LOGIC, SETS AND THE TECHNIQUES OF MATHEMATICAL PROOFS

About the Book

As its title indicates, this book is about logic, sets and mathematical proofs. It is a careful, patient and rigorous introduction for readers with very limited mathematical maturity. It teaches the reader not only how to read a mathematical proof, but also how to write one. To achieve this, we carefully lay out all the various proof methods encountered in mathematical discourse, give their logical justifications, and apply them to the study of topics [such as real numbers, relations, functions, sequences, fine sets, infinite sets, countable sets, uncountable sets and transfinite numbers] whose mastery is important for anyone contemplating advanced studies in mathematics. The book is completely self-contained; since the prerequisites for reading it are only a sound background in high school algebra. Though this book is meant to be a companion specifically for senior high school pupils and college undergraduate students, it will also be of immense value to anyone interested in acquiring the tools and way of thinking of the mathematician.

About the Author

Brahima Mbodje is an educator, mathematician, control system engineer, and researcher. He has taught mathematics, computer science, electronics, and control theory for many schools. Among these institutions are: Universite Paul Sabatier, Saint Mary's University, Fordham University, Chowan University, The University of South Dakota, Rust College, Lenoir-Rhyne University, Gambia Technical Training Institute, Sukuta Secondary Technical School and Holly Springs High School. He holds an Associate degree in Mathematics, Computer Science and Physics; a Bachelor degree in Control Engineering; and a Ph.D. in Mathematical Control Theory from Universite Paul Sabatier [Toulouse III] in Toulouse, France. He now lives in Charlotte NC. His passion, as an educator, is to help high school pupils and college undergraduates demystify the so-called advanced or higher mathematics, by rendering this more accessible to them. He can be reached by e-mail at: mbodjeb@gmail.com.