The syllabus of the course will mostly go through the
contents
of the textbook :
SYLLABUS
GROUP THEORY
Preliminaries
- 0.2 , 0.3
Introduction to Groups
- 1.1 - 1.7
Subgroups
- 2.1 - 2.5
MIDTERM 1 , Tuesday February 24th in Class , See below for
details
Quotient Groups and Homomorphisms
- 3.1 - 3.5
Group Actions and Sylow Theory
- 4.1 - 4.5
MIDTERM 2 , Tuesday April 7th in Class , See below for
details
Direct and Semidirect Products and Abelian Groups (Review/Skipped)
- 5.1 , 5.2 , 5.5
RING THEORY
Introduction
- 7.1 - 7.6
Euclidean Domains , PIDs , UFDs
- 8.1 - 8.3
Polynomial Rings
- 9.6
FINAL , 5/14/2009 , Thursday at 10:05AM - 12:05PM in
usual classroom B219 VV
HOMEWORK:
HW01 : 0.2-1(abc),4,5
0.3-5,15(ab)
1.1-1,2,7,9,10,14
Optional:
0.3-3,4
1.1-11,12
HW02 : 1.1-25,29,30
1.2-1(c),3,10
1.3-1,9(b)
Optional:
1.1-29,30,33
1.2-4,5,9,11-13
1.3-5,9,11,13,16,17,18
HW03 : 1.4-4,10(abc)
1.6-1,4
1.7-4,18,19
Optional:
1.4-11
1.5-1,3
1.6-9,17,25,26
1.7-20-23
HW04 : 2.1-1(abc),7,11(ac)
2.2-5,6(b),12(acde)
2.3-1
Optional:
1.7-20-22
2.2-6(a),7,12(f),14
Hint: You can use Lagrange's Theorem for the problem
2.2-5
HW05 : 2.3-3,8,10,11,12
2.4-7
2.5-7
3.1-7,9
Optional:
2.3-13,15
HW06 : 3.1-10,22(a),24,36,41,42
3.2-4,14
3.3-1
Optional:
3.1-14,23,34
3.2-5,6,15,21,22,23
HW07 : 3.3-3,7,9
3.5-4
4.1-1
4.2-4,7(b)
Optional:
3.3-10
3.4-1
3.5-3,7
4.1-2,4,6
HW08 : 4.2-11
4.3-2,8,10(a),11(ab)
HW09 : 4.4-3,4,8
4.5-3,13,18,22
Problem: Show that for finite G, G is a p-group iff
every element
of G has
order a power of the prime p.
Optional:
4.4-1,2,6,7
HW10 : 7.1-1,5,12,26
7.2-1,2,10
Optional:
7.1-6,8,25,27
7.2-6,7,9,11,12
HW11 : 7.3-1,4,10,34(ab)
7.4-9,15,16
Optional:
7.3-2,3,13,21,34(cd)
7.4-10,11
HW12 : 7.4-7
7.5-4
8.1-1(a),2(a)
8.2-5
Optional:
7.4-4,33,37,38
7.6-5
8.2-1
Optional problems are for bonus points.
MIDTERM 1 INSTRUCTIONS:
- Exam Locations: Midterm is going to take place in class , B219 Van Vleck.
- You're supposed to be ready in class at 2:25.
- Here 1 ,
2 ,
3 ,
4
are some exams from previous years.
- Study the old exams and the assigned homework problems.
Understand the Examples 1-5 on page 50 of the textbook.
MIDTERM 2 INSTRUCTIONS:
- Midterm 2 covers the sections 3.1 to 4.5
- Here is an exam from previous
years.
- Study the old exam and the assigned homework problems.
- Exam Locations: Midterm is going to take place in class ,
B219 Van Vleck
- You're supposed to be ready in class at 2:25
- Leave spare seats between you and your friend in the exam room.
FINAL INSTRUCTIONS:
- Here is an exam from previous
years.
- Final exam covers the topics we covered in class between the
sections 7.1-8.3.
- Exam Locations: Final is going to take place in class ,
B219 Van Vleck
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