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E-grāmata: Mathematics and Technology

4.00/5 (4 ratings by Goodreads)

Christiane Rousseau, Yvan Saint-Aubin, Contributions by Hélčne Antaya, Translated by Chris Hamilton, Contributions by Isabelle Ascah-Coallier

Formāts: PDF+DRM
Sērija : Springer Undergraduate Texts in Mathematics and Technology
Izdošanas datums: 29-Oct-2008
Izdevniecība: Springer-Verlag New York Inc.
Valoda: eng
ISBN-13: 9780387692166

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Formāts: PDF+DRM
Sērija : Springer Undergraduate Texts in Mathematics and Technology
Izdošanas datums: 29-Oct-2008
Izdevniecība: Springer-Verlag New York Inc.
Valoda: eng
ISBN-13: 9780387692166

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The authors present useful, elegant mathematical concepts such as Markov chains, function iteration and simple groups, and develop these concepts in the context of applications to important, practical problems such as web-navigation, data compression and error correcting codes. The authors highlight how mathematical modeling, together with the power of mathematical tools and abstraction, have been crucial for innovation in technology. The topics are presented with clarity, and the mathematics is expressed in a straightforward manner. Numerous exercises at the end of every section provide practice and reinforce the material in the chapter. An engaging quality of this book is that the authors also put the mathematical material in a historical context and not just a practical one. Mathematics and Technology is intended for undergraduate students, instructors and high school teachers. Prerequisites are essentially linear algebra and Euclidean geometry. Additionally, its lack of calculus centricity as well as a clear indication of the more difficult topics and relatively advanced references make it suitable for any curious individual with a decent command of high school math.

This book introduces the student to numerous modern applications of mathematics in technology. The authors write with clarity and present the mathematics in a clear and straightforward way making it an interesting and easy book to read. Numerous exercises at the end of every section provide practice and reinforce the material in the chapter. An engaging quality of this book is that the authors also present the mathematical material in a historical context and not just the practical one.Mathematics and Technology is intended for undergraduate students in mathematics, instructors and high school teachers. Additionally, its lack of calculus centricity as well as a clear indication of the more difficult topics and relatively advanced references make it suitable for any curious individual with a decent command of high school math.

Recenzijas

From the reviews:

"Christiane Rousseau and Yvan Saint-Aubin here present a valuable collection of diverse and detailed applied mathematics examples. presented to work as a standalone guide to mathematics at work today, usable for self-study and enlightenment or as a text for coursework. Chapters conclude with a rich collection of exercises followed by references for further study. together with the clear signposts to help students get around and through the more difficult topics, make Mathematics and Technology suitable for any diligent reader ." (Tom Schulte, MAA Online, February, 2009)

"This book takes a more detailed view of mathematics in action, in several areas of technology . This is an excellent book for a varied audience. This book will also be attractive to college students and to researchers in mathematics, computer science (CS), and technology, who want to acquire a more thorough understanding of the applications covered in the book. the authors give several pointers and suggestions to instructors. I like this book and I recommend it." (Edgar R. Chavez, ACM Computing Reviews, June, 2009)

The authors highlight how mathematical modeling, together with the power of mathematical tools, has been crucial for innovation in technology. The text is written for students who have a familiarity with Euclidean geometry and have mastered multivariable calculus, linear algebra, and elementary probability theory. undergraduates in their junior or senior years are the ideal audience for the course. (Tzvetan Semerdjiev, Zentralblatt MATH, Vol. 1211, 2011)

Preface

Positioning on Earth and in Space

(44)

Introduction

(1)

Global Positioning System

(10)

Some Facts about GPS

(1)

The Theory Behind GPS

(3)

Dealing with Practical Difficulties

(6)

How Hydro-Quebec Manages Lightning Strikes

(7)

Locating Lightning Strikes

(3)

Threshold and Quality of Detection

(3)

Long-Term Risk Management

(1)

Linear Shift Registers

(8)

The Structure of the Field Fr2

(2)

Proof of Theorem 1.4

(3)

Cartography

(9)

Exercises

(9)

References

(2)

Friezes and Mosaics

(40)

Friezes and Symmetries

(4)

Symmetry Group and Affine Transformations

(6)

The Classification Theorem

(6)

Mosaics

(3)

