Preface to Discrete Mathematics: Mathematical Reasoning and Proof with Puzzles, Patterns, and Games pdf
This book is written for students who are prepared to make a first departure from the deeply worn path that leads from arithmetic to calculus in the typical mathematics curriculum. Because of its deliberate pace and emphasis on student readability as well as its treatment of engaging topics, this book is suitable for courses taught at several different levels.
• This text originated as notes for an enrichment course in discrete mathematics for talented high school students. This course has been taught for over ten years as part of the core curriculum of the Pennsylvania Governor’s School for the Sciences.
•The book has been used for five years for a discrete math course at Shippensburg University. This course is required for students majoring in mathematics or computer science as well as those students majoring in elementary education with a concentration in mathematics.
•In its most recent life, this book has also been used by several instructors as the basis for a “transition” course in a mathematics major program. The gentle introduction to abstraction and the emphasis on written proof have been well received by students at this level as well.
Discrete Mathematics: Mathematical Reasoning and Proof with Puzzles, Patterns, and Games pdf download
Discrete mathematics suffers somewhat from having no historically established place in the K-12 mathematics curriculum. According to the National Council of Teachers of Mathematics, discrete math should be emphasized at every level of mathematics. Meanwhile college curriculum committees struggle with what one-semester course ought to be used to address basic discrete math concepts. Since it seems unlikely that there will be a trend in colleges to create a three or four semester sequence in discrete mathematics, perhaps the best one can do is to apply some careful thought and sound pedagogy to what will happen in the crucial one or two semesters.
The approach taken in our book is one of establishing fundamental skills and building connections between basic concepts instead of surveying as many topics as possible in one semester. There is enough variety of topics for the instructor to have some choice for the emphasis of his or her course. However, the instructor might find that a favorite topic is treated only in a specific context instead of more generally For example, in our book, instead of an entire chapter on binary relations, there are three non-contiguous sections placed at different points in the overall development. By stressing connections between topics, we believe we are enhancing student understanding and avoiding the time-consuming task of thoroughly discussing every aspect of each topic before moving on.
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