MATH GU4042 Introduction to Modern Algebra II
Fall 2016
Time and place: MW 2:40-3:55, location 417 Mathematics.
Instructor: Robert Friedman (x4-4355). Office: 605 Mathematics.
Office hours: My office hours are Mondays, 10--11 AM and Thursdays, 2:30--3:30 PM in 605 Math, but feel free to drop by at any time.
Email: rf@math.columbia.edu
Teaching Assistant: Samuel Mundy srm2185@columbia.edu. Office hours: Mondays, 10 AM--1 PM 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. 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 (Ninth Edition), Cengage Learning 2016. ISBN-13: 978-1305657960
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
T. Judson, Abstract Algebra: Theory and Applications. There is a free online edition available here, with instructions on how to purchase a hard copy.
S. Lang, Undergraduate Algebra (Third Edition), Springer 2005. ISBN: 0-387220259
Of these, the books by Fraleigh, Gallian, and Judson are 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, September 12. 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. Homework will be collected in class on the date that it is due. Late homework can be dropped off in the box outside 417 Mathematics until 5 PM on the due date. After that, you will need to request permission for an extension. Graded homework can be picked up in the appropriately marked box outside 605 Mathematics.
Exams: There will be two 75-minute midterm exams and a final.
Grading: The final course grade will be determined by:
Homework: 20%;
Midterm exams: 20% each;
Final exam: 40%.
Help: My office hours are Mondays, 10--11 AM and Thursdays, 2:30--3:30 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.
September 7: First day of class
October 5: Midterm exam 1
October 11: Drop date (most schools)
November 7--8: Election break
November 9: Midterm exam 2
December 12: Last day of class
December 21: Final exam (tentative)
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