My apologies for making this page local access only. I’d just had enough of seeing my unpolished notes, intended for private consumption by people attending the courses, appear on the web as “Free e-books”. They weren’t intended that way. If I’d wanted to write a book, I would have done so, and polished these notes accordingly. Worse still is when people who download these notes are then invited by certain websites to “rate” the notes. These notes were placed on the internet as a courtesy to people attending the course; in some cases, despite their unpolished appearance, it took me a very long time to digest the theory, and to prepare, and for strangers to pass judgement on them, when they hadn’t attended the course, and sat through additional explanations and so on, seems rather rude.
Here’s the kind of site I hate (there are others, but this one was the one which made my mind up).
Some links to course home pages can still be accessed from this page for those using computers within the University network.
Others who are interested in the notes for my Sheffield courses should e-mail me (department policy is that web access to printed notes should only be available from within the university!).
| Semester | Course |
|---|---|
| Spring 1999 | PMA327 Galois Theory (20 lectures) |
| Autumn 1999 | PMA347 Commutative Algebra (20 lectures) |
| Autumn 2000 | PMA347 Commutative Algebra (20 lectures) |
| Spring 2001 | PMA327 Galois Theory (20 lectures) |
| Autumn 2001 | PMA344 Real Analysis (20 lectures) |
| Autumn 2002 | PMA330 Analytic Number Theory (20 lectures) |
| Spring 2003 | PMA327 Galois Theory (20 lectures) |
| Autumn 2003 | PMA215 Metric Spaces (22 lectures) |
| Spring 2004 | PMA427 Galois Theory (20 lectures) |
| Autumn 2004 | PMA110 Numbers and Proofs (22 lectures) |
| Autumn 2004 | PMA215 Metric Spaces (22 lectures) |
| Autumn 2005 | PMA110 Numbers and Proofs (22 lectures) |
| Autumn 2005 | PMA344 Real Analysis (20 lectures) |
| Autumn 2006 | PMA110 Numbers and Proofs (22 lectures) |
| Autumn 2008 | MAS105 Numbers and Proofs (22 lectures) |
| Spring 2009 | PMA220 Vector Spaces and Fourier Theory (22 lectures) |
| Autumn 2009 | MAS105 Numbers and Proofs (22 lectures) |
| Spring 2010 | MAS277 Vector Spaces and Fourier Theory (22 lectures) |
| Given | Course |
|---|---|
| Oxford, 1995-6 | Introduction to modular forms (16 lectures) |
| Oxford, 1996-7 | Zeta functions of number fields (12 lectures) |
| Oxford, 1997-8 | Braid groups and Galois theory (14 lectures) |
| Sheffield, Spring 2000 | Topics in algebraic number theory (24 lectures) |
| Sheffield, Spring 2006 | Topics in algebraic number theory (28 lectures) |
| Sheffield, Autumn 2007 | The Serre conjectures (?? lectures) |
Zeta functions of number fields I (Sheffield: more or less self-contained proof of the analytic class number formula)
Zeta functions of number fields II (Sheffield: slightly less self-contained proof of the functional equation, following Tate's thesis)
Both of these form parts of the course in Oxford alluded to above, which also went on to discuss the Beilinson conjectures very briefly. I haven't rewritten this part of the notes for public consumption yet. But a more natural continuation would be to go through Borel's work on ranks of K-groups of number fields.
Galois theory of number fields (Sheffield: quite lengthy treatment of the representation theory of Galois groups of local and global nuber fields, containing a classification of 2-dimensional representations, amongst other things.)
A brief introduction to étale cohomology (Sheffield: short intoduction to étale cohomology, starting with the Weil conjectures. A very sketchy account - there are much more complete accounts elsewhere on the web.)