About the Program
Bachelor of Arts (BA)
The Department of Mathematics offers an undergraduate major program in mathematics, leading to the Bachelor of Arts (BA) degree. Major programs within the department provide excellent preparation for advanced degrees in math, physical sciences, economics, and industrial engineering as well as graduate study in business, education, law, and medicine. They also prepare students for postbaccalaureate positions in business, technology, industry, teaching, government, and finance.
Students majoring in Mathematics may choose to major with a teaching concentration. The teaching concentration is designed to increase the number and quality of math teachers.
Admission to the Major
Students should contact a mathematics undergraduate adviser. Contact information is available on the contact tab or here.
Honors Program
In addition to completing the requirements for the major in mathematics, students in the honors program must:
 Earn a grade point average (GPA) of at least 3.5 in upper division and graduate courses in the major and at least 3.3 in all courses taken at the University.
 Complete either MATH 196, in which they will write a senior honors thesis, or pass two graduate mathematics courses with a grade of at least A.
 Receive the recommendation of the head major adviser.
Students interested in the honors program should consult with an adviser early in their program, preferably by their junior year.
Minor Program
The department offers a minor in Mathematics.
Other Major Offered by the Department of Mathematics
Applied Mathematics (Major only)
Major Requirements
In addition to the University, campus, and college requirements, listed on the College Requirements tab, students must fulfill the below requirements specific to their major program.
General Guidelines
 All courses taken to fulfill the major requirements below must be taken for graded credit, other than courses listed which are offered on a Pass/No Pass basis only.
 No more than one upper division course may be used to simultaneously fulfill requirements for a student's major and minor programs, with the exception of minors offered outside of the College of Letters & Science.
 A minimum grade point average (GPA) of 2.0 must be maintained in both upper and lower division courses used to fulfill the major requirements.
For information regarding residence requirements and unit requirements, please see the College Requirements tab.
Major Requirements: Mathematics
Code  Title  Units 

Lower Division  
MATH 1A  Calculus  4 
MATH 1B  Calculus  4 
MATH 53  Multivariable Calculus  4 
MATH 54  Linear Algebra and Differential Equations  4 
MATH 55  Discrete Mathematics ^{1}  4 
Upper Divison  
MATH 104  Introduction to Analysis  4 
MATH 110  Linear Algebra  4 
MATH 113  Introduction to Abstract Algebra  4 
MATH 185  Introduction to Complex Analysis  4 
Two semielectives  
Select one course from two of the following three areas:  
Computing  
Numerical Analysis [4]  
Geometry  
The Classical Geometries [4]  
Metric Differential Geometry [4]  
Elementary Differential Topology [4]  
Elementary Algebraic Topology [4]  
Elementary Algebraic Geometry [4]  
Logic and Foundations  
Mathematical Logic [4]  
Introduction to the Theory of Sets [4]  
Incompleteness and Undecidability [4]  
Two electives, select at least two additional upper division or graduate mathematics courses must be taken ^{2} 
^{1}  COMPSCI 70 can be substituted for MATH 55 for students with a double major in Computer Science or Electrical Engineering and Computer Science 
^{2}  These two electives must receive the Faculty Adviser's written approval on the Course Approval Form which is then returned to an Undergraduate Adviser in 964 or 965 Evans for the student's file. Courses in other departments may count toward this requirement provided they have substantial mathematical content and are offered for at least 3 units each. 
