Graduate Undergraduate Learning Program (G.U.L.P)

Description of program

    During the spring quarter of 2012, the AWM began to administer the Graduate-Undergraduate Learning Program. This program pairs undergraduates with a graduate student mentor. Together, mentors and mentees explore a topic in mathematics of their choosing. Usually this involves reading and discussing a textbook or papers on the subject. At the end of the quarter, mentees present what they have learned for one another at an AWM-sponsored party.

    By participating in this program, undergraduates are able to learn more about a topic of their choice, gain experience presenting mathematical ideas to their peers, and bond with a graduate student who has experience working as a mathematician. Students of all levels are encouraged to apply. Whether you are a calculus student hoping to see what advanced math is all about or a senior who wants to get some more background before heading off to graduate school, AWM wants to help you in your study of mathematics.

    This program will run for the second time during the winter quarter of 2013.

Winter 2013 Topics

  • Metamathematics

    Book: Godel-Escher-Bach
    Minimum Prerequisites: The student should be willing to think about math outside of just equations and numbers.
    Preferred Prerequisites: 109 Mathematical Reasoning

  • Learning Biomath through Programming

    Minimum Prerequisites: The student should be interested in learning to program.
    Preferred Prerequisite: 109 Mathematical Reasoning

  • Homological Algebra

    Details: This topic would start with basic homological algebra and would hopefully continue on to Hochschild homology and cyclic homology.
    Minimum Prerequisites: 100 Abstract Algebra
    Preferred Prerequisites: None

  • The PageRank algorithm

    Details: PageRank is the algorithm used by the Google search engine. This topic would include a study of this or other similar ranking systems.
    Minimum Prerequisites: 20F Linear Algebra, 180A Probability
    Preferred Prerequisites: 109 Mathematical Reasoning, 184 Combinatorics

  • Game Analysis

    Minimum Prerequisites: 20F Linear Algebra, 180A Probability
    Preferred Prerequisites: 109 Mathematical Reasoning, 184 Combinatorics

  • Introductory Combinatorics

    Book: Concrete Mathematics
    Minimum Prerequisites: None
    Preferred Prerequisites: 109 Mathematical Reasoning

  • Knots & Graphs

    Minimum Prerequisites: 109 Mathematical Reasoning
    Preferred Prerequisites: 190 Introduction to Topology from the Fall of 2012 or 2010 (with Professor Roberts)

  • Matrix Groups

    Minimum Prerequisites: 100 Abstract Algebra
    Preferred Prerequisites: None

  • Commutative Algebra

    Minimum Prerequisites: 100 Abstract Algebra
    Preferred Prerequisites: None

  • Number Theory

    Minimum Prerequisites: 100 Abstract Algebra
    Preferred Prerequisites: None

  • Algebraic Geometry

    Minimum Prerequisites: 100 Abstract Algebra
    Preferred Prerequisites: None

  • Cryptography

    Minimum Prerequisites: 109 Mathematical Reasoning
    Preferred Prerequisites: 100 Abstract Algebra

  • Graph Theory

    Minimum Prerequisites: 109 Mathematical Reasoning
    Preferred Prerequisites: 100 Abstract Algebra

Application

    All interested students should fill out the application found below. In order to match as many students as possible, you may be asked to work in a small group with a few other undergraduates and one graduate mentor. Applications for the GULP program to start in Winter 2013 are now open.

Past Topics

  • The Wright-Fischer model of genetic drift (BioMath)
  • The Generalized Linear Model (Statistics)
  • Markov chains in Biology (Probability & BioMath)
  • Topics in graph theory: planarity, colorings, matchings, and more
  • Bounds on Van der Waerden numbers (Combinatorics)
  • Representation theory (Algebra & Combinatorics)
  • P-adic numbers (Numerical Analysis)
  • Mathlib: a mathematical app for the Android (Proof Theory & Computer Science)
  • Generating functions (Combinatorics)
  • Topics in combinatorics: fractals, game theory, taxi-cab geometry, and more
  • Introduction to Algebraic Geometry
  • Knotted DNA (Topology and BioMath)
  • Godel Escher Bach (Metamathematics)
  • The fundamental group and applications (Topology)
  • Plane algebraic curves (Algebraic Geometry)
  • Approximation methods for differential equations (Numerical Analysis)