Math 413(W), Introduction to Abstract Algebra




Instructor: Pavel Guerzhoy

The class meets Tuesdays and Thursdays, 12:00 - 1:15pm at 314, 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 1:30-2:30


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
    is twofold. 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.
    Prerequisites
    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 format of the exam will be quite similar to that of the midterm.
  • 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 is approximate, and will be updated regularly.



    Remarks on the homework.






    Date Sections Homework Assignment Writing Homework Assignment
    Tue, 9 Jan Ch. 7.1A A,16-21,23-31 on p180-183
    Thu, 11 Jan Ch. 7.2 A,22-25,27-32
    Tue, 16 Jan Ch. 7.3 A,B
    Thu, 18 Jan Ch. 7.4 A,24-46,48-53,55,58,60,61
    Tue, 23 Jan Ch. 7.5 A,18-24
    Thu, 25 Jan problem session
    Tue, 30 Jan Ch 8.1 A,23-31,34-37
    Thu, 1 Feb Ch. 8.2 A,16-23,26-27,30,32 HW 1 assignment
    Tue, 6 Feb Ch. 8.3 A,15-17,19-29,31,34
    Thu, 8 Feb Ch. 8.4,85 A,22-27,30-33
    Tue, 13 Feb problem session
    Thu 15 Feb Ch. 9.1 A, 10,11,13,16,17,18,21,22,24 HW 1 REDO assignment
    Tue 20 Feb Ch. 9.2 A
    Thu 22 Feb Ch. 9.2 7,8,9,10,11,12,13,14,15,16,17,18,19,20 HW 2 assignment
    Tue 27 Feb Ch. 9.3 A,8,9,11,13,14,16,17
    Thu 1 Mar Ch. 9.4
    Tue 6 Mar problem session
    Thu 8 Mar problem session ... review for midterm
    Tue 13 Mar midterm
    Thu 15 Mar recall: Ch. 5.1-5.3 HW 3 assignment (Mar 18)
    Tue Mar 20 Ch. 11.1 A,B(all of them)
    Thu Mar 22 Ch. 11.2 A,B(all of them)
    Tue Apr 3 Ch. 11.3 A,10-16
    Thu Apr 5 Ch. 11.4 A,B(all of them)
    Tue Apr 10 problem session
    Thu Apr 12 Ch. 11.5
    Tue Apr 17 Ch. 11.6
    Thu Apr 19 problem session
    Tue Apr 24 Ch. 12.1
    Thu Apr 26 Ch. 12.2
    Tue May 1 Ch. 12.3