommended or consent of instructor.

MTH 113 Probability and Statistics (3)

Probability as a mathematical system, random variables and their distributions, limit theorems, statistical applications, hypotheses testing. Prerequisite: MTH 5C or consent of instructor.

MTH 119 Differential Equations (3)

Linear equations, series solutions, Laplace transforms, numerical methods, existence and uniqueness of solutions. Prerequisite: MTH 5B.

MTH 120 Discrete Mathematics (3)

Logic, proof writing (including induction), set theory, functions and relations, algorithms and recursion, elementary number theory, combinatorics, probability, graph theory, and trees. Prerequisite: MTH 5B. GS-VIIB

MTH 125 Programming (3)

Intermediate level programming methods including vector and array manipulations, classes, functions, and subroutines. Applications in science, mathematics, and business. Prerequisite: CIS 2 and MTH 5A or concurrent enrollment in MTH 5A or consent of the instructor. GS-IIIE

MTH 128AB Numerical Analysis (3,3)

Solutions of large systems of linear algebraic equations. Eigenvalues and eigenvectors of matrices. Interpolation: Lagrange and Newton polynomials. Fourier series and orthogonal polynomials. Introduction to the theory of ordinary differential equations. Heun and Runge-Kutta numerical techniques. Numerical determination of real and complex roots of polynomials; cubic splines; numerical treatment of partial differential equations, techniques of numerical integration. Prerequisites: MTH 5C, CIS 2.

MTH 135 Structure and Comparison of Programming Languages (3)

Basic concepts of syntax and semantics. Comparison of syntax and semantics of selected programming languages. Language design. How to evaluate a computer programming language. Prerequisites: MTH 5A, MTH 125, or consent of instructor.

MTH 140 History of Mathematics (1)

History of mathematics from antiquity to the mid 20th Century. Prerequisites: MTH 5C, MTH 103, and demonstrated mathematical maturity.

MTH 190 Internship (1-3)

An intensive work-study program for qualified upper division students. The student is responsible for setting up the internship in conjunction with the appropriate faculty and the office of Career Planning and Placement. This must be approved by the department chairperson.

MTH 195H Senior Honors Thesis (3)

Open only to students admitted to the Honors Program.