How to Prove It: A Structured Approach
Professor Daniel J. Velleman teaches mathematics and statistics. He has done a lot of work in the subject of mathematical logic, especially set theory. He has, nevertheless, written work on a variety of topics, including combinatorics, probability, topology, analysis, mathematics philosophy, and quantum mechanics foundations.
Although proofs are important in advanced mathematics and theoretical computer science, many students struggle the first time they take a course that includes them. The third edition of this best-selling text teaches students how to shift from solving problems to proving theorems by teaching them how to read and write proofs. This new edition exposes students to the world of advanced mathematics through the mastering of proofs, with over 150 new tasks and a new chapter on number theory.
To familiarize students with the language of mathematics and how it is interpreted, the book begins with basic ideas of logic and set theory. These ideas serve as the foundation for an examination of approaches for gradually constructing sophisticated proofs, with detailed scratch work' parts exposing the mechanism of proofs regarding numbers, sets, relations, and functions. How to Prove It: A Structured Approach will be valuable to everyone interested in logic and proofs, including computer scientists, philosophers, linguists, and, of course, mathematicians, as it assumes no prior knowledge beyond normal high school arithmetic.
Some reviews about this book: “This book is my go-to resource for students struggling with how to write mathematical proofs. Beyond its plentiful examples, Velleman lays out the techniques and principles so often glossed over in other texts.”
Author: Daniel J. Velleman
Link to buy: https://www.amazon.com/-/es/Daniel-J-Velleman/dp/1108439535/ref=sr_1_1?
