No products in the cart.
(
ratings
)
1
students
Created by:
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
5
5
Instructor Rating
1
Reviews
1520
Courses
1823
Students
Massachusetts Institute of Technology
