Algorithms with Numbers

About the Course

This course represents an introduction to algorithms with numbers, including linear algebra problems and arbitrary precision arithmetic, that appear virtually everywhere, from cryptography to audio processing. You will learn how to:

— implement the basic number theory algorithms like Euclidean algorithm that are basic building blocks for modern cryptography;

— work with large numbers arising in cryptography and high precision arithmetic;

— solve systems of linear equations that appear in many areas from designing electrical circuits to computer graphics;

— implement Fast Fourier Transform that is inevitable in signal processing.

Each module includes a programming assignment that will improve both your understanding of the topics and your programming skills.

Programme

1. Prime numbers and Euclid’s Algorithm.
2. Arbitrary Precision Arithmetic and Polynomials.
3. Systems of Linear Equations.
4. Matrices and Fast Fourier Transform.