Math 412(W)-1, Introduction to Abstract Algebra

Instructor: Pavel Guerzhoy

Due to the unexpected rise in COVID-19 cases, I have asked and been approved to change this course to a hybrid format. We will start out online. My hope is that at a later point in the semester, we will be able to come together safely in-person. Meeting in-person is not a guarantee, but the hybrid format allows us the greatest flexibility in these challenging and uncertain times.

e-mail: pavel(at)math(dot)hawaii(dot)edu (usually, I respond to e-mail messages within a day)
Office hours: at this zoom meeting room Please send me an e-mail to schedule a meeting.
Meeting ID: 347 745 6800

A general introduction to this class

A detailed instruction on the homework assignments

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. This course is a prerequisite for the consequent introduction to abstract algebra course (413). It is among the objectives to build a solid basis for this course.

A first course in linear algebra (Math 311) and, most importantly, Intro to advanced math (Math 321) 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 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 cumulative (it covers all the material).
  • Three Quizzes. The average grade for the quizzes counts for 30% of the final grade.
  • Four writing homework assignments count together for 40% of the final grade.

  • Contents and 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 Assignement
    Aug, 23 Chapter 1
    A,6,7,8,9,10 on p8-9
    A,16-27 on p16
    A, 21,23,25,26,30 on p24
    chapter 1_v-1 chapter 1_v-1
    chapter 1_v-2 chapter 1_v-2
    chapter 1_v-3 chapter 1_v-3
    chapter 1_v-4 chapter 1_v-4
    chapter 1_v-5 chapter 1_v-5
    chapter 1_v-6 chapter 1_v-6
    third-party video
    Aug 30 Chapter 2
    A(p30-31), 11,12,14,15,16,20 on p31
    A(p36-37), 14,15,16 on p37
    A,B on p41-42
    chapter 2_v-1 chapter 2_v-1
    chapter 2_v-2 chapter 2_v-2
    chapter 2_v-3 chapter 2_v-3
    chapter 2_v-4 chapter 2_v-4
    chapter 2_v-5 chapter 2_v-5
    chapter 2_v-6 chapter 2_v-6
    chapter 2_v-7 chapter 2_v-7
    problem session
    part 1 25,16,26 on p 16; 16 on p31
    part 2 17,18,27,19,21 on p16
    Sep 6 Section 3.1
    A(pp53-55),20-29,35,36,39,43 on pp55-58
    chapter 3.1_v-1 chapter 3.1_v-1
    chapter 3.1_v-2 chapter 3.1_v-2
    Sep 13 Section 3.2
    chapter 3.2_v-1 chapter 3.2_v-1
    chapter 3.2_v-2 chapter 3.2_v-2
    chapter 3.2_v-3 chapter 3.2_v-3
    chapter 3.2_v-4 chapter 3.2_v-4
    Sep 20 Section 3.3
    A,16-23,30,35,38 (pp80-82)
    chapter 3.3_v-1 chapter 3.3_v-1
    problem session
    part 1 26 p56, hints for 20,21,22,23 pp81-82
    part 2 14,25 p66; 25 p68
    part 3 21,17 p68; 38 p70
    Sep 27 Sections 4.1 and 4.2
    A,11,12,13,15,16,18,20 (ppn93-95)
    A,7,8,9 (pp99-100)
    chapter 4.1_v-1 chapter 4.1_v-1
    chapter 4.1_v-2 chapter 4.1_v-2
    chapter 4.1_v-3 chapter 4.1_v-3
    chapter 4.1_v-4 chapter 4.1_v-4
    chapter 4.2_v-1 chapter 4.2_v-1
    Oct 4 Sections 4.3 and 4.4
    15,16,20,21,22,23 (pp103-104)
    A, 12,13,15,16,17,18,23,24,27,28 on pp 109-112
    chapter 4.3_v-1 chapter 4.3_v-1
    chapter 4.4_v-1 chapter 4.4_v-1
    chapter 4.4_v-2 chapter 4.4_v-2
    Oct 11 Sections 4.5 and 4.6
    A on p119
    A on p 123
    chapter 4.5_v-1 chapter 4.5_v-1
    chapter 4.6_v-1 chapter 4.6_v-1
    problem session
    part 1 15,16,18 p 95; 21 p 104; 23, 24 p 111
    part 2 9,14 p 100; 15, 22a p 104; 15,17 p 111
    Oct 18 Sections 5.1 and 5.2 A,8-13 on p129; A,5-11 on p134
    chapter 5.1_v-1 chapter 5.1_v-1
    chapter 5.2_v-1 chapter 5.2_v-1
    Oct 25 Section 5.3 A,2-12 on pp 138-139
    chapter 5.3_v-1 chapter 5.3_v-1
    problem session
    part 1 12,13 p 129
    part 2 6,11 p 134
    part 3 9,14 p 100; 15, 22a p 104; 15,17 p 111
    Nov 1 Section 6.1 A(1-3,6,8-13,15-23),B(24-32,36,37,38,40-43) pp 148-152
    chapter 6.1_v-1 chapter 6.1_v-1
    Nov 8 Section 6.2 A(1-8,10,11,12,16,17,18) on pp 159-161
    chapter 6.2_v-1 chapter 6.2_v-1
    chapter 6.2_v-2 chapter 6.2_v-2
    Nov 15 Section 6.3 A(1-9),B(10-12,15,17,19,20) on pp 166-167
    chapter 6.3_v-1 chapter 6.3_v-1
    chapter 6.3_v-2 chapter 6.3_v-2
    problem session
    part 1 22 p 149
    part 2 6 p 159, 8,12 p 160
    part 3 9,11 p 166, 20 p 167
    Nov 22 Section 10.1
    A,B on pp 330-331
    chapter 10.1_v-1 chapter 10.1_v-1
    chapter 10.1_v-2 chapter 10.1_v-2
    Nov 29
    A, B(1-21) p 341-343
    chapter 10.2_v-1 chapter 10.2_v-1
    chapter 10.2_v-2 chapter 10.2_v-2
    Dec 6
    chapter 10.3_v-1 chapter 10.3_v-1
    chapter 10.3_v-2 chapter 10.3_v-2
    final exam the final exam is due Thursday Dec 16 at noon