Supervision Timetable
Here is my supervision timetable for the Easter 2010 term.
Also, here is the lecture list for 2009-2010.
Here is my supervision timetable for the Easter 2010 term.
Also, here is the lecture list for 2009-2010.
* My IA introductory sheet, given out in the first week of Michaelmas term.
* Some brief notes on hyperbolic functions, written by Kerry Maunder.
* Everyone (indeed, not just those doing IA) should read at least some of Tim Gowers' discussions of miscellaneous mathematical topics.
In the stuff below, things crossed out will appear at the relevant points during the year.
Groups
* Some stuff about associativity.
* Some stuff about homomorphisms.
* How to find groups of order 10.
* A solution to 2004/3/5, about finding subgroups of D12.
* A dodecahedron showing the
five cubes inscribed in it. This picture was made by Simon, who
has also produced a net you can
print and build. Simon's original page about this is here.
Vectors & Matrices
* Some stuff about suffix notation.
Numbers & Sets
* A practice sheet for the first half of Numbers & Sets.
* My own version of examples sheet 4 from Michaelmas 2008, and my bonus sheet 4½ from Michaelmas 2009.
* A sheet of additional questions, for enthusiasts.
* Partial solutions to two past paper questions (2005/4/7 and 1999/4/5) about the Inclusion-Exclusion Principle.
Vector Calculus
* My set of examples sheets, compiling lots of good bits from various places.
* Notes by Matthias Dörrzapf, who lectured the course in 2005 and 2006.
* A solution to a Planet Zog question (2004/3/11).
Linear Algebra
* The Michaelmas 2009 preliminary sheet.
* A good summary of minimal polynomials and JNFs I found online, written by Tom Leinster.
* And some sketch notes on minimal
polynomials and JNFs I scribbled down hastily one morning.
Groups, Rings & Modules
* A selection of group theory questions from Algebra & Geometry, for people starting GR&M but who have forgotten everything.
* "Rings & Things", a
summary of some results in GR&M.
Complex Methods
* Summary notes by Fernando Quevedo, who lectured the course in 2006 and 2007.
* Some notes written by Richard Smith:
about arctan;
conformal maps;
isolated singularities;
calculating residues;
the indentation lemma;
Jordan's Lemma;
Jordan's Lemma for Laplace Inversion.
I don't supervise Parts II and III. However, here are some notes for various courses.
Examples sheets can be found on the DPMMS or DAMTP pages.
Below are the most recent sheets for the courses I supervise. (Sheets in brackets are from last year.)
| Groups | one | two | three | four |
| Vectors & Matrices | one | two | three | four |
| Numbers & Sets | one | two | three | four |
| Analysis I | one | two | three | four |
| Vector Calculus | one | two | three | four |
| Linear Algebra | one | two | three | four |
| Groups Rings & Modules | one | two | three | four |
| Complex Methods | one | two | three | |
| Metric & Topological Spaces | one | two |
Some older examples sheets can be found on my "old things" page. (Requires Raven login.)
Past Papers for recent years can also be found on the university maths website.
Some older past papers can be found on my "old things" page. (Requires Raven login.)
Below are links to those recent papers. I have also separated out the questions for the courses I supervise.
| IA Past Papers | |||||||||
| 2010 | I | II | III | IV | Gps | V&M | An.1 | V.C. | N&S |
| 2009 | I | II | III | IV | Gps | V&M | An.1 | V.C. | N&S |
| 2008 | I | II | III | IV | Gps | V&M | An.1 | V.C. | N&S |
| 2007 | I | II | III | IV | A&G | An.1 | V.C. | N&S | |
| 2006 | I | II | III | IV | A&G | An.1 | V.C. | N&S | |
| 2005 | I | II | III | IV | A&G | An.1 | V.C. | N&S | |
| 2004 | I | II | III | IV | A&G | An.1 | V.C. | N&S | |
| 2003 | I | II | III | IV | A&G | An.1 | V.C. | N&S | |
| 2002 | I | II | III | IV | A&G | An.1 | V.C. | N&S | |
| 2001 | I | II | III | IV | A&G | An.1 | V.C. | N&S | |
| IB Past Papers | ||||||||
| 2010 | I | II | III | IV | L.A. | GR&M | C.M. | M&T |
| 2009 | I | II | III | IV | L.A. | GR&M | C.M. | M&T |
| 2008 | I | II | III | IV | L.A. | GR&M | C.M. | M&T |
| 2007 | I | II | III | IV | L.A. | GR&M | C.M. | M&T |
| 2006 | I | II | III | IV | L.A. | GR&M | C.M. | M&T |
| 2005 | I | II | III | IV | L.A. | GR&M | C.M. | M&T |
| 2004 | I | II | III | IV | L.A. | GR&M | C.M. | |
| 2003 | I | II | III | IV | L.A.* | GR&M past qns + |
C.M. | |
| 2002 | I | II | III | IV | L.A.* | C.M. | ||
| 2001 | I | II | III | IV | L.A.* | C.M. | ||
* Linear Algebra appeared for the first time in 2004. Before that, there were two courses: Linear Maths and Quadratic Maths. Not all the questions will be relevant to the new course.
+ Groups Rings & Modules appeared for the first time in 2004. This is a selection of past Tripos questions handed out that year to give revision practice.
My Ph.D. thesis: "Zeta Functions of Algebras and Resolution of Singularities". It's really not very interesting, I'm afraid.
"The Zeta Function of sl2 and Resolution of Singularities", a paper by Marcus du Sautoy and me.
The project I did for the Diploma in Computer Science: "Solving Certain p-adic Integrals"
A juggling theorem
"Given a collection of positive integers with integer average, there is some permutation of them which is a valid siteswap."
Here is a proof. And here is an implementation of the algorithm, written in Python by Simon.
Solitaire Army
Simon and I came up with a fun extension to "Solitaire Army". Simon has produced a page with pretty animations of our result.
