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Equations in Number Theory

Offered By: Brilliant

Tags

Diophantine Equations Courses Number Theory Courses Linear Equations Courses Modular Arithmetic Courses

Course Description

Overview

This course was written in collaboration with Andrea Marino, a two-time math olympiad gold medalist and mathematics PhD at Tor Vergata University.

In this course, you'll learn one of the most fundamental techniques in number theory: solving Diophantine (integer) equations. You'll apply these techniques to both abstract problems, as well as to problems in chemistry, geometry, game theory, and billiards.


Syllabus

  • Introduction:
    • Thinking Discrete: A fundamental tool in number theory involves solving equations where integer solutions are needed.
  • Foundations:
    • Linear Equations: adding descriptions correction
    • Bezout and Billiards: Predict the path of a billiard ball using linear equations.
    • Modular Arithmetic: The mod operation is part of every number theorist's toolbox.

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