Over 300 challenging problems in algebra, arithmetic, elementary number theory and trigonometry, selected from the archives of the Mathematical Olympiads held at Moscow University. Most presuppose only high school mathematics but some are of uncommon difficulty and will challenge any mathematician. Complete solutions to all problems. 27 black-and-white illustrations. 1962 edition.
The USSR Olympiad Problem Book
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Language Notes
Text: English (translation)
Original Language: Russian
Original Language: Russian
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14 of 15 people found the following review helpful
By Jeff Barnes
Format:Paperback
This book consists of "320 unconventional problems in algebra, arithmetic, elementary number theory and trigonometry." The problems are mathematically accessible to students at the high school level or higher, as they call more upon analytical thinking than upon advanced mathematical techniques. There is a range of difficulties, with harder problems marked with stars in the book. (The hardest problems are marked with double stars.) The problems are divided into twelve sections: "Introductory Problems," "Alterations of Digits in Integers," "The Divisibility of Integers," "Some Problems from Arithmetic," "Equations Having Integer Solutions," "Evaluating Sums and Products," "Miscellaneous Problems from Algebra," "The Algebra of Polynomials," "Complex Numbers," "Some Problems of Number Theory," "Some Distinctive Inequalities," and "Difference Sequences and Sums." Much of the book is devoted to providing hints and solutions, which are both thorough and clear. This is a great resource for preparing for competition, for developing your analytical thinking, or just for having fun (that is, if you are the sort of person who finds solving math problems fun).
6 of 6 people found the following review helpful
By A Customer
Format:Paperback
The reason I am giving 5 stars to this book is for its unique collection of problems. It has been very entertaining reading the book so far (I have not completed the book). There however are a few errors which can be easily figured out by the reader. The treatment of each problem is unique.
7 of 8 people found the following review helpful
By Dance Ham
Format:Paperback
This is a great resource for challenging math problems. After getting annoyed with newspaper "problem of the week" type books, this was a refreshing find. Don't let the "high school level" disclaimer fool you - there are some seriously difficult problems in here.
If you're the type to find logic and math problems fun, I would recommend dropping $15 for this text. It's well worth the time.
If you're the type to find logic and math problems fun, I would recommend dropping $15 for this text. It's well worth the time.
6 of 7 people found the following review helpful
By "albatr0s83"
Format:Paperback
I found this book very interesting, because it deals with many many problems of algebra and number theory. You can find many interesting and tough theorems (not all of them are widely known nor taught) with their demonstration. I particularily liked the section about "distinctive inequalities": it deals with a great number of inequalities and you can learn some new techniques for solving them. The book lacks of geometry, that's true (only some trig somewhere), but it gives (in my opinion) really a strong preparation on topics concerning algebra... try it!
3 of 5 people found the following review helpful
By A Customer
Format:Paperback
This books is what every book on math olympiads should be, it deals with high level problems in a way that readers can easily follow; I also liked it because there are some problems who have many interesting solutions and generalizations
0 of 1 people found the following review helpful
Format:Paperback|Amazon Verified Purchase
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.
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.
0 of 1 people found the following review helpful
By olenka
Format:Paperback|Amazon Verified Purchase
We do problems from this book in the math club at my college.
I wish there were more books like this one.
I wish there were more books like this one.
3 of 6 people found the following review helpful
By A Customer
Format:Paperback
If you like challenging math problems then this book is for you. It's ideal if you want to prepare for a national math olympiad or if you just like hard math problems. Get this book and you won't regret it !!!
Most Recent Customer Reviews
2.0 out of 5 stars
Good at first, but tiring
The book is good at first but one tires quickly after reading the heavy syntax and the similar style of many of the problem. Read more
Published on August 14, 1999
5.0 out of 5 stars
Read the following:
This exercise book is great! The collection of the most interessant and exciting problems of elementary Mathematics. Ideal for preparing for the IMO. Read more
Published on June 7, 1998
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