Intermediate Counting and Probability 1st Edition by David Patrick ISBN 1934124060 978-1934124062
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Product details:
ISBN 10:1934124060
ISBN 13:978-1934124062
Author:David Patrick
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.
Table of contents:
1.Review of Counting & Probability Basics
Introduction
Basic Counting Techniques
Basic Probability Techniques
Expected Value
Pascal’s Triangle and the Binomial Theorem
Summation Notation
Summary
2.Sets and Logic
Introduction
Sets
Operations on Sets
Truth and Logic
Quantifiers
Summary
3.A Piece of PIE
Introduction
PIE With 2 Properties
PIE With 3 Properties
Counting Problems With PIE
PIE With Many Properties
Counting Items With More Than 1 of Something
Some Harder PIE Problems
Summary
4.Constructive Counting and 1-1 Correspondences
Introduction
Some Basic Problems
Harder Constructive Counting Problems
1-1 Correspondence Basics
More Complicated 1-1 Correspondences
Clever 1-1 Correspondences
Summary
5.The Pigeonhole Principle
Introduction
It’s Just Common Sense!
Basic Pigeonhole Problems
More Advanced Pigeonhole Problems
Summary
6.Constructive Expectation
Introduction
Basic Examples
Summing Expectations Constructively
A Coat With Many Patches (Reprise)
Summary
7.Distributions
Introduction
Basic Distributions
Distributions With Extra Conditions
More Complicated Distribution Problems
Summary
8.Mathematical Induction
9.Fibonacci Numbers
Introduction
A Motivating Problem
Some Fibonacci Problems
A Formula for the Fibonacci Numbers
Summary
10.Recursion
Introduction
Examples of Recursions
Linear Recurrences
A Hard Recursion Problem
Problems Involving Catalan Numbers
Formulas for the Catalan Numbers
Summary
11.Conditional Probability
Introduction
Basic Examples of Conditional Probability
Some Definitions and Notation
Harder Examples
Let’s Make a Deal!
Summary
12.Combinatorial Identities
Introduction
Basic Identities
More Identities
Summary
13.Events With States
Introduction
State Diagrams and Random Walks
Events With Infinite States
Two-player Strategy Games
Summary
14.Generating Functions
Introduction
Basic examples of Generating Functions
The Binomial Theorem (as a Generating Function)
Distributions (as Generating Functions)
The Generating Function for Partitions
The Generating Function for the Fibonacci Numbers
Summary
15.Graph Theory
Introduction
Definitions
Basic Properties of Graphs
Cycles and Paths
Planar Graphs
Eulerian and Hamiltonian Paths
Summary
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Tags: David Patrick, Intermediate, Counting, Probability