The USSR Olympiad Problem Book: Selected Problems and Theorems of Elementary Mathematics (Dover Books on Mathematics) by D. O. Shklarsky (PDF)

Description

This book contains 320 unconventional problems in algebra, arithmetic, elementary number theory, and trigonometry. Most of the problems first appeared in competitive examinations sponsored by the School Mathematical Society of the Moscow State University and the Mathematical Olympiads held in Moscow. Although most of the problems presuppose only high school mathematics, they are not easy; some are of uncommon difficulty and will challenge the ingenuity of any research mathematician. Nevertheless, many are well within the reach of motivated high school students and even advanced seventh and eighth graders.The problems are grouped into twelve separate sections. Among these are: the divisibility of integers, equations having integer solutions, evaluating sums and products, miscellaneous algebraic problems, the algebra of polynomials, complex numbers, problems of number theory, distinctive inequalities, difference sequences and sums, and more.Complete solutions to all problems are given; in many cases, alternate solutions are detailed from different points of view. Solutions to more advanced problems are given in considerable detail. Moreover, when advanced concepts are employed, they are discussed in the section preceding the problems. Useful in a variety of ways in high school and college curriculums, this challenging volume will be of particular interest to teachers dealing with gifted and advanced classes.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book contains a number of problems in Elementary Mathematics. I don’t know what they mean by that, since most of the problems forced me to think a great deal, but maybe that is because my math is slightly rusty. However, this book also contains detailed solutions, so you aren’t left hanging for anything. Some of the answers contain radicals and other numbers that are irrational, so maybe they mean that no calculus is involved in getting the answers.In any case, the book clearly states the problem and numbers the problem so you can find the answer in the book. This is all I really ask for in a mathematics text; a way to see if I am right or not.

⭐People who already have some background in basic math and find doing math problems relaxing will be happy with the book – problems and solutions are very well done. I’d say worth their investment. Book received in excellent condition and before promised time. Thank you.

⭐This book is a great source of high-quality math olympiad problems with solutions. If you want to have the pleasure of real math, then you should try this book. I liked it very much. Highly recommended.

⭐Great training for the Olympics. I’ve always been lazy to run but every time I see it I ran as far away as possible. Ill be in the Olympics in no time.

⭐It is a problem and solution type of book. The organization is not ideal. The problems are not ordered by difficulties. There are some very difficult problems. The solutions are quite rigorous and mostly well explained. Probably nice for a teacher to use, not good for self study.Almost all the problems are for algebra, which seems narrow for preparation for high school math Olympiad. From the forward, it is stated that they are for 8th and 9th graders in USSR, which probably explain the lack of Euclidean geometry.

⭐The book contains many good and challenging math problems for middle and high school students usually offered in math competitions in the former Soviet Union or socialist countries.

⭐Fond memories from solving problems from this book during my high school years. Re bought it recently to try some of these problems for fun

⭐Great book! I used it as training book in childhood. I solved about half of them independently. I think it shapes my math background pretty well. Most important, it teaches me math and logic thinking skills by brilliant problems.

⭐Excellent collection to have

⭐Para conhecimento.It is very much appreciated, for olympiad.

⭐Good

⭐Nice book if you’re into math problems.

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