• Title: Proof, Sets, and Logic
• Author(s): M. Randall Holmes
• Publisher: Boise State University (12/31/2023)
• Paperback: N/A
• eBook: PDF (481 pages)
• Language: English
• ISBN-10: N/A
• ISBN-13: N/A
• Share This:  

Book Description

Addressing the importance of constructing and understanding mathematical proofs, this book introduces key concepts from logic and set theory as well as the fundamental definitions of algebra to prepare readers for further study in the field of mathematics. The author supplies a seamless, hands-on presentation of number systems, utilizing key elements of logic and set theory and encouraging readers to abide by the fundamental rule that you are not allowed to use any results that you have not proved yet.

Abstraction is introduced as a tool, and special focus is dedicated to concrete, accessible applications, such as public key encryption, that are made possible by abstract ideas.

The book concludes with a self-contained proof of Abel's Theorem and an investigation of deeper set theory by introducing the Axiom of Choice, ordinal numbers, and cardinal numbers.

• M. Randall Holmes is a professor of mathematics at Boise State University.

• Amazon

• Mathematical Logic - Set Theory, Model Theory, Computability, etc
• Theory of Programming Languages
• Theory of Computation
• Introduction to Computer Science

• Proof, Sets, and Logic (M. Randall Holmes)
• The Mirror Site (1) - PDF
• The Mirror Site (2) - PDF, ePub, Kindle, etc.

• Proofs and Types (Jean-Yves Girard, et al.)

  Deals with the mathematical background of the application to computer science of aspects of logic on typed lambda calculus (namely the correspondence between propositions and types). Treats both the traditional logic and its applications to computer science.

• Language, Proof and Logic (Jon Barwise, et al)

  This book covers first-order language in a method appropriate for first and second courses in logic, and is specially useful to undergraduates of philosophy, computer science, mathematics, and linguistics.

• An Introduction to Set Theory (William A. R. Weiss)

  This book covers the basics: relations, functions, orderings, finite, countable, and uncountable sets, and cardinal and ordinal numbers, gives students sufficient grounding in a rigorous approach to the revolutionary results of set theory.

• Introduction to Mathematical Logic (Vilnis Detlovs, et al)

  This book explores the principal topics of mathematical logic. It covers propositional logic, first-order logic, first-order number theory, axiomatic set theory, and the theory of computability. Discusses the major results of Gödel, Church, Kleene, Rosser, and Turing.

• A Friendly Introduction to Mathematical Logic (Chris Leary)

  In this user-friendly book, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory, leading to rigorous proofs of Gödel's First and Second Incompleteness Theorems.

• Book of Proof, 3rd Edtion (Richard H. Hammack)

  This book is an introduction to the language and standard proof methods of mathematics. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra.

• Proofs and Concepts: The Fundamentals of Abstract Mathematics

  This undergraduate textbook provides an introduction to proofs, logic, sets, functions, and other fundamental topics of abstract mathematics. It helps students transition from solving problems to proving theorems.

• Mathematical Reasoning: Writing and Proof (Ted Sundstrom)

  Help students to develop logical thinking skills and to think abstractly, and write mathematical proofs using standard methods of mathematical proof including direct proofs, proof by contradiction, mathematical induction, case analysis, counterexamples.

• An Introduction to Mathematical Reasoning (Peter J. Eccles)

  The purpose of this book is to introduce the basic ideas of mathematical proof to students embarking on university mathematics. It eases students into the rigors of university mathematics.