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 Elias Zakon - The Trillia Group
The book will help students complete the transition from purely manipulative to rigorous mathematics. It covers basic set theory, induction, quantifiers, functions and relations, equivalence relations, properties of the real numbers, fields, etc.
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.
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 Peter J. Eccles - Cambridge University Press
This book introduces basic ideas of mathematical proof to students embarking on university mathematics. The emphasis is on constructing proofs and writing clear mathematics. This is achieved by exploring set theory, combinatorics and number theory.