chartrand gary mathematical proofs

This English translation of a Russian book presents the basic notions of differential and algebraic topology, which are indispensable for specialists and useful for research mathematicians and theoretical physicists. In particular, ideas and results are introduced related to manifolds, cell spaces, coverings and fibrations, homotopy groups, intersection index, etc. The author notes, "The lecture note origins of the book left a significant imprint on its style. It contains very few detailed proofs: I tried to give as many illustrations as possible and to show what really occurs in topology, not always explaining why it occurs." He concludes, "As a rule, only those proofs (or sketches of proofs) that are interesting per se and have important generalizations are presented." ...

Gentzen's cut-elimination theorem is widely used as a tool for meta-mathematical investigations. It is sometimes claimed however that the theorem and its proof have interest which is independent of these applications and derives from the information they supply about the structure of proofs in general. Ungar investigates this claim in the context of first order logic. Ungar gives an account of Gentzen's theorem for various formalisms and discusses the difficulties involved in treating these different versions uniformly, as instances of a single theorem which is not tied to a particular system of rules. By extending the theorem to a natural deduction calculus whose derivations are allowed to have more than one conclusion, Ungar argues that the different versions of the theorem are more or less natural specializations of a single result whose significance can be understood in terms of the proofs represented by formal derivations. A concluding discussion focuses on the relationship between proofs and formal derivations, and the role proofs may play as part of a general theory of evidence. ...

Discrete Mathematics combines a balance of theory and applications with mathematical rigor and an accessible writing style. The author uses a range of examples to teach core concepts, while corresponding exercises allow students to apply what they learn. Throughout the text, engaging anecdotes and topics of interest inform as well as motivate learners. The text is ideal for one- or two-semester courses and for students who are typically mathematics, mathematics education, or computer science majors. Part I teaches student how to write proofs; Part II focuses on computation and problem solving. The second half of the book may also be suitable for introductory courses in combinatorics and graph theory.

Now in its 7th edition, Mathematical Methods for Physicists continues to provide all the mathematical methods that aspiring scientists and engineers are likely to encounter as students and beginning researchers. This bestselling text provides mathematical relations and their proofs essential to the study of physics and related fields. While retaining the key features of the 6th edition, the new edition provides a more careful balance of explanation, theory, and examples.

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This book constitutes the referred proceedings of the First International Conference on Certified Programs and Proofs, CPP 2011, held in Kenting, Taiwan, in December 2011. The 24 revised regular papers presented together with 4 invited talks were carefully reviewed and selected from 49 submissions. They are organized in topical sections on logic and types, certificates, formalization, proof assistants, teaching, programming languages, hardware certification, miscellaneous, and proof perls....