# Mathematics Courses

The program in Mathematics has a threefold objective: to provide courses giving technical mathematical preparation to students in any field of academic endeavor; to provide liberal arts courses which will demonstrate our mathematical heritage from past ages, and point out the impact of mathematical thought and philosophy on our culture in this technological civilization; and to provide courses of advanced mathematical knowledge which will prepare students for graduate work or professional employment in mathematics or related areas.

Students entering the University of San Diego and/or declaring a major during 2015-2016, should follow information contained in the printed course catalog (also known as the "catalog of record") published on October 1, 2015. Access the catalog of record at http://catalogs.sandiego.edu.

MATH 090, MATH 112, MATH 115, MATH 118, MATH 120, MATH 130, MATH 150, MATH 151, MATH 160, MATH 200, MATH 250, MATH 300, MATH 305, MATH 310, MATH 311, MATH 315, MATH 320, MATH 325W, MATH 330, MATH 331, MATH 340, MATH 341, MATH 350, MATH 351, MATH 355, MATH 360, MATH 361, MATH 365, MATH 370, MATH 375, MATH 380, MATH 385, MATH 388, MATH 395, MATH 405, MATH 445, MATH 494, MATH 495W, MATH 496W, MATH 498, MATH 499

### MATH 090 | INTERMEDIATE ALGEBRA

Units: 3

A survey of basic algebraic skills for students with insufficient mathematics preparation. This remedial course counts for “work-load credit” only. That is, its three units are counted as part of the student’s load during the semester in which it is taken, and the grade earned in the course is included in the computation of the student’s grade point average, but it does not satisfy any core curriculum requirement, or for the major or minor in mathematics, and it does not count toward the 124 units required for graduation.

### MATH 112 | INVESTIGATIONS IN MODERN MATHEMATICS

Units: 3

Prerequisites: MATH 090 or Passing the appropriate departmental placement test within the previous year

This core curriculum mathematics course provides a less algebraic alternative to MATH 115 for those students who need to fulfill the mathematical competency requirement, but who are not planning to go on in math. Topics may include: voting theory, graph theory, sequences, population growth, fractals, topology, geometry, and recursion. Note 1: This course does not serve as a prerequisite to MATH 120, MATH 130, MATH 150, or MATH 200. Prereq: MATH 090 or equivalent with a grade of C– or better, or pass Level 1 mathematics placement exam.

### MATH 115 | COLLEGE ALGEBRA

Units: 3

Prerequisites: Passing the appropriate departmental placement test within the previous year or MATH 090

Review of exponents, equations, and inequalities; function notation, composition, and inverses; linear, quadratic, polynomial, exponential, and logarithmic functions and their graphs. Prereq: MATH 090 or equivalent with a minimum grade of C–, or pass Level 1 mathematics placement exam.

### MATH 118 | ESSENTIALS OF TRIGONOMETRY

Units: 1

Definitions, solutions of right triangles, graphs, identities, and inverse trigonometric functions.

### MATH 120 | INTRODUCTION TO STATISTICS

Units: 3

Prerequisites: MATH 115 or MATH 130

Probability as a mathematical system, random variables and their distributions, confidence intervals, hypothesis testing, and other topics in statistical inference.

### MATH 130 | SURVEY OF CALCULUS

Units: 3

Prerequisites: Passing the appropriate departmental placement test within the previous year or MATH 115

A terminal mathematics course giving an introduction to the concepts and techniques of elementary differential and integral calculus. Note 1: This course is not equivalent to MATH 150, and does not serve as a prerequisite to MATH 151. Prereq: MATH 115 with a grade of C- or better, or pass Level 2 mathematics placement exam.

### MATH 150 | CALCULUS I

Units: 4

Prerequisites: Passing the appropriate departmental placement test within the previous year or MATH 115

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

### MATH 151 | CALCULUS II

Units: 4

Prerequisites: MATH 150

Continuation of Calculus I including integration, infinite series, differential equations, applications, and historical references. Prereq: MATH 150 with a grade of C– or better.

### MATH 160 | LOGIC FOR MATHEMATICS AND COMPUTER SCIENCE

Units: 3

Prerequisites: MATH 115 or Passing the appropriate departmental placement test within the previous year

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. Prereq: MATH 115, or pass Level 2 placement exam. This course satisfies the logic core curriculum requirement.

