# Teaching

## Fall 2018

In the Fall semester 2018, I will be teaching MATH-UA.0248-001 Theory of Numbers.### Lectures:

MW 3:30-4:45pm in CIWW 201. Recitation F 3:30-4:45 in CIWW 101.

### Contact information:

Office 604

bilu @ cims.nyu.edu (remove blank spaces around @)

### Office hours:

MT 10:30-11:30am, or by appointment.

### Contents of the course:

Topics include: divisibility theory, Euclidean algorithm, congruences, prime numbers, Fermat's theorem, Pythagorean triples, applications to cryptography, classical number-theoretic functions, perfect numbers, quadratic reciprocity.

### Notes

12/10 version. Remarks or questions welcome! Pay attention to the fact that these notesdo not contain some of the proofs. If you've missed a lecture, make sure to catch up the proofs by borrowing someone's notes

### Homeworks:

Homeworks are always due in the beginning of Monday's class. If you cannot attend class, you can e-mail me your homework before the beginning of class, or leave it in my mailbox (number 38 on the right side of the mailboxes behind the guard's desk in the lobby of WWH). Late homeworks are usually not accepted, except if you have a valid excuse, which you should e-mail me about in advance. The two lowest homework grades will be dropped.

Homework 1 Solution

Homework 2 Solution

Homework 3 Solution

Homework 4 Solution

Homework 5 Solution

Homework 6 Solution

Homework 7 Solution

Homework 8 Solution

Homework 9 Solution

Homework 10 Solution

Homework 11 Solution

The solutions to the homeworks were mostly written up by Antonios-Alexandros Robotis.

### Recitation:

Your TA is Antonios-Alexandros Robotis. Here are some problems you will work on during recitation.

### Quizzes:

There will be short quizzes during recitation on the following dates:

September 28th

October 12th

November 30th

### Exams:

There will be one Midterm exam, on Monday October 29th. Here are some extra practice problems for the Midterm, with some solutions.

The Final exam will be on Wednesday, December 19th, 4-5:50pm. Here are some extra practice problems.

### Grading:

- Homeworks 20%
- Quizzes 20%
- Midterm 30%
- Final 30%

### Recommended books

David Burton,

Elementary Number Theory, available online here or here

Joseph. H. Silverman, A Friendly Introduction to Number Theory. Chapters 1-6 are available online here

### Some advice

**Read your notes**before coming to class: it is hard to follow if you don't remember what has been said last time.**Ask questions**and try to**propose answers**to questions I am asking even if you're not sure: making mistakes is part of the normal process of learning. One remembers something very well if one got it wrong the first time.- If I use some notation or some mathematical notion you're
not familiar with, please ask about it: I come from a
different background and am not completely aware of what you
know.

- Please only answer a question asked in class if you've been prompted to do so, so as to let the others think. Not everyone has the same speed.
- Come to
**office hours**, even if you don't think you have that many questions. You can come by anytime during the specified time range. - This is a course with many
**proofs**. Make sure to go over each proof**actively**, asking yourself: what would I do if I wanted to prove this? How many steps are there, what is the**structure**of this proof? Why do we need to do this? Why are we done at the end? Knowing the proof of a theorem helps you get a deep understanding of the theorem itself, I therefore strongly recommend that you learn the proofs at the same time as you learn the theorems. Many exercises in the homeworks, quizzes and exams may rely on ideas similar to the proof of some theorem seen in class.

**Work in groups**! It's much more fun doing maths with other people than on one's own. Ask questions to your classmates. If you have trouble remembering a proof, try to practice**explaining**it to a classmate: this is the best way to learn it.

## Previous years

For my teaching at Courant during the academic year 2017-2018, see here.For my 2016 and 2017 Algebraic Topology problem sessions at the ENS, see here.