Cargando…
Elements of mathematics : from Euclid to Gödel /
"Elements of Mathematics takes readers on a fascinating tour that begins in elementary mathematics--but, as John Stillwell shows, this subject is not as elementary or straightforward as one might think. Not all topics that are part of today's elementary mathematics were always considered a...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton :
Princeton University Press,
[2016]
|
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000 i 4500 | ||
|---|---|---|---|
| 001 | JSTOR_ocn946359807 | ||
| 003 | OCoLC | ||
| 005 | 20231005004200.0 | ||
| 006 | m o d | ||
| 007 | cr ||||||||||| | ||
| 008 | 160411t20162016njua ob 001 0 eng d | ||
| 040 | |a N$T |b eng |e rda |e pn |c N$T |d N$T |d IDEBK |d YDXCP |d EBLCP |d CDX |d DEBBG |d IDB |d UAB |d MNW |d NRC |d MNW |d OCLCQ |d DEGRU |d OCLCF |d DEBSZ |d MERUC |d MUU |d W2U |d UUM |d OCLCQ |d AU@ |d OCLCQ |d WYU |d JSTOR |d OCLCQ |d UKBTH |d IEEEE |d OCLCO |d S2H |d OCLCO |d OCLCQ | ||
| 066 | |c (S | ||
| 019 | |a 952597225 |a 982200871 |a 987921596 |a 1066464794 | ||
| 020 | |a 9781400880560 |q (electronic bk.) | ||
| 020 | |a 1400880564 |q (electronic bk.) | ||
| 020 | |z 9780691171685 |q (hardcover ; |q alk. paper) | ||
| 020 | |z 0691171688 |q (hardcover ; |q alk. paper) | ||
| 020 | |z 9780691178547 |q (paperback) | ||
| 020 | |z 0691178542 |q (paperback) | ||
| 024 | 7 | |a 10.1515/9781400880560 |2 doi | |
| 029 | 1 | |a AU@ |b 000059223874 | |
| 029 | 1 | |a DEBBG |b BV043892872 | |
| 029 | 1 | |a DEBBG |b BV043640059 | |
| 029 | 1 | |a DEBSZ |b 494304928 | |
| 029 | 1 | |a AU@ |b 000062384669 | |
| 029 | 1 | |a AU@ |b 000065054103 | |
| 035 | |a (OCoLC)946359807 |z (OCoLC)952597225 |z (OCoLC)982200871 |z (OCoLC)987921596 |z (OCoLC)1066464794 | ||
| 037 | |a 4336787 |b Proquest Ebook Central | ||
| 037 | |a 22573/ctvc61nv9 |b JSTOR | ||
| 037 | |a 9452563 |b IEEE | ||
| 050 | 4 | |a QA11.2 | |
| 072 | 7 | |a MAT |x 039000 |2 bisacsh | |
| 072 | 7 | |a MAT |x 023000 |2 bisacsh | |
| 072 | 7 | |a MAT |x 026000 |2 bisacsh | |
| 072 | 7 | |a MAT |x 000000 |2 bisacsh | |
| 072 | 7 | |a MAT |x 015000 |2 bisacsh | |
| 072 | 7 | |a SCI |x 034000 |2 bisacsh | |
| 082 | 0 | 4 | |a 510.71/1 |2 23 |
| 049 | |a UAMI | ||
| 100 | 1 | |a Stillwell, John, |e author. | |
| 245 | 1 | 0 | |a Elements of mathematics : |b from Euclid to Gödel / |c John Stillwell. |
| 264 | 1 | |a Princeton : |b Princeton University Press, |c [2016] | |
| 264 | 4 | |c ©2016 | |
| 300 | |a 1 online resource (xiv, 422 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |b PDF | ||
| 347 | |a text file | ||
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Online resource; title from electronic title page (EBSCOhost, viewed March 14, 2018). | |
| 505 | 0 | |a Elementary topics -- Arithmetic -- Computation -- Algebra -- Geometry -- Calculus -- Combinatorics -- Probability -- Logic -- Some advanced mathematics. | |
| 520 | |a "Elements of Mathematics takes readers on a fascinating tour that begins in elementary mathematics--but, as John Stillwell shows, this subject is not as elementary or straightforward as one might think. Not all topics that are part of today's elementary mathematics were always considered as such, and great mathematical advances and discoveries had to occur in order for certain subjects to become'elementary.'Stillwell examines elementary mathematics from a distinctive twenty-first-century viewpoint and describes not only the beauty and scope of the discipline, but also its limits. From Gaussian integers to propositional logic, Stillwell delves into arithmetic, computation, algebra, geometry, calculus, combinatorics, probability, and logic. He discusses how each area ties into more advanced topics to build mathematics as a whole. Through a rich collection of basic principles, vivid examples, and interesting problems, Stillwell demonstrates that elementary mathematics becomes advanced with the intervention of infinity. Infinity has been observed throughout mathematical history, but the recent development of'reverse mathematics'confirms that infinity is essential for proving well-known theorems, and helps to determine the nature, contours, and borders of elementary mathematics. Elements of Mathematics gives readers, from high school students to professional mathematicians, the highlights of elementary mathematics and glimpses of the parts of math beyond its boundaries"--Publisher's description | ||
| 590 | |a JSTOR |b Books at JSTOR Demand Driven Acquisitions (DDA) | ||
| 590 | |a JSTOR |b Books at JSTOR Evidence Based Acquisitions | ||
