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April 4, 2019
Like its predecessor, Proofs without Words, this book is a collection of pictures or diagrams that help the reader see why a particular mathematical statement may be true, and how one could begin to go about proving it. While in Read more…
March 10, 2019
Structural proof theory is a branch of logic that studies the general structure and properties of logical and mathematical proofs. This book is both a concise introduction to the central results and methods of structural proof theory, and a work Read more…
February 24, 2019
A hands-on introduction to the tools needed for rigorous andtheoretical mathematical reasoningSuccessfully addressing the frustration many students experience asthey make the transition from computational mathematics to advancedcalculus and algebraic structures, Theorems, Corollaries, Lemmas,and Methods of Proof equips students with the Read more…
February 12, 2019
This book reports recent major advances in automated reasoning in geometry. The authors have developed a method and implemented a computer program which, for the first time, produces short and readable proofs for hundreds of geometry theorems.The book begins with Read more…
January 1, 2019
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 Read more…
December 17, 2018
The development of mathematical competence — both by humans as a species over millennia and by individuals over their lifetimes — is a fascinating aspect of human cognition. This book explores when and why the rudiments of mathematical capability first Read more…
December 10, 2018
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 Read more…
December 5, 2018
In 1824 a young Norwegian named Niels Henrik Abel proved conclusively that algebraic equations of the fifth order are not solvable in radicals. In this book Peter Pesic shows what an important event this was in the history of thought. Read more…
December 4, 2018
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 Read more…
November 6, 2018
The Art of Proof is designed for a one-semester or two-quarter course. A typical student will have studied calculus (perhaps also linear algebra) with reasonable success. With an artful mixture of chatty style and interesting examples, the student’s previous intuitive Read more…
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