Code  Title  Units 

Lower division  
STAT 20  Introduction to Probability and Statistics  4 
MATH 1A  Calculus  4 
MATH 1B  Calculus  4 
MATH 53  Multivariable Calculus  4 
MATH 54  Linear Algebra and Differential Equations  4 
MATH 55  Discrete Mathematics ^{1}  4 
Upper division  
MATH 104  Introduction to Analysis  4 
MATH 110  Linear Algebra  4 
MATH 113  Introduction to Abstract Algebra  4 
Select two of the following:  
MATH 128A  Numerical Analysis  4 
MATH 130  The Classical Geometries  4 
MATH 135  Introduction to the Theory of Sets  4 
MATH 136  Incompleteness and Undecidability  4 
MATH 151  Mathematics of the Secondary School Curriculum I  4 
MATH 152  Mathematics of the Secondary School Curriculum II  4 
MATH 160  History of Mathematics  4 
Recommended courses:  
Sudents are encouraged, though not required, to take, the following:  
MATH 115  Introduction to Number Theory  4 
MATH 123  Ordinary Differential Equations  4 
MATH 170  Mathematical Methods for Optimization  4 
MATH 185  Introduction to Complex Analysis  4 
^{1}  COMPSCI 70 can be substituted for MATH 55 for students with a double major in Computer Science or Electrical Engineering and Computer Science. 
Minor Requirements
Students who have a strong interest in an area of study outside their major often decide to complete a minor program. These programs have set requirements and are noted officially on the transcript in the memoranda section, but they are not noted on diplomas.
General Guidelines
 All courses taken to fulfill the minor requirements below must be taken for graded credit.
 A minimum of three of the upper division courses taken to fulfill the minor requirements must be completed at UC Berkeley.
 A minimum grade point average of 2.0 is required for the lower division minor requirements as well as for the five upper division courses used for the minor.
 Courses used to fulfill the minor requirements may be applied toward the SevenCourse Breadth requirement, for Letters & Science students.
 No more than one upper division course may be used to simultaneously fulfill requirements for a student's major and minor programs.
 All minor requirements must be completed prior to the last day of finals during the semester in which the student plans to graduate.
 All minor requirements must be completed within the unit ceiling. (For further information regarding the unit ceiling, please see the College Requirements tab.)
Requirements
Code  Title  Units 

Lower Division  
MATH 1A  Calculus  4 
MATH 1B  Calculus  4 
MATH 53  Multivariable Calculus  4 
MATH 54  Linear Algebra and Differential Equations  4 
Upper Division  
MATH 104  Introduction to Analysis  4 
MATH 110  Linear Algebra  4 
MATH 113  Introduction to Abstract Algebra  4 
MATH 185  Introduction to Complex Analysis  4 
One elective: select one additional upper division math course  4 
College Requirements
Undergraduate students must fulfill the following requirements in addition to those required by their major program.
For detailed lists of courses that fulfill college requirements, please review the College of Letters & Sciences page in this Guide. For College advising appointments, please visit the L&S Advising Pages.
University of California Requirements
Entry Level Writing
All students who will enter the University of California as freshmen must demonstrate their command of the English language by fulfilling the Entry Level Writing requirement. Fulfillment of this requirement is also a prerequisite to enrollment in all reading and composition courses at UC Berkeley.
American History and American Institutions
The American History and Institutions requirements are based on the principle that a US resident graduated from an American university, should have an understanding of the history and governmental institutions of the United States.
Berkeley Campus Requirement
American Cultures
All undergraduate students at Cal need to take and pass this course in order to graduate. The requirement offers an exciting intellectual environment centered on the study of race, ethnicity and culture of the United States. AC courses offer students opportunities to be part of researchled, highly accomplished teaching environments, grappling with the complexity of American Culture.
College of Letters & Science Essential Skills Requirements
Quantitative Reasoning
The Quantitative Reasoning requirement is designed to ensure that students graduate with basic understanding and competency in math, statistics, or computer science. The requirement may be satisfied by exam or by taking an approved course.
Foreign Language
The Foreign Language requirement may be satisfied by demonstrating proficiency in reading comprehension, writing, and conversation in a foreign language equivalent to the second semester college level, either by passing an exam or by completing approved course work.
Reading and Composition
In order to provide a solid foundation in reading, writing, and critical thinking the College requires two semesters of lower division work in composition in sequence. Students must complete parts A & B reading and composition courses by the end of their second semester and a secondlevel course by the end of their fourth semester.
