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Studying Mathematics = The Beauty, the Toil and the Method /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Studying Mathematics/ by Marco Bramanti, Giancarlo Travaglini.
其他題名:	The Beauty, the Toil and the Method /
作者:	Bramanti, Marco.
其他作者:	Travaglini, Giancarlo.
面頁冊數:	XVII, 398 p. 140 illus., 11 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Mathematics—Study and teaching . -
電子資源:	https://doi.org/10.1007/978-3-319-91355-1
ISBN:	9783319913551

Studying Mathematics = The Beauty, the Toil and the Method /
Bramanti, Marco.

Studying MathematicsThe Beauty, the Toil and the Method /[electronic resource] :by Marco Bramanti, Giancarlo Travaglini. - 1st ed. 2018. - XVII, 398 p. 140 illus., 11 illus. in color.online resource.

Part 1. The Language of Mathematics -- A Few Ambiguities of Everyday Language -- To represent by Sets -- Propositions and Properties -- Proofs, Implications and Counterexamples -- Negations and Indirect Proofs -- Formulae and Indices -- Saturation of Indices and Syntactic Consistency of a Formula -- Induction and Natural Numbers -- Part 2. The Study of a Mathematical Book -- To Read a Definition -- To Understand, i.e. to Know How to Reuse -- To Learn How to Correct -- To Sift the Ideas -- To Understand, i.e. to Know How to Explain -- Part 3. Pages and Ideas -- Majorizations -- Uniqueness Proofs (Level B) -- Functions and Set Theoretic Arguments -- Tiles, Polyhedra, Characterizations -- Index. .

This book is dedicated to preparing prospective college students for the study of mathematics. It can be used at the end of high school or during the first year of college, for personal study or for introductory courses. It aims to set a meeting between two relatives who rarely speak to each other: the Mathematics of Beauty, which shows up in some popular books and films, and the Mathematics of Toil, which is widely known. Toil can be overcome through an appropriate method of work. Beauty will be found in the achievement of a way of thinking. The first part concerns the mathematical language: the expressions “for all”, “there exists”, “implies”, “is false”, ...; what is a proof by contradiction; how to use indices, sums, induction. The second part tackles specific difficulties: to study a definition, to understand an idea and apply it, to fix a slightly wrong argument, to discuss suggestions, to explain a proof. The third part presents customary techniques and points of view in college mathematics. The reader can choose one of three difficulty levels (A, B, C).

ISBN: 9783319913551

Standard No.: 10.1007/978-3-319-91355-1doiSubjects--Topical Terms:

1253684
Mathematics—Study and teaching .

LC Class. No.: LC8-6691

Dewey Class. No.: 370

Studying Mathematics = The Beauty, the Toil and the Method /
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