Mathematics and technology:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English French |
| Veröffentlicht: |
New York, NY
Springer
2008
|
| Schriftenreihe: | Springer undergraduate texts in mathematics and technology
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 580 S. Ill., graph. Darst. |
| ISBN: | 9780387692159 0387692150 |
Internformat
MARC
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| 020 | |a 0387692150 |9 0-387-69215-0 | ||
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| 100 | 1 | |a Rousseau, Christiane |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Mathematics and technology |c Christiane Rousseau ; Yvan Saint-Aubin |
| 264 | 1 | |a New York, NY |b Springer |c 2008 | |
| 300 | |a XV, 580 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer undergraduate texts in mathematics and technology | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Technology | |
| 650 | 4 | |a Technology |x Mathematical models | |
| 650 | 0 | 7 | |a Technik |0 (DE-588)4059205-4 |2 gnd |9 rswk-swf |
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| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Saint-Aubin, Yvan |e Verfasser |4 aut | |
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| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| DE-BY-862_location | 2000 |
|---|---|
| DE-BY-FWS_call_number | 2000/SK 950 R864 |
| DE-BY-FWS_katkey | 514874 |
| DE-BY-FWS_media_number | 083000510530 |
| _version_ | 1806176705718517760 |
| adam_text | Contents
Preface
................................................................
V
1
Positioning on Earth and in Space
................................. 1
1.1
Introduction
................................................... 1
1.2
Global Positioning System
....................................... 2
1.2.1
Some Facts about GPS
................................... 2
1.2.2
The Theory Behind GPS
.................................. 3
1.2.3
Dealing with Practical Difficulties
.......................... 6
1.3
How
Hydro-Québec
Manages Lightning Strikes
..................... 12
1.3.1
Locating Lightning Strikes
................................ 12
1.3.2
Threshold and Quality of Detection
........................ 15
1.3.3
Long-Term Risk Management
.............................. 18
1.4
Linear Shift Registers
........................................... 19
1.4.1
The Structure of the Field F£
.............................. 22
1.4.2
Proof of Theorem
1.4..................................... 24
1.5
Cartography
................................................... 27
1.6
Exercises
...................................................... 36
References
............................................................. 43
2
Friezes and Mosaics
............................................... 45
2.1
Friezes and Symmetries
......................................... 48
2.2
Symmetry Group and
Affine
Transformations
...................... 52
2.3
The Classification Theorem
...................................... 58
2.4
Mosaics
....................................................... 64
2.5
Exercises
...................................................... 67
References
............................................................. 83
XII Contents
3
Robotic Motion
.................................................... 85
3.1
Introduction
................................................... 85
3.1.1
Moving a Solid in the Plane
............................... 87
3.1.2
Some Thoughts on the Number of Degrees of Freedom
........ 89
3.2
Movements That Preserve Distances and Angles
.................... 91
3.3
Properties of Orthogonal Matrices
................................ 94
3.4
Change of Basis
................................................ 103
3.5
Different Frames of Reference for a Robot
......................... 106
3.6
Exercises
......................................................
П1
References
............................................................. 117
4
Skeletons and Gamma-Ray Radiosurgery
.......................... 119
4.1
Introduction
................................................... 119
4.2
Definition of Two-Dimensional Region Skeletons
................... 120
4.3
Three-Dimensional Regions
...................................... 130
4.4
The Optimal Surgery Algorithm
................................. 132
4.5
A Numerical Algorithm
......................................... 134
4.5.1
The First Part of the Algorithm
............................ 135
4.5.2
Second Part of the Algorithm
.............................. 139
4.5.3
Proof of Proposition
4.17.................................. 140
4.6
Other Applications of Skeletons
.................................. 142
4.7
The Fundamental Property of the Skeleton
........................ 143
4.8
Exercises
...................................................... 147
References
............................................................. 153
5
Savings and Loans
................................................. 155
5.1
Banking Vocabulary
............................................ 155
5.2
Compound Interest
............................................. 156
5.3
A Savings Plan
................................................ 159
5.4
Borrowing Money
.............................................. 161
5.5
Appendix: Mortgage Payment Tables
............................. 164
5.6
Exercises
...................................................... 168
References
............................................................. 171
6
Error-Correcting Codes
............................................ 173
6.1
Introduction: Digitizing, Detecting and Correcting
................. 173
6.2
The Finite Field F2
............................................. 178
6.3
The C(7,
4)
Hamming Code
..................................... 179
6.4
C(2k
- 1,
2k
-
к
- 1)
Hamming Codes
............................
