# Did You Say Mathematics? (gnv64)

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Did You Say Mathematics

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## Description

Did You Say Mathematics?

By Yakov Khurgin

Mir | October 1985 | ISBN-10: 0828528780 | English | PDF| 360 pages | 19.6 mb

scanned to PDF by gnv64 with OCR, bookmarks, covers & internal links

"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!

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