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Topics and Graduate Course Descriptions

Spring 2019

  • Math 72: Topics in Geometry: An Introduction to Lie groups

    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.

Spring 2017

  • Math 118: Topics in Combinatorics: Language Theory and Applications to Enumerative Combinatorics

    Instructor: Jay Pantone


    Prerequisites: An undergraduate combinatorics course (preferably, some familiarity with generating functions). Ask the instructor if in doubt.

Winter 2017

  • Math 105: Topics in Number Theory

    Instructor: Naomi Tanabe


Fall 2016

  • Math 108: Topics in Combinatorics: Permutations, partitions and lattice paths

    Instructor: Sergi Elizalde


    This course is aimed at graduate students and strong undergraduate students who have taken some combinatorics course before.

Spring 2016

  • Math 115: Elliptic Curves

    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.

Winter 2016

  • Math 118: Combinatorics

    Instructor: Jay Pantone


    Prerequisites: An undergraduate combinatorics course (in particular, familiarity with generating functions). Ask the instructor if in doubt.

  • Math 123: Automorphic forms, representations and C*-algebras

    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.

Fall 2015

  • Math 100—COSC 49/149
    An Introduction to Mathematics Beyond Calculus: Game Theory

    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.

  • Math 112: Geometric Group Theory

    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.

Summer 2015

  • Math 125: Geometry of Discrete Groups

    Instructor: John Voight


Spring 2015

  • Math 116: Applied Mathematics: Mathematical Modeling in Biology

    Instructor: Olivia Prosper


Fall 2014

  • Math 100: Topics in Probability: Large Networks and Graph Limits

    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!

  • Math 105: Algebraic number theory

    Instructor: John Voight


    The prerequisite for the course is one year of abstract algebra (groups, rings, fields) at the advanced undergraduate or graduate level.

Spring 2014

  • Math 96: Mathematical Finance II

    Instructor: Sutton


    1. Math 86 or Permission of the instructor
    2. Some knowledge of analysis at the level of Math 63/35 or 103 will be useful
  • Math 112: Geometry — The Structure and Representation Theory of Compact Lie Groups

    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).

  • Math 116: Applied Mathematics — Great Papers in Numerical Analysis (Alex Barnett)

    Prereqs: programming (eg CS1 or Math26), Math 63, Math 23, Math 22/24. Graduate analysis (73/103) will help.


Winter 2014

  • Math 128: Current Problems in Symmetric Functions (Rosa Orellana)

    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.


  • Math 123: Geometry and Quantization (Erik Van Erp)


  • SPECIAL TOPICS COURSE: Homogeneous Ricci flow and solitons

    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.


Spring 2013

  • Math 17: Imaginary numbers are real! Complex numbers are simple! (Doyle)

    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.

  • Math 102: Topics in Geometry (Doyle)


  • Math 118: Topics in Combinatorics (Elizalde)

    Prerequisites: An "advanced" undergraduate combinatorics course


  • Math 125: Quadratic forms and spaces (Shemanske)

    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.


Winter 2013

  • Math 100: Topics in Probability [Random Walk on a Graph] (Winkler)

    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.


  • Math 112: Topics in Geometry [Introduction to Riemannian Geometry] (Sutton)


  • Math 126: Topics in Applied Mathematics (Gillman)

    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


Fall 2012

  • Math 105: Topics in Number Theory (Pomerance)

    Prerequisites: A knowledge of elementary number theory and some abstract algebra.

    This class has been scheduled for the 10A period.


  • Math 109: Topics in Logic (Groszek)

    Prerequisites: no prerequisites for graduate students.


Spring 2012

  • Math 121: Current problems in algebra (Webb)

  • Math 125: Reflection and Coxeter groups; Buildings and Classical Groups (Shemanske)

    Prerequisites: 101, 111 (suitable for first year students).
    Any number theory needed (not much) will be developed.


  • Math 128: Topics in Combinatorics (Elizalde)

    Prerequisites: Math 118. If you have had an advanced undergraduate course in combinatorics and are interested, talk to Sergi about your preparation.


Winter 2012

  • Math 17: An Introduction to Mathematics Beyond Calculus (Shemanske)

    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.

  • Math 89: Set theory (Weber)

    Prerequisite: Math 39 or Math 69 or familiarity with the language of first-order logic and readiness for an upper level math course.


  • Math 112: Geometry (Gordon)

    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.)


  • Math 122: The Atiyah-Singer index theorem and the heat kernel proof (van Erp)

    Prerequisites: the introductory graduate level analysis and topology sequences (103/113, 124/114).

  • Math 126: Numerical analysis for PDEs and wave scattering (Barnett)

    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.


Fall 2011

  • Math 102: Foundations of Smooth Manifolds (Sutton)

    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.


  • Math 105: Primes and polynomials (Pomerance)

    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.


  • Math 108: Combinatorial Representation Theory (Orellana)

    Prerequisites: Linear algebra and algebra (Math 31, 71, or 101). No prior knowledge of combinatorics or representation theory is expected.


Winter 2011

Winter 2010

Winter 2008

  • Math 17 (An Introduction to Mathematics Beyond Calculus)

    W08 topic: The Isoperimetric Problem

Fall 2007

Winter 2007

Spring 2006

Winter 2006