MATH W4042 Introduction to Modern Algebra II
Spring 2013

Time and place: MW 2:40-3:55, location TBA.
Instructor: Robert Friedman (x4-4355). Office: 605 Mathematics.
Office hours: My office hours are Mondays, 8:30--9:30 AM and Tuesdays and Thursdays, 2--3 PM in 605 Math, but feel free to drop by at any time.
Email: rf@math.columbia.edu
Teaching Assistants: Joao Guerreiro guerreiro@math.columbia.edu and Josh Tobin jpt2118@columbia.edu. Office hours: Joao Mondays 10--1; Josh Tuesdays 10--12

This is the second semester of a two-semester sequence on Abstract Algebra. This semester will concentrate on rings, fields, polynomials, and Galois theory. Modern Algebra I (Math W4041) or the equivalent is a prerequisite for this course.

Text: There is no required text. Problem sets and occasional class notes will be posted.

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
D. Dummit and R. Foote, Abstract Algebra, (Third edition), John Wiley and Sons, 2004. ISBN-13: 978-0471433347
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
Thomas Hungerford, Abstract Algebra: An Introduction (Second Edition), Brooks Cole 1996. ISBN-13: 978-0030105593
I. Herstein, Abstract Algebra, John Wiley 1996. ISBN-13: 978-0471368793
S. Lang, Undergraduate Algebra (Third Edition), Springer 2005. ISBN: 0-387220259

Of these, the book by Fraleigh is the most elementary, the book by Artin is at an intermediate level, and the book by Dummit and Foote is the most advanced. The material we will cover corresponds to the following: Fraleigh, Chapters IV, V, VI, IX, X. Artin, Chapters 11, 12, 15, 16. Dummit and Foote, Chapters 7, 8, 9, 13 and 14. If you are reading one of these books, I will be happy to provide more guidance as to what to read on a week-by-week basis.


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 28. 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 Mondays, 8:30--9:30 AM and Tuesdays 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 23: First day of class
February 20: Midterm exam 1
February 26: Drop date (most schools)
March 18--24: Spring break
April 3: Midterm exam 2
May 6: Last day of class
May 15: Final exam (tentative)

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