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Proofs and fundamentals : a first course in abstracts mathematics / Ethan D. Bloch

Main Author Bloch, Ethan D., 1956- Country Estados Unidos. Publication Boston : Birkhäuser, cop. 2000 Description XX, 424 p. : il. ; 25 cm ISBN 0-8176-4111-4 CDU 510.2
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Monografia Biblioteca Geral da Universidade do Minho
BGUM 510.2 - B Checked out 2022-01-27 281375

Licenciatura em Ciências da Computação Tópicos de Matemática 1º semestre

Licenciatura em Matemática Tópicos de Matemática 1º semestre

Mestrado em Ensino de Matemática no 3º Ciclo do Ensino Básico e no Secundário A Prova em Matemática 1º semestre

Monografia Biblioteca Geral da Universidade do Minho
BGUM 510.2 - B Não requisitável | Not for loan 281376
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Enhanced descriptions from Syndetics:

The aim of this book is to help students write mathematics better. Throughout it are large exercise sets well-integrated with the text and varying appropriately from easy to hard. Basic issues are treated, and attention is given to small issues like not placing a mathematical symbol directly after a punctuation mark. And it provides many examples of what students should think and what they should write and how these two are often not the same.

Reviews provided by Syndetics


These three books expand the pedagogical literature for what is known as "transition" or "introduction to abstraction" courses. Intended to span the conceptual gap between calculus and upper-level courses, and to prepare students for the abstractions and more rigorous arguments of linear algebra, abstract algebra, and analysis, such courses frequently attempt to develop an understanding of fundamentals of set theory, logic, and proof. This understanding is then applied to various areas of mathematics to help students attain a facility with the construction of proofs. Thus, the fundamentals are not developed in a vacuum. All three books adhere more or less closely to this description. Liebeck writes for a British audience and spends the least time on set theory and notions of proof, preferring rather to jump right into applications. As a result, Liebeck has geometric and analytic topics that the others do not; that said, the length of the book does not allow for discussion of any topic to the lengths at which Bloch and Hummel are able to go. Bloch and Hummel spend similar effort (about half their respective books) on fundamentals of logic, proof, and proof techniques (including induction, although in Hummel it is treated earlier than in Bloch), set theory (including infinite sets), and functions. Both Hummel and Bloch also discuss number systems and order, working up to ^BR from ^BN, and both also discuss orderings. Bloch and Liebeck, however, have discussions of (among others) counting and divisibility that Hummel does not. All three books have suggested lists for further reading, with that of Bloch quite comprehensive. The problem sets in Bloch and Hummel are more extensive than those in Liebeck, and these also have solutions or hints. Upper-division undergraduates. D. Robbins Trinity College (CT)

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