Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

A Logical Introduction to Proof is a unique textbook that uses a logic-first approach to train and guide undergraduates through a transition or “bridge” course  between calculus and advanced mathematics courses.  The author’s approach  prepares the student for the rigors required in future mathematics courses and is appropriate for majors in mathematics, computer science, engineering, as well as other applied mathematical sciences. It may also be beneficial as a supplement for students at the graduate level who need guidance or reference for writing proofs.   Core topics covered are logic, sets, relations, functions, and induction, where logic is the instrument for analyzing the structure of mathematical assertions and is a tool for composing mathematical proofs. Exercises are given at the end of each section within a chapter. Chapter 1 focuses on propositional logic while Chapter 2 is devoted to the logic of quantifiers. Chapter 3 methodically presents the key strategies that are used in mathematical proofs; each presented as a proof diagram. Every proof strategy is carefully illustrated by a variety of mathematical theorems concerning the natural, rational, and real numbers. Chapter 4 focuses on mathematical induction and concludes with a proof of the fundamental theorem of arithmetic. Chapters 5 through 7 introduce students to the essential concepts that appear in all branches of mathematics. Chapter 8 introduces the basic structures of abstract algebra: groups, rings, quotient groups, and quotient rings. Finally, Chapter 9 presents proof strategies that explicitly show students how to deal with the fundamental definitions that they will encounter in real analysis, followed by numerous examples of proofs that use these strategies.  The appendix provides a useful summary of strategies for dealing with proofs.

Proof theory -- Data processing. --- Proof theory -- History. --- Proof theory. --- Logic, Symbolic and mathematical --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Logic, Symbolic and mathematical. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics. --- Mathematical logic. --- Mathematics, general. --- Mathematical Logic and Foundations. --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Math --- Science

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Commemorating the 50th anniversary of the first time a mathematical theorem was proven by a computer system, Freek Wiedijk initiated the present book in 2004 by inviting formalizations of a proof of the irrationality of the square root of two from scientists using various theorem proving systems. The 17 systems included in this volume are among the most relevant ones for the formalization of mathematics. The systems are showcased by presentation of the formalized proof and a description in the form of answers to a standard questionnaire. The 17 systems presented are HOL, Mizar, PVS, Coq, Otter/Ivy, Isabelle/Isar, Alfa/Agda, ACL2, PhoX, IMPS, Metamath, Theorema, Leog, Nuprl, Omega, B method, and Minlog.

Proof theory --- Algebra --- Algèbre --- Data processing. --- Computer programs. --- Logiciels --- Computer programs --- Computer Science --- Mechanical Engineering - General --- Engineering & Applied Sciences --- Mathematics --- Mechanical Engineering --- Physical Sciences & Mathematics --- Information Technology --- Artificial Intelligence --- Computer science. --- Software engineering. --- Mathematical logic. --- Artificial intelligence. --- Computer Science. --- Artificial Intelligence (incl. Robotics). --- Software Engineering. --- Mathematical Logic and Formal Languages. --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Computer software engineering --- Engineering --- Informatics --- Science --- Artificial Intelligence. --- Proof theory - Data processing --- Algebra - Computer programs