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.
Assessment
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.
Certification
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- Show it to prove your success
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 | ||
| Assessment | |||
| Submit Your Assignment | 00:00:00 | ||
| Certification | 00:00:00 | ||
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