Mathematics
OFFICE: 7018 Applied Physics and Mathematics Building, Muir College
http://math.ucsd.edu
Professors
Courses
The Undergraduate Program
The mathematics department offers a wide range of courses in pure
and applied mathematics for its majors and for students in other
disciplines. The department offers six majors leading to the B.A.
degree: mathematics, applied mathematics, mathematicsapplied
science, mathematicscomputer science, joint major in mathematics
and economics, and mathematics secondary education, and one
leading to the B.S. Degree: mathematicsscientific computation.
In addition, students can minor in mathematics. The department also
has an Honors Program for exceptional students in any of the seven
majors. See the sections on major programs and the other areas mentioned
above as well as the course descriptions at the end of this section
for more specific information about program requirements and the
courses that are offered by the department. You may visit our Web
site, math.ucsd.edu for more
information including course Web pages, career advising, and research
interests of our faculty.
First-Year Courses
Entering students must take the Mathematics Placement Exam prior
to orientation unless they have either an appropriate score on
a
Calculus AP exam, a score of 650 or higher on the SAT II Math Level
2C exam, or transferable credit in calculus. The purpose of the
Mathematics Place-ment Exam is to assess the student’s readiness
to enter the department’s calculus courses. Some students
will be required to take precalculus courses before beginning
a
calculus sequence.
Effective fall 2004, all prerequisites for Math. 10A-B-C and Math.
20A-B-C-D-E-F will be enforced through TritonLink. Students need
to ensure that test scores and transferable credit are submitted
to the Registrar prior to enrollment through WebReg.
Math. 3C is the departments preparatory course for the Math.
10 sequence, providing a review of algebraic skills, facility in
graphing, and working with exponential and logarithmic functions.
Math. 4C is the departments preparatory course for the Math.
20 sequence, providing a brief review of college algebra followed
by an introduction to trigonometry and a more advanced treatment
of graphing and functions.
Math. 10A-B-C is one of two calculus sequences. The students in
this sequence have completed a minimum of two years of high school
mathematics. This sequence is intended for majors in liberal arts
and the social and life sciences. It fulfills the mathematics requirements
of Revelle College and the option of the general-education requirements
of Muir College. Completion of two quarters fulfills the requirement
of Marshall College and the option of Warren College and Eleanor
Roosevelt College.
The other first-year calculus sequence, Math. 20A-B-C, is taken
mainly by students who have completed four years of high school
mathematics or have taken a college level precalculus course such
as Math. 4C. This sequence fulfills all college level requirements
met by Math. 10A-B-C and is required of many majors, including chemistry
and biochemistry, bioengineering, cognitive science, economics,
mathematics, molecular biology, psychology, MAE, CSE, ECE, and physics.
Students with adequate backgrounds in mathematics are strongly encouraged
to take Math. 20 since it provides the foundation for Math. 20D-E-F
which is required for some science and engineering majors. Note:
As of summer 2003, Math. 21C and 21D have been renumbered to Math.
20C and 20D.
Certain transfers between the Math. 10 and Math. 20 sequences are
possible, but such transfers should be carefully discussed with
an adviser. Able students who begin the Math. 10 sequence and who
wish to transfer to the Math. 20 sequence, may follow one of three
paths:
- Follow Math. 10A with Math. 20A, with two units of credit given
for Math. 20A. This option is not available if the student has
credit for Math. 10B or Math. 10C.
- Follow Math. 10B with Math. 20B, receiving two units of credit
for Math. 20B.
- Follow Math. 10C with Math. 20B, receiving two units of credit
for Math. 20B and two units of credit for Math. 20C.
Credit will not be given for courses taken simultaneously from
the Math. 10 and the Math. 20 sequence.
Major Programs
The department offers six different majors leading to the Bachelor
of Arts degree: (1) mathematics, (2) applied mathematics, (3) mathematicsapplied
science, (4) mathematicscomputer science, (5) joint major
in mathematics and economics, (6) mathematicssecondary education;
and one leading to a B.S. Degree: mathematics-scientific computation.