Exercises

(18)

References

(2)

Robotic Motion

(34)

Introduction

(6)

Moving a Solid in the Plane

(2)

Some Thoughts on the Number of Degrees of Freedom

(2)

Movements That Preserve Distances and Angles

(3)

Properties of Orthogonal Matrices

(9)

Change of Basis

103

(3)

Different Frames of Reference for a Robot

106

(5)

Exercises

111

(8)

References

117

(2)

Skeletons and Gamma-Ray Radiosurgery

119

(36)

Introduction

119

(1)

Definition of Two-Dimensional Region Skeletons

120

(10)

Three-Dimensional Regions

130

(2)

The Optimal Surgery Algorithm

132

(2)

A Numerical Algorithm

134

(8)

The First Part of the Algorithm

135

(4)

Second Part of the Algorithm

139

(1)

Proof of Proposition 4.17

140

(2)

Other Applications of Skeletons

142

(1)

The Fundamental Property of the Skeleton

143

(4)

Exercises

147

(8)

References

153

(2)

Savings and Loans

155

(18)

Banking Vocabulary

155

(1)

Compound Interest

156

(3)

A Saving Plan

159

(2)

Borrowing Money

161

(3)

Appendix: Mortagage Payment Tables

164

(4)

Exercises

168

(5)

References

171

(2)

Error-Correcting Codes

173

(36)

Introduction: Digitizing, Detecting and Correcting

173

(5)

The Finite Field F2

178

(1)

The C(7,4) Hamming Code

179

(3)

C(2k - 1, 2k- k - 1) Hamming Codes

182

(3)

Finite Fields

185

(8)

Reed-Solomon Codes

193

(5)

Appendix: The Scalar Product and Finite Fields

198

(2)

Exercises

200

(9)

References

207

(2)

Public Key Cryptography

209

(32)

Introduction

209

(1)

A Few Tools from Number Theory

210

(3)

The Idea behind RSA

213

(8)

Constructing Large Primes

221

(10)

The Shor Factorization Algorithm

231

(3)

Exercises

234

(7)

References

239

(2)

Random-Number Generators

241

(24)

Introduction

241

(4)

Linear Shift Registers

245

(3)

Fp-Linear Generators

248

(7)

The Case p = 2

248

(5)

A Lesson on Gambling Machines

253

(1)

The General Case

253

(2)

Combined Multiple Recursive Generators

255

(2)

Conclusion

257

(1)

Exercises

258

(7)

References

263

(2)

Google and the PageRank Algorithm

265

(26)

Search Engines

265

(3)

The Web and Markov Chains

268

(10)

An Improved PageRank

278

(3)

The Frobenius Theorem

281

(3)

Exercises

284

(7)

References

289

(2)

Why 44,100 Samples per Second?

291

(34)

Introduction

291

(1)

The Musical Scale

292

(4)

The Last Note (Introduction to Fourier Analysis)

296

(11)

The Nyquist Frequency and the Reason for 44,100

307

(10)

Exercises

317

(8)

References

323

(2)

Image Compression: Iterated Function Systems

325

(44)

Introduction

325

(2)

Affine Transformations in the Plane

327

(3)

Iterated Function Systems

330

(6)

Iterated Contractions and Fixed Points

336

(4)

The Hausdorff Distance

340

(5)

Fractal Dimension

345

(5)

Photographs as Attractors

350

(11)

Exercises

361

(8)

References

367

(2)

Image Compression: The JPEG Standard

369

(34)

Introduction

369

(3)

Zooming in on a JPEG-Compressed Digital Image

372

(1)

The Case of 2 x 2 Blocks

373

(5)

The Case of N x N Blocks

378

(10)

The JPEG Standard

388

(8)

Exercises

396

(7)

References

401

(2)

The DNA Computer

403

(44)

Introduction

403

(2)

Adleman's Hamiltonian Path Problem

405

(4)

Turing Machines and Recursive Functions

409

(17)

Turing Machines

409

(7)

Primitive Recursive Functions and Recursive Functions

416

(10)

Turing Machines and Insertion-Deletion Systems

426

(4)

NP-Complete Problems

430

(5)

The Hamiltonian Path Problem

430

(1)

Satisfiability

431

(4)

E-grāmata: Mathematics and Technology

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