Math 30a Fall 2009
Algebra I: Group Theory



What is new: Revised HW10, Notes on Finite simple groups, part a.


Instructor


Syllabus (for Fall 2009)


Calendar


Quizzes
 
Date Questions/problems Answers Comments
  9/24     Practice Quiz 1.1  answers   Good job everyone! But it doesn't count.
  10/1     Review problems   Answers, part A  
  10/7     Quiz 1 in class  Answers to Quiz 1  
  11/5     Practice Quiz 2   Answers  
  11/5     Review for Quiz 2    
  11/8     Problem Session for quiz 2     Sunday 2-4pm.
  11/11     Second Review Sheet for Quiz 2    
  11/12     Quiz 2 in class    


Lecture Notes
 
Dates of lectures Description Notes Comments
      Notes on elementary group theory with table of contents.   Math 30a sec 1-18   Now complete.
  8/27, 8/31     Sec 0: Sets and relations (p. 1-8 in book)   First day, Second day (preliminary), Complete sec 0 notes (renumbered)  
  9/2     Sec 1: Introduction and examples (p. 11-18 in book)   Section 1 notes  
  9/3     Sec 2: Binary operations (p. 20-25 in book)   Section 2 notes  
  9/9     Sec 3: Isomorphic binary structures (p. 28-33 in book)   Section 3 notes  
  9/10     Sec 4: Groups (p. 36-45 in book)   Section 4 notes   We finally get to groups
  9/14     Discussion day   Worksheet 1  
  9/16     Sec 5: Subgroups (p. 49-55 in book)   Section 5 notes  
  9/17, 9/21     Sec 6: Cyclic groups (p. 59-65 in book)   Section 6 notes   We continue this on Monday.
  9/23     Sec 7: Generating sets (p. 68-72 in book)   Section 7 notes extended. Also the symmetry of a square handout gives two examples.  
  9/23, 9/24, 9/29     Sec 8: Permutation groups (p. 75-83 in book)   Section 8 parts a,b,c which took us three days!  
  9/29, 9/30     Sec 9: Orbits, cycles and alternating group (p. 87-93 in book)   Section 9 part a orbits and cycles Section 9 part b   We will postpone section 10 until after the quiz
  10/8     Sec 10: Cosets (p. 96-101 in book)   Section 10 Cosets and Lagrange  
  10/12     Sec 11: Direct product   Section 11a Direct product   The second half of this section will be covered later.
  10/14     Sec 13: Homomorphisms   Section 13a, Section 13b  
  10/15     Sec 14: Factor groups   Section 14   This is the key idea of groups.
  10/19,21     Sec 16: Group actions   Section 16 (notes by Max)   Prof. Lian
  10/22     Sec 17a: Burnside's Theorem   Section 17a (notes by Max)   Prof. Lian
  10/26     Sec 15: Simple groups   Section 15  
  10/28     Sec 17b: More on group actions   Section 17b  
      Part 2 of the course: Rings and Fields   Notes on sec 18+   Continuously updated with table of contents
  10/28     Sec 18a: Rings and Fields   Section 18a  
  11/02-04     Sec 18b: Rings and Fields, 19a: Integral domains   Section 18b and 19a
  Section 19b (chart) 		 
  11/05     Sec 20: Fermat and Euler   Section 20
  
  11/09     Sec 20b: Proof of Euler's formula   Section 20b
  
  11/16     Sec 33a: Finite Fields   Section 33a
  
  11/16     Sec 33b: Finite Fields, continued   Section 33b
  
  11/19     Finite simple groups   part a
  


Homework (Answers on LATTE)

Home page: Kiyoshi Igusa Started: March  31, 2009  Last modified: Nov   19, 2009
Department:  Mathematics URL: http://people.brandeis.edu/~igusa/Math30aF09/Math30aF2009.htm