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OVERVIEW

Welcome to 6.S096! This is the webpage for 6.S096, offered in IAP 2024. We plan to offer the same course again in IAP 2025.

DESCRIPTION

Many applications in cryptography and theoretical computer science rely on number theory, which is often not taught with detail in introductory classes. In this class, we try to provide an exposition to these concepts. We begin with a quick review of the basics: Euclidean algorithm and modular arithmetic. We will then cover multiplicative modular arithmetic (Euler, Fermat), elements of group theory, the discrete logarithm problem, and elementary analytic number theory if time permits. There will be a slight focus on computational methods as well, using Sage and other Computer Algebra Systems.

The assessments will consist of weekly homeworks with a small, optional final project. The expectation is that students are familiar with the basics of mathematical proofs (it is sufficient to have taken 6.042/6.1200 or a class at a similar level in discrete mathematics), as well as some coding experience.

Piazza

This class will be using Piazza for class discussion. We encourage you to post your questions (whether about content or logistics) on Piazza.

The class sign-up link: https://piazza.com/mit/spring2024/6s096.

SIGN-UP FORM

Please fill in this google form if you’re interested in the class so we can gauge interest https://forms.gle/HKUuC7LAyuQXN3NN8

STAFF

A. Anas Chentouf Mohamed Wacyl Meddour Mohammed Ali Othman
Abdellatif Anas Chentouf (Instructor) Mohamed Wacyl Meddour (Instructor) Mohammed Ali Othman (Instructor)

LOGISTICS

LECTURE

  • Starting from Monday, January 22: Lectures Tuesday through Thursday @ 10:30am - 12pm in 32.255 (note the updated enrollment)
  • Lectures are in-person and over Zoom, but will not be recorded, although lecture notes will be released.
  • Attendance and active participation is highly encouraged to facilitate an enriching learning environment for everyone.
  • The schedule for lecture, as well as some of the notes, is provided in Schedule. We expect that most, but not all, lectures will be scribed.

    OFFICE HOURS

  • See Piazza for details.

GRADING

  • 100% psets or 70% psets and 30% a mini-expository paper abut a topic you learned (graded on completion) - whichever is best for the student.
  • The cutoff for passing is 60%.

QUICK ACCESS

  • Contacting Instructors: for concerns, issues, and questions (not course content). Note that there is no period in 6s096 in the email address.

ENROLLMENT

Please pre-register! The class is offered as a U/G class and will be graded on a P/F basis for 6 units.

PREREQUISITES

For 6.S096, you need experience and skill with mathematical concepts, theorems, and proofs. If you did well in 18.062/6.042, 18.200, 18.090, or any proof-oriented mathematics class, you should be fine! Some exposure to elementary number theory (modular arithmetic) and programming (e.g. Python) is also strongly recommended but not required. We based these on 18.404’s recommended background

COURSE NAME

Disclaimer: The course title “Number Theory – All You Need to Know” is intended for promotional purposes. While the class covers a wide range of topics in the field, its main goal is to spark your interest and curiosity in the subject. In many ways, ‘Applied Group Theory’ is also an accurate name for most of the class.

ACKNOWLEDGEMENT

This website is based on the excellent website template from MIT’s Quantitative Methods for NLP course.