Math 499 CRN 82705 (imitating 413W), Introduction to Abstract Algebra II

Instructor: Pavel Guerzhoy

The class is asynchronous online.

e-mail: pavel(at)math(dot)hawaii(dot)edu (usually, I respond to e-mail messages within a day)
Office hours: by appointment; please send me an e-mail to schedule a meeting.

General Expectations
The Department of Mathematics has a general expectations statement, which we are assumed to follow in this class.


In this class we use the book

Thomas W. Hungerford, Abstract Algebra, An Introduction, third edition

Brooks/Cole Cengage Learning

The book is really unavoidable, and cannot be replaced with another textbook!

There are, however, many abstract algebra textbooks which may be useful. The books listed below may be difficult to read. However, they contain a huge amount of interesting material, and are useful for those who want to continue further with algebra.

Course Objective

The first and foremost objective is to learn the basic ideas and notions of abstract algebra.

The class is designated as writing-intensive. As a consequence, mathematical writing, and particularly, the writing of clear and correct proofs is a subject of emphasis.

A grade of B or better in the Math412 Introduction to Abstract Algebra or consent.

Grading Policy
The course contains a combination of concepts, ideas and techniques which the students must be able to apply in solving specific problems. Most of these problems require proving or disproving a certain statements. Since this is a writing-intensive class, we simultaneously learn how to write mathematical texts.

At the end of the day, your grade will reflect your ability to solve specific problems. This assumes your ability to read and understand the textbook. To understand, in this context, means to be able to create arguments which are similar to those provided in the text. To create an argument, in this context, means to be able to write it down properly. More specifically, the following rules are to be taken.

  • Final exam will count for 30% of the final grade. The exam is cummulative (i.e. it includes questions related to ALL material covered during the semester). The final exam will be a "take home" exam (you may choose to call it "final paper"). The assignment will be posted approximately a week before the end of the semester. There will be no make-ups for the final.
  • Four writing homework assignments count together for 40% of the final grade.
  • Midterm exam covers the material of chapters 7,8 and 9. It counts for 30% of the final grade.

  • Contents and regular Homework assignments

    This table will be updated regularly. Please check it often!.

    Remarks on the non-graded homework exercises

    Week of Sections Lectures Lecture Notes Homework Exercises -- never collected/graded Writing Homework Assignment
    Jan 10 Sections 7.1 and 7.2
    A,16-21,23-31 on p180-183
    A,22-25,27-32 on p201-202
    chapter 7.1A_v-1 chapter 7.1_v-1
    chapter 7.1A_v-2 chapter 7.1_v-2
    chapter 7.2_v-1 chapter 7.2_v-1
    chapter 7.2_v-2 chapter 7.2_v-2
    Jan 17 Section 7.3
    A,B on p211-213
    chapter 7.3_v-1 chapter 7.3_v-1
    chapter 7.3_v-2 chapter 7.3_v-2
    chapter 7.3_v-3 chapter 7.3_v-3
    Jan 24 Sections 7.4 and 7.5
    A,24-46,48-53,55,58,60,61 on p223-227

    A, 18-24 on p234-235
    chapter 7.4_v-1 chapter 7.4_v-1
    chapter 7.4_v-2 chapter 7.4_v-2
    chapter 7.5_v-1 chapter 7.5_v-1
    chapter 7.5_v-2 chapter 7.5_v-2
    Jan 31 Chapter 8
    A,23-31,34-37 on p245-247
    HW 1 assignment (due Jan 31)
    chapter 8.1_v-1 chapter 8.1_v-1
    chapter 8.1_v-2 chapter 8.1_v-2
    chapters 8.2-8.4_v-1 chapters 8.2-8.4_v-1
    chapters 8.2-8.4_v-2 chapters 8.2-8.4_v-4
    Feb 7 Chapter 8
    A,16-23,26-27,30,32 on p 252-255
    A,15-17,19-29,31,34 on p260-262
    A,22-27,30-33 on p270-273
    redo HW 1 assignment (due Feb 7)
    chapters 8.2-8.4_v-3 chapters 8.2-8.4_v-3
    chapters 8.2-8.4_v-4 chapters 8.2-8.4_v-3
    chapters 8.2-8.4_v-5 chapters 8.2-8.4_v-3
    chapters 8.4_v-1 chapter 8.4_v-1
    Feb 14 Sections 9.1-9.3
    10,11,13,16,17,18,21,22,24 on p255-287
    7,8,9,10,11,12,13,14,15,16,17,18,19,20 on p297-298

    A,8,9,11,13,14,16,17 on p302-303
    chapter 9.1_v-1 chapter 9.1_v-1
    chapter 9.2_v-1 chapter 9.2_v-1
    chapter 9.2_v-2 chapter 9.2_v-2
    chapter 9.3_v-1 chapter 9.3_v-1
    Feb 21 Section 9.4 HW 2 assignment (due Feb 21)
    chapter 9.4_v-1 chapter 9.4_v-1
    chapter 9.4_v-2 chapter 9.4_v-2
    chapter 9.4_v-3 chapter 9.4_v-3
    chapter 9.4_v-4 chapter 9.4_v-4
    Feb 28 Reviews -- problem sessions
    section 7.1 section 7.1_v-1
    section 7.2 section 7.2_v-1
    section 7.3-7.4 sections 7.3-7.4_v-1
    section 8.1 section 8.1_v-1
    section 8.2 section 8.2_v-1
    Mar 7 Sections 11.1-11.2
    A,B(all of them) on p374-376
    redo HW 2 assignment (due Mar 7)
    HW 3 assignment (due Mar 17)
    chapter 11.1_v-1 chapter 11.1_v-1
    chapter 11.2_v-1 chapter 11.2_v-1
    Mar 21 Section 11.2 A,B(all of them) on p381-382
    chapter 11.2_v-2 chapter 11.2_v-2
    chapter 11.2_v-3 chapter 11.2_v-3
    midterm the midterm is due Monday March 28
    Mar 28 Sections 11.3 and 11.4 A,10-16 on p 387

    A,B(all of them) on p393-394
    chapter 11.3_v-1 chapter 11.3_v-1
    chapter 11.4_v-1 chapter 11.4_v-1
    chapter 11.4_v-2 chapter 11.4_v-2
    Apr 4 Sections 11.5 and 11.6
    A,B (all of them) on p397-398
    A,B (all of them) on p404-406
    redo HW 3 assignment (due Apr 5)
    chapter 11.5_v-1 chapter 11.5_v-1
    chapter 11.5_v-2 chapter 11.5_v-2
    chapter 11.6_v-1 chapter 11.6_v-1
    Apr 11 Sections 12.1, 12.2 A,B(all of them) on p413-414
    chapter 12.1_v-1 chapter 12.1_v-1
    chapter 12.2_v-1 chapter 12.2_v-1
    Apr 18 Section 12.2 HW 4 assignment (due Apr 19)
    chapter 12.2_v-2 chapter 12.2_v-2
    chapter 12.2_v-3 chapter 12.2_v-3
    chapter 12.2_v-4 chapter 12.2_v-4
    Apr 25 Section 12.2
    chapter 12.2_v-5 chapter 12.2_v-5
    chapter 12.2_v-6 chapter 12.2_v-6
    May 3 redo HW 4 assignment (due May 3)
    final the final is due Monday May 9