The Nuts and Bolts of Proofs

The Nuts and Bolts of Proof instructs students on the basic logic of mathematical proofs, showing how and why proofs of mathematical statements. It provides them with an inside of them, and it gives them the opportunity to give them the opportunity to do so. excellent examples illustrate the method and detail necessary.

* The "List of Symbols" has been extended.
* Set Theory section has been strengthened with more examples and exercises.
* Addition of "A Collection of Proofs"

Introduction and Basic Terminology
General Suggestions
Some basic Techniques Used in Proving and Theorem of the Form: If and then B "
Direct Proof
Related Statements
Proof by Contra positive
How to Construct the Negation of a Statement
Special Kinds of Theorems
"If and only if" or Equivalence Theorems
Use of Counterexamples
Mathematical Induction
Existence Theorems
Uniqueness Theorems
Equality of Sets
Equality of Numbers
Composite Statements
Limits
Review Exercises
Exercises without Soultions
Collection of Proofs
. Solutions for the Exercises at the End of the Sections
Other Books on the Subject of Proofs and Mathematical Writing