- Math Major
- Computer Science Major
- Math Minor
- Computer Science Minor
- Course Descriptions
- Current Courses
- Learning Outcomes
University of San Diego
Mathematics and Computer Science
Serra Hall 133
5998 Alcalá Park
San Diego, CA 92110
Phone: (619) 260-4706
Fax: (619) 260-4293
aprout@sandiego.edu
Department Chair
Perla Myers,
pmyers@sandiego.edu
Media Contact
Liz Harman
harman@sandiego.edu
(619) 260-4682
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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 (3)
MATH 150, 151, 160*, 250 (15)
MATH 320 (3)
MATH 350 or 361 or 380 (3)
MATH 360 (3)
MATH 375 or 385 (3)
PHYS 270, 271 (8)
Upper-division mathematics electives (12)
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) |
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, 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
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.
