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The Art of Proof Basic Training for Deeper Mathematics /
The Art of Proof is designed for a one-semester or two-quarter course. A typical student will have studied calculus (perhaps also linear algebra) with reasonable success. With an artful mixture of chatty style and interesting examples, the student's previous intuitive knowledge is placed on sol...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York, NY :
Springer New York : Imprint: Springer,
2010.
|
| Edición: | 1st ed. 2010. |
| Colección: | Undergraduate Texts in Mathematics,
|
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
| LEADER | 00000nam a22000005i 4500 | ||
|---|---|---|---|
| 001 | 978-1-4419-7023-7 | ||
| 003 | DE-He213 | ||
| 005 | 20221122210038.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 100825s2010 xxu| s |||| 0|eng d | ||
| 020 | |a 9781441970237 |9 978-1-4419-7023-7 | ||
| 024 | 7 | |a 10.1007/978-1-4419-7023-7 |2 doi | |
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| 100 | 1 | |a Beck, Matthias. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 4 | |a The Art of Proof |h [electronic resource] : |b Basic Training for Deeper Mathematics / |c by Matthias Beck, Ross Geoghegan. |
| 250 | |a 1st ed. 2010. | ||
| 264 | 1 | |a New York, NY : |b Springer New York : |b Imprint: Springer, |c 2010. | |
| 300 | |a XXI, 182 p. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a Undergraduate Texts in Mathematics, |x 2197-5604 | |
| 505 | 0 | |a The Discrete -- Integers -- Natural Numbers and Induction -- Some Points of Logic -- Recursion -- Underlying Notions in Set Theory -- Equivalence Relations and Modular Arithmetic -- Arithmetic in Base Ten -- The Continuous -- Real Numbers -- Embedding Z in R -- Limits and Other Consequences of Completeness -- Rational and Irrational Numbers -- Decimal Expansions -- Cardinality -- Final Remarks -- Further Topics -- Continuity and Uniform Continuity -- Public-Key Cryptography -- Complex Numbers -- Groups and Graphs -- Generating Functions -- Cardinal Number and Ordinal Number -- Remarks on Euclidean Geometry. | |
| 520 | |a The Art of Proof is designed for a one-semester or two-quarter course. A typical student will have studied calculus (perhaps also linear algebra) with reasonable success. With an artful mixture of chatty style and interesting examples, the student's previous intuitive knowledge is placed on solid intellectual ground. The topics covered include: integers, induction, algorithms, real numbers, rational numbers, modular arithmetic, limits, and uncountable sets. Methods, such as axiom, theorem and proof, are taught while discussing the mathematics rather than in abstract isolation. Some of the proofs are presented in detail, while others (some with hints) may be assigned to the student or presented by the instructor. The authors recommend that the two parts of the book -- Discrete and Continuous -- be given equal attention. The book ends with short essays on further topics suitable for seminar-style presentation by small teams of students, either in class or in a mathematics club setting. These include: continuity, cryptography, groups, complex numbers, ordinal number, and generating functions. | ||
| 650 | 0 | |a Mathematical logic. | |
| 650 | 0 | |a Algebra. | |
| 650 | 0 | |a Mathematical analysis. | |
| 650 | 0 | |a Mathematics. | |
| 650 | 1 | 4 | |a Mathematical Logic and Foundations. |
| 650 | 2 | 4 | |a Algebra. |
| 650 | 2 | 4 | |a Analysis. |
| 650 | 2 | 4 | |a Mathematics. |
| 700 | 1 | |a Geoghegan, Ross. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9781441970220 |
| 776 | 0 | 8 | |i Printed edition: |z 9781441970244 |
| 776 | 0 | 8 | |i Printed edition: |z 9781493940868 |
| 830 | 0 | |a Undergraduate Texts in Mathematics, |x 2197-5604 | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-1-4419-7023-7 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||