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Go to: Program Requirements
Director of Undergraduate Studies: Paul Sally, E 405, 702-8535
Associate Director of Undergraduate Studies: Diane L. Herrmann, E 212,
702-7332
Secretary for Undergraduate Studies: Stephanie Walthes, E 211, 702-7331
The requirements for a degree in mathematics or in applied mathematics express
the educational intent of the Department of Mathematics; they are drawn with an
eye toward the cumulative character of an education based in mathematics, the
present emerging state of mathematics, and the scholarly and professional
prerequisites of an academic career in mathematics.
Requirements for the bachelor's degree look to the advancement of students'
general education in modern mathematics and their knowledge of its relation
with the other sciences (Bachelor of Science) or with the other arts (Bachelor
of Arts).
Descriptions of the detailed requirements that give meaning to these
educational intentions follow. Students should understand that any particular
degree requirement can be modified if persuasive reasons are presented to the
department; petitions to modify degree requirements are submitted in person to
the director of undergraduate studies or the departmental counselor.
Placement. At what level does an entering student begin mathematics at the
University of Chicago? This question is answered individually for students on
the basis of their performance on placement tests in mathematics administered
during Orientation Week in September: a precalculus mathematics placement test
required of all entering students and an optional calculus
placement test. Scores on the mathematics placement test determine the
appropriate beginning mathematics sequence for each student: a precalculus
sequence (100-101-102 or 105-106) or one of three other sequences (Mathematics
110-111, Mathematics 131-132-133, or Mathematics 151-152-153). Students who
wish to begin at a level higher than Mathematics 151 must take the
calculus placement test, unless they receive Advanced Placement credit as
described below.
Students with suitable achievement on the calculus placement test are invited
to begin Honors Calculus (Mathematics 161-162-163). Admission to Honors
Analysis (Mathematics 207-208-209) is by invitation only to those first-year
students who show an exceptional performance on the calculus placement test or
to those sophomores who receive a strong recommendation from their instructor
in Mathematics 161-162-163. Mathematics 257-258-259 is designated as an honors
section of Basic Algebra. Registration for this course is the option of the
individual student. Consultation with the departmental counselor is strongly
advised.
Students who submit a score of 5 on the AB Advanced Placement exam in
mathematics or a score of 4 on the BC Advanced Placement exam in mathematics
receive credit for Mathematics 151. Students who submit a score of 5 on the BC
Advanced Placement exam in mathematics receive credit for Mathematics 151 and
152.
NOTE: It is the policy of the Division of Physical Sciences that students
concentrating in mathematics or applied mathematics may not use Physical
Sciences placement credit to fulfill the general education requirement.
Students are required to complete both a 100-level sequence in calculus (or to
demonstrate equivalent competence on the optional calculus placement test) and
a three-quarter sequence in analysis (Mathematics 203-204-205 or 207-208-209).
The normal procedure is to take calculus in the first year and analysis in the
second.
Students taking a bachelor's degree in mathematics or in applied mathematics
should know that by judicious employment of courses from another field for
extradepartmental requirements or for electives, a minor field can be developed
which is often in itself a sufficient base for graduate or professional work in
that field. A notable example is furnished by the field of statistics: the core
programs are Statistics 230 and 242 for theory and Statistics 244 and 245 for
methods. For an emphasis on statistical methods, students would add Statistics
222, 224, or 226; while for an emphasis on probability they would add
Statistics 312 or perhaps Statistics 381-382.
What is noted here for statistics can also be applied to computer science (see
below), chemistry, geophysical sciences, physics, biophysics, theoretical
biology, economics, and education.
While these remarks apply to all bachelor's degree programs in the Department
of Mathematics, their force is particularly evident in programs looking to
bachelor's degrees in applied mathematics, where minor fields are strongly
urged.
Degree Programs in Mathematics. Candidates for the B.A. and B.S. in
mathematics all take a sequence in basic algebra. Candidates for the B.S.
degree must take the three-quarter sequence (Mathematics 254-255-256 or
Mathematics 257-258-259), whereas B.A. candidates may opt for a two-quarter
sequence (Mathematics 254-255 or Mathematics 257-258). The remaining
mathematics courses needed in the concentration programs (three for the B.A.,
two for the B.S.) must be selected, with due regard for prerequisites, from the
following list: Mathematics 175, 211, 241, 242, 261, 262, 263, 270, 272, 273,
274, 275, 277, 278, 279, 280, 281, 284, 299 (as approved), 300, 301, 302, 303,
309, 310, 312, 313, 314, 317, 318, 319, 325, 326, 327, and Statistics 230. B.A.
candidates may include Mathematics 256 or 259.
