Math 31 Summer 2009

Math 31, Topics in Algebra (Summer 2009)

General Information

Examinations	Textbook	Deadlines	Instructor	Homework
Grades	Honor Principle	Disabilities	Schedule of Lectures

Examinations

There will be one midterm examination and a final examination (which will not be cummulative). These exams are scheduled as follows:

Midterm Thursday, July 30
Kemeny 006
5:00 pm to 7:00 pm

Final Exam Sunday, August 30
Kemeny 007
11:30 am to 2:30 pm

If you have a legitimate conflict with these exam dates and times, please contact your instructor as soon as possible. Please do not wait until shortly before the exam.

Textbook

Abstract Algebra (3rd edition) by I. N. Herstein
(Available at Wheelock Books)

Deadlines

It is each student's responsibility to be aware of academic deadlines as stated by the Registrar. In particular, please note these deadlines:

July 10: Final day for electing use of the Non-Recording option.
August 12: Final day to withdraw from a course (see the ORC); any later request to withdraw from a course requires petition to a special committee.
August 19: Final day to alter grade limit filed under the Non-Recording Option.

Instructor

Vince Vatter, 314 Kemeny

Blitz: vincent.vatter

Office hours: Mondays and Wednesdays, 11:00 to 12:00 and Thursdays, 2:00 to 3:00

Homework

Homework will be assigned weekly and will be due Monday at the beginning of class. Late homework will NOT be accepted, except in extreme circumstances. You must individually write up your own solutions, but you are highly encouraged to work together in groups on the homework! Please note that this applies only to the homework; exams must be done independently.

In the table below, homework problems are listed in the format chapter.section.problem.

Homework 1
due Monday, June 29 1.1.3, 1.2.11, 1.2.12, 1.2.22, 1.3.7, 1.3.14

Homework 2
due Monday, July 6 1.4.9, 1.4.12, 1.4.27, 1.5.1, 1.5.7, 1.5.13

Homework 3
due Monday, July 13 1.6.8, 1.6.11, 1.7.2, 1.7.3, 1.7.22, 2.1.1, 2.1.17, 2.1.18, 2.3.1, 2.3.3, 2.3.12

Homework 4
due Monday, July 20 2.4.4, 2.4.5, 2.4.6, 2.4.7, 2.4.16, 2.4.33, 2.5.6, 2.5.14, 2.5.15, 2.5.17

Homework 5
due Monday, July 27 2.6.2, 2.6.6 (for those two, brief answers suffice), 2.6.11, 2.6.18, 2.7.4, 2.4.31, 2.7.6, 3.2.2, 3.2.9, 3.2.13

Homework 6
due Monday, August 3 3.2.22, 3.3.5, 3.3.8, 4.1.1, 4.1.18, 4.1.20, 4.2.1

Homework 7
due Monday, August 10 4.3.3, 4.3.25, 4.3.2, 4.3.4, 4.4.2, 4.4.8

Homework 8
due Monday, August 17 4.5.3, 4.5.13, 4.5.10 (a-c), 4.6.3, 4.6.5, 5.1.7

Homework 9
due Wednesday, August 26 5.2.3, 5.2.7, 5.2.13, 5.3.1, 5.3.13

Grades

The grades in this course will be calculated as follows:

Midterm 35%

Final Exam 35%

Homework and Quizzes
30%

The Honor Principle

On Exams: Exams are closed-book. No help is to be given or received. No calculators or computers are allowed.
On Homework: Collaboration is both permitted and encouraged, but you must indiviually write up your own solutions.

Disabilities

Students with learning, physical, or psychiatric disabilities enrolled in this course who may need disability-related accommodations are encouraged to meet with your instructor before the end of the second week of the term. All discussions will remain confidential, although the Student Accessibility Services office may be consulted.

Schedule of Lectures

The course meets MWF 1:45 to 2:50 in Kemeny 006.

The x-hour (Th 1:00 to 1:50) will be used occasionally and you will be informed in advance as to when it will be used.

Please note that the below is a very tentative schedule. I will update it as we cover lectures, so past lectures are listed with what was covered.

