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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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