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Math 237 Fall, 2010.
Syllabus

Tentative class schedule with reading and homework assignments. Homework is due at the start of class each Wednesday (after the week in which it is assigned) unless otherwise stated. Late homework will not be accepted.


Week
Date Text Topic Homework from Text Additional Homework
0
W Sept 1 Introduction, preview of coming attractions and the tragic life of Evariste Galois (1811-1832)
1
W Sept 8 6.1, 6.2,6.3 Rings, Integral domains, Fields 6.1: 11, 16
6.2: 12, 13
6.3: 23, 33, 39
2
MSept 13 6.3Fields6.3: 25, 31, 34
W Sept 15 7.1, 7.2 Ring homomorphisms, Ideals 7.2: 8, 16, 19, 23, 26 7.3: 19, 20, 21
3 M Sept 208.1, 8.2Polynomial rings 8.1: 9
8.2: 2
W Sept 22 8.3, 8.4 The division algorithm
Irreducible polynomials
8.3: 14
8.4: 1, 9, 28
4
M Sept 27 8.6 Ideals and quotients in polynomial rings 8.6: 9,11
W Sept 29 8.7 Quotients in polynomial rings 8.7: 4, 5, 7, 8, 21
5
M Oct 4 10.1, 10.2Vector spaces
algebraic extensions
10.1:20
10.2: 2, 4, 12, 18
W Oct 6 10.2Algebraic extensions
10.2:
6
M Oct 11 Fall break
W Oct 13 10.3 Splitting fields 10.3: 2, 3, 6, 12, 15, 22, 27
7
M Oct 18 Review for first midterm exam
W Oct 20 FIRST MIDTERM EXAM in class Further Information
8
M Oct 25 10.4 Finite fields
10.4: 1, 5, 8, 20, 21, 22, 25
W Oct 27 11.1 Ruler and Compass Constructions 11.1: 1, 2, 6
11.3: 7
9
M Nov 1 11.2 Classical Problems
11.2:
W Nov 3 12.1 Galois groups 12.1: 1, 2, 3, 4, 6, 9, 15
10
M Nov 8 12.1 Galois Groups
12.1:
W Nov 10 12.2 Galois Theory 12.2: 5, 6, 7, 8, 19, 20, 21, 22 12.1: 18, 20
11
M Nov 15 12.2 Galois Theory
12.2:
W Nov 17 Review for second midterm exam
No HW due. However, I suggest instead that you do the sample exam problems.
12
M Nov 22 SECOND MIDTERM EXAM in class Further Information
W Nov 24 NO CLASS, Thanksgiving recess
13
M Nov 29 5.3 Solvable Groups 5.3: 1, 3, 4, 11
W Dec 1 12.5 Solvability by radicals 12.5:
14
M Dec 6 12.5 Solvability by radicals 12.5: 1, 2, 4, 12 ,14 This assignment is due on Monday 12/13.
W Dec 8 12.5 Solvability by radicals 12.5:
15 M Dec 13 12.5 Galois' Theorem at last! 12.5:
Take Home Final exam due at 2 pm, Friday December 17. Further Information

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