Final Exam

due noon Thursday, Dec. 19

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

Instructor: Pavel Guerzhoy

The class meets Tuesdays and Thursdays, 10:30 - 11:45am 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 12:00-1:00 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.
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. 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) 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).
  • Five 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. Remark on the homework. All part A exercises are very simple. Students must always make sure that they are able to easily do these exercises.

    Date Sections Homework Assignment Writing Homework Assignement
    Tue, 27 Aug Ch. 1.1,1,2,1.3 4,5,6,7,8,9 on p6
    Thu, 29 Aug Ch. 1.1,1,2,1.3 7,10 on p12; 12-23 on p18
    Tue, 3 Sep problem session
    Thu, 5 Sep Ch. 2.1,2.2 19-32 on p30; 8,9,10 on p36
    Tue, 10 Sep Ch. 2.3 6,7,8 on p40 assignment
    Thu, 12 Sep quiz
    Tue, 17 Sep Ch 3.1 1-35 on p54
    Thu, 19 Sep Ch. 3.2 18-34,36 on p64
    Tue, 24 Sep problem session
    Thu, 26 Sep Ch. 3.3 18-37 on p77
    Tue, 1 Oct problem session
    Thu, 3 Oct Ch 4.1 10-18,20,21 on p89 assignment
    Tue, 8 Oct Ch 4.2 7-16 on p94
    Thu, 10 Oct Ch 4.3 16-26 on p99
    Thu, 15 Oct quiz
    Thu, 17 Oct problem session
    Tue, 22 Oct Ch 4.4 12-28 on p105
    Thu, 24 Oct Ch 4.5,4.6 11-21 on p114,5-8 on p118 assignment
    Tue, 29 Oct problem session
    Thu, 31 Oct Ch 5.1,5.2 8-13 on p123,5-14 on p128
    Thu, 7 Nov Ch 5.3/problem session 2-12 on p 132
    Thu 14 Nov Ch 6.1 22-43 on p143 redo HW 3 assignment
    Tue, 19 Nov Ch 6.2, 6.3 10-31 on p151; 10-19 on p158
    Thu, 21 Nov problem session
    Tue, 26 Nov quiz
    Tue, 3 Dec 9.1,9.2 18-28 on p294; 9-12 on p305 assignment
    Thu, 5 Dec 9.3,9.5 6-21 on p316; 5-12 on p328
    Tue, 10 Dec problem session/review for the final exam