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Analysis with an Introduction to Proof
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Steven R Lay
For courses in undergraduate Analysis (an easy one) and Transition to Advanced Mathematics. This text helps fill in the groundwork students need to succeed in real analysis--often considered the most difficult course in the undergraduate curriculum. By introducing logic and by emphasizing the structure and nature of the arguments used, Lay helps ...
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How to Read and Do Proofs: An Introduction to Mathematical Thought Processes
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Daniel Solow
When engineers, computer scientists, and economists need to learn how to read, think about, and create proofs, they turn to Solow. In order to make the material more relevant, the exercises in each chapter have been revised and expanded. New and more complete discussions are included on how to use a previously-proved proposition in both the ...
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Q.E.D.: Beauty in Mathematical Proof
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Burkard Polster
Q.E.D. presents some of the most famous mathematical proofs in a charming book that will appeal to nonmathematicians and math experts alike. Grasp in an instant why Pythagoras's theorem must be correct. Follow the ancient Chinese proof of the volume formula for the frustrating frustum, and Archimedes' method for finding the volume of a sphere. ...
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Math Proofs Demystified
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Stan Gibilisco
Almost every student has to study some sort of mathematical proofs, whether it be in geometry, trigonometry, or with higher-level topics. In addition, mathematical theorems have become an interesting course for many students outside of the mathematical arena, purely for the reasoning and logic that is needed to complete them. Therefore, it is not ...
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Mathematical Proofs: A Transition to Advanced Mathematics
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Gary Chartrand, Albert D Polimeni, Ping Zhang
Mathematical Proofs: A Transition to Advanced Mathematics, Second Edition, prepares students for the more abstract mathematics courses that follow calculus. This text introduces students to proof techniques and writing proofs of their own. As such, it is an introduction to the mathematics enterprise, providing solid introductions to relations, ...
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The Nuts and Bolts of Proofs: An Introduction to Mathematical Proofs
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Antonella Cupillari
"The Nuts and Bolts of Proof" instructs students on the basic logic of mathematical proofs, showing how and why proofs of mathematical statements work. It provides them with techniques they can use to gain an inside view of the subject, reach other results, remember results more easily, or rederive them if the results are forgotten. A flow chart ...
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An Introduction to Mathematical Reasoning
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by
Peter Eccles
The purpose of this book is to introduce the basic ideas of mathematical proof to students embarking on university mathematics. The emphasis is on helping the reader in understanding and constructing proofs and writing clear mathematics. This is achieved by exploring set theory, combinatorics and number theory, topics which include many ...
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Tracking Reason: Proof, Consequence, and Truth
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Jody Azzouni
When ordinary people - mathematicians among them - take something to follow (deductively) from something else, they are exposing the backbone of our self-ascribed ability to reason. Jody Azzouni investigates the connection between that ordinary notion of consequence and the formal analogues invented by logicians. One claim of the book is that, ...
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The Nuts and Bolts of Proofs
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by
Antonella Cupillari
This book leads readers through a progressive explanation of what mathematical proofs are, why they are important, and how they work, along with a presentation of basic techniques used to construct proofs. The Second Edition presents more examples, more exercises, a more complete treatment of mathematical induction and set theory, and it ...
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Journey Into Mathematics: An Introduction to Proofs
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by
Joseph J Rotman
The book is designed for self study or "bridge courses" that prepare students finishing calculus for first courses in real variables and abstract algebra.Prompting students to do mathematics, not merely read about it, this interesting and uniquely enjoyable text prepares students for reading and writing proofs by having them do just that at the ...
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Mathematical Reasoning: Writing and Proof
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by
Ted Sundstrom
For one-semester courses in Transition to Advanced Mathematics that emphasize the construction and writing of mathematical proofs. Focusing on the formal development of mathematics, this text teaches students how to read and understand mathematical proofs and to construct and write mathematical proofs. Developed as a text for a writing course ...
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Proofs and Fundamentals: A First Course in Abstract Mathematics
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by
Ethan D Bloch
This text is designed as a "transition" textbook to introduce undergraduates to the writing of vigorous mathematical proofs, and to such fundamental mathematical ideas as sets, functions, relations, and cardinality. It serves as a bridge between computational courses, e.g. calculus, and more theoretical, proofs-oriented courses such as linear ...
