Time and place: MW 2:40-3:55, location 207 Mathematics.
Instructor: Robert Friedman (x4-4355). Office: 605 Mathematics.
Office hours: My office hours are Tuesdays, 1--2 PM and Thursdays, 2--3 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 Assistants: Nguyen Dung nguyendung@math.columbia.edu, Adiba Ejaz adiba.ejaz@columbia.edu. and Jacob Weinstein jmw2281@columbia.edu. Office hours Nguyen Tuesday 12--3pm, Adiba Monday 11am--1pm, Jacob Friday 9--11am, all in the Mathematics 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 or the internet is recommended 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. 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 on Mondays, and typically posted after class on the previous Wednesday. The first problem set will be due on Monday, September 20. 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 outside 417 Mathematics. Graded homework will be available once it is graded in the box outside 605 Mathematics. For late homework, you will need to request permission for an extension.

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

• Midterm Exam 1: Monday, October 11, in class (tentative date)
• Midterm Exam 2: Wednesday, November 17, in class (tentative date)
• Final: this is centrally scheduled by the University. The tentative time is Wednesday, December 22, 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%.

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 (tentatively) Tuesdays and Thursdays, 1--2 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.

September 13: First day of class
October 11: Midterm exam 1
November 1--2: Election break break
November 17: Midterm exam 2
November 24--26: Thanksgiving break
December 13: Last day of class
December 22: Final exam (tentative)

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