Grant Walker's Home Page

Grant Walker
School of Mathematics
University of Manchester
Oxford Road
Manchester M13 9PL
UK

Email address: grant@ma.man.ac.uk

Telephone: (+44)(0)161 306 8951
Fax: (+44)(0)161 275 5819

Research interests

Algebraic topology; the structure of the Steenrod algebra, the action of the Steenrod algebra on polynomials
Combinatorics; symmetric functions, Young diagrams and tableaux
Algebra; Modular representation theory of general linear groups in the defining characteristic

MT3522 Knot Theory

This is a third level course unit which provides an introduction to knot theory at an elementary level.

The central theme is polynomial invariants of knots and links.

  • Course Notes for Chapter 1 (Postscript file)
  • Course Notes for Chapter 1 (PDF file)
  • Exercises for Chapter 1 (Knot Theory, Examples 1 (Postscript file)
  • Exercises for Chapter 1 (Knot Theory, Examples 1 (PDF file)
  • Solutions for Chapter 1 (Knot Theory, Solutions 1 (Postscript file)
  • Solutions for Chapter 1 (Knot Theory, Solutions 1 (PDF file)
  • Course Notes for Chapter 2 (Knot Theory, Chapter 2 (Postscript file)
  • Course Notes for Chapter 2 (Knot Theory, Chapter 2 (PDF file)
  • Exercises for Chapter 2 (Knot Theory, Examples 2 (Postscript file)
  • Exercises for Chapter 2 (Knot Theory, Examples 2 (PDF file)
  • Solutions for Chapter 2 (Knot Theory, Solutions 2 (Postscript file)
  • Solutions for Chapter 2 (Knot Theory, Solutions 2 (PDF file)
  • Course Notes for Chapter 3 (Knot Theory, Chapter 3 (Postscript file)
  • Course Notes for Chapter 3 (Knot Theory, Chapter 3 (PDF file)
  • Exercises for Chapter 3 (Knot Theory, Examples 3 (Postscript file)
  • Exercises for Chapter 3 (Knot Theory, Examples 3 (PDF file)
  • Solutions for Chapter 3 (Knot Theory, Solutions 3 (Postscript file)
  • Solutions for Chapter 3 (Knot Theory, Solutions 3 (PDF file)
  • Course Notes for Chapter 4 (Knot Theory, Chapter 4 (Postscript file)
  • Course Notes for Chapter 4 (Knot Theory, Chapter 4 (PDF file)
  • Course Notes for Chapter 5 (Knot Theory, Chapter 5 (Postscript file)
  • Course Notes for Chapter 5 (Knot Theory, Chapter 5 (PDF file)
  • Exercises for Chapters 4/5 (Knot Theory, Examples 4 (Postscript file)
  • Exercises for Chapters 4/5 (Knot Theory, Examples 4 (PDF file)
  • Solutions for Chapters 4/5 (Knot Theory, Solutions 4 (Postscript file)
  • Solutions for Chapter 4/5 (Knot Theory, Solutions 4 (PDF file)
  • Course Notes for Chapter 6 (Knot Theory, Chapter 6 (Postscript file)
  • Course Notes for Chapter 6 (Knot Theory, Chapter 6 (PDF file)
  • Exercises for Chapter 6 (Knot Theory, Examples 5 (Postscript file)
  • Exercises for Chapter 6 (Knot Theory, Examples 5 (PDF file)
  • Solutions for Chapter 6 (Knot Theory, Solutions 5 (Postscript file)
  • Solutions for Chapter 6 (Knot Theory, Solutions 5 (PDF file)
  • Menu Page for Knots Exhibition
  • Borromean rings
  • The Knot Plot Site
  • Knots on the Web
  • Math Forum Library, Knot Theory

    MT30512 Polynomials

    This course aims to provide a concrete approach to standard topics in commutative algebra by focussing on polynomial algebras over a field of scalars. The topic up to Easter is Groebner bases for ideals. Results on factorisation and irreducible polynomials will be introduced as required. The topic after Easter is symmetric and alternating polynomials. Chapter 5 of the book "Concrete Abstract Algebra" by Niels Lauritzen (Cambridge University Press, 2003) follows a similar approach to Groebner bases to that given in the lectures, and is recommended.

  • Course Notes for session 2006--2007 (PDF file)
  • Course Notes for session 2006--2007 (Postscript file)
  • Examples 1, 2006--2007 Session , Polynomials Examples 1 (Postscript file)
  • Examples 1, 2006--2007 Session , Polynomials Examples 1 (PDF file)
  • Examples 2, 2006--2007 Session , Polynomials Examples 2 (Postscript file)
  • Examples 2, 2006--2007 Session , Polynomials Examples 2 (PDF file)
  • Examples 3, 2006--2007 Session , Polynomials Examples 3 (Postscript file)
  • Examples 3, 2006--2007 Session , Polynomials Examples 3 (PDF file)
  • Examples 4, 2006--2007 Session , Polynomials Examples 4 (Postscript file)
  • Examples 4, 2006--2007 Session , Polynomials Examples 4 (PDF file)
  • Examples 5, 2006--2007 Session , Polynomials Examples 5 (Postscript file)
  • Examples 5, 2006--2007 Session , Polynomials Examples 5 (PDF file)
  • Examples 6, 2006--2007 Session , Polynomials Examples 6 (Postscript file)
  • Examples 6, 2006--2007 Session , Polynomials Examples 6 (PDF file)
  • Examples 7, 2006--2007 Session , Polynomials Examples 7 (Postscript file)
  • Examples 7, 2006--2007 Session , Polynomials Examples 7 (PDF file)
  • Examples 8, 2006--2007 Session , Polynomials Examples 8 (Postscript file)
  • Examples 8, 2006--2007 Session , Polynomials Examples 8 (PDF file)

    • Recent papers and preprints