і
182
6.5
Finite Fields
................................................... 185
6.6
Reed-Solomon Codes
........................................... 193
Contents XIII
6.7 Appendix:
The Scalar Product and Finite Fields
................... 198
6.8
Exercises
...................................................... 200
References
............................................................. 207
7
Public Key Cryptography
......................................... 209
7.1
Introduction
................................................... 209
7.2
A Few Tools from Number Theory
............................... 210
7.3
The Idea behind RSA
........................................... 213
7.4
Constructing Large Primes
...................................... 221
7.5
The Shor Factorization Algorithm
................................ 231
7.6
Exercises
...................................................... 234
References
............................................................. 239
8
Random-Number Generators
...................................... 241
8.1
Introduction
................................................... 241
8.2
Linear Shift Registers
........................................... 245
8.3
Fp-Linear Generators
........................................... 248
8.3.1
The Case
ρ
= 2.......................................... 248
8.3.2
A Lesson on Gambling Machines
........................... 253
8.3.3
The General Case
........................................ 253
8.4
Combined Multiple Recursive Generators
.......................... 255
8.5
Conclusion
.................................................... 257
8.6
Exercises
...................................................... 258
References
............................................................. 263
9
Google and the PageRank Algorithm
.............................. 265
9.1
Search Engines
................................................. 265
9.2
The Web and Markov Chains
.................................... 268
9.3
An Improved PageRank
......................................... 278
9.4
The Frobenius Theorem
......................................... 281
9.5
Exercises
...................................................... 284
References
............................................................. 289
10
Why
44,100
Samples per Second?
.................................. 291
10.1
Introduction
................................................... 291
10.2
The Musical Scale
.............................................. 292
10.3
The Last Note (Introduction to Fourier Analysis)
.................. 296
10.4
The Nyquist Frequency and the Reason for
44,100.................. 307
10.5
Exercises
...................................................... 317
References
............................................................. 323
XIV Contents
11
Image Compression:
Iterated Function Systems
................... 325
11.1
Introduction
................................................... 325
11.2
Affine
Transformations in the Plane
.............................. 327
11.3
Iterated Function Systems
....................................... 330
11.4
Iterated Contractions and Fixed Points
........................... 336
11.5
The Hausdorff Distance
......................................... 340
11.6
Fractal Dimension
.............................................. 345
11.7
Photographs as Attractors
....................................... 350
11.8
Exercises
...................................................... 361
References
............................................................. 367
12
Image Compression: The JPEG Standard
......................... 369
12.1
Introduction
................................................... 369
12.2
Zooming in on a JPEG-Compressed Digital Image
.................. 372
12.3
The Case of
2
χ
2
Blocks
........................................ 373
12.4
The Case of
Ν χ Ν
Blocks
...................................... 378
12.5
The JPEG Standard
............................................ 388
12.6
Exercises
...................................................... 396
References
............................................................. 401
13
The
DNA
Computer
............................................... 403
13.1
Introduction
................................................... 403
13.2
Adleman s Hamiltonian Path Problem
............................ 405
13.3
Turing Machines and Recursive Functions
......................... 409
13.3.1
Turing Machines
......................................... 409
13.3.2
Primitive Recursive Functions and Recursive Functions
....... 416
13.4
Turing Machines and Insertion-Deletion Systems
................... 426
13.5
NP-Complete Problems
......................................... 430
13.5.1
The Hamiltonian Path Problem
............................ 430
13.5.2
Satisfiability
............................................. 431
