Math 31, Topics in Algebra (Summer 2009)

## General Information

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)

• 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 1due Monday, June 29 1.1.3, 1.2.11, 1.2.12, 1.2.22, 1.3.7, 1.3.14 Homework 2due Monday, July 6 1.4.9, 1.4.12, 1.4.27, 1.5.1, 1.5.7, 1.5.13 Homework 3due 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 4due 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 5due 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 6due 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 7due Monday, August 10 4.3.3, 4.3.25, 4.3.2, 4.3.4, 4.4.2, 4.4.8 Homework 8due Monday, August 17 4.5.3, 4.5.13, 4.5.10 (a-c), 4.6.3, 4.6.5, 5.1.7 Homework 9due Wednesday, August 26 5.2.3, 5.2.7, 5.2.13, 5.3.1, 5.3.13

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 1Friday, June 26 Introduction, set theory (Sections 1.1 and 1.2 in Herstein) Lecture 2Saturday, June 2711:45 to 12:50 Mappings (Section 1.3 in Herstein)

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

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

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

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

 Lecture 15Monday, July 27 Even and Odd Permutations (Section 3.3 in Herstein) Lecture 16Wednesday, July 29 Introduction to Rings (Section 4.1 in Herstein) Thursday, July 30x-hour, 1:00 to 1:50 Optional: review for midterm Thursday, July 305:00 to 7:00 pm Midterm Lecture 17Friday, July 31 More Introduction to Rings (Section 4.1 in Herstein)

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

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

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

 Monday, August 24 Class cancelled Lecture 26Wednesday, 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