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Algebra

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This book is about algebra. This is a very old science and its gems have lost their charm for us through everyday use. We have tried in this book to refresh them for you. The main part of the book is made up of problems. The best way to deal with them is: Solve the problem by yourself - compare your solution with the solution in the book (if it exists) - go to the next problem. However, if you have difficulties solving a problem (and some of them are quite difficult), you may read the hint or start to read the solution. If there is no solution in the book for some problem, you may skip it (it is not heavily used in the sequel) and return to it later. The book is divided into sections devoted to different topics. Some of them are very short, others are rather long. Of course, you know arithmetic pretty well. However, we shall go through it once more, starting with easy things. 2 Exchange of terms in addition Let's add 3 and 5: 3+5=8. And now change the order: 5+3=8. We get the same result. Adding three apples to five apples is the same as adding five apples to three - apples do not disappear and we get eight of them in both cases. 3 Exchange of terms in multiplication Multiplication has a similar property. But let us first agree on notation.

Authors: Gelfand I.M., Shen Alexander
Publisher: BIRKHAUSER
Pages: 160
ISBN: 9780817636777
Cover: Paperback
Edition Number: 1
Release Year: 1993

Israel Gelfand (1913-2009) is often considered one of the greatest mathematicians of the Twentieth Century.  He published dozens of books and over 400 articles in a variety of mathematical fields, including group theory, representation theory, and functional analysis.  Gelfand was known internationally as an outstanding and passionate teacher, as well as for his famous seminars in mathematics and biology, which were attended by the most prominent specialists in the field.  He had a remarkable ability to adapt his presentation of difficult concepts so they would be easily understood by his audience, whether that was children or experienced professors. In 1964, he created the Correspondence School in Mathematics (ZMSH) in Moscow, and later on, the Gelfand Correspondence Program in Mathematics (GCPM) at Rutgers University, both of which made mathematics available to a broad range of students.  His goal was to pass on to students his belief that mathematics is simple, beautiful, and a part of human culture which anyone can learn and enjoy, just like literature, poetry, art, and music.

Transfer, Russian Academy of Sciences Inst. Problems of Information, Moskva, Russia

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