The specific emphases and course requirements for these majors are
described in the following sections. All majors must obtain a minimum
2.0 grade-point average in the upper-division courses used to satisfy
the major requirements. Further, the student must receive a grade
of C or better in any course to be counted toward fulfillment
of the major requirements. Any mathematics course numbered 100194
may be used as an upper-division elective. (Note: 195, 196,
197, 198, 199, and 199H cannot be used towards any mathematics major.)
All courses used to fulfill the major must be taken for a letter
grade.
It is strongly recommended that all mathematics majors review their
programs at least annually with a departmental adviser, and that
they consult with the Advising Office in AP&M 6016 before making
any changes to their programs. Current course offering information
for the entire academic year is maintained on the departments
Web page at http://math.ucsd.edu.
Special announcements are also emailed to all majors.
Students who plan to go on to graduate school in mathematics should
be advised that only the best and most motivated students are admitted.
Many graduate schools expect that students will have completed a
full sequence of abstract algebra (Math. 100A-B-C) as well as a
full sequence of analysis (Math. 140A-B-C). The advanced Graduate
Record Exam (GRE) often has questions that pertain to material covered
in the last quarter of analysis or algebra. In addition, it is advisable
that students consider Summer Research Experiences for Undergraduates.
This is a program funded by the National Science Foundation to introduce
students to math research while they are still undergraduates. In
their senior year or earlier, students should consider taking some
graduate courses so that they are exposed to material taught at
a higher level. In their junior year, students should begin to think
of obtaining letters of recommendation from professors who are familiar
with their abilities.
Education Abroad
Students may be able to participate in the UC Education Abroad
Program (EAP) and UCSDs Opportunities Abroad Program (OAP)
while still making progress towards the major. Students interested
in this option should contact the Programs Abroad Office in the
International Center and discuss their plans with the mathematics
advising officer before going abroad.
The department must approve courses taken abroad. Information on
EAP/OAP can be found in the Education Abroad Program section of
the UCSD General Catalog and the Web site http://orpheus.ucsd.edu/icenter/pao.
Major in Mathematics
The upper-division curriculum provides programs for mathematics
majors as well as courses for students who will use mathematics
as a tool in the biological, physical and behavioral sciences, and
the humanities.
Required Courses:
Lower-Division
- Calculus: Math. 20A-B-C-D-E-F
Upper-Division
- Mathematical Reasoning: Math. 109
- One of the following
sequences:
- Foundations of Analysis: Math. 140A-B
- Advanced Calculus:
Math. 142A-B and Math. 120A (Math. 140A-B-C recommended
for graduate school)
- One of the following sequences:
- Modern Algebra: Math.
100A-B
- Modern Applied Algebra: Math. 103A-B and Math. 102
(Math. 100A-B-C recommended for graduate school)
- Upper-division electives to complete thirteen four-unit courses,
chosen from any mathematics
course numbered
between 100 and 194 (including those
taken from
the requirements listed above.)
As with all departmental requirements, more advanced courses on
the same material may be substituted with written approval from
the departmental adviser.
To be prepared for a strong major curriculum, students should complete
the last three quarters of the 20 sequence and Math. 109 before
the end of their sophomore year. Either Math. 140A-B or 100A-B should
be taken during the junior year.
Major in Applied Mathematics
A major in applied mathematics is also offered. The program is
intended for students planning to work on the interface between
mathematics and other fields.
Required Courses:
Lower-Division
- Calculus: Math. 20A-B-C-D-E-F
- Programming (one of the following)
- CSE 8A-B (Intro to
Computer Sci: Java)
- CSE 11 (Intro to Computer Sci: Java,
Accelerated Pace)
- MAE 9 (C/C++ Programming)
- MAE 10 (FORTRAN for Engineers)
Upper-Division
- Mathematical Reasoning: Math. 109
- Linear Algebra: Math.
102 or Math. 170A
- Advanced Calculus: Math. 140A-B or Math.
142A-B
- One of the following sequences:
- Math. 180A-B-C-181A
- Math. 180A-181A and any two from Math.
181B-C-D-E
- (Math. 183 or Math. 180A-181A) and any three
from Math. 170A-B-C-172-173\
- One additional sequence which
may be chosen from the list (#6) above or the following list:
Math. 110-120A-130A, 120A-B, 130A-132A, 155A-B, 171A-B,
193A-B.
