Final Exam

Math 412(W), Introduction to Abstract Algebra

Instructor: Pavel Guerzhoy

The class meets Tuesdays and Thursdays, 1:30 - 2:45pm at 404, 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 3:00-4:00pm
Tutoring office hours Wednesday 1:30-2:30 pm, and Thursday 9-10am by Quinn Culver at PS 320

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. 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 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).

The final exam will be a "take home" exam (you may choose to call it "final paper"). The assignment will be distributed approximately a week before the end of the semester. There will be no make-ups for the final.

Five writing homework assignments count together for 40% of the final grade.

It will be possible to make up these assignments. Moreover, it is recommended to redo them until a certain level of quality is achieved.

Three Quizzes. The average grade for the quizzes counts for 30% of the final grade.

Every quiz consists of problems similar (maybe even identical) to those from the regular homework and/or the ones discussed in class. For this reason, it is highly recommended to solve homework problems, and to attend the classes, where many of these problems will be discussed. The precise date of every quiz will be announced in class approximately one week in advance. In general, there will be no make-ups for the quizzes. A make-up quiz will only be given in very unusual circumstances, with one week prior notification (or in the event of an emergency, "very" strong documentation of that emergency). Not attending class, and hence not being present when a quiz is announced or administered is not an acceptable excuse.

Contents and regular Homework assignments

This table is approximate, and will be updated regularly.

An example of how to read the table.

Thursday, 4 Sep is the due date for the writing assignment, and you have to submit your solutions of exercises 24,25 p19.
On Thursday, 4 Sep we covered Chapter 2.1 and 2.2 in class.
For Tuesday, 9 San your assignment is to do exercises 19-32 on p30; 8,9,10 on p36.

Remark on the homework. All part A exercises from 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, 26 Aug	Ch. 1.1,1,2,1.3	4,5,6,7,8,9 on p6
Thu, 28 Aug	Ch. 1.1,1,2,1.3	7,10 on p12; 12-23 on p18
Tue, 2 Sep	problem session
Thu, 4 Sep	Ch. 2.1,2.2	19-32 on p30; 8,9,10 on p36	24,25 p19
Tue, 9 Sep	Ch. 2.3	6,7,8 on p40
Thu, 11 Sep	quiz
Tue, 16 Sep	Ch 3.1	1-35 on p54
Thu, 18 Sep	Ch. 3.2	18-34,36 on p64
Tue, 23 Sep	problem session
Thu, 25 Sep	Ch. 3.3	18-37 on p77	37,38 on p 66
Tue, 30 Sep	problem session
Thu, 2 Oct	quiz
Tue, 7 Oct	Ch 4.1	10-18,20,21 on p89
Thu, 9 Oct	Ch 4.2	7-16 on p94
Tue, 14 Oct	Ch 4.3	16-26 on p99
Thu, 16 Oct	problem session
Tue, 21 Oct	Ch 4.4	12-28 on p105
Thu, 23 Oct	Ch 4.5,4.6	11-21 on p114,5-8 on p118
Tue, 28 Oct	problem session
Thu, 30 Oct	Ch 5.1,5.2	8-13 on p123,5-14 on p128
Thu, 6 Nov	Ch 5.3/problem session	2-12 on p 132	29,30,31 on p107
Thu 13 Nov	Ch 6.1	22-43 on p143
Tue, 18 Nov	Ch 6.2, 6.3	10-31 on p151; 10-19 on p158
Thu, 20 Nov	problem session		44,45 on p145
Tue, 25 Nov	quiz
Tue, 2 Dec	9.1,9.2	18-28 on p294; 9-12 on p305
Thu, 4 Dec	9.3,9.5	6-21 on p316; 5-12 on p328	20,21,22,23,24 on p 159
Tue, 9 Dec	problem session/review for the final exam