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Contents & Using This Site

What is a Set, a Group, a Ring, and a Field?

The Discrete Logarithm Problem

Elliptic Curves over ℝ

Theorem / Proof: A line connecting P and Q always intersects a third point

The Additive Inverse

Adding Points, Doubling Points: P, 2P, 3P, 4P, 8P etc.

Expanding from Weierstrass To General Form

Associativity

The Projective Plane

Homogenous Equations

Elliptic Curves In a Finite Field

The Modular Multiplicative Inverse

The Slope of an Elliptic Curve (Formal Derivatives)

Arithmetic in a Finite field

Doubling Points in A Finite Field

Acknowledgements and Bibliography

What is a Set, a Group, a Ring, and a Field?

Exploring Fundamental Abstract Algebra

Set

A set is a collection of distinct objects, considered as an object in its own right. These objects are called the elements or members of the set. (Set - Wolfram MathWorld

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What is a Set, a Group, a Ring, and a Field?

Set

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