"Chapter five is the shortest but the most interesting and helpful. I could see this as a book used for both a freshman seminar and a senior level capstone course . . . Students could use the book as a reference or exercises could be assigned from each chapter. I would also recommend this book to a senior math major planning on attending graduate school as a reference or for summer reading." Maa This book introduces students to the art and craft of writing proofs, beginning with the basics of writing proofs and logic, and continuing on with more in-depth issues and examples of creating proofs in different parts of mathematics, as well as introducing proofs-of-correctness for algorithms. The creation of proofs is covered for theorems in both discrete and continuous mathematics, and in difficulty ranging from elementary to beginning graduate level. Just beyond the standard introductory courses on calculus, theorems and proofs become central to mathematics. Students often find this emphasis difficult and new. This book is a guide to understanding and creating proofs. It explains the standard “moves” in mathematical proofs: direct computation, expanding definitions, proof by contradiction, proof by induction, as well as choosing notation and strategies.

In this major contribution to the intellectual history of Cambridge University, Dr Garland takes as her main theme the rise of a specific educational ideal in early Victorian Cambridge, how it enjoyed a moment of triumph, and then how it fell under the impact of a new set of challenges. The story revolves around the careers of a group of 'conservative reformers', led by the Trinity dons Whewell and Sedgwick. They were the self-designated providers of a refurbished version of traditional Cambridge values in the new environment of a rapidly industrializing England, and took as their ideal a general unified core of knowledge based upon mathematics, classics and moral philosophy. They wished to retain this general structure because they believed it corresponded to the structure of the human mind and its mental faculties. For them, belief in the harmony of science and religion was part and parcel of their basically Broad Church religious views.

Product Description: This radical, profoundly scholarly book explores the purposes and nature of proof in a range of historical settings. It overturns the view that the first mathematical proofs were in Greek geometry and rested on the logical insights of Aristotle by showing how much of that view is an artefact of nineteenth-century historical scholarship...read more

Product Description: After being an open question for sixty years the Tarski conjecture was answered in the affirmative by Olga Kharlampovich and Alexei Myasnikov and independently by Zlil Sela. This book is an examination of the material on the general elementary theory of groups that is necessary to begin to understand the proofs...read more

Product Description: Although sequent calculi constitute an important category of proof systems, they are not as well known as axiomatic and natural deduction systems. Addressing this deficiency, Proof Theory: Sequent Calculi and Related Formalisms presents a comprehensive treatment of sequent calculi, including a wide range of variations...read more

This book continues from where the authors' previous book, Structural Proof Theory, ended. It presents an extension of the methods of analysis of proofs in pure logic to elementary axiomatic systems and to what is known as philosophical logic. A self-contained brief introduction to the proof theory of pure logic is included that serves both the mathematically and philosophically oriented reader. The method is built up gradually, with examples drawn from theories of order, lattice theory and elementary geometry. The aim is, in each of the examples, to help the reader grasp the combinatorial behaviour of an axiom system, which typically leads to decidability results. The last part presents, as an application and extension of all that precedes it, a proof-theoretical approach to the Kripke semantics of modal and related logics, with a great number of new results, providing essential reading for mathematical and philosophical logicians.

Product Description: This book treats bounded arithmetic and propositional proof complexity from the point of view of computational complexity. The first seven chapters include the necessary logical background for the material and are suitable for a graduate course...read more

The notion of burden of proof and its companion notion of presumption are central to argumentation studies. This book argues that we can learn a lot from how the courts have developed procedures over the years for allocating and reasoning with presumptions and burdens of proof, and from how artificial intelligence has built precise formal and computational systems to represent this kind of reasoning. The book provides a model of reasoning with burden of proof and presumption, based on analyses of many clearly explained legal and non-legal examples. The model is shown to fit cases of everyday conversational argumentation as well as argumentation in legal cases. Burden of proof determines (1) under what conditions an arguer is obliged to support a claim with an argument that backs it up and (2) how strong that argument needs to be to prove the claim in question.

Focusing on the formal development of mathematics, this book shows readers how to read, understand, write, and construct mathematical proofs. Uses elementary number theory and congruence arithmetic throughout. Focuses on writing in mathematics. Reviews prior mathematical work with “Preview Activities” at the start of each section. Includes “Activities” throughout that relate to the material contained in each section. Focuses on Congruence Notation and Elementary Number Theorythroughout. For professionals in the sciences or engineering who need to brush up on their advanced mathematics skills.     Mathematical Reasoning: Writing and Proof, 2/E Theodore Sundstrom

Product Description: “Proofs and Fundamentals: A First Course in Abstract Mathematics” 2nd edition is designed as a "transition" course to introduce undergraduates to the writing of rigorous mathematical proofs, and to such fundamental mathematical ideas as sets, functions, relations, and cardinality...read more

For "baby" analysis with single variable only. Appropriate for one term courses in analysis and advanced calculus. Text starts with a little logic and how to construct a proof. Revision features: material on the topology of the reals has been expanded and divided into two sections. Two optional sections on metric spaces and continuity in metric spaces have been added.

Product Description: This helpful workbook-style "bridge" book introduces students to the foundations of advanced mathematics, spanning the gap between a practically oriented calculus sequence and subsequent courses in algebra and analysis with a more theoretical slant...read more

Product Description: The primary purpose of this undergraduate text is to teach students to do mathematical proofs. It enables readers to recognize the elements that constitute an acceptable proof, and it develops their ability to do proofs of routine problems as well as those requiring creative insights...read more

Product Description: This is the first book-length treatment of hybrid logic and its proof-theory. Hybrid logic is an extension of ordinary modal logic which allows explicit reference to individual points in a model (where the points represent times, possible worlds, states in a computer, or something else)...read more