Mathematics

Lukasz Pruski, Ph.D., Area Coordinator
John H. Glick, Ph.D., Chair
Dwight R. Bean, Ph.D.
Jane E. Friedman, Ph.D.
Jennifer Gorsky, Ph.D.
Stanley J. Gurak, Ph.D.
Diane Hoffoss, Ph.D.
Eric Jiang, Ph.D.
Simon G. M. Koo, Ph.D.
Stacy Langton, Ph.D.
Luby Liao, Ph.D.
Lynn McGrath, Ph.D.
Perla Myers, Ph.D.
Cameron Parker, Ph.D.
Jack W. Pope, Ph.D.
Lynne B. Small, Ph.D.
Ani Velo, Ph.D.
Jeff Wright, Ph.D.

Mathematics Placement Exam

It is important for the success of students in mathematics courses that they have the proper background. Students, therefore, are required to take a placement exam that determines their placement. The only exceptions are for students who have 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. Placement exam scores are good for one year after they are taken, and students can take the placement exam at most twice during any 12 month period.

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.

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 / 3 units
MATH 150, 151, 160*, 250 / 15 units
MATH 320 / 3 units
MATH 350 or 361 or 380 / 3 units
MATH 360 / 3 units
MATH 375 or 385 / 3 units
PHYS 270, 271 / 8 units

Upper-division mathematics electives / 12 units

Students interested in obtaining the Single Subject Teaching Credential in mathematics are required to major in mathematics with a secondary education emphasis. For this option, the student must satisfy the core curriculum requirements and complete the following courses:

COMP 150 / 3 units
MATH 115 (or the Level 2 placement exam), 120, 150, 151, 160*, 250 / 18-21 units
MATH 305 / 2 units
MATH 320 / 3 units
MATH 325W / 3 units
MATH 350 / 3 units
MATH 360 / 3 units
MATH 375 / 3 units
MATH 380 / 3 units
MATH 405 / 3 units
PHYS 270 / 4 units

Upper-division mathematics electives / 6 units

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

The mathematics department also offers a major in mathematics with an applied emphasis having somewhat different requirements. For the applied option, the student must satisfy the core curriculum requirements and complete the following courses:

COMP 150, 151 / 6 units
MATH 150, 151, 160*, 250 / 15 units
MATH 320 / 3 units
MATH 330 / 3 units
MATH 340 / 3 units
MATH 350 / 3 units
MATH 445 / 3 units
MATH 495W / 1 unit
MATH 496W / 2 units
PHYS 270 / 4 units

Two upper-division electives** chosen from MATH 331, 341, 351, 360, or 365 / 6 units

One additional upper-division elective / 3 units

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 – Advanced Calculus 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 6 units of upper-division work as well as MATH 150, 151, and 250.

MATHEMATICS Courses (MATH)

090 Intermediate Algebra / 3 UNITS
A survey of basic algebraic skills for students with insufficient mathematics preparation. This remedial course counts for “work-load credit” only. That is, its 3 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. (every semester)

112 Investigations in Modern Mathematics / 3 UNITS
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, and recursion. Note 1: This course does not serve as a prerequisite to MATH 130, MATH 150, or MATH 200. Prerequisite: MATH 090 at USD with a grade of C– or better, or pass Level 1 mathematics placement exam within the previous year. (every semester)

114 Modeling with Algebra and Statistics / 3 UNITS
Statistical and algebraic methods of modeling quantitative data and analyzing the models. Includes the study of two-variable data using ideas of regression, correlation and bias, and the study of linear, quadratic, polynomial, exponential and logarithmic functions and their graphs.

Note: Students may not take both MATH 114 and MATH 115 for credit.

Prerequisite: MATH 090 at USD with a grade of C- or better, or pass Level 1 mathematics placement exam within the previous year.

115 College Algebra / 3 UNITS
Review of exponents, equations, and inequalities; function notation, composition, and inverses; linear, quadratic, polynomial, exponential, and logarithmic functions and their graphs. Prerequisite: MATH 090 at USD with a grade of C– or better, or pass Level 1 mathematics placement exam within the previous year. (every semester)

118 Essentials of Trigonometry / 1 UNIT
Definitions, solutions of right triangles, graphs, identities, and inverse trigonometric functions. (every semester)

120 Introduction to Statistics / 3 UNITS
Probability as a mathematical system, random variables and their distributions, confidence intervals, hypothesis testing, and other topics in statistical inference. Prerequisite: MATH 114, or MATH 115 or equivalent.

130 Survey of Calculus / 3 UNITS
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 will not serve as a prerequisite to MATH 151. Prerequisite: MATH 114 with a grade of C– or better, MATH 115 with a grade of C– or better, or pass Level 2 mathematics placement exam within the previous year. (every semester)

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)

200 Mathematical Concepts for Elementary Teachers I / 3 UNITS
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 114, or MATH 115 or equivalent.

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)

300 Mathematical Concepts for Elementary Teachers II / 3 UNITS
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.

305 Seminar in Teaching Mathematics / 2 UNITS
Senior seminar for single subject credential students in mathematics. Contributions to mathematics by various ethnic, racial, and cultural groups by both men and women. Equity considerations in mathematics education. Variations in how students learn mathematics. Diverse methods of communication and assessment in mathematics. Practical aspects of teaching diverse students. Students will be required to do some tutoring in mathematics. This course is offered exclusively on a pass/fail basis. This course will not apply toward the major or minor in Mathematics.

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, every year)

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, division rings, fields, vector spaces, and algebras, and applications of these 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 instructor.

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.