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This course is an elementary introduction to number theory with no algebraic prerequisites.
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English
English [CC]
FREE
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Description
Topics covered include primes, congruences, quadratic reciprocity, diophantine equations, irrational numbers, continued fractions, and partitions.
Course content
- 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
Instructor
Massachusetts Institute of Technology
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