Introduction to Number Theory AOPS

Introduction to Number Theory AOPS PDF in high quality for good readability, with its fundamentals of number theory from former Mathcounts

Introduction to Number Theory AOPS PDF

PDF NameIntroduction to Number Theory AOPS
Published/Updated On
Category,
RegionGlobal
No. of Pages192
PDF Size28.73 MB
LanguageEnglish
Source(s) / CreditsOliPDF

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Introduction to Number Theory AOPS PDF - Overview

Introduction to Number Theory AOPS – 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, base numbers, modular arithmetic, divisibility rules, linear congruences, how to develop number sense, and much more.

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 motivated solutions to these problems, through which concepts and curriculum of number theory are taught.

Important facts and powerful problem solving approaches are highlighted throughout the text. In addition to the instructional material, the book contains hundreds of problems. The solutions manual contains full solutions to nearly every problem, not just the answers.

Introduction to Number Theory AOPS

CONTENTS of Introduction to Number Theory AOPS
Number Theory
How to Use This Book
Acknowledgements

  • 1 Integers: The Basics of Introduction to Number Theory AOPS
    1.1 Introduction
    1.2 Making Integers Out of Integers
    1.3 Integer Multiples
    1.4 Divisibility of Integers
    1.5 Divisors
    1.6 Using Divisors
    1.7 Mathematical Symbols
    1.8 Summary
  • 2 Primes and Composites of Introduction to Number Theory AOPS
    2.1 Introduction
    2.2 Primes and Composites
    2.3 Identifying Primes I
    2.4 Identifying Primes II
    2.5 Summary
  • 3 Multiples and Divisors of Introduction to Number Theory AOPS
    3.1 Introduction
    3.2 Common Divisors
    3.3 Greatest Common Divisors (GCDs)
    3.4 Common Multiples
    3.5 Remainders
    3.6 Multiples, Divisors, and Arithmetic
    3.7 The Euclidean Algorithm
    3.8 Summary
  • 4 Prime Factorization of Introduction to Number Theory AOPS
    4.1 Introduction
    4.2 Factor Trees
    4.3 Factorization and Multiples
    4.4 Factorization and Divisors
    4.5 Rational Numbers and Lowest Terms
    4.6 Prime Factorization and Problem Solving
    4.7 Relationships Between LCMs and GCDs
    4.8 Summary
  • 5 Divisor Problems
    5.1 Introduction
    5.2 Counting Divisors
    5.3? Divisor Counting Problems
    5.4? Divisor Products
    5.5 Summary
  • 6 Special Numbers
    6.1 Introduction
    6.2 Some Special Primes
    6.3 Factorials, Exponents and Divisibility
    6.4 Perfect, Abundant, and Deficient Numbers
    6.5 Palindromes
    6.6 Summary
  • 7 Algebra With Integers
    7.1 Introduction
    7.2 Problems
    7.3 Summary
  • 8 Base Numbers
    8.1 Introduction
    8.2 Counting in Bundles
    8.3 Base Numbers
    8.4 Base Number Digits
    8.5 Converting Integers Between Bases
    8.6? Unusual Base Number Problems
    8.7 Summary
  • 9 Base Number Arithmetic
    9.1 Introduction
    9.2 Base Number Addition
    9.3 Base Number Subtraction
    9.4 Base Number Multiplication
    9.5 Base Number Division and Divisibility
    9.6 Summary
  • 10 Units Digits
    10.1 Introduction
    10.2 Units Digits in Arithmetic
    10.3 Base Number Units Digits
    10.4 Unit Digits Everywhere
    10.5 Summary
  • 11 Decimals and Fractions
    11.1 Introduction
    11.2 Terminating Decimals
    11.3 Repeating Decimals
    11.4 Converting Decimals to Fractions
    11.5? Base Numbers and Decimal Equivalents
    11.6 Summary
  • 12 Introduction to Modular Arithmetic
    12.1 Introduction
    12.2 Congruence
    12.3 Residues
    12.4 Addition and Subtraction
    12.5 Multiplication and Exponentiation
    12.6 Patterns and Exploration
    12.7 Summary
  • 13 Divisibility Rules
    13.1 Introduction
    13.2 Divisibility Rules
    13.3? Divisibility Rules With Algebra
    13.4 Summary
  • 14 Linear Congruences
    14.1 Introduction
    14.2 Modular Inverses and Simple Linear Congruences
    14.3 Solving Linear Congruences
    14.4 Systems of Linear Congruences
    14.5 Summary
  • 15 Number Sense
    15.1 Introduction
    15.2 Familiar Factors and Divisibility
    15.3 Algebraic Methods of Arithmetic
    15.4 Useful Forms of Numbers
    15.5 Simplicity
    15.6 Summary

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