IMMERSE Summer 2005

IMMERSE Summer 2005


From the IMMERSE webpage:

For the pre-grads, the main component of the program consists of two intensive courses: one in algebra and one in analysis. The courses will be at the advanced undergraduate/beginning graduate level. However, rather than working through a textbook, the courses will be structured around the reading of research papers. The IMMERSE course coordinators (two UNL faculty) will select papers that use as tools some of the topics which typically appear in first-year graduate algebra and analysis courses, and then structure the IMMERSE courses around the material of the papers. Each course is team-taught by a pair of early-career faculty, with a mixed group of three first-year and advanced graduate students serving as teaching assistants. There will also be several special presentations / colloquiums / workshops throughout the six weeks, which will provide additional forums for exploring issues the pre-grads are likely to face as they begin graduate school. We will have at least three guest speakers, each of whom will give an overview of current research topics in his/her mathematical area.

IMMERSE Summer 2005 - Algebra Course


Instructors:
Tracy Hamilton (CSU - Sacramento)
Jackie Jensen (Sam Houston State University)

Graduate Mentors:
Andrew Crabbe
Melissa Luckas
Terri Moore
Ed Loeb
Deanna Turk

Jackie Jensen and Tracy Hamilton


General Information

The syllabus
The paper - Gutan, M. and Kisielewicz, A. Reversible group rings. J. Algebra 279 (2004), no. 1, 280--291.
Notes from Don Passman's lectures - 12-13 July, 2005


Homework Assignments

  • Introduction and Rings - Homework 1, assigned Monday, 27 June
  • Groups and Symmetric Groups - Homework 2, assigned Tuesday, 28 June
  • Supplementary ring and group problems
  • P_n(R) - Homework 3, assigned Thursday, 30 June
  • Quaternions - Homework 4, assigned Friday, 1 July
  • Power Series, Polynomial, and Group Rings - Homework 5, assigned Tuesday, 5 July
  • Group Rings, continued - Homework 6, assigned Thursday, 7 July
  • Normal Subgroups - Homework 7, assigned Friday, 8 July
  • Normal Subgroups and Hamiltonian Groups - Homework 8, assigned Monday, 11 July
  • Prime and Semi-prime - Homework 9, assigned Tuesday, 12 July
  • Discussion questions 1
  • Theorem 2.1 discussion worksheet
  • Orders of elements and Groups, Torsion Groups - Homework 10, assigned Thursday, 14 July
  • Characteristic - Homework 11, assigned Friday, 15 July
  • Exponent of a Group - Homework 11, cont, assigned Friday, 15 July
  • Quotient Structures - Homework 12, assigned Monday, 18 July
  • Direct Products and Sums - Homework 13, assigned Tuesday, 19 July
  • Discussion worksheet 2
  • Fields, Part 1 - Homework 14, assinged Friday, 22 July
  • Fields, Part 2 - Homework 15, assigned Tuesday, 26 July
  • Fields, Part 3 - Homework 16, assigned Thursday, 28 July
  • Fields, Part 4 - Homework 17, assigned Friday, 29 July
  • Paper Revisited - Discussion worksheet
    Homework Solutions

    Solutions - thanks to Andrew Crabbe, Terri Moore, and Deanna Turk
    .TeX - the .TeX code
    Solutions - thanks to Andrew Crabbe, Terri Moore, and Deanna Turk
    .TeX - the .TeX code