Instructor: Craig Sutton
Audience and prerequisites: This course will be of interest to students who are curious about geometry, (theoretical) physics, robotics, computer animation and/or applications of geometric techniques. I will assume you have a working knowledge of multivariable calculus, (abstract) linear algebra and abstract algebra, or possess the willingness to fill in any gaps on the fly.
Instructor: Jay Pantone
Prerequisites: An undergraduate combinatorics course (preferably, some familiarity with generating functions). Ask the instructor if in doubt.
Instructor: Naomi Tanabe
Instructor: Sergi Elizalde
This course is aimed at graduate students and strong undergraduate students who have taken some combinatorics course before.
Instructor: John Voight
The prerequisites for the course are one year of abstract algebra (groups, rings, fields), preferably at the graduate level, and some complex analysis. The course may be suitable for first-year graduate students--please see the instructor.
Instructor: Jay Pantone
Prerequisites: An undergraduate combinatorics course (in particular, familiarity with generating functions). Ask the instructor if in doubt.
Instructor: Pierre Clare
Prerequisites: a good acquaintance with linear and general algebra (as provided for instance in Math 71) is necessary. Some exposure to complex and functional analysis is preferable. No prior knowledge of representation theory or C*-algebras will be assumed. Contact the instructor for more details.
Instructor: Peter Winkler
Prerequisites: Mathematical background of a senior mathematics major or a beginning graduate student in mathematics or theoretical computer science; including a course in probability (e.g., MATH 20 or Math 60). If in doubt, please see the instructor.
Instructor: Bjoern Muetzel
Prerequisites: Math 71 and 101 and a solid background in topology (point set topology, fundamental group, covering space theory). This course aims at second year graduate students, but will be accessible to other students with the appropriate background.
Instructor: John Voight
Instructor: Olivia Prosper
Instructor: Peter Winkler
Prerequisites: A solid background in mathematics, including calculus and at least one course in probability. Exposure to graph theory or measure theory will be handy but won't be assumed. Graduate students and advanced undergraduates studying mathematics or the theory of computing will most likely have adequate mathematical sophistication, but fair warning: this stuff is at the frontier of research; it isn't easy!
Instructor: John Voight
The prerequisite for the course is one year of abstract algebra (groups, rings, fields) at the advanced undergraduate or graduate level.
Instructor: Sutton
Instructor: Sutton
Prerequisites: familiarity/comfort with manifolds (e.g. Math 124) & a solid background in linear algebra (e.g., Math 24) and groups (e.g., Math 71).
Prereqs: programming (eg CS1 or Math26), Math 63, Math 23, Math 22/24. Graduate analysis (73/103) will help.
Prerequisite: An algebra course ( e.g., M71 or M101) and a basic combinatorics course (M28) as well as a desire to learn and solve problems. If you have not had a course in combinatorics and would like to take the course, talk to Rosa.
Instructor: Jorge Lauret (visiting from University of Cordoba, Argentina). Preparation lectures: Carolyn Gordon
Prerequisite: Differential topology. Students should have had some exposure to Riemannian geometry. However, if you are interested in the course and have not had a course in Riemannian geometry, we can include an introduction in January. Please discuss your background in advance with Carolyn Gordon.
We will survey the role of complex numbers across the mathematical spectrum, from the central limit theorem of probability, to the distribution of prime numbers, to hyperbolic geometry, to the mathematical apparatus of quantum mechanics.
Prerequisites: An "advanced" undergraduate combinatorics course
Prerequisites: Everyone should have adequate algebra by spring, and while it would be nice to be acquainted with number fields and their (p-adic) completions, the essentials can be picked up with reasonable ease.
Prerequisites: Basic probability (e.g. Math 20 or 60), and some experience with proofs; graph theory or combinatorics will be useful but not necessary. Graduate students at all levels in math and in computer science are welcome, as are advanced undergrad majors.
Prerequisites: Graduate students at all levels in math and in computer
science are welcome, as are advanced undergrad majors who have taken Math 23.
Suggested background: Some coding experience (Matlab, Fortran, or C), Math 46, Math 63
Prerequisites: A knowledge of elementary number theory and some abstract algebra.
This class has been scheduled for the 10A period.
Prerequisites: no prerequisites for graduate students.
Prerequisites: 101, 111 (suitable for first year students).
Any number theory needed (not much) will be developed.
Prerequisites: Math 118. If you have had an advanced undergraduate course in combinatorics and are interested, talk to Sergi about your preparation.
Prerequisite: Math 8, or placment into Math 11.
Details: This year's offering will be
“From Caculus to Elliptic Curve Cryptography in ten weeks”
See the web site.
Prerequisite: Math 39 or Math 69 or familiarity with the language of first-order logic and readiness for an upper level math course.
Prerequisite: A course in differential topology, including vector fields and their flows. (The course that used to be called Math 124 and is called Math 102 this fall is ideal.)
Prerequisites: the introductory graduate level analysis and topology sequences (103/113, 124/114).
Prerequisite: some programming experience (preferred: Matlab/octave, C, or fortran; esp. the first).
Recommended background: some PDEs (could be at undergrad level, eg Math 46) and real analysis (Math 63 and some graduate-level functional analysis). However the background is flexible: a motivated advanced undergrad or other science/engineering/CS student (undergrad or grad) could pick up enough to learn a lot and do well.
Prerequisites: Linear algebra (Math 24), point-set topology (math 54) and multivariable analysis (Math 73). It will also help to be familiar with covering spaces and the fundamental group.
Prerequisites: An undergrad number theory course, as well as some abstract algebra. I'll be happy to try and fill in gaps for motivated students.
Prerequisites: Linear algebra and algebra (Math 31, 71, or 101). No prior knowledge of combinatorics or representation theory is expected.