Mathematics Galore!: Masterclasses, Workshops and Team Projects in Mathematics and Its Applications

Cover
OUP Oxford, 17.05.2001 - 254 Seiten
This book is a series of self-contained workshops in mathematics which aim to enthuse and inspire young people, their parents and teachers with the joy and excitement of modern mathematics. Written in an informal style, each chapter describes how novel mathematical ideas relate directly to real life. The chapters contain both a description of the mathematics and its applications together with problem sheets, their solutions and ideas for further work, project and field trips. Topics include; mazes, folk dancing, sundials, magic, castles, codes, number systems, and slide rules. This book should be accessible to young people from age thirteen upwards and yet contains material which should stretch the brightest students.
 

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Inhalt

Where we start
10
How does a masterclass work?
10
What is this book all about?
10
The classes
10
Acknowledgments
10
Amazing mazes
10
13 The mathematics of the Cretan Labyrinth
11
14 The rise of the maze
15
52 Early fortifications circles and the isoperimetric theorem
127
53 Medieval castles
137
54 More recent fortifications
142
55 How to defend a castle
145
56 Exercises
151
57 Further problems
153
58 Answers
159
59 Mathematical notes
162

15 How to solve a maze with your hand on a hedge
17
16 How to solve a maze with a little network topology
21
17 How to solve a maze using a packet of peanuts and a bag of crisps
27
18 Modern mazes
28
19 Exercises
29
110 Further problems
33
111 Answers
35
112 Mathematical notes
36
Dancing with mathematics
38
22 Symmetry and group theory
39
23 Back to dancing
43
24 Bellringing and knitting
48
25 Exercises
51
26 Further problems
53
27 Answers
55
28 Mathematical notes
60
29 References
61
Sundials how to tell the time without a digital watch
62
33 The motion of the sun
64
34 The Equatorial sundial
72
35 The horizontal sundial
74
36 The vertical sundial
79
37 The analemmatic sundial
81
38 What time does a sundial show?
85
39 Exercises
92
310 Further problems
94
311 Answers
99
313 References
100
Magical mathematics
102
42 Magical mathematics
103
43 Mathematical magic
105
44 Conclusions
115
46 Further problems
117
47 Answers
121
48 Mathematical notes
123
49 References
125
Castles mathematics in defence and attack
126
510 References
163
How to be a spy the mathematics of codes and ciphers
165
62 What are codes and ciphers and what is the difference?
168
63 The Caesar cipher
169
64 Was Caesar a mathematician?
171
65 Statistics and more general ciphers
174
66 Multiple substitution ciphers
177
67 Transposition ciphers
181
68 Modernday ciphers
184
69 Exercises
185
610 Further problems
187
611 Answers
191
Some properties of the English language
193
613 References
194
Whats in a name?
195
72 Number bases and base ten
199
73 Other number bases
202
74 The counting board
207
75 Negative number bases
208
76 Exercises
212
77 Further problems
215
78 Answers
216
79 Mathematical notes
218
710 References
219
Doing the sums
220
82 Before logarithms
221
83 The life of John Napier
222
84 What are logarithms?
224
85 Using tables of logarithms
228
86 The slide rule
231
87 Who invented the slide rule?
235
88 Exercises
236
89 Answers
241
810 Mathematical notes
242
811 References
244
Index
249
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Über den Autor (2001)

Christopher Budd is at Royal Institution. Christopher Sangwin is at University of Birmingham.

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