- Instructor: Robert Young (ryoung@cims.nyu.edu)
- Office: WWH 601
- Office hours: Mondays, 1-3, WWH 601
- Lectures: (check Albert for location) TTh 11:00-12:15
- Recitations: (check Albert for location) F 9:30-10:45 (starting February 8)
- TA: Rodion Deev
- Office hours: Tuesdays, 5-6, WWH 608
- Textbook: Judson, Abstract Algebra: Theory and Applications
The textbook is available freely online and cheaply in print at many retailers. Any print edition has similar content, but editions before 2014 may have different numbering of theorems, figures, etc.

Please consider buying a print edition rather than downloading it and printing it out; the cost of printing the PDF yourself is generally more than buying a paperback copy, and the paperback is easier to carry and use.

Assignments | 20% |

Midterm | 25% |

Quizzes | 15% |

Final exam | 40% |

- Quiz 1: Friday, February 15th, in recitation
- Quiz 2: Friday, March 8th, in recitation
- Midterm: Friday, March 29th, in recitation
- Quiz 3: Friday, April 19th, in recitation
- Quiz 4: Friday, May 3th, in recitation
- Final: Thursday, May 16th, 10-11:50 AM

Assignments will usually be given on Tuesdays and handed in at class the next Tuesday. Collaboration is encouraged, but each student must write up and hand in their own solutions. If you work closely with someone else, please identify them on your assignment (e.g., "I worked with __________").

Late assignments will not be accepted except in the case of an emergency. If you expect to be absent on a day when an assignment is due, you can give your assignment to a classmate to turn in for you. At the end of the semester, your two lowest assignment grades will be dropped from your average. This is meant to accommodate non-emergency absences, so try not to use this unless you have to.

**Solving problems is important! Doing exercises and understanding
the assignments is the best way to master the material.**

- Come to class and recitation!
- Solve problems!
- Ask me questions: Feel free to ask me questions in class, after class, at office hours, or by email. Feel free to ask questions in recitation.
- Ask your classmates questions: Mathematics is about collaboration. Explaining something to someone else is one of the best ways to learn.
**Read actively and study diligently!**The true goal of this course is to learn how to prove theorems. So, as you read the textbook or review your notes, read actively. Make up your own examples. Check calculations and check each step of a proof. Fill in any gaps. Solve exercises. Try explaining the proof to someone else. Try proving a theorem yourself before looking at the proof. Ask yourself questions like:- What would happen if I changed one of the hypotheses of this theorem?
- What new tricks and techniques does this proof use?
- What's a simple example of this definition?
- What's a complicated example of this definition?

- Problem Set 1 (due Tuesday, February 5)
- Problem Set 2 (due Tuesday, February 12)
- Problem Set 3 (due Tuesday, February 19)
- Problem Set 4 (due Tuesday, February 26)
- Problem Set 5 (due Tuesday, March 5)
- Problem Set 6 (due Tuesday, March 12)
- Problem Set 7 (due Tuesday, March 26)
- Midterm Study Guide
- Problem Set 8 (due Tuesday, April 2)
- Problem Set 9 (due Tuesday, April 9)
- Problem Set 10 (due Tuesday, April 16)
- Problem Set 11 (due Tuesday, April 23)
- Problem Set 12 (due Tuesday, April 30)
- Problem Set 13 (due Tuesday, May 6)
- Final Study Guide

1/29, 1/31 | Sets and functions, what is a group? | Ch. 1, 2, 3.1-3.2 | |

2/5, 2/7 | Subgroups and cyclic groups | Ch. 3.3, 4.1-4.2 | |

2/12, 2/14 | Permutations and symmetries | Ch. 5 | Quiz 1 |

2/19, 2/21 | Odd and even permutations, the alternating group | Ch. 5 | |

2/26, 2/28 | Cosets | Ch. 6 | |

3/5, 3/7 | Number theory, Euler and Fermat's Theorems, isomorphisms | Ch. 6, 9.1 | Quiz 2 |

3/12, 3/14 | Cayley's theorem, products, homomorphisms | Ch. 9.2, 11.1 | |

Break | |||

3/26, 3/28 | Kernels and images, factor groups | Ch. 10 | Midterm |

4/2, 4/4 | Isomorphism theorems, finite abelian groups | Ch. 11.2, Navarro | |

4/9, 4/11 | Rings | ||

4/16, 4/18 | Polynomials and polynomial rings | Quiz 3 | |

4/23, 4/25 | Factorization | ||

4/30, 5/2 | Vector spaces and fields | Quiz 4 | |

5/7, 5/9 | Vector spaces and fields |