There will be weekly problem sets, each of which typically contain three to five multi-part problems. Typically you will not be required to solve all of the problems, you be given the option to choose a subset that sums to 100 points. Some problems are purely theoretical in nature, while others are more computationally focused; those who prefer proofs to programming (or vice versa) can choose problems that appeal to there interests.

Several of the problems require the use of the Sage computer algebra system. You will find relevant of examples of Sage usage in the problem descriptions themselves, and in the worksheets listed in the lectures section. There is also a wealth of useful information to be found on the Sage website, including tutorials. You can download a copy of Sage to run on your own machine if you wish, or create an account for free on the SageMathCloud™.

Problem sets are to be prepared in typeset form (typically via LaTeX) and submitted electronically as PDF files. Collaboration is encouraged, but you must write up your own solutions; there will be computational problems for which the correct answer will be different for every student, based on a unique identifier derived from your MIT ID number.

Lectures 1 and 2 Problem Set 1 (PDF)   Lec 4
Lectures 3 and 4 Problem Set 2 (PDF)   Lec 5
Lectures 5 and 6 Problem Set 3 (PDF)   Lec 7
Lectures 7 and 8 Problem Set 4 (PDF)   Lec 9
Lectures 9 and 10 Problem Set 5 (PDF)

18.783 Problem Set 5 Problem 2 (SWS)

18.783 Lecture 9: Schoof's Algorithm (SWS)

Lec 11
Lectures 11 and 12 Problem Set 6 (PDF) 18.783 Problem Set 6 Problem 2 (SWS) Lec 13
Lectures 13 and 14 Problem Set 7 (PDF)   Lec 15
Lectures 15 and 16 Problem Set 8 (PDF)   Lec 17
Lectures 17 and 18 Problem Set 9 (PDF)   Lec 19
Lectures 18 and 19 Problem Set 10 (PDF)   Lec 20
Lectures 18 through 21 Problem Set 11 (PDF) 18.783 Isogeny Neighbors (SWS) Lec 22
Lectures 22 and 23 Problem Set 12 (PDF) 18.783 Problem Set 12 (SWS) Lec 24
Lectures 23 and 25 Problem Set 13 (PDF)   Lec 26