Niels Henrik Abel and Abelian Group

Abelian Groups are named after early 19th century mathematician Niels Henrik Abel.

Abelian Groups are named after early 19th century mathematician Niels Henrik Abel. Here is how Wikipedia describes him at en.wikipedia.org/wiki/Niels_Henrik_Abel:

Niels Henrik Abel (/ˈɑːbəl/; Norwegian: [ˈɑːbl̩]; 5 August 1802 - 6 April 1829) was a Norwegian mathematician who made pioneering contributions in a variety of fields. His most famous single result is the first complete proof demonstrating the impossibility of solving the general quintic equation in radicals. This question was one of the outstanding open problems of his day, and had been unresolved for over 350 years. He was also an innovator in the field of elliptic functions, discoverer of Abelian functions. Through the great works from Abel's hand he was known to the world's mathematicians; he made his discoveries while living in poverty and died at the age of 26 from tuberculosis.

Mathematician: Niels Henrik Abel
Mathematician: Niels Henrik Abel

Here is what Niels Henrik Abel is known for:

   Abel's binomial theorem
   Abelian category
   Abelian variety
   Abel equation
   Abel equation of the first kind
   Abelian extension
   Abel function
   Abelian group
   Abel's identity
   Abel's inequality
   Abel's irreducibility theorem
   Abel-Jacobi map
   Abel-Plana formula
   Abel-Ruffini theorem
   Abelian means
   Abel's summation formula
   Abelian and tauberian theorems
   Abel's test
   Abel's theorem
   Abel transform
   Abel transformation
   Abelian variety
   Abelian variety of CM-type
   Dual Abelian variety

Last update: 2019.

Table of Contents

 About This Book

 Geometric Introduction to Elliptic Curves

 Algebraic Introduction to Elliptic Curves

Abelian Group and Elliptic Curves

 What Is Abelian Group

Niels Henrik Abel and Abelian Group

 Multiplicative Notation of Abelian Group

 Additive Notation of Abelian Group

 Modular Addition of 10 - Abelian Group

 Modular Multiplication of 10 - Not Abelian Group

 Modular Multiplication of 11 - Abelian Group

 Abelian Group on Elliptic Curve

 Discrete Logarithm Problem (DLP)

 Finite Fields

 Generators and Cyclic Subgroups

 Reduced Elliptic Curve Groups

 Elliptic Curve Subgroups

 tinyec - Python Library for ECC

 EC (Elliptic Curve) Key Pair

 ECDH (Elliptic Curve Diffie-Hellman) Key Exchange

 ECDSA (Elliptic Curve Digital Signature Algorithm)

 ECES (Elliptic Curve Encryption Scheme)

 Terminology

 References

 Full Version in PDF/EPUB