### MATH 200 | MATHEMATICAL CONCEPTS FOR ELEMENTARY TEACHERS I

Units: 3

Prerequisites: MATH 115

Problem solving, sets, numeration systems, a development of the whole number system, geometric figures, and computers. Note: This course does not count toward either the major or minor in mathematics. Prereq: MATH 115 with a grade of C– or better.

### MATH 250 | CALCULUS III

Units: 4

Prerequisites: MATH 151

Calculus of several variables, partial derivatives, multiple integration, elements of vector calculus, elements of differential equations, applications, and historical references. Prereq: MATH 151 with a grade of C– or better.

### MATH 300 | MATHEMATICAL CONCEPTS FOR ELEMENTARY TEACHERS II

Units: 3

Prerequisites: MATH 200

Measurement concepts, development of the real number system, algebra, geometric mappings, probability, and statistics. Note: This course does not count toward either the major or minor in Mathematics. Prereq: MATH 200 with a grade of C– or better.

### MATH 305 | SEMINAR IN TEACHING MATHEMATICS

Units: 2

Senior seminar for single subject credential students in mathematics. Issues in mathematics education including: Contribution to mathematics by men and women of various ethnic, racial, and cultural groups; equity considerations in mathematics education; variations in how students learn mathematics; diverse methods of communication and assessment in mathematics; and practical aspects of teaching diverse students. Students will be required to do some tutoring in mathematics. This course does not count toward the minor in mathematics or toward the upper division mathematics electives of the mathematics major (even for the secondary education emphasis).

### MATH 310 | APPLIED MATHEMATICS FOR SCIENCE AND ENGINEERING I

Units: 3

Prerequisites: MATH 151

Matrix algebra, ordinary differential equations, and operational techniques. Prereq: MATH 151. Students may not take MATH 310 concurrently with MATH 330 or after having taken MATH 330.

### MATH 311 | APPLIED MATHEMATICS FOR SCIENCE AND ENGINEERING II

Units: 3

Prerequisites: MATH 250 and MATH 310

Boundary value problems, partial differential equations, Fourier methods, and introduction to complex analysis. Prereq: MATH 250 and 310. Students may not take MATH 311 concurrently with MATH 331 or after having taken MATH 331.

### MATH 315 | APPLIED PROBABILITY AND STATISTICS

Units: 3

Prerequisites: MATH 250

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.

### MATH 320 | LINEAR ALGEBRA

Units: 3-4

Prerequisites: MATH 151

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. Prereq: MATH 151 with a grade of C- or better. It is recommended that students take MATH 160 before taking MATH 320.

### MATH 325W | HISTORY OF MATHEMATICS

Units: 3

Prerequisites: MATH 250

Selected topics from the history of mathematics. The course includes a variety of writing assignments. Emphasis is on the history of mathematical ideas, rather than on personalities or social background. Prereq: MATH 250 with a grade of C- or better.

### MATH 330 | ORDINARY DIFFERENTIAL EQUATIONS

Units: 3

Prerequisites: MATH 250

Preliminary ideas, differential equations of the first and second order, linear equations with constant coefficients, operational techniques, simultaneous equations, series solutions, and applications. Prereq: MATH 250 with a grade of C- or better.

### MATH 331 | PARTIAL DIFFERENTIAL EQUATIONS

Units: 3

Prerequisites: MATH 330

Preliminary notions, techniques for solving well-known partial differential equations of physics, orthogonal functions, and applications. Prereq: MATH 330 with a grade of C- or better.

### MATH 340 | NUMERICAL ANALYSIS I

Units: 3

Prerequisites: MATH 151 and COMP 150

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. Prereq: MATH 151 with a grade of C- or better and COMP 150 with a grade of C- or better. Cross-listed as COMP 340.

### MATH 341 | NUMERICAL ANALYSIS II

Units: 3

Prerequisites: MATH 250 and MATH 320 and MATH 330 (Can be taken Concurrently) and MATH 340

Estimation of eigenvalues and eigenvectors of matrices; numerical solutions of differential equations, existence, and stability theory; and computer lab assignments. Prereq: MATH 250, 320, 330 (may be taken concurrently), and 340, all with a grade of C- or better. Cross-listed as COMP 341.

### MATH 350 | PROBABILITY

Units: 3

Prerequisites: MATH 250

Probability axioms, conditional probability, discrete and continuous sample spaces, random variables and common distributions, jointly distributed random variables, and central limit theorem.

