Did You Say Mathematics?
By Yakov Khurgin
Mir | October 1985 | ISBN-10: 0828528780 | English | PDF| 360 pages | 19.6 mb

"In the chapters that follow I will attempt to tell the story of mathematics and weave into an integral whole the various discussions I have had with my non-mathematical friends. This will be a story of mathematics in popular language so that the non-mathematician will see what it is all about. This is not a course in mathematics but merely a series of sketches concerning ideas and methods. There will be no proofs to carry out and no need for paper and pencil. What I want to do
is sketch a picture of the development of mathematics and show what mathematicians are presently engaged in—to some extent. It is hardly possible to examine the whole field, but the fragments 1 hope to present will cover a rather wide range of outwardly unrelated mathematical theories and their applications. It is best to read one chapter after another as they occur in the book, since they are all linked together. If some parts are uninteresting, don't throw the book down. Go over the earlier chapters once again. I'm sure you will find something that will hold your attention."

About the Author
Dr. Yakov Khurgin is professor of mathematics at the Chair of Applied Mathematics at the Gubkin Institute of the Petrolium and Gas Industry. He has written over a hundred scientific papers in pure and applied mathematics and has been particularly productive in the fields of radio-engineering, radiophysics, cybernetics, neurophysiology and psychiatry. At the present time (1984), Professor Khurgin heads the laboratory of applied mathematics. He is also a member of the USSR National Committee of Automatic Control.His extensive knowledge and wide range of activities have helped to make his popular science books a great success.


CONTENTS
A FEW WORDS WITH THE READER 9
Mathematician and physiologist get together in September 12
Mathematician and physiologist get together in December 20
A radio engineer needs math 25
One last word to the reader 31

WHAT DO YOU THINK ABOUT MATHEMATICS? 33
What is mathematics all about? 35
A little historical background 36

RUBBER-SHEET MATHEMATICS 41
Mathematics and art 47
Continuous transformations 47
A remarkable surface 55
Graphs 58

NUMBERS AND POINTS 71
THE MATHEMATICS OF A SADDLE 88
Extrema 96
Extremal curves 106
The epoch of Euler 108
Soap bubbles 110

MATHEMATICIANS ARE NOT ALL ALIKE 114
Where do axioms come from? 116
Two ways of reasoning 117
Induction and mathematical induction 125
The drama of equation solving—an historical sketch 129

ENGINEER CONSULTS MATHEMATICIAN 136
What is better? 141
Criteria 147
Optimization 150
How close? 152
Mary and Maude 155
Integrals—not so terrible after all 157
Space, distance, norm 162
Terms and where they come from 169
The problems of an oil engineer 172
Choosing a job 174
Model building 184
Mathematical models 187
Events and their models 191
Does one really need a mathematical model? 197
Modelling the oil-refining process 206

YOU PROBABLY LIKE THIS BOOK 209
Probability theory. Some background 212
Random events 213
Probability 214
An experiment and what came of it 216
Engineer consults mathematician 222
Experimenter and statistician 227
Decision making 231
Intuition and birthdays 234
Intuition and luck 239
Random walks 246
The drunkard's walk 258
The random-walk student 260

INFORMATION 268
Memory and codes 271
Information and what it's all about 278
Quantitative measures 282
The capacity of a communication channel 288
Coding 290
A language model and the transmission of information 295
Basic principle of the theory of the transmission of information 297
What about the content? 300

MATHEMATICAL MACHINES AND WHAT THEY CAN DO 303
The psychiatrist drops in for a talk 310
Pattern recognition 318
Technical diagnostics 327
Medical diagnostics 338
Replacing doc with a diagnostic machine 347
What is our life? A game... 349
One final word to the reader 360

I had always postponed scanning this book as its tightly bound paperback format was preventing me from getting good scans. But finally I decided to go at it as this rare book, which I had purchased exactly 23 years back, was not available anywhere on the web. Its not a perfect scan but I hope its good enough!