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Numbers and Proofs
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by
Reg Allenby
'Numbers and Proofs' presents a gentle introduction to the notion of proof to give the reader an understanding of how to decipher others' proofs as well as construct their own. Useful methods of proof are illustrated in the context of studying problems concerning mainly numbers (real, rational, complex and integers). An indispensable guide to all ...
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The Moment of Proof
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by
Donald C Benson
When Archimedes, while bathing, suddenly hit upon the principle of buoyancy, he ran wildly through the streets of Syracuse, stark naked, crying "eureka!" In The Moment of Proof, Donald Benson attempts to convey to general readers the feeling of eureka--the joy of discovery--that mathematicians feel when they first encounter an elegant proof. This ...
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Metamathematics, Machines, and Godel's Proof
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by
N Shankar
Mathematicians from Leibniz to Hilbert have sought to mechanise the verification of mathematical proofs. Developments arising out of Godel's proof of his incompleteness theorem showed that no computer program could automatically prove true all the theorems of mathematics. In practice, however, there are a number of sophisticated automated ...
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An Accompaniment to Higher Mathematics
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by
George Exner
This text prepares undergraduate mathematics students to meet two challenges in the study of mathematics, namely, to read mathematics independently and to understand and write proofs. The book begins by teaching how to read mathematics actively, constructing examples, extreme cases, and non-examples to aid in understanding an unfamiliar theorem or ...
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The Moment of Proof: Mathematical Epiphanies
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by
Donald C Benson
This text attempts to show the power of mathematics to a readership with a background in only elementary algebra, by presenting in a very accessible form some fundamental proofs, mostly having to do with number theory. The goal is to recreate for the lay reader a facsimile of the pleasure and excitement that mathematicians experience through ...
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Logic of Provability
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by
George S Boolos
This book, written by one of the most distinguished of contemporary philosophers of mathematics, is a fully rewritten and updated successor to the author's earlier The Unprovability of Consistency (1979). Its subject is the relation between provability and modal logic, a branch of logic invented by Aristotle but much disparaged by philosophers and ...
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Basic Proof Theory
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by
Anne S Troelstra
This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; ...
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The Age of Alternative Logics: Assessing Philosophy of Logic and Mathematics Today
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by
Johan Van Benthem (Editor), Gerhard Heinzmann (Editor), Manuel Rebuschi (Editor)
In the last century, developments in mathematics, philosophy, physics, computer science, economics and linguistics have proven important for the development of logic. There has been an influx of new ideas, concerns, and logical systems reflecting a great variety of reasoning tasks in the sciences. This volume reflects the multi-dimensional nature ...
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Proof Theory: A Selection of Papers from the Leeds Proof Theory Programme 1990
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Harold Simmons (Editor), Stanley S Wainer (Editor), Peter Aczel
The lecture courses in this work are derived from the SERC 'Logic for IT' Summer School and Conference on Proof Theory held at Leeds University. The contributions come from acknowledged experts and comprise expository and research articles; put together in this book they form an invaluable introduction to proof theory that is aimed at both ...
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Sets and Proofs
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by
S Barry Cooper (Editor), John K Truss (Editor), N J Hitchin (Editor)
Together, Sets and Proofs and its sister volume Models and Computability will provide readers with a comprehensive guide to the current state of mathematical logic. All the authors are leaders in their fields and are drawn from the invited speakers at 'Logic Colloquium '97' (the major international meeting of the Association of Symbolic Logic). It ...
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Iterated Inductive Definitions and Subsystems of Analysis: Recent Proof-Theoretical Studies
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Wilfried Buchholz
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Axiomatising the logic of computer programming
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by
R Goldblatt
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Reductive Logic and Proof-Search: Proof Theory, Semantics, and Control
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David J Pym, Eike Ritter
This book is a specialized monograph on the development of the mathematical and computational metatheory of reductive logic and proof-search, areas of logic that are becoming important in computer science. A systematic foundational text on these emerging topics, it includes proof-theoretic, semantic/model-theoretic and algorithmic aspects. The ...
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