College of Letters & Science 7 Course Breadth Requirements
Breadth Requirements
The undergraduate breadth requirements provide Berkeley students with a rich and varied educational experience outside of their major program. As the foundation of a liberal arts education, breadth courses give students a view into the intellectual life of the University while introducing them to a multitude of perspectives and approaches to research and scholarship. Engaging students in new disciplines and with peers from other majors, the breadth experience strengthens interdisciplinary connections and context that prepares Berkeley graduates to understand and solve the complex issues of their day.
Unit Requirements

120 total units

Of the 120 units, 36 must be upper division units
 Of the 36 upper division units, 6 must be taken in courses offered outside your major department
Residence Requirements
For units to be considered in "residence," you must be registered in courses on the Berkeley campus as a student in the College of Letters & Science. Most students automatically fulfill the residence requirement by attending classes here for four years. In general, there is no need to be concerned about this requirement, unless you go abroad for a semester or year or want to take courses at another institution or through UC Extension during your senior year. In these cases, you should make an appointment to meet an adviser to determine how you can meet the Senior Residence Requirement.
Note: Courses taken through UC Extension do not count toward residence.
Senior Residence Requirement
After you become a senior (with 90 semester units earned toward your BA degree), you must complete at least 24 of the remaining 30 units in residence in at least two semesters. To count as residence, a semester must consist of at least 6 passed units. Intercampus Visitor, EAP, and UC BerkeleyWashington Program (UCDC) units are excluded.
You may use a Berkeley Summer Session to satisfy one semester of the Senior Residence requirement, provided that you successfully complete 6 units of course work in the Summer Session and that you have been enrolled previously in the college.
Modified Senior Residence Requirement
Participants in the UC Education Abroad Program (EAP), Berkeley Summer Abroad, or the UC Berkeley Washington Program (UCDC) may meet a Modified Senior Residence requirement by completing 24 (excluding EAP) of their final 60 semester units in residence. At least 12 of these 24 units must be completed after you have completed 90 units.
Upper Division Residence Requirement
You must complete in residence a minimum of 18 units of upper division courses (excluding UCEAP units), 12 of which must satisfy the requirements for your major.
Student Learning Goals
Learning Goals for the Major
Mathematics is the language of science. In Galileo’s words:
Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures, without which it is impossible to understand a single word of it. Without those, one is wandering in a dark labyrinth.
Mathematics majors learn the internal workings of this language, its central concepts and their interconnections. These involve structures going far beyond the geometric figures to which Galileo refers. Majors also learn to use mathematical concepts to formulate, analyze, and solve realworld problems. Their training in rigorous thought and creative problemsolving is valuable not just in science, but in all walks of life.
Skills
By the time of graduation, majors should have acquired the following knowledge and skills:
 Analytical skills
 An understanding of the basic rules of logic.
 The ability to distinguish a coherent argument from a fallacious one, both in mathematical reasoning and in everyday life.
 An understanding of the role of axioms or assumptions.
 The ability to abstract general principles from examples.
 Problemsolving and modeling skills (important for all, but especially for majors in Applied Mathematics)
 The ability to recognize which realworld problems are subject to mathematical reasoning.
 The ability to make vague ideas precise by representing them in mathematical notation, when appropriate.
 Techniques for solving problems expressed in mathematical notation.
 Communication skills
 The ability to formulate a mathematical statement precisely.
 The ability to write a coherent proof.
 The ability to present a mathematical argument verbally.
 Majors in Mathematics with a Teaching Concentration should acquire familiarity with techniques for explaining K12 mathematics in an accessible and mathematically correct manner.
 Reading and research skills
 Sufficient experience in mathematical language and foundational material to be wellprepared to extend one’s mathematical knowledge further through independent reading.
 Exposure to and successful experience in solving mathematical problems presenting substantial intellectual challenge.
Advising
The Math Department has a small team of undergraduate advisers that information on requirements, policies, procedures, resources, opportunities, untying bureaucratic knots, developing study plans, attending commencement, certifying degrees and minors. Students are strongly encouraged to see an undergraduate adviser at least twice a year.
