"A textbook for students who are learning how to write a mathematical proof, a validation of the truth of a mathematical statement"--
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"This book offers an introduction to the art and craft of proof writing. The author, a leading research mathematician, presents a series of engaging and compelling mathematical statements with interesting elementary proofs. These proofs capture a wide range of topics, including …
A classical beginning -- Multiple proof -- Number theory -- Mathematical induction -- Discrete mathematics -- Proofs without words -- Theory of games -- Pick's theorem -- Lattice-point polygons -- Polygonal dissection -- Functions and relations -- Graph theory -- Infinity -- Ord…
"A textbook for students who are learning how to write a mathematical proof, a validation of the truth of a mathematical statement"--
"This book provides an accessible step-by-step account of Arnold's classical proof of the Kolmogorov-Arnold-Moser (KAM) Theorem. It begins with a general background of the theorem and proves the famous Liouville-Arnold theorem for integrable systems and introduces Kneser's tori …
INTRODUCTION TO ARNOLD'S PROOF OF THE KOLMOGOROV-ARNOLD-MOSER THEOREM This book provides an accessible step-by-step account of Arnold's classical proof of the Kolmogorov-Arnold-Moser (KAM) Theorem. It begins with a general background of the theorem, proves the famous Liouville-A…
Hamilton theory -- Preliminaries -- Outline of the KAM proof -- Proof of the KAM theorem -- Analytic lemmas -- Geometric lemmas -- Convergence lemmas -- Arithmetic lemmas. "This book provides an accessible step-by-step account of Arnold's classical proof of the Kolmogorov-Arnol…
This book is a monograph on the topic of Proof-Theoretic Semantics, a theory of meaning constituting an alternative to the more traditional Model-Theoretic Semantics. The latter regards meaning as truth-conditions (in arbitrary models), the former regards meaning as canonical de…
The volume is dedicated to the 60th birthday of Professor Gerhard Jager, who has been instrumental in shaping and promoting logic in Switzerland for the last 25 years. It comprises contributions from the symposium Advances in Proof Theory, which was held in Bern in December 2013.
The volume is dedicated to the 60th birthday of Professor Gerhard Jäger, who has been instrumental in shaping and promoting logic in Switzerland for the last 25 years. It comprises contributions from the symposium Advances in Proof Theory, which was held in Bern in December 2013.
How the concept of proof has enabled the creation of mathematical knowledge. The Story of Proof investigates the evolution of the concept of proof--one of the most significant and defining features of mathematical thought--through critical episodes in its history. From the Pytha…
How the concept of proof has enabled the creation of mathematical knowledge. The Story of Proof investigates the evolution of the concept of proof--one of the most significant and defining features of mathematical thought--through critical episodes in its history. From the Pytha…
How the concept of proof has enabled the creation of mathematical knowledgeThe Story of Proof investigates the evolution of the concept of proof--one of the most significant and defining features of mathematical thought--through critical episodes in its history. From the Pythago…
There are many bits and pieces of folklore in mathematics that are passed down from advisor to student, or from collaborator to collaborator, but which are too fuzzy and nonrigorous to be discussed in the formal literature. Traditionally, it was a matter of luck and location as …