Philosophy of Mathematics: A Contemporary Introduction to the World of Proofs and PicturesRoutledge, 2010. márc. 17. - 264 oldal In his long-awaited new edition of Philosophy of Mathematics, James Robert Brown tackles important new as well as enduring questions in the mathematical sciences. Can pictures go beyond being merely suggestive and actually prove anything? Are mathematical results certain? Are experiments of any real value? This clear and engaging book takes a unique approach, encompassing non-standard topics such as the role of visual reasoning, the importance of notation, and the place of computers in mathematics, as well as traditional topics such as formalism, Platonism, and constructivism. The combination of topics and clarity of presentation make it suitable for beginners and experts alike. The revised and updated second edition of Philosophy of Mathematics contains more examples, suggestions for further reading, and expanded material on several topics including a novel approach to the continuum hypothesis. |
Tartalomjegyzék
The Mathematical Image | 1 |
CHAPTER 2 Platonism | 9 |
CHAPTER 3 Pictureproofs and Platonism | 26 |
CHAPTER 4 What is Applied Mathematics? | 51 |
CHAPTER 5 Hilbert and Gödel | 67 |
CHAPTER 6 Knots and Notation | 84 |
CHAPTER 7 What is a Definition? | 99 |
CHAPTER 8 Constructive Approaches | 118 |
CHAPTER 9 Proofs Pictures and Procedures in Wittgenstein | 136 |
CHAPTER 10 Computation Proof and Conjecture | 160 |
CHAPTER 11 How to Refute the Continuum Hypothesis | 178 |
CHAPTER 12 Calling the Bluff | 198 |
Notes | 220 |
226 | |
236 | |
Más kiadások - Összes megtekintése
Philosophy of Mathematics: A Contemporary Introduction to the World of ... James Robert Brown Korlátozott előnézet - 2010 |
Philosophy of Mathematics: A Contemporary Introduction to the World of ... James Robert Brown Nincs elérhető előnézet - 2008 |
Philosophy of Mathematics: A Contemporary Introduction to the World of ... James Robert Brown Nincs elérhető előnézet - 2008 |