- Upper-division electives to complete
at least thirteen four-unit courses, chosen from any mathematics
course
numbered between
100 and 194 (including
those taken from the requirements listed
above) except:
- Up to twelve units may be taken from
outside the department in an approved applied mathematical
area.
A petition
specifying the
courses
to be used
must be approved by an applied mathematics
adviser. No such units may also be
used for a minor or program of concentration.
- MAE 107, Econ. 120A-B-C, cannot be counted toward the thirteen
required courses.
To be prepared for a strong major curriculum, students should complete
the last three quarters of the 20 sequence and Math. 109 before
the end of their sophomore year.
Major in MathematicsScientific Computation
This major is designed for students with a substantial interest
in scientific computation. The program is a specialized applied
mathematics program with a concentration in computer solutions of
scientific problems.
Required Courses:
Lower-Division
- Calculus: Math. 20A-B-C-D-E-F
- Computer Programming: MAE 9 or MAE 10 and CSE 8A-B or CSE 11
- Basic Computation: Math. 15A (or CSE 20) and Math. 15B (or
CSE 21) and CSE 12
Upper-Division
- Mathematical Reasoning: Math. 109
- Linear Algebra: Math. 102
- Probability and Statistics: Math. 183 or 180A-181A (Note: No
credit for Math. 183 if Math. 180A or 181A taken prior or concurrently.)
- Analysis: Math. 140A-B or 142A-B (Note: Students planning to
go to grad school should take 140A-B)
- Numerical Analysis: Math. 170A-B-C or Math. 170A-B/Math. 172
- Optimization: Math. 171A-B
- Scientific Computing: Math. 173
- Additional elective upper-division courses to total 15 chosen
from the following: Math. 107A-B, 110, 120A-B, 130A-B, 131,
132A-B,
152, 155A-B, 170C, or 172.
At least 15 upper-division mathematics courses are required for
the major, except:
- Up to 3 upper-division courses may be taken outside the department
in an approved scientific computation area in the sciences or
engineering. A petition specifying the courses to be used must
be approved by a mathematics-scientific computation adviser. No
such units may also be used by a minor or program of concentration.
- MAE 107, Econ. 120A-B-C, Math. 195, 196, 197, 199, and 199H
cannot be counted toward the 13 four-unit upper-division courses.
Major in MathematicsApplied Science
This major is designed for students with a substantial interest
in mathematics and its applications to a particular field such as
physics, biology, chemistry, biochemistry, cognitive science, computer
science, economics, management science, or engineering.
Required Courses:
Lower-Division
- Calculus: Math. 20A-B-C-D-E-F
- Programming (one of the following
is recommended):
- CSE 8A-B (Intro to Computer Sci: Java)
- CSE 11 (Intro
to Computer Sci: Java, Accelerated Pace)
- MAE 9 (C/C++ Programming)
- MAE 10 (FORTRAN for Engineers)
Upper-Division Mathematics
Requirements:
- Mathematical Reasoning: Math. 109
- Linear Algebra: Math.
102 or Math. 170A
- Any two-quarter, upper-division math sequence
- Upper-division
electives to complete at least seven four-unit courses, chosen
from any mathematics course
numbered between 100 and 194 (including those taken
from the requirements listed above.)
Upper-Division Applied
Science Requirements:
- Seven upper-division courses selected
from one or two other departments (these cannot be from mathematics).
At least three
of these seven
upper-division courses
must require at least Math. 20C as a prerequisite.
Students must submit an individual plan for approval in advance
by a mathematics department adviser, and all subsequent changes
in the plan must be approved by a mathematics department adviser.
Major in MathematicsComputer Science
The program provides for a major in computer science within the
Department of Mathematics. Graduates of this program will be mathematically
oriented computer scientists who have specialized in the mathematical
aspects and foundations of computer science or in the computer applications
of mathematics.
As of fall 2000, a mathematics-computer science major is not allowed
to also minor in computer science in the Computer Science and Engineering
department.
The detailed curriculum is given in the list below:
MathematicsComputer Science Pre-Major
In October 2001, the Academic Senate approved a minimum GPA requirement
of 2.5 in the lower-division mathematics courses required for the
mathematicscomputer science major. The 2.5 minimum GPA in
the lower-division math courses reflects minimal preparation for
the upper-division courses required for the major.
