Time and place: MW 2:40-3:55, location 312 Mathematics.
Instructor: Robert Friedman (x4-4355). Office: 605 Mathematics.
Office hours: My office hours are (tentatively) Tuesdays and Thursdays, 1--2 PM in 605 Math, but feel free to drop by at any time.
Email: rf@math.columbia.edu
Teaching Assistants: Shizhang Li sl3744@columbia.edu, Quang Dao qvd2000@columbia.edu, and Bharatha Rankothge bmr2147@columbia.edu. Office hours Shizhang: Wednesdays 10AM--1PM, Quang: Fridays 2--4PM, Bharatha: Mondays 4--6PM, all in the Columbia Help Room.

This is the first semester of a two-semester sequence on Abstract Algebra. This semester will concentrate on group theory. Math UN1202 (Multivariable Calculus) and Math UN2010 (Linear Algebra), or equivalent courses, are prerequisites for this course. You should also be familiar with complex numbers, mathematical induction and other methods of proof, and in general have a certain confidence in your abilities to handle abstract mathematical reasoning. A prior course which involves writing proofs such as Honors Math A/B or Introduction to Higher Mathematics is strongly recommended.

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. Most of what we will cover this semester can be found in Chapters 2, 6, and 7.
D. Dummit and R. Foote, Abstract Algebra, (Third edition), John Wiley and Sons, 2004. ISBN-13: 978-0471433347. Most of what we will cover this semester can be found in Chapters 1 through 5.
John Fraleigh, A First Course in Abstract Algebra (Seventh Edition), Addison Wesley 2002. ISBN-13: 978-0201763904. Most of what we will cover this semester can be found in Sections 1 through 17 and 34 through 37.
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

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 10. 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 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.

• Midterm Exam 1: Monday, October 8, in class (tentative date)
• Midterm Exam 2: Monday, November 12, in class (tentative date)
• Final: this is centrally scheduled by the University. The tentative time is Wednesday, December 19, 1:10 PM --4:00 PM, in the usual classroom. It must be taken at the scheduled time.

Grading: The final course grade will be determined by:

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

Help: My office hours are (tentatively) Tuesdays and Thursdays, 1--2 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 5: First day of class
October 8: Midterm exam 1
October 9: Drop date (most schools)
November 5--6: Election break
November 12: Midterm exam 2
November 21--23: Thanksgiving break
December 10: Last day of class
December 19: Final exam (tentative)

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