Perla Myers, PhD, CHAIR

Dwight R. Bean, PhD

Jane E. Friedman, PhD

Jennifer Gorsky, PhD

Diane Hoffoss, PhD

Eric Jiang, PhD

Simon G. M. Koo, PhD

Stacy Langton, PhD

Luby Liao, PhD

Lynn McGrath, PhD

Cameron Parker, PhD

Jack W. Pope, PhD

Lukasz Pruski, PhD

Michael Shulman, PhD

Ani Velo, PhD

Jeff Wright, PhD

### Mathematics Placement

For students to succeed in mathematics courses, it is important that they have the proper background. Students will be placed into their first math course at USD based on their SAT/ACT score. A student may take our mathematics placement exam in order to be placed into a higher level course the SAT/ACT score will allow. Students can take the placement exam at most twice during any 12 month period.

An exception to the above is: students who have either 1) scored 3 or higher on an AP calculus exam; 2) transferred a course that satisfies USD’s core curriculum mathematical competency requirement; or 3) earned 4 or higher on the HL5 IB exam or 3 or higher on the SL5 IB exam will have fulfilled their core mathematics requirement, and will be placed into future mathematics courses at USD based on those scores.

## The Mathematics Major

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.

### Preparation for the Major

COMP 150; MATH 150, 151, 160*, 250; PHYS 270; one of COMP 151, PHYS 271 or ECON 380

### Major Requirements

In order to obtain a major in mathematics, the student must satisfy the core curriculum requirements as set forth in this course catalog and complete the following courses:

MATH 320 (3)

MATH 350 or 361 or 380 (3)

MATH 360 (3)

MATH 375 or 385 (3)

Upper division mathematics electives (chosen from courses numbered 300 or above except for Math 300, 305, 405 and 498) (12 units)

At least 15 of the Upper-Division Units in the major must be completed at USD.

## Secondary Education Emphasis

Students interested in obtaining the Single Subject Teaching Credential in mathematics are required to major in mathematics with a secondary education emphasis.

### Preparation for the Major

COMP 150; MATH 115 (or the Level 2 placement exam), 120, 150, 151, 160*, 250; PHYS 270

### Major Requirements

For the mathematics major with secondary education emphasis, the student must satisfy the core curriculum requirements and complete the following courses:

MATH 305 (2)

MATH 320 (3)

MATH 325W (3)

MATH 350 (3)

MATH 360 (3)

MATH 375 (3)

MATH 380 (3)

MATH 405 (3)

Upper-Division Mathematics Electives (chosen from courses numbered 300 or above except for Math 300*(6)

At least 15 of the Upper-Division Units in the major must be completed at USD.

To obtain the professional preliminary teaching credential, consult the School of Leadership and Education Sciences for further requirements.

## Applied Emphasis

The mathematics department also offers a major in mathematics with an applied emphasis.

### Preparation for the Major

COMP 150 and COMP 151; MATH 150, 151, 160*, 250; PHYS 270

### Major Requirements

For the mathematics major with applied emphasis, the student must satisfy the core curriculum requirements and complete the following courses:

MATH 320 (3)

MATH 330 (3)

MATH 340 (3)

MATH 350 (3)

MATH 445 (3)

MATH 495W (1)

MATH 496W (2)

Two Upper-Division Electives** chosen from MATH 331, 341, 351, 360, or 365 (6 units)

One additional upper division elective (chosen from courses numbered 300 or above except for Math 300, 305, 405, and 498) (3 units)

At least 15 of the Upper-Division Units in the major must be completed at USD.

Substitutions in this list may be granted with the approval of the department chair.

For the applied emphasis, a minor in a natural science, computer science, engineering, or economics is also required.

Other minors can be substituted but require a proposal from the student explaining the connection between that discipline and mathematics that must be approved in advance by the department chair.

*Students are encouraged to complete MATH 160 – Logic for Mathematics and Computer Science before taking MATH 320 – Linear Algebra. In addition, students are strongly advised to complete both MATH 160 and MATH 320 before taking upper division courses numbered above 331. MATH 160 satisfies the core curriculum logic competency requirement. Students majoring in mathematics should take this course instead of PHIL 101 or 102.