Therefore, students entering UCSD as first- year students for the
fall 2002 quarter and later and students entering as transfer students
for the fall 2003 quarter and later will be held to this requirement.
Applications from students entering UCSD on or after the effective
dates above will be held until all lower-division math courses for
the major are completed and the minimum GPA in those courses of
2.5 can be verified. Students meeting the 2.5 minimum GPA requirement
will be accepted into the mathematicscomputer science major.
Required Courses:
Lower-Division:
- Calculus: Math. 20A-B-C-D-E-F
- Intro to Computer ScienceCSE 8A-B Introduction to Computer
Science: Java, or CSE 11 Introduction to Computer Science: Java
(Accelerated)
- Basic Data Structures and Object-oriented Programming: CSE
12
- Computer Organization and Systems Programming: CSE 30 (Note:
CSE 30 requires CSE 20 or Math. 15A as a prerequisite.)
Upper-Division:
- Mathematical Reasoning: Math. 109
- Modern Applied Algebra: Math. 103A-B or Modern Algebra: Math.
100A-B
- Theory of Computability: Math. 166 (or CSE 105)
- Intro to Probability: Math. 180A or 183
- Mathematical Foundations of Computer Science: Math. 184A
- Computer Implementations of Data Structures: Math. 176 (or
CSE 100)
- Design & Analysis of Algorithms: Math. 188 (or CSE 101)
- Eight units from: Math. 170A-B-C, 172, 173, 174 (Note duplication
of credit between Math. 174 and 170A-B-C)
- Eight units from: Math. 107A-B, 152, 154, 155A-B, 160A-B,
166, 168A-B, 187, CSE 120-121, 130, 131A-B, 140-140L,
141-141L, 167
- Eight additional units from: any course in list #12 or #13
above or Math. 102, 110, 111A-B, 120A-B, 130A-B, 131, 132A-B,
140A-B, 142A-B, 150A-B, 181A-B-C
In order to graduate by the end of their senior year, students
should complete Math. 103A-B by the end of their junior year.
Joint Major in Mathematics and Economics
Majors in mathematics and the natural sciences often feel the need
for a more formal introduction to issues involving business applications
of science and mathematics. Extending their studies into economics
provides this application and can provide a bridge to successful
careers or advanced study. Majors in economics generally recognize
the importance of mathematics to their discipline. Undergraduate
students who plan to pursue doctoral study in economics or business
need the more advanced mathematics training prescribed in this major.
This major is considered to be excellent preparation for Ph.D.
study in economics and business administration, as well as for graduate
studies for professional management degrees, including the MBA.
The major provides a formal framework making it easier to combine
study in the two fields.
Course requirements of the Joint Major in Mathematics and Economics
consist principally of the required courses of the pure mathematics
major and the economics/management science major.
Required Courses:
Lower-Division
- Calculus: Math. 20A-B-C-D-F
- Intro to Economics: Econ. 1-2-3
Upper-Division
Fifteen upper-division courses in mathematics and economics, with
a minimum of seven courses in each department, chosen from the courses
listed below (prerequisites are strictly enforced):
- Mathematical Reasoning: Math. 109
- One of the following: Applied Linear Algebra: Math. 102 Numerical
Linear Algebra: Math. 170A Modern Algebra: Math. 100A-B
- One of the following: Foundations of Analysis: Math. 140A Advanced
Calculus: Math. 142A
- One of the following: Ordinary Differential Equations: Math.
130A, Foundations of Analysis: Math. 140B Advanced Calculus: Math.
142B
- One of the following: Microeconomics: Econ. 100A-B or Management
Science Microeconomics: Econ. 170A-B
- Econometrics: Econ. 120A-B-C or Math. 180A and Econ. 120B-C
or Probability: Math. 180A, 181A and Econ. 120C
- One of the following:
Macroeconomics: Econ. 110A-B
Mathematical Programming: Numerical Optimization: Math. 171A-B
or
Two courses from the following:
Decisions Under Uncertainty: Econ. 171
Introduction to Operations Research: Econ. 172A-B-C, (Note:
172A is a prerequisite for 172BC)
Other courses which are strongly recommended are: Math. 130B,
131, 181B, 193A-B and 194 and Econ. 109, 113, 175, and 178.
