'19 Spring: Number Theory and Cryptography (UN3020)

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TR 1:10-2:25pm in 312 Mathematics Building

Instructor: Shotaro Makisumi (516 Mathematics, makisumi@math.columbia.edu)
Please contact me by email using your UNI@columbia.edu address (not a firstname.lastname@columbia.edu vanity address). I cannot promise to read any messages/comments sent through Canvas.

Topics: This is a course in elementary number theory, with some excursions into cryptographic applications. Topics include primes and unique factorization of integers, congruences and arithmetic "mod n," primitive roots, quadratic residues and quadratic reciprocity, RSA encryption, Diffe-Hellmann key exchange, Miller-Rabin primality testing. For details, see the syllabus.

Prerequisites: Some familiarity with proofs or a willingness to learn

Texts:
We will primarily follow the notes

You may find it helpful to read multiple books to get a variety of viewpoints on the same material. If you choose to do this, here are some books you might look at:

Exams

There will be one 75-minute in-class midterm and a final.

Make-up midterms will not be given. Under special circumstances (e.g. with a note from a doctor or a dean), students may miss the midterm. In this case, the weight of the final will be increased proportionally. (The weight of homeworks stays the same.) The final must be taken at the scheduled time. If you have two final exams scheduled at the same time, it is the responsibility of the other department to provide an alternate exam. Exams will not be rescheduled because of travel arrangements. It is your responsibility to schedule travel appropriately.

The use of electronic devices during exams is not allowed and will automatically result in a zero for the exam. In addition, anyone found to have cheated on an exam will receive a failing grade for the course and be subject to administrative discipline.

Homework

Problem sets (available under Files on Canvas) every 7-10 days, due in the homework box on the fourth floor of the Mathematics building. For a problem to receive full credit, you must show all your work, explain your work as necessary, and present your work in a clean and clear format that is easily understood. Collaboration and discussion with your classmates is encouraged, but I encourage you to attempt the problems on your own before you discuss them with friends. You must write up assignments individually. Late homework will not be accepted. Instead, the lowest two homework grades will be dropped when computing the homework grade.

Grades

Accommodation

Students requiring special accommodation should contact the Office of Disability Services (ODS) promptly. You can find more information here.