Instructor: Pavel Guerzhoy

The class meets Tuesdays and Thursdays, 9:00 - 10:15am at 413, Keller Hall.


Office: 501, Keller Hall (5-th floor) e-mail: pavel(at)math(dot)hawaii(dot)edu (usually, I respond to e-mail messages within a day)
Office hours: Tuesdays and Thursdays 11:30-1:00 and 3:45-5:00pm


General Expectations
The Department of Mathematics has a general expectations statement, which we are assumed to follow in this class.
Reading
In this class we use the book
  • Thomas W. Hunderford, 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.

  • Dummit, David S.; Foote, Richard M., Abstract algebra , Third edition. John Wiley & Sons, Inc., Hoboken, NJ, 2004. xii+932 pp. ISBN: 0-471-43334-9. This is probably the best contemporary standard textbook in abstract algebra.
  • Lang, Serge, Algebra , Revised third edition. Graduate Texts in Mathematics, 211. Springer-Verlag, New York, 2002. xvi+914 pp. ISBN: 0-387-95385-X This is, in a sense, the best mathematics textbook ever. However, I would not recommend it as a textbook even for an advanced graduate class.
  • van der Waerden, B. L. Algebra. Vol.I,II. Translated from the fifth German edition by John R. Schulenberger. Springer-Verlag, New York, 1991. This is a rare example of a classic which survives many decades and does not become obsolete.

    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.
    Prerequisites
    A first course in linear algebra (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 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 cumulative (it covers all the material).
  • Four writing homework assignments count together for 40% of the final grade.
  • Three Quizzes. The average grade for the quizzes counts for 30% of the final grade.






    Contents and Homework assignments

    This table is approximate, and will be updated regularly.

    An example of how to read the table.

    Remarks on the homework.






    Date Sections Homework Assignment Writing Homework Assignement
    Tue, 22 Aug Ch. 1.1 A,6,7,8,9,10 on p8-9
    Thu, 24 Aug Ch. 1.2,1.3 A(p14-15 and p22-23), 16-27 on p16; 21,23,25,26,28,30 on p24
    Tue, 29 Aug Ch. 2.1,2.2 A(p30-31 and p36-37), 11,12,14,15,16,20 on p31; 14,15,16 on p37 A,B on p41-42
    Thu, 31 Aug Ch. 2.3 HW 1 assignment
    Tue, 5 Sep canceled
    Thu, 7 Sep quiz
    Tue, 12 Sep Ch 3.1 A(pp53-55),20-43 on pp55-58
    Thu, 14 Sep Ch. 3.2 A,B(pp66-70),44 on p70
    Tue, 19 Sep Ch. 3.3 A,B (pp80-83) redo HW 1 assignment
    Thu, 21 Sep problem session
    Tue, 26 Sep Ch 4.1 A,11,13,15,16,18,19,20
    Thu, 28 Sep Ch 4.2,4.3 A,B (pp99-100); 15-24 (pp103-104)
    Tue, 3 Oct problem session HW 2 assignment
    Thu, 5 Oct quiz on Chapter 3
    Tue, 10 Oct Ch 4.4 A, 12-19,23,24,27,28 on pp 109-112
    Thu, 12 Oct Ch 4.5 A,B (pp119-120)
    Tue, 17 Oct Ch 4.6/problem session A,B on pp123-123
    Thu, 19 Oct problem session on 4.4,4.5,4.6 redo HW 2 assignment
    Tue, 24 Oct Ch 5.1, 5.2 A,8-13 on p129, A,5-14 on p134
    Thu, 26 Oct Ch 5.3/problem session
    Tue, 31 Oct problem session HW 3 assignment
    Thu, 2 Nov Ch 6.1 A(1-3,6-13,15-23),B(24-31,37,40-43) pp 148-152
    Tue, 7 Nov Ch 6.2, 6.3 A(1-8,10,11) on pp 159-161, A(1-9),B(10-12,15,20) on pp 166-167
    Thu, 9 Nov problem session
    Tue, 14 Nov quiz redo HW 3 assignment
    Thu, 16 Nov 10.1 A,B on pp 330-331
    Tue, 21 Nov 10.2 A, B(1-21)
    Tue 28 Nov 10.3 HW 4 assignment
    Thu 30 Nov 10.4
    Tue 5 Nov 10.5
    Thu 7 Nov problem session/review for the final exam