Major in MathematicsSecondary Education
This major offers excellent preparation for teaching mathematics
in secondary schools. Students interested in earning a California
teaching credential from UCSD should contact the Teacher Education
Program (TEP) for information regarding prerequisites and requirements.
It is recommended you contact TEP as early as possible.
Lower-Division Requirements
- Calculus 20A-B-C-D-E-F
Recommended:
- One of the following: Introduction to Computer Science: Java:
CSE 8A-B, FORTRAN: MAE 10 C/C++ Programming: MAE 9
Upper-Division Requirements:
- Mathematical Reasoning: Math. 109
- Number Theory: Math 104A
- History of Mathematics: Math. 163
- Practicum in Learning: TEP 129A-B-C
- One of the following: Computer Algebra: Math. 107A, Computer
Graphics: Math. 155A, Mathematical Computing: Math. 161, Numerical
Linear Algebra: Math. 170A, Intro. to Cryptography: Math. 187
- One of the following: Intro. to Probability: Math. 180A, Statistical
Methods: Math. 183
- One of the following: Differential Geometry: Math. 150A, Topics
in Geometry: Math 151, Geometry for Secondary Teachers: Math.
153, Intro. to Topology: Math. 190
- One of the Following: Modern Algebra: Math. 100A, Applied Linear
Algebra: Math. 102, Modern Applied Algebra: Math. 103A
- One of the following: Foundations of Analysis: Math. 140A,
Advanced Calculus: Math. 142A
- Upper-division courses must total thirteen upper-division courses
chosen from items 1 to 10. Upper-division courses must include
at least one two-quarter sequence from the following list:
100A-B; 103A-B, 103A-102; 104A-B; 110-120A; 110-130A-B; 110-132A;
110-131; 120A-B; 130A-132A; 130A-B; 140A-B;142A-B; 150A-B;
155A-B;
160A-B; 170A-B; 170A-172; 170A-173; 170A-171A; 171A-B; 180A-B;
180A-181A; 184A; 193A-B.
Minor in Mathematics
The minor in mathematics consists of seven or more courses. At
least four of these courses must be upper-division courses taken
from the UCSD Department of Mathematics. Acceptable lower-division
courses are Math. 20D, 20E, and 20F.
Math. 195, 196, 197, 198, 199, and 199H are not acceptable courses
for the mathematics minor. A grade of C or better (or P if
the Pass/No Pass option is used) is required for all courses used
to satisfy the requirements for a minor. There is no restriction
on the number of classes taken with the P/NP option. Upper-division
courses cannot overlap between major and minor programs.
Mathematics Honors Program
The Department of Mathematics offers an honors program for those
students who have demonstrated excellence in the major. Successful
completion of the honors program entitles the student to graduate
with departmental honors (see Department Honors in the Academic
Regulations section). Application to the program should be made
the spring quarter before the student is at senior standing.
Requirements for admission to the program are:
- Junior standing
- An overall GPA of 3.0 or higher
- A GPA in the major of 3.5 or higher
- Completion of Math. 109 (Mathematical Reasoning) and at least
one of Math. 100A, 103A, 140A, or 142A. (Completion of additional
major courses is strongly recommended.)
Completion of the honors program requires the following:
- At least one quarter of the student colloquium, Math. 196 (Note:
Math. 196 is only offered in the fall quarter.)
- The minimum 3.5 GPA in the major must be maintained
- An Honors Thesis. The research and writing of the thesis will
be conducted over at least two quarters of the junior/senior years
under the supervision of a faculty adviser. This research will
be credited as eight to twelve units of Math. 199H. The completed
thesis must be approved by the departments Honors Committee,
and presented orally at the Undergraduate Research Conference
or another appropriate occasion.
The departments Honors Committee will determine the level
of honors to be awarded, based on the students GPA in the
major and the quality of the honors work. Applications for the mathematics
departments Honors Program can be obtained at the mathematics
department Undergraduate Affairs Office (AP&M 7018) or the Mathematics
Advising Office (AP&M 6016). Completed applications can be returned
to the Mathematics Advising Office.
