Proofs in Mathematics
by Alexander Bogomolny
Publisher: Interactive Mathematics Miscellany and Puzzles 2013
Number of pages: 272
I'll distinguish between two broad categories. The first is characterized by simplicity. In the second group the proofs will be selected mainly for their charm. Most of the proofs in this book should be accessible to a middle grade school student.
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by Joseph Fields - Southern Connecticut State University
The point of this book is to help you with the transition from doing math at an elementary level (concerned mostly with solving problems) to doing math at an advanced level (which is much more concerned with axiomatic systems and proving statements).
by Patrick Keef, David Guichard, Russ Gordon - Whitman College
Contents: Logic (Logical Operations, De Morgan's Laws, Logic and Sets); Proofs (Direct Proofs, Existence proofs, Mathematical Induction); Number Theory (The Euclidean Algorithm); Functions (Injections and Surjections, Cardinality and Countability).
by James Franklin, Albert Daoud - Kew Books
This is a small (98 page) textbook designed to teach mathematics and computer science students the basics of how to read and construct proofs. The book takes a straightforward, no nonsense approach to explaining the core technique of mathematics.
by Farshid Hajir - University of Massachusetts
Problem Solving, Inductive vs. Deductive Reasoning, An introduction to Proofs; Logic and Sets; Sets and Maps; Counting Principles and Finite Sets; Relations and Partitions; Induction; Number Theory; Counting and Uncountability; Complex Numbers.