Sophie Germain: mathématicienne extraordinaire - Scripps College

More documents

Recommendations

Info

Abstract Sophie Germain lived in Paris during the French Revolution. She educated herself about circulating theories in what we now call number theory by collecting lecture notes from the newly created École Centrale des Travaux Publics in Paris, now called l’École Polytechnique, and by corresponding with Gauss, Legendre, and other mathematicians–all under the pseudonym, M. Le Blanc. Her contributions to the theory of vibrating elastic plates has influenced the way we think about these surfaces even now. In addition, Cases 1 and 2 of Fermat’s Last Theorem developed following publications of Legendre’s version of Germain’s proof. She proved the first case of Fermat’s Last Theorem for all primes under 100 and for primes p where q = 2p + 1 is also prime; hers is considered one of the first “good approaches” to Fermat’s Last Theorem.
Contents Abstract Acknowledgments iii vii 1 Introduction 1 2 La Femme 3 2.1 Sa Biographie . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Modestie supposée . . . . . . . . . . . . . . . . . . . . . . . . 9 3 Ses Oeuvres, Ses Travaux 21 3.1 La mathématicienne . . . . . . . . . . . . . . . . . . . . . . . 21 3.2 Le philosophe . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.3 La scientifique . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4 Mathematical Background 31 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.2 The First Attempts . . . . . . . . . . . . . . . . . . . . . . . . 34 4.3 The First Proof . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 5 Sophie Germain 53 5.1 Case 1, Case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 5.2 Sophie Germain’s Theorems . . . . . . . . . . . . . . . . . . . 54 5.3 What then . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 6 Conclusion 69 6.1 And Beyond . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 6.2 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Bibliography 73
Page 1: Sophie Germain: mathématicienne ex
Page 5 and 6: Chapter 1 Introduction Marie-Sophie
Page 7 and 8: Chapter 2 La Femme 2.1 Sa Biographi
Page 9 and 10: Sa Biographie 5 maths et ils lui in
Page 11 and 12: Sa Biographie 7 Florens Friedrich C
Page 13 and 14: Modestie supposée 9 2.2 Modestie s
Page 15 and 16: Modestie supposée 11 2.2.1 Lalande
Page 17 and 18: Modestie supposée 13 (Bucciarelli
Page 19 and 20: Modestie supposée 15 sa préséanc
Page 21 and 22: Modestie supposée 17 Il est évide
Page 23 and 24: Modestie supposée 19 délai [. . .
Page 25 and 26: Chapter 3 Ses Oeuvres, Ses Travaux
Page 27 and 28: Le philosophe 23 C’est un peu iro
Page 29 and 30: Le philosophe 25 nomènes qu’elle
Page 31 and 32: La scientifique 27 la théorie d’
Page 33 and 34: La scientifique 29 crédibilité, e
Page 35 and 36: Introduction 31 a truly remarkable
Page 37 and 38: The First Attempts 33 4.2 The First
Page 39 and 40: The First Attempts 35 4.1.2. Withou
Page 41 and 42: The First Attempts 37 If we substit
Page 43 and 44: The First Proof 39 the previous 3 c
Page 45 and 46: The First Proof 41 We plug these eq
Page 47 and 48: The First Proof 43 us 5 3 r 4 + 2
Page 49 and 50: The First Proof 45 Returning to the
Page 51 and 52: The First Proof 47 write P 0 = A 16
Page 53 and 54:
The First Proof 49 are positive int
Page 55 and 56:
Chapter 5 Sophie Germain 5.1 Case 1
Page 57 and 58:
Sophie Germain’s Theorems 53 Cube
Page 59 and 60:
Sophie Germain’s Theorems 55 Clai
Page 61 and 62:
Sophie Germain’s Theorems 57 We h
Page 63 and 64:
Sophie Germain’s Theorems 59 fied
Page 65 and 66:
Sophie Germain’s Theorems 61 if n
Page 67 and 68:
What then 63 Germain prime, discove
Page 69 and 70:
What then 65 This means that if P i
Page 71 and 72:
Chapter 6 Conclusion 6.1 And Beyond
Page 73 and 74:
Conclusion 69 the Frey curve must n
Page 75 and 76:
Bibliography [1] Bucciarelli, Louis
Page 77 and 78:
Bibliography 73 [10] James, Ioan. R
Page 79:
Bibliography 75 1990. v. 41 no. 2,
show all

Sophie Germain: mathématicienne extraordinaire - Scripps College

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?