Math 413(W), Introduction to Abstract Algebra




Instructor: Pavel Guerzhoy

The class meets Tuesdays and Thursdays, 12:00 - 1:15pm at 413, Keller Hall.


Office: 501, Keller Hall (5-th floor)
tel: (808)-956-6533
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 and 4:30-5:30pm


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 , second edition, Books/Cole
    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.
  • Five (?) writing homework assignments count together for 40% of the final grade.
  • Midterm exam covers the material of chapters 7 and 8. 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, 14 Jan Ch. 7.1 A,12,14-19,21-23,25,26,27,29-32 on p171-173
    Thu, 16 Jan Ch. 7.2 A,20,21-26,28-32 on p178-180
    Tue, 21 Jan Ch. 7.3 A,22,23-29,31,32-36,40,41,42,43,44,46,48,49 on p187-191
    Thu, 23 Jan problem session
    Tue, 28 Jan Ch. 7.4 A,16-19,21-30,32,35,37,38,41,42 on p196-199
    Thu, 30 Jan Ch. 7.5 A,11-13,15,17-19,21,25 on p206-208
    Tue, 4 Feb Ch 7.6 A,15-26,29,32 p213-216 assignment 1
    Thu, 6 Feb Ch. 7.7 A,12-17,20,23,26 on p220-221
    Tue, 11 Feb Ch. 7.8 A,8-11,15,16,19,20,22 on p226-229
    Thu, 13 Feb Ch. 7.9 A,9,10,14,16 on p236-237
    Tue, 18 Feb problem session redo assignment 1
    Thu, 20 Feb Ch. 8.1 A,10,12-14,17,18,22,27-30 on p248-251
    Tue, 25 Feb Ch. 8.2 A,7-16 on p260-261 assignment 2
    Thu, 27 Feb Ch. 8.3 A,8,9,11,13,16-22 on p265-266
    Tue, 4 Mar Ch. 8.4 A,9,12,15,18,19 on p273-275
    Thu, 6 Mar Ch. 8.5 A,7,10,11,12 on p281-282
    Tue, 11 Mar recall: Ch. 5.1-5.3
    Thu, 13 Mar Ch. 10.1 A,21,22,24-28,31,35 on p337-340 redo assignment 2
    Tue, 18 Mar Ch. 10.2 A,15-18,20-23 on p345-346
    Thu, 20 Mar problem session ... review for midterm assignment 3
    Tue, 1 Apr midterm
    Thu 3 Apr Ch. 10.3 A,10-16 on p350-352
    Tue, 8 Apr problem session
    Thu, 10 Apr Ch. 10.4 A,10-17 on p357-358
    Tue, 15 Apr Ch. 10.5 A,4,5,8,9,12,13,15 on p362-363
    Thu, 17 Apr Ch. 10.6 A,8-14,18-22 on p368-370 redo assignment 3
    Tue, 22 Apr problem session
    Thu, 24 Apr Ch. 11.1 A,7-15 on p377-378
    Tue, 29 Apr Ch. 11.2 A,7-12 on p385-386
    Thu, 1 May Ch. 11.3 A on p395-398
    Tue, 6 May problem session/review for the final exam assignment 4
    Tue, 13 May FINAL EXAM redo assignment 4