B.S. candidates are further required to select a minor field, which consists of
an additional three-course sequence outside the Department of Mathematics,
chosen in consultation with the departmental counselor.
Summary of Requirements:
Mathematics
General Chem 111-112-113 or 121-122-123 or
Education Phys 121-122-123 or higher
Math 131-132, 151-152, or 161-162
Concentration 1 third quarter of a calculus sequence
3 Math 203-204-205 or 207-208-209
2 mathematics courses chosen from an approved list
4 courses within the PSCD but outside of
mathematics, at least 2 of which should
form a sequence from a single department
Plus the following requirements:
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Summary of Requirements:
Applied Mathematics
General Chem 111-112-113 or 121-122-123 or
Education Phys 121-122-123 or higher
Math 131-132, 151-152, or 161-162
Concentration 1 third quarter of a calculus sequence
3 Math 203-204-205 or 207-208-209
1 Math 211
2 Math 254-255 or 257-258
3 Math 270-273-275
6 courses within the PSCD but outside of
mathematics, at least 3 of which should
form a sequence from a single department
16 (total)
Degree Program in Mathematics with Specialization in Computer Science. The
concentration program leading to a B.S. in mathematics with a specialization in
computer science is a version of the B.S. in mathematics. The degree will be in
mathematics with the designation "with specialization in computer science"
included on the final transcript. Candidates are required to complete a
yearlong sequence in calculus (Mathematics 151-152-153 or 161-162-163 strongly
recommended), in analysis (Mathematics 203-204-205 or 207-208-209), and in
abstract algebra (Mathematics 254-255-256 or 257-258-259), and earn a grade of
at least C- in each course. The remaining two mathematics courses may be
chosen from the list of approved courses in the section Degree Programs in
Mathematics except for Mathematics 175 and Statistics 230; students are urged
to take at least one of Mathematics 242, 262, 277, or 284. A C average
must be earned in these two courses.
The seven courses required outside the Department of Mathematics must all be in
the computer science department. A two-quarter sequence in programming is
required; Computer Science 115-116 is recommended. (Students may substitute
Computer Science 105-106, although this is not encouraged.) Five additional
courses must be selected from among computer science courses numbered 200 or
higher, except 274. Students who take Computer Science 105-106 are encouraged
to include Computer Science 221 here. Students must earn a grade of at least
C in each course taken in computer science to be eligible for this
degree. For more information, see the computer science section of this
catalog.
Summary of Requirements: Mathematics
with Specialization in Computer Science
General Chem 111-112-113 or 121-122-123 or
Education Phys 121-122-123 or higher
Math 131-132, 151-152, or 161-162
Concentration 1 third quarter of calculus sequence
3 Math 203-204-205 or 207-208-209
3 Math 254-255-256 or 257-258-259
2 ComSci 115-116
2 approved mathematics courses
5 approved computer science courses
16 (total)
Grading. Subject to College and division regulations and with the consent
of the instructor, all students, except concentrators in mathematics or
applied mathematics, may register for regular letter grades, P/N
grades, or P/F grades in any course beyond the second quarter of
calculus. A Pass grade is given only for work of C- quality or
higher.
Concentrators in mathematics or applied mathematics may take any 200-level
mathematics courses elected beyond concentration requirements for a grade of
P. However, a grade of at least C- must be earned in each
calculus, analysis, or algebra course, and an overall grade average of C
must be earned in the remaining mathematics courses that a student uses to
fulfill concentration requirements. PSCD courses taken to fulfill concentration
requirements in mathematics must be taken for quality grades.
Incompletes are given in the Department of Mathematics only to those students
who have done some work of passing quality and who are unable to complete all
the course work by the end of the quarter. Arrangements are made between the
instructor and the student.
Honors. There are two alternative routes to a B.A. or B.S. honors degree.
