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Description
The USSR Olympiad Problem Book: Selected Problems and Theorems of Elementary MathematicsThis 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
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.
Binding Type: Paperback
Publisher: Dover Publications
Published: 09/28/1993
ISBN: 9780486277097
Pages: 480
Weight: 1.03lbs
Size: 8.76h x 5.16w x 0.90d
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Product Reviews
★★★★★ 3
Not as good as chuck it anymore
Style: Fetch Balls (Pack of 10), Size: 2.5 inch
I have bought these before and the where just like the chuck it balls. These are not those balls. The are lighter and my dog has already cause damage to one
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Reviewed in the United States on March 16, 2026
★★★★★ 5
Is this the CURE!
Size: Regular, Color: Cream
I have a skin disease called Ichthyosis Vulgaris. Yes, SCALEY FISH! Thanks MOM! This unfortunate crud leaves my heels an embarrassing mess! They are cracked and dry and literally like concrete. I have had this disease all my life and there is NO cure. It's hideous! Anyway, I have tried so many different experiments to help improve my situation. So much time and money I will never get back. So when I saw these, I had to give them a try too because I am a forever optimist and love being disappointed. Here's how it went.
First I put my dermatologist recommended AmLactin on my crusty heels. Then, I put the socks on. By the way, with no problem at all, and went to bed. I was not too hot, which is usually what happens when I sleep with socks on. I never even realized that I had them on. When I woke up, I took them off and immediately used a "Heel File" over a towel removing all the yuck!. Then, I sand papered them to smooth the skin out. Then, I doused them with Shea and Aloe foot lotion I found at the bottom of my experiment drawer in my bathroom. Oh, they felt like someone else's feet. I am very hopeful at this moment! Is this the cure to my embarrassing situation? I sure hope so. Spring is here and I would really like to wear my cute flip-flops when I go to the Waffle House and set at the bar. Wasn't that a picture on Facebook of someone nasty heels? It made me gag. Then, I had to make sure that picture wasn't me! I am going to do this for a week and come back for another review. Wish me luck ya'll!
UPDATE!
So it’s been about two weeks. I wish that I had taken a before and after picture. I guess I figure that this too will be a waste of money. NO! These little socks are a God send for me. I did buy AmLactin foot repair cream and that I highly recommend. It’s the best so far. They also offer an option with heel socks. They are soft and work very well also but one negative. They leave fuzzies on you feet and tools. Guys this is it for me. My search is over! I went to my mani/pedi queen yesterday and she was shocked when she saw my feet. She is spreading the word!
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Reviewed in the United States on March 23, 2025
★★★★★ 5
Great reusable moisturizing
Size: Regular, Color: Cream
Love these! Use them often to help moisturize my heels with my favorite moisturizer. Comfortable and easy to use
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Reviewed in the United States on May 21, 2026
★★★★★ 5
Buy these!
Size: Regular, Color: Cream
I only write a review when I have a strong opinion and want to help others decide. I've been having trouble with cracked heels for months. Previously I had just been using regular socks, but these slip-ons have been game changers! They don't make my feet hot at night. They are comfortable and in the morning my heels feel soft, and I don't need to use them everyday. They look good and fit well even if I want to wear them under socks or in shoes during the day. They really do help if you have cracked heels along with some kind of lotion. Definitely effective!
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Reviewed in the United States on May 19, 2025
★★★★★ 5
Cracked heels are gone after 5 applications
Size: Regular, Color: Cream
These moisturizing socks work great. My heels are happy again. The open toe design makes it so my feet don’t overheat at night. It only took 5 times to get rid of my painful cracked heels. Now I wear them 1-2 times a week to keep my heels healthy.
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Reviewed in the United States on January 6, 2026