Programming and Mathematical Thinking
Programming and Mathematical Thinking
A Gentle Introduction to Discrete Math Featuring Python
Allan M. Stavely
The New Mexico Tech Press
Socorro, New Mexico, USA
Programming and Mathematical Thinking
A Gentle Introduction to Discrete Math Featuring Python
Allan M. Stavely
Copyright ? 2014 Allan M. Stavely First Edition
Content of this book available under the Creative Commons Attribution-Noncommercial-ShareAlike License. See for details.
Publisher's Cataloguing-in-Publication Data
Stavely, Allan M Programming and mathematical thinking: a gentle introduction to discrete math featuring Python / Allan M. Stavely. xii, 246 p.: ill. ; 28 cm ISBN 978-1-938159-00-8 (pbk.) -- 978-1-938159-01-5 (ebook) 1. Computer science -- Mathematics. 2. Mathematics -- Discrete Mathematics. 3. Python (Computer program language).
QA 76.9 .M35 .S79 2014 004-dc22
OCLC Number: 863653804 Published by The New Mexico Tech Press, a New Mexico nonprofit corporation
The New Mexico Tech Press Socorro, New Mexico, USA
Once more, to my parents, Earl and Ann i
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Table of Contents
Preface ........................................................................................................ vii 1. Introduction ............................................................................................. 1
1.1. Programs, data, and mathematical objects ..................................... 1 1.2. A first look at Python .................................................................... 3 1.3. A little mathematical terminology ................................................ 10 2. An overview of Python ........................................................................... 17 2.1. Introduction ................................................................................. 17 2.2. Values, types, and names ............................................................. 18 2.3. Integers ........................................................................................ 19 2.4. Floating-point numbers ................................................................ 23 2.5. Strings .......................................................................................... 25 3. Python programs .................................................................................... 29 3.1. Statements ................................................................................... 29 3.2. Conditionals ................................................................................ 31 3.3. Iterations ..................................................................................... 35 4. Python functions ..................................................................................... 41 4.1. Function definitions ..................................................................... 41 4.2. Recursive functions ...................................................................... 43 4.3. Functions as values ...................................................................... 45 4.4. Lambda expressions ..................................................................... 48 5. Tuples ..................................................................................................... 51 5.1. Ordered pairs and n-tuples .......................................................... 51 5.2. Tuples in Python .......................................................................... 52 5.3. Files and databases ...................................................................... 54 6. Sequences ............................................................................................... 57 6.1. Properties of sequences ................................................................ 57 6.2. Monoids ...................................................................................... 59 6.3. Sequences in Python ..................................................................... 64 6.4. Higher-order sequence functions .................................................. 67 6.5. Comprehensions .......................................................................... 73 6.6. Parallel processing ....................................................................... 74 7. Streams ................................................................................................... 83 7.1. Dynamically-generated sequences ................................................ 83 7.2. Generator functions ..................................................................... 85
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