How to Count

An Introduction to Combinatorics and Its Applications

How to Count

Providing a self-contained resource for upper undergraduate courses in combinatorics, this text emphasizes computation, problem solving, and proof technique. In particular, the book places special emphasis the Principle of Inclusion and Exclusion and the Multiplication Principle. To this end, exercise sets are included at the end of every section, ranging from simple computations (evaluate a formula for a given set of values) to more advanced proofs. The exercises are designed to test students' understanding of new material, while reinforcing a working mastery of the key concepts previously developed in the book. Intuitive descriptions for many abstract techniques are included. Students often struggle with certain topics, such as generating functions, and this intuitive approach to the problem is helpful in their understanding. When possible, the book introduces concepts using combinatorial methods (as opposed to induction or algebra) to prove identities. Students are also asked to prove identities using combinatorial methods as part of their exercises. These methods have several advantages over induction or algebra.

How to Count

An Introduction to Combinatorics, Second Edition

How to Count

Emphasizes a Problem Solving Approach A first course in combinatorics Completely revised, How to Count: An Introduction to Combinatorics, Second Edition shows how to solve numerous classic and other interesting combinatorial problems. The authors take an easily accessible approach that introduces problems before leading into the theory involved. Although the authors present most of the topics through concrete problems, they also emphasize the importance of proofs in mathematics. New to the Second Edition This second edition incorporates 50 percent more material. It includes seven new chapters that cover occupancy problems, Stirling and Catalan numbers, graph theory, trees, Dirichlet’s pigeonhole principle, Ramsey theory, and rook polynomials. This edition also contains more than 450 exercises. Ideal for both classroom teaching and self-study, this text requires only a modest amount of mathematical background. In an engaging way, it covers many combinatorial tools, such as the inclusion-exclusion principle, generating functions, recurrence relations, and Pólya’s counting theorem.

How to Count Coins

For Kids Ages 3-10

How to Count Coins

How to Count Coins is designed with simple basic lessons to help young children learn to recognize coins and count. Includes coin quizzes.

How to Count to Infinity

How to Count to Infinity

Do something amazing and learn a new skill thanks to the Little Ways to Live a Big Life books! Birds do it, bees do it, even educated fleas do it... Not falling in love, but counting. Animals and humans have been using numbers to navigate their way through the jungle of life ever since we all evolved on this planet. But this book will help you to do something that humans have only recently understood how to do: to count to regions that no animal has ever reached. By the end of this book you'll be able to count to infinity...and beyond. On our way to infinity we'll discover how the ancient Babylonians used their bodies to count to 60 (which gave us 60 minutes in the hour), how the number zero was only discovered in the 7th century by Indian mathematicians contemplating the void, why in China going into the red meant your numbers had gone negative and why numbers might be our best language for communicating with alien life. But for millennia contemplating infinity has sent even the greatest minds into a spin. Then at the end of the nineteenth century mathematicians discovered a way to think about infinity that revealed that it is a number that we can count. Not only that. They found that there are an infinite number of infinities, some bigger than others. Just using the finite neurons in your brain and the finite pages in this book, you'll have your mind blown discovering the secret of how to count to infinity.

How to Count It All Joy

When Faced with Insurmountable Circumstances!

How to Count It All Joy

In September 2002 she married the man of her dreams. In June 2005 they purchased their home in paradise. It was the perfect love nest, the kind of home most people can only dream about. Their private get-a-way was nestled in 5.75 acres of plush exotic land, with a towering forest of landscape and natural habitat, overlooking several creeks and streams with breath taking sunset views from every angle. It was secretly hidden from the world, a place where deer's and rabbits seek refuge; where the falcons soared and roamed freely without fear of discovery. It was the summer of their lives, with a newly built wrap-around deck that lit up the night. They were the envy of all their friends and neighbors. Until one day the perfect dream they once shared came crashing down around them! Their once perfect marriage would be put to the test. Voluntary humility is an honor and privilege best served with a willing, sincere and open heart. To be humbled by God, is an indescribable devastation of heartache and pain for which they would soon discover. September 2009 the flood they once mocked and avoided two years prior, returns with a wicked vengeance, only this time it would take most of the city and their home in paradise with it! Being homeless with only the clothes on their backs, they did not sin nor did they charge God with wrong. They were hard-pressed on every side, but not crushed; perplexed, but not in despair; persecuted, but not forsaken; struck down, but not destroyed. In this faith based book, Bernita Weston shares with the world how they were able to turn their tragedy into triumph. Find out, "How to Count it ALL Joy, When Faced with Insurmountable Circumstances!"

