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 work. It provides them with techniques they can use to gain an inside view of the subject, reach other results, remember results more easily, or rederive them if the results are forgotten.A flow chart graphically demonstrates the basic steps in the construction of any proof and numerous examples illustrate the method and detail necessary to prove various kinds of theorems.

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

Intended as a supplement for undergraduate courses in higher mathematics (including Linear Algebra and Geometry), discrete mathematics courses in computer science, and as a primer to assist engineering and physical science students on fundamental proof techniques

Introduction and Basic Terminology General Suggestions Some basic Techniques Used in Proving a Theorem of the Form :If A 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 of the Exercises at the End of the Sections and the Review Exercises Other Books on the Subject of Proofs and Mathematical Writing