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Created by:

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Last updated:

December 27, 2022

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration

Description

This course is an elementary introduction to number theory with no algebraic prerequisites.

Topics covered include primes, congruences, quadratic reciprocity, diophantine equations, irrational numbers, continued fractions, and partitions.

Course Curriculum

  • Introduction, Diophantine Equations, Divisibility, GCD Unlimited
  • Euclidean Algorithm, Primes Unlimited
  • Binomial Coefficients, Congruences Unlimited
  • FFermat, Euler, Wilson, Linear Congruences Unlimited
  • Linear Congruences, Chinese Remainder Theorem, Algorithms Unlimited
  • Primality, Factoring, RSA, Hensel’s Lemma Unlimited
  • Congruences mod Primes, Order, Primitive Roots Unlimited
  • Primitive Roots (Prime Powers), Index Calculus Unlimited
  • Quadratic Residues, Quadratic Reciprocity Unlimited
  • Jacobi Symbol, Computation, Zolotareff’s Definition Unlimited
  • Square Roots, Tonelli’s Algorithm, Number of Consecutive Pairs of Squares mod p Unlimited
  • Cyclotomic Polynomials, Primes Congruent to 1 mod n Unlimited
  • Arithmetic Functions Unlimited
  • Mobius Inversion Formula, Zeta Functions Unlimited
  • Linear Recurrences Unlimited
  • Generating Functions Unlimited
  • More on Generating Functions, Two Squares Theorem Unlimited
  • Continued Fractions I Unlimited
  • Continued Fractions II: Inequalities Unlimited
  • Periodic Continued Fractions, Quadratic Irrationalities Unlimited
  • Brahmagupta-Pell Equation Unlimited
  • Four Squares Theorem Unlimited
  • Pythagorean Triples, Fermat Descent Unlimited
  • Rational Points on Conics Unlimited

About the instructor

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Massachusetts Institute of Technology
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