13.6
More on
DNA
Computers
....................................... 435
13.6.1
The Hamiltonian Path Problem and Insertion-Deletion Systems
435
13.6.2
Current Limits
........................................... 435
13.6.3
A Few Biological Explanations Concerning Adleman s
Experiment
............................................. 437
13.7
Exercises
...................................................... 441
References
........................................................ 445
Contents
XV
14
Calculus of Variations
............................................. 447
14.1
The Fundamental Problem of Calculus of Variations
................ 448
14.2
Euler-Lagrange Equation
....................................... 451
14.3
Fermat s Principle
.............................................. 455
14.4
The Best Half-Pipe
............................................. 457
14.5
The Fastest Tunnel
............................................. 460
14.6
The Tautochrone Property of the Cycloid
......................... 465
14.7
An Isochronous Device
.......................................... 468
14.8
Soap Bubbles
.................................................. 471
14.9
Hamilton s Principle
............................................ 475
14.10
Isoperimetric Problems
.......................................... 479
14.11
Liquid Mirrors
................................................. 486
14.12
Exercises
...................................................... 490
References
............................................................. 499
15
Science Flashes
.................................................... 501
15.1
The Laws of Reflection and Refraction
............................ 501
15.2
A Few Applications of Conies
.................................... 508
15.2.1
A Remarkable Property of the Parabola
..................... 508
15.2.2
The Ellipse
.............................................. 518
15.2.3
The Hyperbola
.......................................... 520
15.2.4
A Few Clever Tools for Drawing Conies
..................... 521
15.3
Quadratic Surfaces in Architecture
............................... 521
15.4
Optimal Cellular Antenna Placement
............................. 528
15.5
Voronoi Diagrams
.............................................. 532
15.6
Computer Vision
............................................... 537
15.7
A Brief Look at Computer Architecture
........................... 539
15.8
Regular Pentagonal Tiling of the Sphere
.......................... 544
15.9
Laying Out a Highway
.......................................... 551
15.10
Exercises
...................................................... 552
References
............................................................. 567
Index
.................................................................. 569
|
| adam_txt |
Contents
Preface
.
V
1
Positioning on Earth and in Space
. 1
1.1
Introduction
. 1
1.2
Global Positioning System
. 2
1.2.1
Some Facts about GPS
. 2
1.2.2
The Theory Behind GPS
. 3
1.2.3
Dealing with Practical Difficulties
. 6
1.3
How
Hydro-Québec
Manages Lightning Strikes
. 12
1.3.1
Locating Lightning Strikes
. 12
1.3.2
Threshold and Quality of Detection
. 15
1.3.3
Long-Term Risk Management
. 18
1.4
Linear Shift Registers
. 19
1.4.1
The Structure of the Field F£
. 22
1.4.2
Proof of Theorem
1.4. 24
1.5
Cartography
. 27
1.6
Exercises
. 36
References
. 43
2
Friezes and Mosaics
. 45
2.1
Friezes and Symmetries
. 48
2.2
Symmetry Group and
Affine
Transformations
. 52
2.3
The Classification Theorem
. 58
2.4
Mosaics
. 64
2.5
Exercises
. 67
References
. 83
XII Contents
3
Robotic Motion
. 85
3.1
Introduction
. 85
3.1.1
Moving a Solid in the Plane
. 87
3.1.2
Some Thoughts on the Number of Degrees of Freedom
. 89
3.2
Movements That Preserve Distances and Angles
. 91
3.3
Properties of Orthogonal Matrices
. 94
3.4
Change of Basis
. 103
3.5
Different Frames of Reference for a Robot
. 106
3.6
Exercises
.
П1
References
. 117
4
Skeletons and Gamma-Ray Radiosurgery
. 119
4.1
Introduction
. 119
4.2
Definition of Two-Dimensional Region Skeletons
. 120
4.3
Three-Dimensional Regions
. 130
4.4
The Optimal Surgery Algorithm
. 132
4.5
A Numerical Algorithm
. 134
4.5.1
The First Part of the Algorithm
. 135
4.5.2
Second Part of the Algorithm
. 139
4.5.3
Proof of Proposition
4.17. 140
4.6
Other Applications of Skeletons
. 142
4.7
The Fundamental Property of the Skeleton
. 143
4.8
Exercises
. 147
References
. 153
5
Savings and Loans
. 155
5.1
Banking Vocabulary
. 155
5.2
Compound Interest
. 156
5.3
A Savings Plan
. 159
5.4
Borrowing Money
. 161
5.5
Appendix: Mortgage Payment Tables
. 164
5.6
Exercises
. 168
References
. 171
6
Error-Correcting Codes
. 173
6.1
Introduction: Digitizing, Detecting and Correcting
. 173
6.2
The Finite Field F2
. 178
6.3
The C(7,
4)
Hamming Code
. 179
6.4
C(2k
- 1,
2k
-
к
- 1)
Hamming Codes
.