Duplication of Credit
In the circumstances listed below, a student will not receive full
credit for a Department of Mathematics course. The notation Math.
20A [2 if Math. 10A previously/0 if Math. 10A concurrently/0 if
Math. 10B or 10C] means that a student already having credit
for Math. 10A will receive only two units of credit for Math. 20A,
but will receive no units if he or she has credit for Math. 10B
or 10C, and no credit will be awarded for Math. 20A if Math. 10A
is being taken concurrently.
- Math. 4C [2 if 3C previously/0 if Math. 10A or Math. 20A
previously or concurrently]
- Math. 10A [0 if Math. 20A previously or concurrently]
- Math. 10B [0 if Math. 20B previously or concurrently]
- Math. 10C [0 if Math. 20C previously or concurrently]
- Math. 15A [0 if CSE20 previously or concurrently]
- Math. 15B [0 if CSE21 previously or concurrently]
- Math. 20A [2 if Math. 10A previously/0 if Math. 10A concurrently/0
if Math. 10B or 10C]
- Math. 20B [2 if Math. 10B or 10C previously/0 if Math. 10B
concurrently]
- Math. 20C [2 if Math. 10C previously/0 if Math. 10C concurrently]
- Math. 20D [0 if Math. 2DA previously]
- Math. 20E [0 if Math. 2F previously]
- Math. 20F [0 if Math. 2EA previously]
- Both Math. 100 and Math. 103 cannot be taken for credit
- Math. 140A-B and Math. 142A-B cannot both be taken for credit
- Math. 155A [0 if CSE 167]
- Math. 166 [0 if CSE105]
- Math. 174 [0 if 170A or B or C previously]
- Math. 176 [0 if CSE 100 previously or concurrently]
- Math. 180A [2 if Econ. 120A previously/ 0 if Econ. 120A concurrently]
- Math. 181A [2 if Econ. 120B/0 if Econ. 120B concurrently]
- Math. 183 [0 if Econ. 120A or Math. 180A or Math. 181A has
been taken previously or concurrently. Full credit for Math. 183
will be given if taken previously to Math. 180A or Math. 181A.]
Advisers
Advisers change yearly. Contact the undergraduate office at (858)
534-3590 for current information.
The Graduate Program
The Department of Mathematics offers graduate programs leading
to the M.A. (pure or applied mathematics), M.S. (statistics), and
Ph.D. degrees.
The application deadline for fall admission is January 15. Candidates
should have a bachelors or masters degree in mathematics
or a related field from an accredited institution of higher education
or the equivalent. A minimum scholastic average of B or better is
required for course work completed in upper-division or prior graduate
study. In addition, the department requires all applicants to submit
scores no older than twelve months from both the GRE General Test
and Advanced Subject Test in Mathematics. Completed files are judged
on the candidates mathematical background, qualifications,
and goals.
Departmental support is typically in the form of teaching assistantships,
research assistantships, and fellowships. These are currently only
awarded to students in the Ph.D. program.
General Requirements
All student course programs must be approved by a faculty adviser
prior to registering for classes each quarter, as well as any changes
throughout the quarter.
Full-time students are required to register for a minimum of twelve
(12) units every quarter, eight (8) of which must be graduate-level
mathematics courses taken for a letter grade only. The remaining
four (4) units can be approved upper-division or graduate-level
courses in mathematics-related subjects (Math. 500 may not be used
to satisfy any part of this requirement). After advancing to candidacy,
Ph.D. candidates may take all course work on a Satisfactory/Unsatisfactory
basis. Typically, students should not enroll in Math. 299 until
they have satisfactorily passed both qualifying examinations (see
Ph.D. in Mathematics) or obtained approval of their faculty adviser.
Master of Arts in Pure Mathematics
[Offered only under the Comprehensive Examination Plan.] The degree
may be terminal or obtained on the way to the Ph.D. A total of forty-eight
units of credit is required. Twenty-four of these units must be
graduate-level mathematics courses approved in consultation with
a faculty adviser.
In the selection of course work to fulfill the remaining twenty-four
units, the following restrictions must be followed:
- No more than eight units of upper-division mathematics courses.
