Math 499 CRN 82705 (imitating 413W), Introduction to Abstract Algebra II
Instructor: Pavel Guerzhoy
The class is asynchronous online.
e-mail: pavel(at)math(dot)hawaii(dot)edu (usually, I respond to e-mail messages within a day)
Office hours: by appointment; please send me an e-mail to schedule a meeting.
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. Hungerford, 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.
Aluffi, Paolo Algebra: Chapter 0 Graduate Studies in Mathematics, Vol. 104, American Mathematical Society, Providence, RI, 2009. This is a relatively recent textbook which promotes a highly conceptual approach to algebra. I absolutely recommend this textbook to anyone who intends to continue studies in mure math.
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.
A grade of B or better in the Math412 Introduction to Abstract Algebra or consent.
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 final exam will be a "take home" exam (you may choose to call it "final paper"). The assignment will be posted approximately a week before the end of the semester. There will be no make-ups for the final.
It will be possible to make up these assignments. Moreover, it is recommended to redo them until a certain level of quality is achieved.
Specifically, for every assignment, two attempts will be given, and the score comes out as a maximum of the two.
Midterm exam covers the material of chapters 7,8 and 9. It counts for 30% of the final grade.
The midterm will be posted online as a pdf-file; the due date to submit the midterm will be announced.
Contents and regular Homework assignments
This table will be updated regularly. Please check it often!.
Remarks on the non-graded homework exercises
All group A exercises are very simple and straightforward, although sometimes tedious. They check basic understanding of the material. Students must always make sure that they are able to easily do these exercises.
In most cases, a non-graded homework assignment essentially consists of group B exercises. Some of these exercises require a certain amount of creativity. Doing these exercises is a way to really learn the material. It is expected that a student succeeds with a majority of these exercises. Some of them will be considered in detail in "problem sessions" lectures.
Homework Exercises -- never collected/graded
Writing Homework Assignment
Sections 7.1 and 7.2
A,16-21,23-31 on p180-183 A,22-25,27-32 on p201-202