і
182
6.5
Finite Fields
. 185
6.6
Reed-Solomon Codes
. 193
Contents XIII
6.7 Appendix:
The Scalar Product and Finite Fields
. 198
6.8
Exercises
. 200
References
. 207
7
Public Key Cryptography
. 209
7.1
Introduction
. 209
7.2
A Few Tools from Number Theory
. 210
7.3
The Idea behind RSA
. 213
7.4
Constructing Large Primes
. 221
7.5
The Shor Factorization Algorithm
. 231
7.6
Exercises
. 234
References
. 239
8
Random-Number Generators
. 241
8.1
Introduction
. 241
8.2
Linear Shift Registers
. 245
8.3
Fp-Linear Generators
. 248
8.3.1
The Case
ρ
= 2. 248
8.3.2
A Lesson on Gambling Machines
. 253
8.3.3
The General Case
. 253
8.4
Combined Multiple Recursive Generators
. 255
8.5
Conclusion
. 257
8.6
Exercises
. 258
References
. 263
9
Google and the PageRank Algorithm
. 265
9.1
Search Engines
. 265
9.2
The Web and Markov Chains
. 268
9.3
An Improved PageRank
. 278
9.4
The Frobenius Theorem
. 281
9.5
Exercises
. 284
References
. 289
10
Why
44,100
Samples per Second?
. 291
10.1
Introduction
. 291
10.2
The Musical Scale
. 292
10.3
The Last Note (Introduction to Fourier Analysis)
. 296
10.4
The Nyquist Frequency and the Reason for
44,100. 307
10.5
Exercises
. 317
References
. 323
XIV Contents
11
Image Compression:
Iterated Function Systems
. 325
11.1
Introduction
. 325
11.2
Affine
Transformations in the Plane
. 327
11.3
Iterated Function Systems
. 330
11.4
Iterated Contractions and Fixed Points
. 336
11.5
The Hausdorff Distance
. 340
11.6
Fractal Dimension
. 345
11.7
Photographs as Attractors
. 350
11.8
Exercises
. 361
References
. 367
12
Image Compression: The JPEG Standard
. 369
12.1
Introduction
. 369
12.2
Zooming in on a JPEG-Compressed Digital Image
. 372
12.3
The Case of
2
χ
2
Blocks
. 373
12.4
The Case of
Ν χ Ν
Blocks
. 378
12.5
The JPEG Standard
. 388
12.6
Exercises
. 396
References
. 401
13
The
DNA
Computer
. 403
13.1
Introduction
. 403
13.2
Adleman's Hamiltonian Path Problem
. 405
13.3
Turing Machines and Recursive Functions
. 409
13.3.1
Turing Machines
. 409
13.3.2
Primitive Recursive Functions and Recursive Functions
. 416
13.4
Turing Machines and Insertion-Deletion Systems
. 426
13.5
NP-Complete Problems
. 430
13.5.1
The Hamiltonian Path Problem
. 430
13.5.2
Satisfiability
. 431
13.6
More on
DNA
Computers
. 435
13.6.1
The Hamiltonian Path Problem and Insertion-Deletion Systems
435
13.6.2
Current Limits
. 435
13.6.3
A Few Biological Explanations Concerning Adleman's
Experiment
. 437
13.7
Exercises
. 441
References
. 445
Contents
XV
14
Calculus of Variations
. 447
14.1
The Fundamental Problem of Calculus of Variations
. 448
14.2
Euler-Lagrange Equation
. 451
14.3
Fermat's Principle
. 455
14.4
The Best Half-Pipe
. 457
14.5
The Fastest Tunnel
. 460
14.6
The Tautochrone Property of the Cycloid
. 465
14.7
An Isochronous Device
. 468
14.8
Soap Bubbles
. 471
14.9
Hamilton's Principle
. 475
14.10
Isoperimetric Problems
. 479
14.11
Liquid Mirrors
. 486
14.12
Exercises
. 490
References
. 499
15
Science Flashes
. 501
15.1
The Laws of Reflection and Refraction
. 501
15.2
A Few Applications of Conies
. 508
15.2.1
A Remarkable Property of the Parabola
. 508
15.2.2
The Ellipse
. 518
15.2.3
The Hyperbola
. 520
15.2.4
A Few Clever Tools for Drawing Conies
. 521
