The Nuts and Bolts of Proofs: An Introduction to Mathematical Proofs explains the fundamental logic of mathematical arguments and demonstrates how they function. It provides methods for proofreading and writing. The methods for proving if/then statements by contradiction and contrapositive are covered in the book’s second chapter. Additionally, it has the negation clause and/or. It looks at a number of theorems, including the if and only-if, equivalence, existence, and uniqueness theorems. This chapter also discusses the use of counterexamples, mathematical induction, composite statements with many hypotheses and conclusions, and numerical equality. Additionally, the book offers mathematical material for practicing proof strategies. The Cartesian products, indexed families, functions, and relations are all included here. Exercises for review on a variety of subjects are provided in the book’s last chapter. This book is a goldmine for undergraduate engineering and physical science students.