MATHEMATICAL METHODS II

Phys 509 Spring 2023

The worm

Tuesday, Thursday 09:30am to 10:50am in 276 Loomis Laboratory.

Syllabus Outline

The course will have three related components:

Below are links to various course-related documents. These files will now be in PDF format only

Homework Sets

The solutions to the hw sets should be placed in the yellow 508/509 homework box near the passage from Loomis to MRL on the second floor of Loomis Lab.

Homework number 0, due 4pm Jan 25th. , ( Porter's solution. )
Homework number 1, due 4pm Feb 1st. , ( Porter's solutions. )
Homework number 2, due 4pm Feb 8th, ( Porter's solutions. )
Homework number 3, due 4pm Feb 22nd. ( Porter's solutions. )
Homework number 4, due 4pm March 1st. ( Porter's solutions. )
Homework number 5, due 4pm March 8th. ( Porter's's solutions. )
Homework number 6, due 4.pm March 22nd . ( Porter's solutions. )
Homework number 7, due 4pm April 12th . ( Porter's solutions. )
Homework number 8, due 4pm April 19. ( Porter's solutions. )
Homework number 9, due 9am April 26th. ( Porter's solutions. )
Homework number 10, optional.

Lecture notes

The lecture notes are available to the general public. Please give me feedback - tell me of typos, sign errors, obscurities, or plain conceptual errors.

My notes on torsion can be found near the bottom of this page

Textbooks

I recommend (but do not require) that you purchase Mathematics for Physics: A guided tour for graduate students by myself and Paul Goldbart. (Cambridge University Press 2009). The list price is $90, but Amazon has it for $72 (+shipping). I do not yet know what the UI bookstore is selling it for. This beautifully produced book is an expanded version of the lecture notes for both PHYS 508 and PHYS 509.

If you do not want to shell out $90, I recommend three other books: Differential Forms with applications to the Physical Sciences by Harley Flanders, Group Theory by Morton Hammermesh, and Mathematics for Physicists by Phillipe Dennery and Andre Krzywicki. All three are published by Dover Publications, and should cost no more than $15 or so each.

Grades

Grades for the course will be based on you total score on the homework (60%), and a term paper (40%). You may choose your own term paper topic, but I will wish to check its suitability. Here is short list of papers that might provide some inspiration.

Please e-mail me with your suggested topics by the end of the spring break. The papers should be in the order of five pages long --- although there will be no penalty for longer works if you need the space --- and should be typeset in TeX (or LaTex). You may find this this essay on the art of writing mathematics to be of use. Another useful article is this article by N. David Mermin.

The term papers will be due at the end of the scheduled time for the final exam: 4:30 pm on Tuesday May 11th. Please email a PDF version of them to me before that time.

People who figure in our story:

Elie Cartan
Cauchy
De Rham
Frobenius
H. Hopf
W. Killing
Laurent
Sophus Lie
Riemann
Issai Schur
Stokes
Hermann Weyl

Finding me:

Office: 2117 ESB.
Phone: 3-2891.
e-mail: m-stone5@uiuc.edu
My office hour is Tuesday 8-9am.
Location: Outside 2117 ESB (except first week)

Grader:
Porter Howland
pbh2@illinois.edu
Office Hour: 1pm Monday
Location:ESB 4109 (except first week)


P> Last updated /10/01/2023