MATH GU4041 Introduction to
Modern Algebra II

Fall 2021

Time and place: TR 2:40-3:55, location 407 Mathematics.
Instructor: Robert Friedman. Office: 605 Mathematics.
Office hours: My office hours are Mondays, 2--3 PM and Wednesdays, 3--4 PM, in 605 Mathematics, but feel free to email me if you need to set up another time, either in person or on Zoom.
Email: rf@math.columbia.edu
Teaching Assistant: Kevin Yaolin Chang kyc2130@columbia.edu. Office hours Tuesdays 4--6 PM and Wednesdays 4--5 PM in the Mathematics 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 GU4041) 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 or the internet is encouraged for further examples, history, or different approaches to 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 on Tuesdays, and typically posted after class on the previous Thursday. The first problem set will be due on Tuesday, September 13. 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 and in your own words. Homework is due by 5 PM on the due date and can either be handed in directly to me before class or placed in the mailbox on the fourth floor. For late homework, you will need to request permission for an extension.

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.

Grading: The final course grade will be determined by:

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

Disability Issues: In order to receive disability-related academic accommodations for this course, students must first be registered with their school Disability Services (DS) office. Detailed information is available online for both the Columbia and Barnard registration processes. Refer to the appropriate website for information regarding deadlines, disability documentation requirements, and drop-in hours (Columbia) (Barnard).

For this course, students registered with the Columbia DS office can refer to the "Courses that do not require professor signature" section of the DS Testing Accommodations page for more information about accessing their accommodations.

Help: My office hours are Mondays and Wednesdays, 2--3 PM, and you should always feel free to email. Help is also available without appointment in the Mathematics Help Room 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:

September 6: First day of class
October 11: Midterm exam 1
November 7--8: Election break break
November 17: Midterm exam 2
November 23--25: Thanksgiving break
December 8: Last day of class
December 22: Final exam (tentative)

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