MAT215

Elementary Number Theory & Cryptography

Information

Instructor: Dr Manjil P. Saikia

Contact: [email protected] (please only use this email address to send me emails related to this course)

Lecture Time & Place: Mondays & Fridays 1430 to 1545 (Room XXX, SAS)

Office Hours: XXX

Attendance Policy: Attendance is mandatory, check the institute’s attendance policy on AURIS (please note, we have a new policy from last semester). If you are low on attendance then you should talk to me (at least 3 weeks before the end-semester examination).

Course Details

Available on AURIS, we will follow the syllabus (more or less), but there will be a few digressions. So, I encourage you to keep notes.

Reading Materials

Textbook: I will cover a majority of the material from the following textbooks:

  • Elementary Number Theory, David M. Burton, 7th Edition, McGraw Hill India, 2023.
  • The Mathematics of Encryption: An Elementary Introduction, Margaret Cozzens and Steven J. Miller, American Mathematical Society, 2013.

I will use other resources from time to time, which I will list below as the course progresses. If you wish to get a high-level introduction to the topics that will be discussed then you can read the following short introductory books:

  • Number Theory: A Very Short Introduction, Robin Wilson, Oxford University Press, 2020.
  • Cryptography: A Very Short Introduction, Fred Piper and Sean Murphy, Oxford University Press, 2002.

Grading

  • Assignments: Regular homework assignments will be given, which will count towards 20% of the total score. Approximately one assignment will be given for every 3 lecture sessions. At least some of them will use WebWork (details about this will be shared via email).
  • Quiz: There will be two 20-minute quizzes, which will count towards 20% of the total score.
  • Project: A group project will be assigned to students in groups of 2 - 3 students; they will have to submit a written report. This will count towards 10% of the total score.
  • Presentation: A presentation on the project component above will have to be made by the students. This will count towards 10% of the total score.
  • Mid-Semester Examination: We will have a 60-minute written exam (closed book), this will count towards 20% of the total score.
  • End-Semester Examination: We will have a 120-minute written exam (with one cheat sheet allowed), this will count towards 20% of the total score.

To get an A grade, you must score atleast 80% overall. However, this doesn’t automatically guarantee an A.

Lectures

W 04/08: Introduction to the course, historical overview of number theory & cryptography

Assignments

  • The problem set will be updated over the semester. I will announce this in class when I post a set here.
  • To get the most out of this course, you are expected to spend at least twice the amount of lecture hours on your own.

Submissions

  • Due time: 11:59 am of each due date
  • Must be submitted as PDF (via email) or printed/written (slide under my office door)
  • Begin each solution on a new page, and use only blank or dotted pages (not ruled)
  • Staple the submission, if submitting a paper version
  • State your sources at the top of each problem (even if you worked independently)

Late Policy

  • Penalty: Late submissions will be penalized by 25% per each late day
  • Extensions: There will be no extensions given

Collaborations

  • You are encouraged to first work on the problems independently before seeking collaboration.
  • Meaningful collaboration is allowed and is encouraged for this course.
  • You must write up your solutions.

Acknowledging collaborators and sources

It is required to acknowledge your sources (even if you worked independently).

  • At the beginning of the submission for each problem, write Collaborators and sources: followed by a list of collaborators and sources consulted (people, books, papers, websites, software, etc.), or write none if you did not use any such resources.
  • Failure to acknowledge will result in an automatic 20% penalty per problem.
  • Acceptable uses of resources include: looking up a standard theorem/formula/technique; using Wolfram Alpha/Mathematica/Python for a calculation (no need to mention lectures)
  • Unacceptable uses of resources include: directly looking up the problem online or in the research literature for a solution. (Once you have solved a problem, it is fine to seek and learn alternate solutions.)

Intentional violations of the above policies may be considered academic dishonesty/misconduct.

(Thanks to Professor Yufei Zhao for his extensive course policy page, from which I have created my policies.)