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A Spiral Workbook for Discrete Mathematics

A Spiral Workbook for Discrete Mathematics

A Spiral Workbook for Discrete Mathematics

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Detalles del libro:

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Año:2015
Editor:Open SUNY Textbooks
Páginas:307 páginas
Idioma:inglés
Desde:20/04/2016
Tamaño:1.87 MB
Licencia:CC-BY-NC-SA

Contenido:

There are many discrete mathematics textbooks available, so why did I decide to invest my time and energy to work on something that perhaps only I myself would appreciate?

Mathematical writings are full of jargon and conventions that, without proper guidance, are difficult for beginners to follow. In the past, students were expected to pick them up along the way on their own. Those who failed to do so would be left behind. Looking back, I consider myself lucky. It was by God’s grace that I survived all those years. Now, when I teach a mathematical concept, I discuss its motivation, explain why it is important, and provide a lot of examples. I dissect the proofs thoroughly to make sure everyone understands them. In brief, I want to show my students how to analyze mathematical problems.

Most textbooks typically hide all these details. They only show you the final polished products. By training, mathematicians love short and elegant proofs. This is reflected in their own writing. Yes, the results are beautiful, but it is a mystery how mathematicians come up with such ideas. I want a textbook that discusses mathematical concepts in greater detail. I want to teach my students how to read and write mathematical arguments. Since I could not find a textbook that suited my needs, I started writing lecture notes to supplement the main text. Marginal notes, hands-on exercises, summaries, and section exercises were subsequently added at different stages. The lecture notes have evolved into a full-length text.

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Why do I call this a workbook? There are many hands-on exercises designed to help students understand a new concept before they move on to the next. I believe the title Workbook reflects the nature of the book, because I expect the students to work on the hands-on exercises. But why spiral? Because the pedagogy is inspired by the spiral method. The idea is to revisit some themes and results several times throughout the course and each time further deepen your understanding. You will find some problems pop up more than once, and are solved in a different way each time. In other instances, a concept you learned earlier will be viewed from a new perspective, thus adding a new dimension to it.

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