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010   $a3-319-91355-7
024 7 $a10.1007/978-3-319-91355-1
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035   $a(DE-He213)978-3-319-91355-1
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035   $a(EXLCZ)994100000005323552
100   $a20180723d2018      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aStudying Mathematics $eThe Beauty, the Toil and the Method /$fby Marco Bramanti, Giancarlo Travaglini
205   $a1st ed. 2018.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018.
215   $a1 online resource (XVII, 398 p. 140 illus., 11 illus. in color.) 
311   $a3-319-91354-9 
327   $aPart 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. .
330   $aThis 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).
606   $aMathematics?Study and teaching 
606   $aLearning
606   $aInstruction
606   $aMathematics Education$3https://scigraph.springernature.com/ontologies/product-market-codes/O25000
606   $aLearning & Instruction$3https://scigraph.springernature.com/ontologies/product-market-codes/O22000
615  0$aMathematics?Study and teaching .
615  0$aLearning.
615  0$aInstruction.
615 14$aMathematics Education.
615 24$aLearning & Instruction.
676   $a370
700   $aBramanti$b Marco$4aut$4http://id.loc.gov/vocabulary/relators/aut$0284761
702   $aTravaglini$b Giancarlo$4aut$4http://id.loc.gov/vocabulary/relators/aut
906   $aBOOK
912   $a9910299502303321
996   $aStudying Mathematics$92523936
997   $aUNINA