Both require a minimum grade of B- in each of the following courses:
Mathematics 207-208-209 and Mathematics 257-258-259. If, in addition, the
student passes an approved sequence of three graduate courses with no grade
below B-, he or she is eligible to receive a B.A. or B.S. honors degree.
Normally, these three 300-level courses should be chosen from Mathematics
312-313-314, 317-318-319, or 325-326-327.
An alternative to taking one of these graduate sequences is to register for
Mathematics 298 (Bachelor's Thesis) and to write a bachelor's thesis based on
an approved research project. This is ordinarily done in consultation with an
individual faculty member and must be approved by the director and associate
director of undergraduate studies.
Students interested in the honors degree should consult with the departmental
counselor no later than their third year.
B.A. (B.S.)/M.A.T. Concentrators in mathematics or applied mathematics
seeking to prepare for secondary school teaching and possible futures in
mathematics education may be eligible for admission to the joint B.A.
(B.S.)/M.A.T. programs. These enable qualified students to complete the M.A.T.
degree by beginning in the summer quarter following their third year, utilizing
four electives in their fourth year for the required education courses
(including two in the winter quarter for student teaching), and finishing in
the summer quarter after their fourth year. Admission to the joint programs is
conditioned on a positive recommendation to the Department of Education from
the Coordinating Committee for Mathematics. Interested students should consult
with the departmental counselor no later than the autumn quarter of their third
year.
ROBERT ALMGREN, Assistant Professor, Department of Mathematics and the
College
JONATHAN L. ALPERIN, Professor, Department of Mathematics and the College
GREGORY ARENE, L. E. Dickson Instructor, Department of Mathematics and the
College
WALTER L. BAILY, JR., Professor, Department of Mathematics and the College
JONATHAN BECK, Assistant Professor, Department of Mathematics and the College
SPENCER J. BLOCH, Robert Maynard Hutchins Distinguished Service Professor,
Department of Mathematics and the College
ALBERTO CANDEL, L. E. Dickson Instructor, Department of Mathematics and the
College
PETER CONSTANTIN, Professor, Department of Mathematics and the College
KEVIN CORLETTE, Professor, Department of Mathematics and the College
ALESSIO CORTI, L. E. Dickson Instructor, Department of Mathematics and the
College
OVIDIU COSTIN, L. E. Dickson Instructor, Department of Mathematics and the
College
JACK D. COWAN, Professor, Department of Mathematics and the College
TODD DUPONT, Professor, Departments of Computer Science and Mathematics and the
College
ALEX ESKIN, L. E. Dickson Instructor, Department of Mathematics and the
College
BENSON FARB, L. E. Dickson Instructor, Department of Mathematics and the
College
ROBERT A. FEFFERMAN, Professor, Department of Mathematics and the College;
Chairman, Department of Mathematics
WILLIAM FULTON, Professor, Department of Mathematics
VICTOR GINZBURG, Professor, Department of Mathematics
GEORGE I. GLAUBERMAN, Professor, Department of Mathematics and the College
DONGGENG GONG, L. E. Dickson Instructor, Department of Mathematics and the
College
WILLIAM GRAHAM, L. E. Dickson Instructor, Department of Mathematics and the
College
DIANE L. HERRMANN, Senior Lecturer, Department of Mathematics and the College
XIAOJUN HUANG, L. E. Dickson Instructor, Department of Mathematics and the
College
ELIZABETH JURISICH, L. E. Dickson Instructor, Department of Mathematics and the
College
LEO P. KADANOFF, John D. MacArthur Distinguished Service Professor, Departments
of Physics and Mathematics, James Franck Institute, Enrico Fermi Institute, and
the College
CARLOS E. KENIG, Professor, Department of Mathematics
ROBERT KOTTWITZ, Professor, Department of Mathematics
IGOR KUKAVICA, Assistant Professor, Department of Mathematics and the College
NORMAN R. LEBOVITZ, Professor, Department of Mathematics and the College
ARUNAS L. LIULEVICIUS, Professor, Department of Mathematics and the College
J. PETER MAY, Professor, Department of Mathematics and the College
MATAM P. MURTHY, Professor, Department of Mathematics
RAGHAVAN NARASIMHAN, Professor, Department of Mathematics
ANDREI NIES, Assistant Professor, Department of Mathematics and the College
WIESLAWA NIZIOL, L. E. Dickson Instructor, Department of Mathematics and the
College
MADHAV NORI, Professor, Department of Mathematics
NIELS O. NYGAARD, Professor, Department of Mathematics and the College
RAHUL PANDHARIPANDE, L. E. Dickson Instructor, Department of Mathematics and
the College