| 590 | |a JSTOR |b Books at JSTOR All Purchased | ||
| 650 | 0 | |a Mathematics |x Study and teaching (Higher) | |
| 650 | 7 | |a MATHEMATICS |x Essays. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Pre-Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Reference. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x General. |2 bisacsh | |
| 650 | 7 | |a Mathematics |x Study and teaching (Higher) |2 fast |0 (OCoLC)fst01012286 | |
| 776 | 0 | 8 | |i Print version: |n Druck-Ausgabe |a Stillwell, John. Elements of Mathematics . |t From Euclid to Godel |
| 776 | 0 | 8 | |i Print version: |a Stillwell, John. |t Elements of mathematics. |d Princeton : Princeton University Press, [2016] |z 9780691171685 |w (DLC) 2015045022 |w (OCoLC)933596228 |
| 856 | 4 | 0 | |u https://jstor.uam.elogim.com/stable/10.2307/j.ctvc77h7p |z Texto completo |
| 880 | 0 | |6 505-00/(S |a Cover -- Title -- Copyright -- Dedication -- Contents -- 1 Elementary Topics -- 1.1 Arithmetic -- 1.2 Computation -- 1.3 Algebra -- 1.4 Geometry -- 1.5 Calculus -- 1.6 Combinatorics -- 1.7 Probability -- 1.8 Logic -- 1.9 Historical Remarks -- 1.10 Philosophical Remarks -- 2 Arithmetic -- 2.1 The Euclidean Algorithm -- 2.2 Continued Fractions -- 2.3 Prime Numbers -- 2.4 Finite Arithmetic -- 2.5 Quadratic Integers -- 2.6 The Gaussian Integers -- 2.7 Euler's Proof Revisited -- 2.8 √2 and the Pell Equation -- 2.9 Historical Remarks -- 2.10 Philosophical Remarks -- 3 Computation -- 3.1 Numerals -- 3.2 Addition -- 3.3 Multiplication -- 3.4 Division -- 3.5 Exponentiation -- 3.6 P and NP Problems -- 3.7 Turing Machines -- 3.8 *Unsolvable Problems -- 3.9 *Universal Machines -- 3.10 Historical Remarks -- 3.11 Philosophical Remarks -- 4 Algebra -- 4.1 Classical Algebra -- 4.2 Rings -- 4.3 Fields -- 4.4 Two Theorems Involving Inverses -- 4.5 Vector Spaces -- 4.6 Linear Dependence, Basis, and Dimension -- 4.7 Rings of Polynomials -- 4.8 Algebraic Number Fields -- 4.9 Number Fields as Vector Spaces -- 4.10 Historical Remarks -- 4.11 Philosophical Remarks -- 5 Geometry -- 5.1 Numbers and Geometry -- 5.2 Euclid's Theory of Angles -- 5.3 Euclid's Theory of Area -- 5.4 Straightedge and Compass Constructions -- 5.5 Geometric Realization of Algebraic Operations -- 5.6 Algebraic Realization of Geometric Constructions -- 5.7 Vector Space Geometry -- 5.8 Introducing Length via the Inner Product -- 5.9 Constructible Number Fields -- 5.10 Historical Remarks -- 5.11 Philosophical Remarks -- 6 Calculus -- 6.1 Geometric Series -- 6.2 Tangents and Differentiation -- 6.3 Calculating Derivatives -- 6.4 Curved Areas -- 6.5 The Area under y = x^n -- 6.6 *The Fundamental Theorem of Calculus -- 6.7 Power Series for the Logarithm -- 6.8 *The Inverse Tangent Function and π. | |
| 880 | 8 | |6 505-00/(S |a 6.9 Elementary Functions -- 6.10 Historical Remarks -- 6.11 Philosophical Remarks -- 7 Combinatorics -- 7.1 The Infinitude of Primes -- 7.2 Binomial Coefficients and Fermat's Little Theorem -- 7.3 Generating Functions -- 7.4 Graph Theory -- 7.5 Trees -- 7.6 Planar Graphs -- 7.7 The Euler Polyhedron Formula -- 7.8 Nonplanar Graphs -- 7.9 *The Kőnig Infinity Lemma -- 7.10 Sperner's Lemma -- 7.11 Historical Remarks -- 7.12 Philosophical Remarks -- 8 Probability -- 8.1 Probability and Combinatorics -- 8.2 Gambler's Ruin -- 8.3 Random Walk -- 8.4 Mean, Variance, and Standard Deviation -- 8.5 *The Bell Curve -- 8.6 Historical Remarks -- 8.7 Philosophical Remarks -- 9 Logic -- 9.1 Propositional Logic -- 9.2 Tautologies, Identities, and Satisfiability -- 9.3 Properties, Relations, and Quantifiers -- 9.4 Induction -- 9.5 *Peano Arithmetic -- 9.6 *The Real Numbers -- 9.7 *Infinity -- 9.8 *Set Theory -- 9.9 *Reverse Mathematics -- 9.10 Historical Remarks -- 9.11 Philosophical Remarks -- 10 Some Advanced Mathematics -- 10.1 Arithmetic: the Pell Equation -- 10.2 Computation: the Word Problem -- 10.3 Algebra: the Fundamental Theorem -- 10.4 Geometry: the Projective Line -- 10.5 Calculus: Wallis's Product for π -- 10.6 Combinatorics: Ramsey Theory -- 10.7 Probability: de Moivre's Distribution -- 10.8 Logic: the Completeness Theorem -- 10.9 Historical and Philosophical Remarks -- Bibliography -- Index. | |
| 938 | |a De Gruyter |b DEGR |n 9781400880560 | ||
| 938 | |a Coutts Information Services |b COUT |n 34172282 | ||
| 938 | |a EBL - Ebook Library |b EBLB |n EBL4336787 | ||
| 938 | |a YBP Library Services |b YANK |n 12758962 | ||
| 938 | |a ProQuest MyiLibrary Digital eBook Collection |b IDEB |n cis34172282 | ||
| 938 | |a EBSCOhost |b EBSC |n 1107942 | ||
| 994 | |a 92 |b IZTAP | ||