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Mathematics

Departmental Counselor: Diane L. Herrmann, E 212, 702-7332, diane@math.uchicago.edu
Director of Undergraduate Studies: Paul Sally, E 405, 702-8535, sally@math.uchicago.edu
Associate Director of Undergraduate Studies: Diane L. Herrmann, E 212, 702-7332
Secretary for Undergraduate Studies: Stephanie Walthes, E 211, 702-7331, steph@math.uchicago.edu

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.

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 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.

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.

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 242 and 251 for probability theory and Statistics 244 and 245 for statistical theory. 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 (consult following section), 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 251. 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

              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           in a minor      field outside      
                                   mathematics  16

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.

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 three of which

should form a sequence from a single

department

16

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 or better 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 C or better in each course taken in computer science to be eligible for this degree. For more information, consult the Computer Science section of this catalog.

Summary of Requirements: Mathematics

with Specialization in Computer Science

General Education Chem 111-112-113 or 121-122-123 or

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

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- or better.

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 C- or better be earned in each calculus, analysis, or algebra course, and an overall grade average of C or better 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 grade of B- or better 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.

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.

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.

Faculty

ROBERT ALMGREN, Assistant Professor, Department of Mathematics and the College

JONATHAN L. ALPERIN, Professor, Department of Mathematics and the College

GREGORY ARONE, 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

PETER CONSTANTIN, Professor, Department of Mathematics and the College

KEVIN CORLETTE, Professor, 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, Assistant Professor, Department of Mathematics and the College

BENSON FARB, Assistant Professor, 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 and the College

GEORGE I. GLAUBERMAN, Professor, 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

FANG HUA LIN, Professor, Department of Mathematics and the College

ARUNAS L. LIULEVICIUS, Professor, Department of Mathematics and the College

YUAN LOU, L. E. Dickson Instructor, 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

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

RICHARD SCHWARTZ, Assistant Professor, Department of Mathematics and the College

BROOKE SHIPLEY, L. E. Dickson Instructor, 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

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

ROBERT J. ZIMMER, Professor, Department of Mathematics and the College

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