MATH W4042
Introduction to Modern Algebra II
Spring 2012

Time and place: MW 2:40-3:55, in 417 Mathematics.
Instructor: Robert Friedman (x4-4355). Office: 605 Mathematics.
Office hours: My office hours are (tentatively) Mondays, 10--11 AM and Thursdays, 2--3 PM in 605 Math, but feel free to drop by at any time.
Email: rf@math.columbia.edu
Teaching Assistants: Ioan Filip ioanf@math.columbia.edu, office hours: Tuesdays 11--12 and Fridays 2--4 in the Help Room and Josh Tobin jpt2118@columbia.edu , office hours: Mondays and Wednesdays, 12--1 in the Help Room.

This is the second semester of a two-semester sequence on Abstract Algebra. This semester will concentrate on rings, fields, polynomials, and Galois theory. We plan to cover roughly the material of chapters 7, 8, 9, 13 and 14 of the textbook (Dummit and Foote, 3rd edition). Modern Algebra I (Math W4041) or the equivalent is a prerequisite for this course.

Text: Dummit and Foote, Abstract Algebra, third edition, John Wiley and Sons, 2004. ISBN-13: 978-0471433347. Available at the University bookstore.

Other recommended texts. There are very many texts in Abstract Algebra; browsing the library is recommended for further examples, history, or different treatment of the material. Here is a selection of some recommended ones.


Michael Artin, Algebra (Second Edition), Prentice-Hall 2011. ISBN-13: 978-01324137-0
John Fraleigh, A First Course in Abstract Algebra (Seventh Edition), Addison Wesley 2002. ISBN-13: 978-0201763904
Joseph Gallian, Contemporary Abstract Algebra (Seventh Edition), Houghton-Mifflin 2009. ISBN-13: 978-0547165097
I. Herstein, Abstract Algebra, John Wiley 1996. ISBN-13: 978-0471368793
Thomas Hungerford, Abstract Algebra: An Introduction (Second Edition), Brooks Cole 1996. ISBN-13: 978-0030105593
S. Lang, Undergraduate Algebra (Third Edition), Springer 2005. ISBN: 0-387220259

Homework: There will be weekly problem sets, due at the beginning of class on Mondays. The first problem set will be due on Monday, January 23. You should attempt every homework problem and eventually understand how to do every problem correctly. Collaboration and discussion with your classmates is encouraged, but you must write up assignments individually.

Exams: There will be two 75-minute midterm exams and a final.

If you have two final examinations scheduled at the same time, it is the responsibility of the other department to provide an alternate exam. Examinations will not be rescheduled because of travel arrangements -- it is your responsibility to schedule travel appropriately. Makeup midterms will be given only under exceptional circumstances and you will need a note from a doctor or a dean.

Grading: The final course grade will be determined by:

Homework: 20%;
Midterm exams: 20% each;
Final exam: 40%.

Help: My office hours are (tentatively) Mondays, 10--11 AM and Thursdays, 2--3 PM, and you should always feel free to make an appointment or just drop by. Help is also available without appointment in the Mathematics Help Room (406 Mathematics) whenever it is open.

Academic Dishonesty: The vast majority of students do not cheat. Anyone who does so devalues the hard work of the rest of the class and creates a bad atmosphere for all. Anyone found to have cheated on an exam will receive a failing grade for the course and be subject to administrative discipline. If you are struggling with the material or have a problem about an upcoming exam, please discuss it with me instead of resorting to cheating.

Important dates:

January 18: First day of class
February 15: Midterm exam 1
February 21: Drop date (most schools)
March 10--18: Spring Break
March 28: Midterm exam 2
April 30: Last day of class
May 9: Final exam (tentative)

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