DANIEL POLLACK, Assistant Professor, Department of Mathematics and the
College
XIAOCHUN RONG, Assistant Professor, Department of Mathematics and the College
MELVIN G. ROTHENBERG, Professor, Department of Mathematics and the College
PAUL J. SALLY, JR., Professor, Department of Mathematics and the College
THEODORE A. SLAMAN, Professor, Department of Mathematics and the College
ROBERT I. SOARE, Paul Snowden Russell Distinguished Service Professor,
Departments of Computer Science and Mathematics and the College
RICHARD G. SWAN, Louis Block Professor, Department of Mathematics
TATIANA TORO, Assistant Professor, Department of Mathematics and the College
BURT TOTARO, Assistant Professor, Department of Mathematics and the College
SIDNEY WEBSTER, Professor, Department of Mathematics EFIM ZELMANOV, Professor, Department of Mathematics and the College
ROBERT J. ZIMMER, Professor, Department of Mathematics and the College
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Go to: Summary of Requirements
Go to: Faculty
Mathematics
Departmental Counselor: Diane L. Herrmann, E 212, 702-7332
Program of Study
The Department of Mathematics provides an environment of research and
comprehensive instruction in mathematics and applied mathematics at both
undergraduate and graduate levels. Degrees available in mathematics include two
baccalaureate degrees, the Bachelor of Arts and the Bachelor of Science (the
Bachelor of Science is also available in applied mathematics), and two
postgraduate degrees, the Master of Arts and the Doctor of Philosophy. In
addition, the degree of Master of Science in Teaching is available in
mathematics; this degree is offered through the Department of Education in
cooperation with the Department of Mathematics. A later section describes the
joint B.A. (B.S.)/M.A.T. programs.
Program Requirements
Undergraduate Programs. Four bachelor's degrees are available in the
Department of Mathematics: the Bachelor of Arts in mathematics, the Bachelor of
Science in mathematics, the Bachelor of Science in applied mathematics, and the
Bachelor of Science in mathematics with specialization in computer science.
Course programs qualifying students for the degree of Bachelor of Arts provide
more elective freedom, while programs qualifying students for the degrees of
Bachelor of Science require more emphasis in the physical sciences. All degree
programs, whether qualifying students for a degree in mathematics or in applied
mathematics, require fulfillment of the College's general education
requirements. The Common Core sequence in the physical sciences must be
selected from either first-year basic chemistry or first-year basic physics.
The courses that make up the concentration program include at least nine
courses in mathematics (detailed descriptions follow for each degree), plus at
least four courses within the Physical Sciences Collegiate Division (PSCD) but
outside mathematics, at least two of which should form a sequence of courses
from a single department. These PSCD courses may not include any of the
first-year physical sciences sequences. We particularly call attention to the
degree of Bachelor of Science in mathematics with specialization in computer
science, which was introduced in 1987-88, and is described in more detail
below. B.A. B.S.
2 Math 254-255 or 257-258 1 3 Math 254-255-256 or
Math 256, 259, or an 257-258-259 3 course sequence
approved alternative 13 (total) in a minor field outside
mathematics 16 (total)
Degree
Program in Applied Mathematics. Candidates for the B.S. in applied
mathematics all take prescribed courses in numerical analysis, algebra, complex
variables, ordinary differential equations, and partial differential equations.
In addition, candidates are required to select, in consultation with the
departmental counselor, a minor field, which consists of a three-course
sequence outside the Department of Mathematics.
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Joint Degree Programs
B.A. (B.S.)/M.S. in Mathematics. Qualified College students may receive
both a bachelor's and a master's degree in mathematics concurrently at the end
of their years in the College. Qualification consists of satisfying all the
requirements of each degree in mathematics. With the help of placement tests
and honors sequences, able students can be engaged in 300-level Mathematics
(usually Mathematics 312-313-314) as early as their third year and, through an
appropriate use of free electives, can complete the master's requirements by
the end of their fourth year. Interested students should apply to the
departmental counselor as soon as possible and in any event no later than the
winter quarter of the third year.
Faculty