- No more than twelve units of graduate courses in a related
field outside the department (approved by the Department of Mathematics).
- No more than four units of Math. 295 (Special Topics) or Math.
500 (Apprentice Teaching).
- No units of Math. 299 (Reading and Research) may be used in
satisfying the requirements for the masters degree.
Comprehensive Examinations
Seven written departmental examinations are offered in three areas
(refer to Ph.D. In Mathematics, Areas 1, 2, and 3, for
list of exams). A student must complete two examinations, one from
Area 1 and one from Area 2, both with an M.A. pass or better.
Foreign Language Requirement
A reading knowledge of one foreign language (French, German, or
Russian) is required. In exceptional cases other languages may be
substituted. Testing is administered by faculty in the department
who select published mathematical material in one of these languages
for a student to translate.
Time Limits
Full-time students are permitted seven quarters in which to complete
all degree requirements. While there are no written time limits
for part-time students, the department has the right to intervene
and set individual deadlines if it becomes necessary.
Master of Arts in Applied Mathematics
[Offered only under the Comprehensive Examination Plan] The degree
may be terminal or obtained on the way to the Ph.D. Out of the total
forty-eight units of required credit, two applied mathematics sequences
comprising twenty-four units must be chosen from the following list
(not every course is offered each year):
202A-B-C. (Applied Algebra)
210A-B-C. (Mathematical Methods in Physics and Engineering)
261A-B-C. (Combinatorial Algorithms)
264A-B-C. (Combinatorics)
270A-B-C. (Numerical Mathematics)
271A-B-C. (Numerical Optimization)
272A-B-C. (Numerical Partial Differential Equations)
273A-B-C. (Scientific Computation)
In certain cases, a petition may be approved to substitute one
of these requirements from the following list of sequences:
220A-B-C. (Complex Analysis)
231A-B-C. (Partial Differential Equations)
240A-B-C. (Real Analysis)
280A-B-C. (Probability Theory)
281A-B-C. (Mathematical Statistics)
282A-B. (Applied Statistics)
In choosing course work to fulfill the remaining twenty-four units,
the following restrictions must be followed:
- At least eight units must be approved graduate courses in mathematics
or other departments [a one-year sequence in a related area outside
the department such as computer science, engineering, physics,
or economics is strongly recommended];
- A maximum of eight units can be approved upper-division courses
in mathematics; and
- A maximum of eight units can be approved upper-division courses
in other departments.
- A maximum of four units of Math. 500 (Apprentice Teaching).
- NO UNITS of Math. 295 (Special Topics) or Math. 299 (Reading
and Research) may be used.
Students are strongly encouraged to consult with a faculty adviser
in their first quarter to prepare their course of study.
Comprehensive Examinations
Two written comprehensive examinations must be passed at the masters
level in any of the required applied mathematics sequences listed
above. The instructors of each course should be contacted for exam
details.
Foreign Language Requirement
There is no foreign language requirement for the M.A. in applied
mathematics.
Time Limits
Full-time M.A. students are permitted seven quarters in which to
complete all requirements. While there are no written time limits
for part-time students, the department has the right to intervene
and set individual deadlines if it becomes necessary.
Master of Science in Statistics
[Offered only under the Comprehensive Examination Plan] The M.S.
in statistics is designed to provide recipients with a strong mathematical
background and experience in statistical computing with various
applications. Out of the forty-eight units of credit needed, required
core courses comprise twenty-four units, including:
Math. 281A-B. (Mathematical Statistics)
Math. 282A-B. Applied Statistics)
and any two topics comprising eight units chosen at will from Math.
287A-B-C-D and 289A-B-C (see course descriptions for topics).
The following guidelines should be followed when selecting courses
to complete the remaining twenty-four units:
- For a theoretical emphasis, Math. 280A-B-C (Probability Theory)
is required.
- For an applied orientation, Math. 270A-B-C (Numerical Mathematics)
is recommended.
- A maximum of eight units of approved upper-division applied
mathematics courses (see faculty adviser) and Math. 500 (Apprentice
Teaching).
Upon the approval of the faculty adviser, all twenty-four units
can be graduate-level courses in other departments.
