Proofs and Fundamentals
Birkhauser Boston Inc (Verlag)
978-0-8176-4111-5 (ISBN)
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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.
Part 1 Proofs: informal logic, introduction, statements, relations between statements, valid arguments quantifiers; strategies for proofs; mathematical proofs - what they are and why we need them; direct proofs, proofs by contrapositive and contradiction; cases, and if and only if, quantifiers in theorems, writing mathematics. Part 2 Fundamentals: sets, introduction, sets - basic definitions; set operations, indexes families of sets; functions, image and inverse image, composition and inverse functions, injectivity, surjectivity and bijectivity, set of functions; relations, congruence, equivalence relations; infinite and finite sets, cardinality of sets, cardinality of the number systems, mathematical induction, recursion. Part 3 Extras: selected topics, binary operations, groups, homomorphisms and isomorphism, partially ordered sets, lattices, counting products and sums, counting - permutations and combinations; number systems, back to the beginning, the natural numbers, further properties of the natural numbers, the integers, the rational numbers, the real numbers and the complex numbers. Appendix: properties of numbers. Hints of selected exercises.
| Erscheint lt. Verlag | 1.6.2000 |
|---|---|
| Zusatzinfo | 1 |
| Verlagsort | Secaucus |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 1770 g |
| Einbandart | gebunden |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika |
| Mathematik / Informatik ► Mathematik ► Algebra | |
| Naturwissenschaften ► Physik / Astronomie | |
| ISBN-10 | 0-8176-4111-4 / 0817641114 |
| ISBN-13 | 978-0-8176-4111-5 / 9780817641115 |
| Zustand | Neuware |
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