Preface Preface to the LaTeX version
This document grew from lecture notes following the seventh edition of Discrete Mathematics and its Applications by Kenneth Rosen [13].
I used various versions of the notes in conjunction with the book over the years whenever I taught MAT 253 Discrete Mathematical Structures. I will continue to develop this document incorporating feedback from readers.
MAT 253 core course in the mathematics curriculum designed for mathematics majors as an early introduction to discrete mathematical structures, rigorous proof techniques, and mathematical programming.
The catalog description of MAT 253 is:
A rigorous introduction to discrete mathematical structures, proof techniques, and programming. Topics include sets, functions, sequences, relations, induction, propositional and predicate logic, modular arithmetic, and mathematical programming.
Upon successful completion of this course, students will be able to:
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define the fundamental discrete mathematical structures.
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identify and describe various types of relations.
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explain how RSA encryption allows for secure message transcription.
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translate pseudocode algorithms into Python scripts.
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compute the number of solutions to several arrangement problems.
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analyze simple algorithms and identify values of variables at various stages of completion.
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combine definitions and results produced in class to create rigorous proofs of basic statements about discrete mathematical structures.
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evaluate an argument for logical validity.
In writing this text, I wanted to produce an streamlined, yet inviting introduction to discrete structures. The text is interspersed with fun, yet (mostly) relevant xkcd comics. The prerequisites for the book are minimal; pre-calculus and an open mind. Foundations are built from definitions.
It is best to pair these notes with additional resources. Some free resources are identified below.
A major goal of this course is to teach you to communicate mathematics clearly. This involves learning precise statements of definitions, and learning to write clear, concise proofs. Here are two books that may help.
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Book of Proofby Richard Hammock: This book is an introduction to the standard methods of proving mathematical theorems. It has been approved by the American Institute of Mathematics’ Open Textbook Initiative.
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www.people.vcu.edu/~rhammack/BookOfProof/ -
The Art of Proofby Matthias Beck and Ross Geoghegan is an excellent introduction to writing good proofs. This book is not open source, but our library has a Springer subscription that includes this book. Go to the UNCG Library Catalog to find this book. You can download a free copy by entering your UNCG iSpartan credentials.
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link.springer.com/book/10.1007%2F978-1-4419-7023-7
I thank Office of the Provost and the University Libraries for the Open Educational Resources Mini-Grant in summer 2018 that allowed me the extra time to adjust the course syllabus to accommodate this text.
Thanks to Cliff Smyth and Sebastian Pauli for piloting the use of these notes in their courses. Thanks to others that found typos and mistakes, including Heather Parlaman.
Dan Yasaki
