More Fun with Prime Numbers

МООК
en
Английский
5 h
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Source
  • From www.edx.org
Conditions
  • Self-paced
  • Free Access
  • Fee-based Certificate
More info
  • 5 Sequences
  • Intermediate Level

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Course details

Syllabus

Week1: What are Prime Numbers?
Introduction to basic concepts and properties of prime numbers, such as infinitude of prime numbers, counting prime numbers, and the Basel problem and its relation with the Riemann Hypothesis.

Week 2: Sums of Two Squares
Introduction to the modular arithmetic and its applications to number theory, including Fermat's Little Theorem, Wilson's Theorem, and Fermat's theorem on sums of two squares.

Week 3: The Reciprocity Laws
Introduction to the quadratic reciprocity laws proved by Gauss. Several generalizations of the quadratic reciprocity laws are also explained.

Week 4: Prime Numbers and Cryptography
Introduction to cryptography, and the construction practical cryptosystems using prime numbers. More recent topics on elliptic curve cryptosystems are also explained.

Week 5: Mystery of Prime Numbers: Past, Present, and Future
Introduction to several open problems and conjectures on prime numbers, including the Birch and Swinnerton-Dyer conjecture and the ABC conjecture.

Prerequisite

Secondary school (high school) level algebra; basic mathematics concepts

Instructors

Tetsushi Ito

Editor

Kyoto University

Platform

EdX est une plateforme d'apprentissage en ligne (dite FLOT ou MOOC). Elle héberge et met gratuitement à disposition des cours en ligne de niveau universitaire à travers le monde entier. Elle mène également des recherches sur l'apprentissage en ligne et la façon dont les utilisateurs utilisent celle-ci. Elle est à but non lucratif et la plateforme utilise un logiciel open source.

EdX a été fondée par le Massachusetts Institute of Technology et par l'université Harvard en mai 2012. En 2014, environ 50 écoles, associations et organisations internationales offrent ou projettent d'offrir des cours sur EdX. En juillet 2014, elle avait plus de 2,5 millions d'utilisateurs suivant plus de 200 cours en ligne.

Les deux universités américaines qui financent la plateforme ont investi 60 millions USD dans son développement. La plateforme France Université Numérique utilise la technologie openedX, supportée par Google.

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