Math 402: GROUP THEORY
Hardy, Godfrey H. (1877 -
1947)
The mathematician's patterns, like the painter's or the poet's must be
beautiful;
the ideas, like the colors or the words must fit together in a harmonious
way.
Beauty is the first test: there is no permanent place in this world for ugly
mathematics.
A Mathematician's Apology, London, Cambridge University Press, 1941.
Office hours: Monday 2:20-3:20, Wednesday 11-12 in my office, PDL C-8K
Exams: Final Fri, Aug 20th; Midterm Wed, July 21st.
CURRENT:
Grades are here.
You can pick up your exam: Monday (August 23rd) 10:30-11 in my office
or by appointment later. I will be unavailable August 27th -September 10th.
Enjoy the break and good luck next quarter!
Solutions to HWK#1, HWK#2, HWK#3, HWK #4, Hwk 5, Hwk 6, Hwk 7
FINAL EXAM: Review Problems
Who was Sylow?
Link about the Classification Theorem of Finite Simple Groups: AMS Article (pdf file: need Adobe Acrobat Reader)
Platonic Solids Links: Dodecahedron
Alternative proof of "A5 is simple"
List of Topics for weeks 1 and 2
Worksheet from Monday 7/12 (w/ partial solutions)
Fun Website:
http://members.tripod.com/~dogschool/index.html (warning: lots of pop-up
ads!)
First Week:
Monday 6/21: Section 2.1 (Groups)
Wednesday 6/23: Section 2.2 (Subgroups) + extra: Dihedral groups
Friday 6/25:Sections 2.4 and 2.3 (Homomorphisms and Isomorphisms) Homework #1 (2.1-2.2) due
Second Week (updated):
Monday 6/28: Catch up (conjugation, normal groups, etc)
Wednesday 6/30: Sections 2.5 and 2.9 (Equivalence Relations and Modular Arithmetic)
SLIDES about Sn
Friday 7/2: Sections 2.6 (Cosets) Homework #2 (2.3--2.5, 2.9) due
Third week:
Monday 7/5: Holiday
Wednesday 7/7: Section 2.10 (Quotients) .
Homework #3 (2.6) due
Friday 7/9: Section 2.7 and more on quotients, subgroups and the three Isomorphism Theorems
Fourth Week:
M: Section 2.8 Products of Groups + Cyclic Groups + Finitely generated abelian groups.
W: More about products.
Rewrites of hwk 2 and 3 due
F: Skimming through Sections 1-2 of Chapter 5: Symmetries of plane figures.
Homework #4 due
Fifth Week:
M: Review for Midterm. Bring Sample Midterm & your questions.
W: Midterm (1hr, 1 index card with notes)
F: Section 5.5
Sixth Week:
M: Section 5.6
W: Section 5.7 + Platonic solids & Rotational symmetries
F: Section 5.8 & wrap up chapter 5
Seventh Week:
M: Section 6.1 Class Equation
W: Section 6.2 Simplicity of A5
F: 6.3 and start 6.4 Sylow's Theorems
Eighth Week:
M: Section 6.4 Prove Sylow Thms 1 and 2
W: Section 6.3, 6.4 Normalizers and the proof of Sylow Thm 3
F: Section 6.4, 6.5 Applications. Groups of order 12. Small order groups
Ninth Week:
M: Elliptic Curves and Cryptography
W: Review
F: Final Exam