Lecture 1
Friday, June 26 Introduction, set theory
(Sections 1.1 and 1.2 in Herstein)

Lecture 2
Saturday, June 27
11:45 to 12:50 Mappings
(Section 1.3 in Herstein)

Lecture 3
Monday, June 29 A(S)
(Section 1.4 in Herstein)

Lecture 4
Wednesday, July 1 The Integers
(Section 1.5 in Herstein)

Friday, July 3 Class cancelled for Independence Day

Lecture 5
Monday, July 6 Induction, Complex Numbers
(Sections 1.6 and 1.7 in Herstein)

Lecture 6
Wednesday, July 8 Introduction to Groups
(Section 2.1 in Herstein)

Lecture 7
Friday, July 10 Subgroups
(Sections 2.2 and 2.3 in Herstein)

Lecture 8
Monday, July 13 Lagrange's Theorem
(Section 2.4 in Herstein)

Lecture 9
Wendesday, July 15 Lagrange's Theorem
(Section 2.4 in Herstein)
Quiz

Lecture 10
Thursday, July 16
x-hour, 1:00 to 1:50 Homomorphisms and Normal Subgroups
(Section 2.5 in Herstein)

Lecture 11
Friday, July 17 Homomorphisms and Normal Subgroups
(Section 2.5 in Herstein)

Lecture 12
Monday, July 20 Factor Groups
(Section 2.6 in Herstein)

Lecture 13
Wednesday, July 22 The Homomorphism Theorems
(Section 2.7 in Herstein)
Quiz on Section 2.5

Thursday, July 23
x-hour, 1:00 to 1:50 Optional: review of groups

Lecture 14
Friday, July 24 The Symmetric Group, Cycle Decomposition
(Sections 3.1 and 3.2 in Herstein)

Lecture 15
Monday, July 27 Even and Odd Permutations
(Section 3.3 in Herstein)

Lecture 16
Wednesday, July 29 Introduction to Rings
(Section 4.1 in Herstein)

Thursday, July 30
x-hour, 1:00 to 1:50 Optional: review for midterm

Thursday, July 30
5:00 to 7:00 pm Midterm

Lecture 17
Friday, July 31 More Introduction to Rings
(Section 4.1 in Herstein)

Lecture 18
Monday, August 3 Ideals, Homomorphisms, and Quotient Rings
(Section 4.3 in Herstein)

Lecture 19
Wednesday, August 5 Ideals, Homomorphisms, and Quotient Rings
(Section 4.3 in Herstein)

Lecture 20
Friday, August 7 Maximal Ideals
(Section 4.4 in Herstein)
Quiz on Section 4.3

Lecture 21
Monday, August 10 Polynomial Rings
(Section 4.5 in Herstein)

Lecture 22
Wednesday, August 12 Polynomial Rings
(Sections 4.5 and 4.6 in Herstein)

Lecture 23
Friday, August 14 Introduction to Fields
(Section 5.1 in Herstein)

Lecture 24
Monday, August 17 Fields and Vector Spaces
(Section 5.2 in Herstein)

Lecture 25
Wednesday, August 19 Field Extensions
(Section 5.3 in Herstein)

Friday, August 21 Class cancelled

Monday, August 24 Class cancelled

Lecture 26
Wednesday, August 26 Finite Extensions
(Sections 5.3 and 5.4 in Herstein)

Thursday, August 27
1:00 to 1:50 Optional: review for final

Sunday, August 30
11:30 to 2:30
Kemeny 007 Final Exam

Midterm	Thursday, July 30	Kemeny 006	5:00 pm to 7:00 pm
Final Exam	Sunday, August 30	Kemeny 007	11:30 am to 2:30 pm