The individually assigned faculty adviser counsels students on the academic content of their mathematics major. The faculty adviser's signature is required for approval of courses that are not already preapproved to be used as major electives. Appropriate questions for the faculty adviser include selection of electives and preparation for graduatelevel courses in a specific mathematical area to be used for honors in the major. Be sure and let him/her know if you are considering graduate work in or related to mathematics, and solicit help in how best to prepare.
Occasionally, the student's adviser goes on sabbatical or is taken off the major advising list and a new official adviser will be appointed by the head major adviser. Requests to change advisers will be accommodated to the extent possible on an individual basis. Please make requests well in advance of the course enrollment period in which the change is to become effective.
We also encourage students to take advantage of the expertise of the peer advisors, who have office hours in Evans. The schedule of Peer Advising office hours will be posted here at the beginning of each semester.
Faculty and Instructors
+ Indicates this faculty member is the recipient of the Distinguished Teaching Award.
Faculty
Mina Aganagic, Professor. Particle physics.
Research Profile
Ian Agol, Professor. Lowdimensional topology.
David Aldous, Professor. Mathematical probability, applied probability, analysis of algorithms, phylogenetic trees, complex networks, random networks, entropy, spatial networks.
Research Profile
Denis Auroux, Professor. Mirror symmetry, symplectic topology.
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Richard H. Bamler, Assistant Professor.
Richard E. Borcherds, Professor. Mathematics, lie algebras, vertex algebras, automorphic forms.
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+ F. Michael Christ, Professor. Mathematics, harmonic analysis, partial differential equations, complex analysis in several variables, spectral analysis of Schrodinger operators.
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James W. Demmel, Professor. Computer science, scientific computing, numerical analysis, linear algebra.
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Semyon Dyatlov, Assistant Professor. Microlocal analysis, scattering theory, quantum chaos, PDE.
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David Eisenbud, Professor. Mathematics, algebraic geometry, commutative algebra, computation.
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Lawrence C. Evans, Professor. Optimization theory, nonlinear partial differential equations, calculus of variations.
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Steven N. Evans, Professor. Genetics, random matrices, superprocesses and other measurevalued processes, probability on algebraic structures particularly local fields, applications of stochastic processes to biodemography, mathematical finance, phylogenetics and historical linguistics.
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Edward Frenkel, Professor. Mathematics, representation theory, integrable systems, mathematical physics.
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Alexander B. Givental, Professor. Mathematics, mathematical physics, symplectic geometry, singularities, mirror symmetry.
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Ming Gu, Professor. Mathematics, scientific computing, numerical linear algebra, adaptive filtering, system and control theory, differential and integral equations.
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Mark D. Haiman, Professor. Mathematics, algebraic geometry, algebra, combinatorics, diagonal coinvariants, Hilbert schemes.
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Alan Hammond, Associate Professor. Statistical mechanics.
Jenny Harrison, Professor. Mathematics, geometric analysis.
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Olga V. Holtz, Professor. Numerical analysis, matrix and operator theory, approximation theory, wavelets and splines, orthogonal polynomials and special functions, analysis of algorithms and computational complexity.
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Michael Hutchings, Professor. Mathematics, low dimensional, symplectic topology, geometry.
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Michael J. Klass, Professor. Statistics, mathematics, probability theory, combinatorics independent random variables, iterated logarithm, tail probabilities, functions of sums.
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Lin Lin, Assistant Professor. Numerical analysis, computational quantum chemistry, computational materials science.
John W. Lott, Professor. Differential geometry.
Antonio Montalban, Associate Professor. Mathematical logic.
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David Nadler, Professor. Geometric representation.
Martin Olsson, Professor. Algebraic geometry, arithmetic geometry.
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PerOlof Persson, Associate Professor. Applied mathematics, numerical methods, computational fluid and solid mechanics.
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James W. Pitman, Professor. Fragmentation, statistics, mathematics, Brownian motion, distribution theory, path transformations, stochastic processes, local time, excursions, random trees, random partitions, processes of coalescence.
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Nicolai Reshetikhin, Professor. Mathematics, representation theory, mathematical physics, lowdimensional topology.
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Fraydoun Rezakhanlou, Professor. Mathematics, probability theory, partial differential equations.
