Math 3510 Information

Fall 2010

Office hours during week of finals:

Monday 8:30-10:00
Tuesday 9:00-11:00
Wednesday 11:00-12:00
Thursday 9:00-11:00

Final Exam: Friday 10:30-12:30

Homework: Homework is to be turned at the beginning of class on the days indicted below. Follow the homework guidelines when preparing your homework to be graded. Soon after class each day the homework assignments will be posted here. You should do all the homework listed, but turn in only the problems listed in bold face type.

August 27
Introduction to abstract algebra
August 30
Introduction to concept of group
Read Section 4 through the middle of Page 31
Eliminate as many possible ending positions for the + puzzle as you can.
September 1
Basic properties of a group
Read Section 4
Prove the left cancellation law.
September 3
Group tables
Prove that for any a,b in a group G, y*a = b has a unique solution.
September 8
Examples of groups, including the dihedral groups
Practice computing products in the dihedral group.
September 10
Basic properties of subgroups
September 13
Identifying subgroups
Page 45 1-6, 8, 9, 10, 11-19, 22, 23, 25, 19, 29, 31, 32, 36, 41
Read Sections 5
September 15
Examples of subgroups
September 17
Introduction to cyclic subgroups
September 20
Subgroups of cyclic groups
Read Section 6
Page 55 1-12, 14,15,27,19,20,22,23,27,37,39,40 Turn in 41, 42, 43, 45, 46, 47
September 22
Cyclic groups and GCD
September 24
Classification of cyclic groups
Introduction to permutation groups
September 27
Class works on problems related to cyclic groups
Page 66 5-11, 17-24, 33-37, 46
Page 55 51, 52, 53
September 29
Review for Exam 1
October 1
Exam 1
Page 67 48, 49, 55
October 4
Homomorphism and Isomorphism
October 6
Cayley’s Theorem
October 8
Alternating group
Review the lecture from October 6 and make sure you understand the connection between the Klein 4-group table and permutations of the Klein 4-group.
Page 83 1,3,5,7,8,11-13,21,,22,30,31,35,40,41,46,48
October 11
Introduction to cosets
Lagrange’s Theorem
Read Section 10
Page 94 1,3,5,13,14,15,16,17,18,23,27,29,33,34
October 13
Products of groups
Orders of elements in product of groups
Fundamental Theorem of Finitely Generated Abelian Groups
October 15
Implications of the FTFGAG
Page 101 1-7, 12, 15, 16, 20, 21, 22, 23, 24, 27, 28, 29, 30, 31, 34, 37, 38, 39, 40
October 18
Kernels of homomorphisms
Normal Subgroups
Read Section 13
October 20
Factor groups (or quotient groups)
Read Section 14
Page 110 1-13,15-25, 39,46,47,49,52
October 22
In class problem solving
Page 133 1-7,8,16-21,22
October 25
First Isomorphism Theorem
October 27
Characterizations of normal subgroups
October 29
Exam 2
November 1
Page 142 1,3,6,7,9,11,12,15,17,18,21,23,24,30
November 3
In-class problem solving session on normal subgroups and quotient groups
November 5
Simple groups, centers and centralizers
Page 142 31,34,35,36
November 8
Work on problems in class
November 10
Work on problems in class
November 12
Introduction to rings
November 15
Properties of rings
Page 151 1,3,4,5,6,7,9,10,14 (center only), 15 (center only)
November 17
Read Section 19
Integral Domains
Page 174 1,3,5,7,8,9,12,16,19,17,37,38 (Recall that a-b means a+(-b).)
November 19
Some number theory and introduction to field extensions
Page 182 1,3,4,5,23 Hint: Move everything to the same side and factor (distributive law)
November 22
Examples of algebraic and transcendental field extensions
November 24
Polynomials and field extensions
Page 189 1-22,27,28,29 Turn in 4,6,8,11,13,15
November 29
Vector spaces
Page 190 27,28, 29
Page 272 1,2,3,7,8
December 1
Algebra and geometric constructions
Page 280 1,2,4,6,8
December 3
Exam 3
December 6
Review and catch up
Page 299 1-10 Turn in 3,5,6,7,10
December 8
Review
December 17 (10:30)
Final Exam

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