Homework 1 due Monday, June 29	1.1.3, 1.2.11, 1.2.12, 1.2.22, 1.3.7, 1.3.14
Homework 2 due Monday, July 6	1.4.9, 1.4.12, 1.4.27, 1.5.1, 1.5.7, 1.5.13
Homework 3 due Monday, July 13	1.6.8, 1.6.11, 1.7.2, 1.7.3, 1.7.22, 2.1.1, 2.1.17, 2.1.18, 2.3.1, 2.3.3, 2.3.12
Homework 4 due Monday, July 20	2.4.4, 2.4.5, 2.4.6, 2.4.7, 2.4.16, 2.4.33, 2.5.6, 2.5.14, 2.5.15, 2.5.17
Homework 5 due Monday, July 27	2.6.2, 2.6.6 (for those two, brief answers suffice), 2.6.11, 2.6.18, 2.7.4, 2.4.31, 2.7.6, 3.2.2, 3.2.9, 3.2.13
Homework 6 due Monday, August 3	3.2.22, 3.3.5, 3.3.8, 4.1.1, 4.1.18, 4.1.20, 4.2.1
Homework 7 due Monday, August 10	4.3.3, 4.3.25, 4.3.2, 4.3.4, 4.4.2, 4.4.8
Homework 8 due Monday, August 17	4.5.3, 4.5.13, 4.5.10 (a-c), 4.6.3, 4.6.5, 5.1.7
Homework 9 due Wednesday, August 26	5.2.3, 5.2.7, 5.2.13, 5.3.1, 5.3.13

Lecture 1 Friday, June 26	Introduction, set theory (Sections 1.1 and 1.2 in Herstein)
Lecture 2 Saturday, June 27 11:45 to 12:50	Mappings (Section 1.3 in Herstein)

Lecture 3 Monday, June 29	A(S) (Section 1.4 in Herstein)
Lecture 4 Wednesday, July 1	The Integers (Section 1.5 in Herstein)
Friday, July 3	Class cancelled for Independence Day

Lecture 5 Monday, July 6	Induction, Complex Numbers (Sections 1.6 and 1.7 in Herstein)
Lecture 6 Wednesday, July 8	Introduction to Groups (Section 2.1 in Herstein)
Lecture 7 Friday, July 10	Subgroups (Sections 2.2 and 2.3 in Herstein)

Lecture 8 Monday, July 13	Lagrange's Theorem (Section 2.4 in Herstein)
Lecture 9 Wendesday, July 15	Lagrange's Theorem (Section 2.4 in Herstein) Quiz
Lecture 10 Thursday, July 16 x-hour, 1:00 to 1:50	Homomorphisms and Normal Subgroups (Section 2.5 in Herstein)
Lecture 11 Friday, July 17	Homomorphisms and Normal Subgroups (Section 2.5 in Herstein)

Lecture 12 Monday, July 20	Factor Groups (Section 2.6 in Herstein)
Lecture 13 Wednesday, July 22	The Homomorphism Theorems (Section 2.7 in Herstein) Quiz on Section 2.5
Thursday, July 23 x-hour, 1:00 to 1:50	Optional: review of groups
Lecture 14 Friday, July 24	The Symmetric Group, Cycle Decomposition (Sections 3.1 and 3.2 in Herstein)

Lecture 15 Monday, July 27	Even and Odd Permutations (Section 3.3 in Herstein)
Lecture 16 Wednesday, July 29	Introduction to Rings (Section 4.1 in Herstein)
Thursday, July 30 x-hour, 1:00 to 1:50	Optional: review for midterm
Thursday, July 30 5:00 to 7:00 pm	Midterm
Lecture 17 Friday, July 31	More Introduction to Rings (Section 4.1 in Herstein)

Lecture 18 Monday, August 3	Ideals, Homomorphisms, and Quotient Rings (Section 4.3 in Herstein)
Lecture 19 Wednesday, August 5	Ideals, Homomorphisms, and Quotient Rings (Section 4.3 in Herstein)
Lecture 20 Friday, August 7	Maximal Ideals (Section 4.4 in Herstein) Quiz on Section 4.3

Lecture 21 Monday, August 10	Polynomial Rings (Section 4.5 in Herstein)
Lecture 22 Wednesday, August 12	Polynomial Rings (Sections 4.5 and 4.6 in Herstein)
Lecture 23 Friday, August 14	Introduction to Fields (Section 5.1 in Herstein)

Lecture 24 Monday, August 17	Fields and Vector Spaces (Section 5.2 in Herstein)
Lecture 25 Wednesday, August 19	Field Extensions (Section 5.3 in Herstein)
Friday, August 21	Class cancelled

Monday, August 24	Class cancelled
Lecture 26 Wednesday, August 26	Finite Extensions (Sections 5.3 and 5.4 in Herstein)
Thursday, August 27 1:00 to 1:50	Optional: review for final
Sunday, August 30 11:30 to 2:30 Kemeny 007	Final Exam