### MATH 351 | MATHEMATICAL STATISTICS

Units: 3

Prerequisites: MATH 350

Statistical models, estimation, hypothesis testing, optimality, linear models, analysis of discrete data, and nonparametric methods. Prereq: MATH 350 with a grade of C- or better.

### MATH 355 | COMBINATORICS

Units: 3

Prerequisites: MATH 151 and MATH 160

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. Prereq: MATH 151 with a grade of C- or better and MATH 160 with a grade of C- or better.

### MATH 360 | REAL ANALYSIS I

Units: 3

Prerequisites: MATH 160 and MATH 250

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. Prereq: MATH 160 with a grade of C- or better and MATH 250 with a grade of C- or better.

### MATH 361 | REAL ANALYSIS II

Units: 3

Prerequisites: MATH 360

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. Prereq: MATH 360 with a grade of C- or better.

### MATH 365 | COMPLEX FUNCTION THEORY

Units: 3

Prerequisites: MATH 160 and MATH 250

Analytic function theory; power series, analytic continuation, conformal mapping, and applications. Prereq: MATH 160 with a grade of C- or better and MATH 250 with a grade of C- or better.

### MATH 370 | THEORY OF NUMBERS

Units: 3

Prerequisites: MATH 151 and MATH 160

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. Prereq: MATH 160 with a grade of C- or better and MATH 151 with a grade of C- or better.

### MATH 375 | ALGEBRAIC SYSTEMS

Units: 3

Prerequisites: MATH 151 and MATH 160

An introduction to groups, rings, integral domains, division rings, fields, vector spaces, and algebras, and applications of these systems to other branches of mathematics. Prereq: MATH 160 with a grade of C- or better and MATH 151 with a grade of C- or better.

### MATH 380 | GEOMETRY

Units: 3

Prerequisites: MATH 160 and MATH 250

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. Prereq: MATH 160 with a grade of C- or better and MATH 250 with a grade of C- or better.

### MATH 385 | TOPOLOGY

Units: 3

Prerequisites: MATH 160 and MATH 250

Metric spaces, topologies, subspaces, continuity, separation axioms, compactness, and connectedness. Prereq: MATH 160 with a grade of C- or better and MATH 250 with a grade of C- or better.

### MATH 388 | MATHEMATICAL LOGIC

Units: 3

Prerequisites: MATH 160 and MATH 151

Abstract structure of logical arguments, theory of the propositional and predicate calculus, and selected topics in modern logic. Prereq: MATH 160 with a grade of C- or better and MATH 151 with a grade of C- or better.

### MATH 395 | MATHEMATICAL PROBLEM SOLVING SEMINAR

Units: 1 Repeatability: Yes (Can be repeated for Credit)

Prerequisites: MATH 151

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. (May be taken twice for credit.).

### MATH 405 | ADVANCED PERSPECTIVE ON HIGH SCHOOL MATHEMATICS

Units: 3

This course is a required course in the Mathematics Single Subject credential program. It provides a capstone experience for future mathematics high school teachers, in which they 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 does not count toward the minor in mathematics or toward the upper division mathematics electives of the mathematics major (even for the secondary education emphasis).

### MATH 445 | MATHEMATICAL MODELING

Units: 3

Prerequisites: MATH 250 and MATH 320 and MATH 330

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. Prereq: MATH 250 with a grade of C- or better, MATH 320 with a grade of C- or better and MATH 330 with a grade of C- or better.

### MATH 494 | SPECIAL TOPICS

Units: 1-4 Repeatability: Yes (Can be repeated for Credit)

Prerequisites: MATH 250

Topics of special interest chosen by the instructor. May be repeated for credit with the consent of the instructor.

### MATH 495W | SENIOR PROJECT A

Units: 1

Prerequisites: MATH 445 (Can be taken Concurrently)

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.

### MATH 496W | SENIOR PROJECT B

Units: 2

Prerequisites: MATH 495W

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. Prereq: MATH 495W with a grade of C– or better.

### MATH 498 | INTERNSHIP

Units: 1-3 Repeatability: Yes (Can be repeated for Credit)

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 three units.

Department of Mathematics

College of Arts and Sciences

### Contact Us

**Phone: **(619) 260-4706**Fax: **(619) 260-4293

tmanabat@sandiego.edu

### Visit Campus

Serra Hall 133

5998 Alcalá Park

San Diego, CA 92110