MIT OpenCourseWare
Theory of Numbers
Art: Johannes Kepler, Konjukce Saturnu a Jupiteru Originál, 1596 · Public domain
- Instructor
- Prof. Abhinav Kumar
- Term
- Spring 2012
- Level
- Undergraduate
- What's inside
- 1 problem set · 6 exams · 13 solutions · 1 lecture note · 33 other files · 4 web pages
- Materials open
- MIT OCW
About this course
Source: MIT OpenCourseWare 18.781 Theory of Numbers, Spring 2012, Prof. Abhinav Kumar — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: none is claimed; materials are grouped by MIT's own sections. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.
Materials are grouped the way MIT organized them. A verified, course-wide order has not been established here.
Has MIT solutions
Before you start
Prerequisites are not listed here. Check MIT's own syllabus for this course.
How this course was organized
What's here, and what isn't
- MIT lists a session calendar for this course, but it could not be verified well enough to build a sequence from it — materials are grouped by section instead.
Not included here
4 items from the source could not be safely included:
- MIT's page format for this item wasn't recognized clearly enough to place it safely. (2 items)
- Referenced in a table, but without MIT's own verified order, so it isn't used to claim a sequence. (2 items)
Materials by section
Grouped by section, as MIT organized them. Not sequenced or ordered.
Lecture Notes
24 files
- Arithmetic Functions, Lecture 13 Notes Download
- Binomial Coefficients, Congruences, Lecture 3 Notes Download
- Brahmagupta-Pell Equation, Lecture 21 Notes Download
- Congruences mod Primes, Order, Primitive Roots, Lecture 7 Notes Download
- Continued Fractions I, Lecture 18 Notes Download
- Continued Fractions II: Inequalities, Lecture 19 Notes Download
- Cyclotomic Polynomials, Primes Congruent to 1 mod n, Lecture 12 Notes Download
- Euclidean Algorithm, Primes, Lecture 2 Notes Download
- Fermat, Euler, Wilson, Linear Congruences, Lecture 4 Notes Download
- Four Squares Theorem, Lecture 22 Notes Download
- Generating Functions, Lecture 16 Notes Download
- Introduction, Lecture 1 Notes Download
- Jacobi Symbol, Computation, Zolotareff's Definition, Lecture 10 Notes Download
- Linear Congruences, Chinese Remainder Theorem, Algorithms, Lecture 5 Notes Download
- Linear Recurrences, Lecture 15 Notes Download
- Mobius Inversion Formula, Zeta Functions, Lecture 14 Notes Download
- More on Generating Functions, Two Squares Theorem, Lecture 17 Notes Download
- Periodic Continued Fractions, Quadratic Irrationalities, Lecture 20 Notes Download
- Primality, Factoring, RSA, Hensel's Lemma, Lecture 6 Notes Download
- Primitive Roots (Prime Powers), Index Calculus, Lecture 8 Notes Download
- Pythagorean Triples, Fermat Descent, Lecture 23 Notes Download
- Quadratic Residues, Quadratic Reciprocity, Lecture 9 Notes Download
- Rational Points on Conics, Lecture 24 Notes Download
- Square Roots, Tonelli's Algorithm, Number of Consecutive Pairs of Squares mod p, Lecture 11 Notes Download
Assignments
20 files
- Problem Set 2 Download
- Theory of Numbers, assignment 1 Download
- Theory of Numbers, assignment 3 Download
- Theory of Numbers, assignment 4-1 Download
- Theory of Numbers, assignment 4-2 Download
- Theory of Numbers, assignment 5 Download
- Theory of Numbers, assignment 6 Download
- Theory of Numbers, assignment 7 Download
- Theory of Numbers, assignment 8 Download
- Theory of Numbers, assignment 9 Download
- Theory of Numbers, solution 1 Download
- Theory of Numbers, solution 2 Download
- Theory of Numbers, solution 3 Download
- Theory of Numbers, solution 4-1 Download
- Theory of Numbers, solution 4-2 Download
- Theory of Numbers, solution 5 Download
- Theory of Numbers, solution 6 Download
- Theory of Numbers, solution 7 Download
- Theory of Numbers, solution 8 Download
- Theory of Numbers, solution 9 Download
Exams
9 files
- Theory of Numbers, Exam Final Guidelines Download
- Theory of Numbers, Exam Final Practice Solutions Download
- Theory of Numbers, Exam Final Practice Download
- Theory of Numbers, Exam 2 Guidelines Download
- Theory of Numbers, Exam 1 Guidelines Download
- Theory of Numbers, Exam 1 Practice Download
- Theory of Numbers, Exam 1 Practice Solutions Download
- Theory of Numbers, Exam 2 Practice Download
- Theory of Numbers, Exam 2 Practice Solutions Download
MIT OpenCourseWare, Prof. Abhinav Kumar, 18.781 Theory of Numbers, Spring 2012.
License: CC BY-NC-SA 4.0 · Edition: Spring 2012 · Open the original course on OCW ↗
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