How to Count Animals, more or less

How to Count Animals, more or less

Most people agree that animals count morally, but how exactly should we take animals into account? A prominent stance in contemporary ethical discussions is that animals have the same moral status that people do, and so in moral deliberation the similar interests of animals and people should be given the very same consideration. In How to Count Animals, more or less, Shelly Kagan sets out and defends a hierarchical approach in which people count more than animals do and some animals count more than others. For the most part, moral theories have not been developed in such a way as to take account of differences in status. By arguing for a hierarchical account of morality - and exploring what status sensitive principles might look like - Kagan reveals just how much work needs to be done to arrive at an adequate view of our duties toward animals, and of morality more generally.

Mathematics of Choice

Or, How to Count Without Counting

Mathematics of Choice

A study of combinatorics--formulas used in solving problems that ask how many

The Child's Understanding of Number

The Child's Understanding of Number

The authors report the results of some half dozen years of research into when and how children acquire numerical skills. They provide a new set of answers to these questions, and overturn much of the traditional wisdom on the subject. Table of Contents: 1. Focus on the Preschooler 2. Training Studies Reconsidered 3. More Capacity Than Meets the Eye: Direct Evidence 4. Number Concepts in the Preschooler? 5. What Numerosities Can the Young Child Represent? 6. How Do Young Children Obtain Their Representations of Numerosity? 7. The Counting Model 8. The Development of the How-To-Count Principles 9. The Abstraction and Order-Irrelevance Counting Principles 10. Reasoning about Number 11. Formal Arithmetic and the Young Child's Understanding of Number 12. What Develops and How Conclusions References Index Reviews of this book: The publication of this book may mark a sea change in the way that we think about cognitive development. For the past two decades, the emphasis has been on young children's limitations... Now a new trend is emerging: to challenge the original assumption of young children's cognitive incapacity. The Child's Understanding of Number represents the most original and provocative manifestation to date of this new trend. --Contemporary Psychology Reviews of this book: Here at last is the book we have been waiting for, or at any rate known we needed, on the young child and number. The authors are at once sophisticated in their own understanding of number and rich in psychological intuition. They present a wealth of good experiments to support and guide their intuitions. And all is told in so simple and unalarming a manner that even the most pusillanimous will be able to read with enjoyment. --Canadian Journal of Psychology

Today I Learn to count - English & Korean [Bilingual]

Today I Learn to count - English & Korean [Bilingual]

"열 까지 셀 수 있니 ?" - This bilingual book aids learning through play of numbers one to ten in English and Korean. Children connect the words' sounds to the appealing pictures and keep them in their memory easily. Both languages are handled equally and assisst early bilingual speech comprehension. This title is the first of the MyFirstEbook-series, new titles following soon. . Early bilingual learning (English and Korean) . Appealing images for children . learning through play . book translations by native speakers . optimized for electronic reading devices can you count to ten? - 이 책은 아이가 놀이를 통해 영어와 동시에 한국어로 1부터 10까지 숫자를 세는 법을 쉽게 배우도록 도와 줍니다. 사물과 숫자를 소리내어 읽음과 동시에 그림을 보면서 좀더 효과적으로 기억을 할 수 있습니다. 한국어와 영어에 동시에 중점을 둠으로서 다문화 가정, 또는 이중언어로 자라는 아이들의 이해를 돕도록 합니다. 이 책은 '내 첫 전자책' 시리즈의 첫 책으로 앞으로 더 많은 책이 출간될 것입니다. . 영어 조기교육 . 흥미로운 그림 . 놀이를 통해 배움 . 원어민을 통한 수준있는 번역 . 전자책을 위한 최적화된 버젼