**Students planning to go to graduate school are advised to take MATH 360 – Real Analysis I.

## The Mathematics Minor

Students may obtain a minor in mathematics by completing 18 units of mathematics course work. These units must include at least six units of upper division work as well as MATH 150, 151, and either MATH 160 or MATH 250.

## Mathematics Courses (MATH)

MATH 090 Intermediate Algebra (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 (3)

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. Prerequisite: MATH 090 or equivalent with a grade of C– or better, or pass Level 1 mathematics placement exam.

MATH 115 COLLEGE ALGEBRA (3)

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

MATH 118 ESSENTIALS OF TRIGONOMETRY (1)

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

MATH 120 INTRODUCTION TO STATISTICS (3)

Probability as a mathematical system, random variables and their distributions, confidence intervals, hypothesis testing, and other topics in statistical inference. Prerequisite: MATH 115 or equivalent.

MATH 130 SURVEY OF CALCULUS (3)

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. Prerequisite: MATH 115 with a grade of C– or better, or pass Level 2 mathematics placement exam.

MATH 150 CALCULUS I (4)

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. Students without a solid trigonometry background are strongly recommended to take MATH 118 prior to or concurrently with MATH 150.

MATH 151 Calculus II (4)

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

MATH 160 Logic for Mathematics and Computer Science (3)

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 core curriculum requirement.

MATH 200 Mathematical Concepts for Elementary Teachers I (3)

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. It covers the mathematical content required by the California state teacher credentialing frameworks. Prerequisite: MATH 115 or equivalent with a grade of C– or better.

MATH 250 Calculus III (4)

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 with a grade of C– or better.

MATH 300 Mathematical Concepts for Elementary Teachers II (3)

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. It covers the mathematical content required by the California state teacher credentialing frameworks. Prerequisite: MATH 200 or equivalent with a grade of C– or better.

MATH 305 Seminar in Teaching Mathematics (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 (3)

Matrix algebra, ordinary differential equations, and operational techniques. Prerequisite: 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 (3)

Boundary value problems, partial differential equations, Fourier methods, and introduction to complex analysis. Prerequisites: 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 (3)

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.

MATH 320 Linear Algebra (3)

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.

MATH 325W History of Mathematics (3)

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. Prerequisite: MATH 250.

MATH 330 Ordinary Differential Equations (3)

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.

MATH 331 Partial Differential Equations (3)

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

MATH 340 Numerical Analysis I (3)

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.

MATH 341 Numerical Analysis II (3)

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. Cross-listed as COMP 341.

MATH 350 Probability (3)

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.

MATH 351 Mathematical Statistics (3)

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

MATH 355 Combinatorics (3)

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.

MATH 360-361 Real Analysis I and II (3-3)

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.

MATH 365 Complex Function Theory (3)

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

MATH 370 Theory of Numbers (3)

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 151, or consent of instructor.

MATH 375 Algebraic Systems (3)

An introduction to groups, rings, integral domains, division rings, fields, vector spaces, and algebras, and applications of these systems to other branches of mathematics. Prerequisites: MATH 160 and 151, or consent of instructor.

MATH 380 Geometry (3)

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.

MATH 385 Topology (3)

Metric spaces, topologies, subspaces, continuity, separation axioms, compactness, and connectedness. Prerequisites: MATH 160 and 250, or consent of instructor.

MATH 388 Mathematical Logic (3)

Abstract structure of logical arguments, theory of the propositional and predicate calculus, and selected topics in modern logic. Prerequisites: MATH 160 and 151, or consent of instructor.

MATH 395 Mathematical Problem Solving Seminar (1)

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.) Prerequisite: MATH 151.

MATH 405 Advanced Perspective on High School Mathematics (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 (3)

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 and 330, or consent of the instructor.

MATH 494 Special Topics (3)

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.

MATH 495W Senior Project A (1)

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.

MATH 496W Senior Project B (2)

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.

MATH 498 Internship (1-3)

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.

MATH 499 Independent Study (3)

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