Basics

Instructor

Prof. Graham Leuschke

Contact

gjleusch@math.syr.edu

Time & Place

MW 2:15—3:35, Carnegie 220

Office Hours

MW 10—11, TR 11—12:30; by appointment; and any time my door is open (206C Carnegie)

Important documents

course syllabus

The course is over! Thanks to everyone for a great semester.

Final Exam

• due Friday, Dec. 15

Exam II

• Due Monday 6 Dec. at 5pm

Exam I

• corrected version

Problem Sets

• #1, due Sept. 6
• #2, due Sept. 13
• #3, due Sept. 27
• #4, due Oct. 4
• #5, due Oct. 11 (corrected typo in problem 2)
• #6, due Nov. 1
• #7, due Nov. 8
• #8, due Nov. 15
• #9, due Nov. 20
• #10, not collected

Links

• Tales of the Dodecahedron (This is a general-audience talk, so a bit basic for us, but groovy nonetheless. Also, I am apparently a big Baez fanboy.)
• Apparently the fact that you could fit five cubes in a dodecahedron was known to Euclid. So I’d guess the answer to David’s question (“Who first noticed the icosahedral group is isomorphic to A₅?”) is: it was even before the word ‘group’ existed.
• Some thoughts on the number 6, by John Baez (again), about the icosahedral group and its relation to A₅.
• biography of Sylow (Adam was right, he was Norwegian. Also a high-school teacher.)
• finite subgroups of SO3 and the ADE syndrome, by John Baez
• Lectures on the Ikosahedron and Solutions of Equations of the Fifth Degree, by Felix Klein (see esp. Chapter 1, where he discusses the rotational symmetries of the regular polyhedra)
• paper-model.com, a Windows program to make cut-out polyhedra.
• geometry junkyard, with a whole bunch of links about symmetry and group theory
• The Use of the Linear Algebra by Web Search Engines [PDF]
• Introduction to the Singular Value Decomposition (we’ll try to work this in later in the semester)
• The Status of the Classification of the Finite Simple Groups (PDF)
• the development of group theory
• biography of Abel, after whom Abelian groups are named
• biography of Galois, who first used the word “group.”