Combinatorics Through Guided Discovery by Kenneth P. Bogart (PDF)

Description

This book is an introduction to combinatorial mathematics, also known as combinatorics. The book focuses especially but not exclusively on the part of combinatorics that mathematicians refer to as “counting.” The book consist almost entirely of problems. Some of the problems are designed to lead you to think about a concept, others are designed to help you figure out a concept and state a theorem about it, while still others ask you to prove the theorem. Other problems give you a chance to use a theorem you have proved. From time to time there is a discussion that pulls together some of the things you have learned or introduces a new idea for you to work with. Many of the problems are designed to build up your intuition for how combinatorial mathematics works. Above all, this book is dedicated to the principle that doing mathematics is fun. As long as you know that some of the problems are going to require more than one attempt before you hit on the main idea, you can relax and enjoy your successes, knowing that as you work more and more problems and share more and more ideas, problems that seemed intractable at first become a source of satisfaction later on. This book is released under an open source licence and is available in electronic form for free at http://bogart.openmathbooks.org/.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Interesting approach. Decent text. Good for someone self learning the material since generally one’s professor should be providing the guided discovery.

⭐I took an upper division combinatorics class about 15 years ago that used this textbook. It was unlike any other book that I had used before, where concepts were introduced through exercises. Lots of exercises. The entire class was basically doing incrementally harder problems that built upon each other. There was only a minor amount of explanation in the book. It’s a great concept, and it actually worked out really well.As a student who used this book, I really enjoyed it and appreciated the prompt to think as we discovered concepts. Now as an educator, I both respect and appreciate the creativity that went into the design of this book. It may require shifting how a course is run, such as using class time to work through problems in groups*, but I think it’s worth it.Also, it’s hard to beat this price. This book could have easily been produced through a standard publisher at 5-10 times its current price. The quality is there. A book being more expensive may correlate with higher quality, but this book breaks the typical mold in that regard, much as it broke the form of a traditional textbook format.*Yes, the pandemic does require a further shift, such as small group calls so students can work together, but it should still work out.

⭐I came across the book while studying integer partitions. The book has a very rich set of exercises. You can entertain yourself and your family and kids with these nice problems. The book is not so heavy, and can be your companion for a sunny day on the beach.

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