Assignments

The weekly problem sets contain three (sometimes four) multi-part problems. Typically the first problem will be required, and you may then choose one of the remaining two problems to solve; one of these will be theoretical in nature, while the other will be more computationally focused, so those who prefer proofs to programming (or vice versa) can suit themselves.

Several of 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.

RELATED LECTURES PROBLEM SETS ASSOCIATED FILES DUE IN
Lectures 1 and 2 Problem Set 1 (PDF) 18.783 Lecture 2: Group law on Edwards curves (SWS) Lec 3
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 10
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 12
Lectures 11, 12, and 13 Problem Set 6 (PDF) 18.783 Problem Set 4 Problem 2 (SWS) Lec 14
Lectures 14 and 15 Problem Set 7 (PDF)   Lec 16
Lectures 16 and 17 Problem Set 8 (PDF)   Lec 18
Lectures 18 and 19 Problem Set 9 (PDF)   Lec 20
Lectures 18, 19, 20, and 21 Problem Set 10 (PDF) 18.783 Problem Set 10 Problem 3 (SWS) Lec 22
Lectures 22 and 23 Problem Set 11 (PDF) 18.783 Problem Set 11 Norm Equation (SWS) Lec 24
Lecture 23 Problem Set 12 (PDF) 18.783 Problem Set 12 (SWS) Lec 25