Comprehensive Examinations
Two written comprehensive examinations must be passed at the masters
level in related course work (approved by a faculty adviser). Instructors
of the relevant courses should be consulted for exam dates as they
vary on a yearly basis.
Foreign Language Requirement
There is no foreign language requirement for the M.S. in statistics.
Time Limits
Full-time M.S. students are permitted seven quarters in which to
complete all requirements. While there are no written time limits
for part-time students, the department has the right to intervene
and set individual deadlines if it becomes necessary.
Ph.D. In Mathematics
Written Qualifying Examinations
The department offers written qualifying examinations in seven
subjects. These are grouped into three areas as follows:
Area #1
Complex Analysis (Math. 220A-B-C) Real Analysis (Math. 240A-B-C)
Area #2
Algebra (Math. 200A-B-C) Applied Algebra (Math. 202A-B-C) Topology
(Math. 290A-B-C)
Area #3
Numerical Analysis (Math. 270A-B-C) Statistics (Math. 281A-B-C)
- Three qualifying exams must be passed. At least one must be
passed at the Ph.D. level, and a second must be passed at either
the Ph.D. or Provisional Ph.D. Level The third exam must be passed
at least at the masters level.
- Of the three qualifying exams, there must be at least one from
each of Areas #1 and #2. Algebra and Applied Algebra do not count
as distinct exams in Area #2.
- Students must pass a least two exams from distinct areas with
a minimum grade of Provisional Ph.D. (For example, a Ph.D. pass
in Real Analysis, Provisional Ph.D. Pass in Complex Analysis,
M.A. pass in Algebra would NOT satisfy this requirement, but a
Ph.D. Pass in Real Analysis, M.A. pass in Complex Analysis, Provisional
Ph.D. Pass in Algebra would, as would a Ph.D. Pass in Numerical
Analysis, Provisional Ph.D. Pass in Applied Algebra, and M.A.
pass in Real Analysis.)
- All exams must be passed by the September exam session prior
to the beginning of the third year of graduate studies. (Thus,
there would be no limit on the number of attempts, encouraging
new students to take exams when they arrive, without penalty.)
Department policy stipulates that a least one of the exams must
be completed with a Provisional Ph.D. Pass or better by September
following the end of the first year. Anyone unable to comply with
this schedule will be terminated from the doctoral program and transferred
to one of our Masters programs.
Any Masters student can submit for consideration a written
request to transfer into the Ph.D. Program when the qualifying exam
requirements for the Ph.D. Program have been met and a dissertation
adviser is found. Approval by the Qualifying Exam and Appeals Committee
(QEAC) is not automatic, however.
Exams are typically offered twice a year, one scheduled late in
the spring quarter and again in early September (prior to the start
of fall quarter). Copies of past exams are made available for purchase
in the Graduate Office.
In choosing a program with an eye to future employment, students
should seek the assistance of a faculty adviser and take a broad
selection of courses including applied mathematics, such as those
in Area #3.
Foreign Language Requirement
A reading knowledge of one foreign language (French, German, or
Russian) is required prior to advancing to candidacy. In exceptional
cases other languages may be substituted. Testing is administered
within the department by faculty who select published mathematical
material in one of these languages for a student to translate.
Advancement to Candidacy
It is expected that by the end of the third year (nine quarters),
students should have a field of research chosen and a faculty member
willing to direct and guide them. A student will advance to candidacy
after successfully passing the oral qualifying examination, which
deals primarily with the area of research proposed but may include
the project itself. This examination is conducted by the students
appointed doctoral committee. Based on their recommendation, a student
advances to candidacy and is awarded the C.Phil. Degree
Dissertation and Final Defense
Submission of a written dissertation and a final examination in
which the thesis is publicly defended are the last steps before
the Ph.D. Degree is awarded. When the dissertation is substantially
completed, copies must be provided to all committee members at least
four weeks in advance of the proposed defense date. Two weeks before
the scheduled final defense, a copy of the dissertation must be
made available in the department for public inspection.
Time Limits
The normative time for the Ph.D. In mathematics is five years.
Students must be advanced to candidacy by the end of eleven quarters.
Total university support cannot exceed six years. Total registered
time at UCSD cannot exceed seven years.
Mathematics
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