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

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. 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.

Course Objective

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) and, most importantly, Intro to advanced math (Math 321) 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 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 posted approximately a week before the end of the semester. There will be no make-ups for the final.

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

The quizzes are take-home; they will be posted online as pdf-files and the due dates to submit the quizzes will be announced.

Four 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 so that 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.

Click here for a very short set of hints on (La)Tex which will help you to type the assignments.