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If you want to know the pure mathematics devoted to the study of the integers because of the foundational place in the discipline, you have to understand Number Theory. By studying this [course_title] as well as properties of objects made out of integers or defined as generalizations of the integers, you will acquire a vast knowledge on primes, congruences, quadratic reciprocity continued fractions, Diophantine equations, irrational numbers, and partitions.


This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.


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Course Credit: MIT

Course Curriculum

Module: 01
Introduction, Diophantine Equations, Divisibility, GCD 00:30:00
Euclidean Algorithm, Primes 00:30:00
Binomial Coefficients, Congruences 00:30:00
FFermat, Euler, Wilson, Linear Congruences 00:30:00
Linear Congruences, Chinese Remainder Theorem, Algorithms 00:30:00
Primality, Factoring, RSA, Hensel’s Lemma 00:30:00
Module: 02
Congruences mod Primes, Order, Primitive Roots 00:30:00
Primitive Roots (Prime Powers), Index Calculus 00:30:00
Quadratic Residues, Quadratic Reciprocity 00:30:00
Jacobi Symbol, Computation, Zolotareff’s Definition 00:15:00
Square Roots, Tonelli’s Algorithm, Number of Consecutive Pairs of Squares mod p 00:30:00
Cyclotomic Polynomials, Primes Congruent to 1 mod n 00:30:00
Module: 03
Arithmetic Functions 00:30:00
Mobius Inversion Formula, Zeta Functions 00:45:00
Linear Recurrences 00:30:00
Generating Functions 00:30:00
More on Generating Functions, Two Squares Theorem 00:30:00
Continued Fractions I 00:30:00
Module: 04
Continued Fractions II – Inequalities 00:30:00
Periodic Continued Fractions, Quadratic Irrationalities 00:30:00
Brahmagupta-Pell Equation 00:30:00
Four Squares Theorem 00:30:00
Pythagorean Triples, Fermat Descent 00:30:00
Rational Points on Conics 00:30:00
Submit Your Assignment 00:00:00
Certification 00:00:00

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