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Kenneth A. Ribet, Professor. Mathematics, algebraic geometry, algebraic number theory.
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Marc Rieffel, Professor. Mathematics, operator algebras, noncommutative geometry, noncommutative harmonic analysis, quantum geometry.
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Thomas Scanlon, Professor. Mathematics, model theory, applications to number theory.
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Vera Serganova, Professor. Mathematics, Superrepresentation theory.
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James A. Sethian, Professor. Mathematics, applied mathematics, partial differential equations, computational physics, level set Methods, computational fluid mechanics and materials sciences. fast marching methods.
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Chris Shannon, Professor. Economics, mathematical economics, economic theory.
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Vivek V. Shende, Assistant Professor. Geometry.
Sug Woo Shin, Associate Professor. Number theory, automorphic forms.
Pierre Simon, Assistant Professor. Mathematical Logic, Model theory.
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Theodore A. Slaman, Professor. Mathematics, recursion theory.
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Nikhil Srivastava, Assistant Professor. Theoretical computer science, random matrices, geometry of polynomials.
Zvezdelina Stankova, Teaching Professor. Algebraic geometry, representation theory, combinatorics, Olympiad problem solving, Berkeley Math Circle.
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John Strain, Professor. Mathematics, numerical analysis, applied mathematics, fast algorithms, materials science.
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Bernd Sturmfels, Professor. Mathematics, combinatorics, computational algebraic geometry.
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Song Sun, Associate Professor. Differential Geometry.
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Daniel Ioan Tataru, Professor. Mathematics, partial differential equations, nonlinear waves.
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Constantin Teleman, Professor. Lie algebras, algebraic geometry, Lie groups, topology, topological quantum field theory.
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Luca Trevisan, Professor. Computational complexity, spectral graph theory.
Dan Voiculescu, Professor. Random matrices, pperator algebras, free probability theory.
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Paul A. Vojta, Professor. Mathematics, algebraic geometry, diophantine geometry, Nevanlinna theory, Arakelov theory.
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Katrin Wehrheim, Associate Professor. Lowdimensional and symplectic topology.
Jon Wilkening, Professor. Applied mathematics, numerical analysis, computational solid and fluid mechanics.
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Lauren K. Williams, Professor. Algebraic combinatorics.
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Mariusz Wodzicki, Professor. Analysis, mathematics, Noncommutative and algebraic geometry, Ktheory.
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Xinyi Yuan, Assistant Professor. Number theory.
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Maciej Zworski, Professor. Mathematics, partial differential equations, mathematical physics, mathematical aspects of quantum mechanics, scattering theory, microlocal analysis.
Research Profile
Lecturers
Emiliano Gomez, Lecturer.
Alexander Paulin, Lecturer.
Kelli Talaska, Lecturer.
Visiting Faculty
Carolyn Abbott, Visiting Assistant Professor.
Semeon Artamonov, Visiting Assistant Professor.
Daniel Bragg, RTG Postdoc.
James Conway, Visiting Assistant Professor.
David Corwin, RTG Postdoc.
Wilfrid Gangbo, Chancellor's Professor.
Charles Hadfield, Visiting Assistant Professor.
Marina Iliopoulou, Visiting Assistant Professor.
Casey Jao, NSF Postdoc.
Tim Laux, Visiting Assistant Professor.
Koji Shimizu, Visiting Assistant Professor.
Slobodan Simic, Visiting Professor.
Dmitry Tonkonog, Visiting Assistant Professor.
Dimitry Vaintrob, Visiting Assistant Professor.
Xuwen Zhu, Visiting Assistant Professor.
Emeritus Faculty
John W. Addison, Professor Emeritus. Mathematics, theory of definability, descriptive set theory, model theory, recursive function theory.
Research Profile
Robert Anderson, Professor Emeritus. Finance, probability theory, mathematical economics, nonstandard analysis.
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Grigory I. Barenblatt, Professor Emeritus. Applied mathematics, Solid mechanics, Fluid mechanics, similarity methods asymptotics, mechanics of deformable solids.