15.3
Quadratic Surfaces in Architecture
. 521
15.4
Optimal Cellular Antenna Placement
. 528
15.5
Voronoi Diagrams
. 532
15.6
Computer Vision
. 537
15.7
A Brief Look at Computer Architecture
. 539
15.8
Regular Pentagonal Tiling of the Sphere
. 544
15.9
Laying Out a Highway
. 551
15.10
Exercises
. 552
References
. 567
Index
. 569 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Rousseau, Christiane Saint-Aubin, Yvan |
| author_facet | Rousseau, Christiane Saint-Aubin, Yvan |
| author_role | aut aut |
| author_sort | Rousseau, Christiane |
| author_variant | c r cr y s a ysa |
| building | Verbundindex |
| bvnumber | BV023124428 |
| callnumber-first | Q - Science |
| callnumber-label | QA37 |
| callnumber-raw | QA37.3 |
| callnumber-search | QA37.3 |
| callnumber-sort | QA 237.3 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 950 |
| ctrlnum | (OCoLC)183915963 (DE-599)HBZHT015447841 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| genre | 1\p (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV023124428 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:52:52Z |
| indexdate | 2024-08-01T11:25:33Z |
| institution | BVB |
| isbn | 9780387692159 0387692150 |
| language | English French |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016326859 |
| oclc_num | 183915963 |
| open_access_boolean | |
| owner | DE-703 DE-355 DE-BY-UBR DE-20 DE-898 DE-BY-UBR DE-11 DE-862 DE-BY-FWS DE-83 DE-188 |
| owner_facet | DE-703 DE-355 DE-BY-UBR DE-20 DE-898 DE-BY-UBR DE-11 DE-862 DE-BY-FWS DE-83 DE-188 |
| physical | XV, 580 S. Ill., graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer undergraduate texts in mathematics and technology |
| spellingShingle | Rousseau, Christiane Saint-Aubin, Yvan Mathematics and technology Mathematik Mathematisches Modell Mathematics Technology Technology Mathematical models Technik (DE-588)4059205-4 gnd Angewandte Mathematik (DE-588)4142443-8 gnd |
| subject_GND | (DE-588)4059205-4 (DE-588)4142443-8 (DE-588)4123623-3 |
| title | Mathematics and technology |
| title_auth | Mathematics and technology |
| title_exact_search | Mathematics and technology |
| title_exact_search_txtP | Mathematics and technology |
| title_full | Mathematics and technology Christiane Rousseau ; Yvan Saint-Aubin |
| title_fullStr | Mathematics and technology Christiane Rousseau ; Yvan Saint-Aubin |
| title_full_unstemmed | Mathematics and technology Christiane Rousseau ; Yvan Saint-Aubin |
| title_short | Mathematics and technology |
| title_sort | mathematics and technology |
| topic | Mathematik Mathematisches Modell Mathematics Technology Technology Mathematical models Technik (DE-588)4059205-4 gnd Angewandte Mathematik (DE-588)4142443-8 gnd |
| topic_facet | Mathematik Mathematisches Modell Mathematics Technology Technology Mathematical models Technik Angewandte Mathematik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016326859&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT rousseauchristiane mathematicsandtechnology AT saintaubinyvan mathematicsandtechnology |
Inhaltsverzeichnis
THWS Schweinfurt Zentralbibliothek Lesesaal
| Signatur: |
2000 SK 950 R864 |
|---|---|
| Exemplar 1 | ausleihbar Verfügbar Bestellen |