Einführung in die AoPS-ReiheReihe
Diese Reihe richtet sich an außergewöhnlich begabte Mathematikstudenten, die eine tiefere und anspruchsvollere Ausbildung suchen. Jedes Buch befasst sich mit fortgeschrittenen Konzepten und entwickelt ausgeprägte analytische und problemlösende Fähigkeiten. Sie bietet einen umfassenden und anregenden Ansatz zur Mathematik, der über den üblichen Lehrplan hinausgeht. Dies ist ideal für diejenigen, die ihre mathematischen Fähigkeiten auf ein neues Niveau heben möchten.
Empfohlene Lesereihenfolge
Learn the fundamentals of number theory from former MATHCOUNTS, AHSME, and AIME perfect scorer Mathew Crawford. Topics covered in the book include primes & composites, multiples & divisors, prime factorization and its uses, simple Diophantine equations, base numbers, modular arithmetic, divisibility rules, linear congruences, how to develop number sense, and much more. This books is ideal for students who have mastered basic algebra, such as solving linear equations. Middle school students preparing for MATHCOUNTS, high school students preparing for the AMC, and other students seeking to master the fundamentals of number theory will find this book an instrumental part of their mathematics libraries.
Learn the basics of counting and probability from former USA Mathematical Olympiad winner David Patrick. Topics covered in the book include permutations, combinations, Pascal's Triangle, basic combinatorial identities, expected value, fundamentals of probability, geometric probability, the Binomial Theorem, and much more.As you'll see in the excerpts below, the text is structured to inspire the reader to explore and develop new ideas. Each section starts with problems, so the student has a chance to solve them without help before proceeding. The text then includes solutions to these problems, through which counting and probability techniques are taught. Important facts and powerful problem solving approaches are highlighted through out the text. In addition to the instructional material, the book contains over 400 problems. The solutions manual contains full solutions to all of the problems, not just answers.This book is ideal for students who have mastered basic algebra, such as solving linear equations. Middle school students preparing for MATHCOUNTS, high school students preparing for the AMC, and other students seeking to master the fundamentals of counting and probability will find this book an instrumental part of their mathematics libraries.