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George Bergman, Professor Emeritus. Mathematics, associative rings, universal algebra, category theory, counterexamples.
Research Profile
Elwyn R. Berlekamp, Professor Emeritus. Computer science, electrical engineering, mathematics, combinatorial game theory, algebraic coding theory.
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Robert Bryant, Professor Emeritus. Symplectic geometry, differential geometry, Lie groups, geometric partial differential equations.
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Alexandre J. Chorin, Professor Emeritus. Applied mathematics, numerical methods, hydrodynamics, sampling and Monte Carlo methods.
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Paul Concus, Professor Emeritus. Fluid mechanics, numerical analysis, applied mathematics, capillarity.
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Heinz O. Cordes, Professor Emeritus. Mathematics, classical analysis.
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F. Alberto Grunbaum, Professor Emeritus. Medical imaging, xray crystallography, imaging of structures of biological interest, classical and quantum random walks, matrix valued orthogonal polynomials, quasi birthanddeath processes.
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+ Ole H. Hald, Professor Emeritus. Mathematics, numerical analysis.
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Leo A. Harrington, Professor Emeritus. Mathematics, model theory, recursion theory, set theory.
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Robert C. Hartshorne, Professor Emeritus. Mathematics, algebraic geometry.
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Morris W. Hirsch, Professor Emeritus. Game theory, dynamical systems, topology, biological models.
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WuYi Hsiang, Professor Emeritus. Mathematics, transformation groups, differential geometry.
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Vaughan F. R. Jones, Professor Emeritus. Mathematics, Von Neumann algebras.
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William M. Kahan, Professor Emeritus. Error analysis, Numerical computations, Computers, Convexity, Large matrices, Trajectory problems.
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Robion C. Kirby, Professor Emeritus. Mathematics, topology of manifolds.
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TsitYuen Lam, Professor Emeritus.
R. Sherman Lehman, Professor Emeritus.
H. W. Lenstra, Professor Emeritus.
Ralph N. McKenzie, Professor Emeritus. Mathematics, logic, universal algebra, general algebra, lattice theory.
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Keith Miller, Professor Emeritus. Mathematics, partial differential equations, numerical methods for PDE's.
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Calvin C. Moore, Professor Emeritus. Operator algebras, ergodic theory, representations and actions of topological groups, foliations and foliated spaces, K theory.
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John Neu, Professor Emeritus.
Andrew Ogg, Professor Emeritus.
Arthur E. Ogus, Professor Emeritus. Mathematics, algebraic geometry, algebraic differential equations, log poles.
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Beresford N. Parlett, Professor Emeritus. Numerical analysis, scientific computation.
Charles C. Pugh, Professor Emeritus. Mathematics, global theory of differential equations.
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John L. Rhodes, Professor Emeritus. Mathematics, algebra, semigroups, automata.
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Rainer K. Sachs, Professor Emeritus. Mathematical biology.
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Isadore M. Singer, Professor Emeritus. Mathematics, physics, partial differential equations, geometry.
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Stephen Smale, Professor Emeritus. Algorithms, mathematics, numerical analysis, global analysis.
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Robert M. Solovay, Professor Emeritus.
John Steel, Professor Emeritus. Mathematics, descriptive set theory, set theory, fine structure.
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Peter Teichner, Professor Emeritus. Topology, quantum field theory.
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John B. Wagoner, Professor Emeritus. Mathematics, dynamical systems, differential topology, algebraic Ktheory.
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Alan Weinstein, Professor Emeritus. Mathematics, mathematical physics, symplectic geometry.
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Joseph A. Wolf, Professor Emeritus. Harmonic analysis, differential geometry, Lie groups.
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W. Hugh Woodin, Professor Emeritus. Mathematics, set theory, large cardinals.
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HungHsi Wu, Professor Emeritus. Real and complex geometry, school mathematics education.
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Contact Information
ViceChair for Undergraduate Affair
Professor Olga Holtz
821 Evans Hall
Phone: 5106422122
Undergraduate Student Adviser
Ana Renteria
964 Evans Hall
Phone: 5106434148