Ed. 3.4, corrected - Independently published, 2025. - 380 p. - ISBN 0989472132. This book is an introduction to the language and standard proof methods of mathematics. It is a "bridge" from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for...
CRC Press, 2025. - 169 p. - ISBN 1032686197. A Beginner’s Guide to Mathematical Proof prepares mathematics majors for the transition to abstract mathematics, as well as introducing a wider readership of quantitative science students, such as engineers, to the mathematical structures underlying more applied topics. The text is designed to be easily utilized by both instructor...
Boca Raton: CRC Press, 2024. — 296 p. — (Textbooks in Mathematics). — ISBN 1032595981. This book introduces readers to the art of doing mathematical proofs. Proofs are the glue that holds mathematics together. They make connections between math concepts and show why things work the way they do. This book teaches the art of proofs using familiar high-school concepts, such as...
CSLI Publications, 1994. — 266 p. Hyperproof is a system for learning the principles of analytical reasoning and proof construction, consisting of a text and a Macintosh software program. Unlike traditional treatments of first-order logic, Hyperproof combines graphical and sentential information, presenting a set of logical rules for integrating these different forms of...
World Scientific Publishing Company, 2023. — 376 p. — eBook ISBN: 978-981-127-210-3. This textbook is aimed at transitioning high-school students who have already developed proficiency in mathematical problem solving from numerical-answer problems to proof-based mathematics. It serves to guide students on how to write and understand mathematical proofs. It covers proof...
Lulu Press, 2019. — 247 p. Metamath is a computer language and an associated computer program for archiving, verifying, and studying mathematical proofs at a very detailed level. The Metamath language incorporates no mathematics per se but treats all mathematical statements as mere sequences of symbols.You provide Metamath with certain special sequences (axioms) that tellit...
Arcler Press, 2023. — 424 p. “The Notion Of Mathematical Proof: Key Rules And Considerations” is an edited book consisting of 16 contemporaneous open-access articles that aim to cover the different aspects of learning and teaching mathematical proof. The first part of this book aims at summing up factors that influence the cognitive development required to successfully...
New York: Springer, 2022. — 498 p. Reverse mathematics studies the complexity of proving mathematical theorems and solving mathematical problems. Typical questions include: Can we prove this result without first proving that one? Can a computer solve this problem? A highly active part of mathematical logic and computability theory, the subject offers beautiful results as well...
Independently published, 2021. — 330 p. This textbook is designed for students. Rather than the typical definition-theorem-proof-repeat style, this text includes much more commentary, motivation and explanation. The proofs are not terse, and aim for understanding over economy. Furthermore, dozens of proofs are preceded by "scratch work" or a proof sketch to give students a...
College Publications, 2004. — 387 p. This book in categorial proof theory formulates in terms of category theory a generalization close to linear algebra of the notions of distributive lattice and Boolean algebra. These notions of distributive lattice category and Boolean category codify a plausible nontrivial notion of identity of proofs in classical propositional logic, which...
New York: Springer, 1994. — 202 p. In the last fiffteen years two seemingly unrelated problems, one in computer science and the other in measure theory, were solved by amazingly similar techniques from representation theory and from analytic number theory. One problem is the - plicit construction of expanding graphs («expanders»). These are highly connected sparse graphs whose...
Cambridge: Cambridge University Press, 2011. — 280 p. 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...
MAA Press, AMS, 2022. — 350 p. — (AMS/MAA Textbooks 68). — ISBN 9781470465148ю Доказательства и идеи: прелюдия к высшей математике Proofs and Ideas serves as a gentle introduction to advanced mathematics for students who previously have not had extensive exposure to proofs. It is intended to ease the student's transition from algorithmic mathematics to the world of mathematics...
Oxford University Press, 2021. — 431 p. — ISBN 978–0–19–289593–6. Введение в теорию доказательств An Introduction to Proof Theory provides an accessible introduction to the theory of proofs, with details of proofs worked out and examples and exercises to aid the reader's understanding. It also serves as a companion to reading the original pathbreaking articles by Gerhard...
Springer, 2021. — 139 p. — ISBN 978-3-030-68374-0. A compact and easily accessible book, it guides the reader in unravelling the apparent mysteries found in doing mathematical proofs. Simply written, it introduces the art and science of proving mathematical theorems and propositions and equips students with the skill required to tackle the task of proving mathematical...
Springer, 2021. — 139 p. — ISBN 978-3-030-68374-0. A compact and easily accessible book, it guides the reader in unravelling the apparent mysteries found in doing mathematical proofs. Simply written, it introduces the art and science of proving mathematical theorems and propositions and equips students with the skill required to tackle the task of proving mathematical...