A Problem Based Journey from Elementary Number Theory to an Introduction to Matrix Theory

The President Problems

By: Abraham Berman

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eText | 18 October 2021

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The book is based on lecture notes of a course 'from elementary number theory to an introduction to matrix theory' given at the Technion to gifted high school students. It is problem based, and covers topics in undergraduate mathematics that can be introduced in high school through solving challenging problems. These topics include Number theory, Set Theory, Group Theory, Matrix Theory, and applications to cryptography and search engines.
Contents:

Introduction
Algebraic Structures
The Natural Numbers
The Integers
The Real Numbers
Introduction to Set Theory
The Pigeonhole Principle and the Base 2 Number System
Introduction to Group Theory
Introduction to Matrix Theory
Fibonacci Numbers, Determinants and Eigenvalues
The Mathematics Behind Google's Page Rank and a Game of Numbers
Bibliography
Index

Readership: High school students who love mathematics and mathematics teachers. Also good for professors of mathematics and maths education, students in the mathematical sciences and pre-service math teachers.

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