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Inequalities: Theorems, Techniques and Selected Problems, by Zdravko Cvetkovski
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This work is about inequalities which play an important role in mathematical Olympiads. It contains 175 solved problems in the form of exercises and, in addition, 310 solved problems. The book also covers the theoretical background of the most important theorems and techniques required for solving inequalities. It is written for all middle and high-school students, as well as for graduate and undergraduate students. School teachers and trainers for mathematical competitions will also gain benefit from this book.
- Sales Rank: #1212169 in Books
- Brand: Brand: Springer
- Published on: 2012-01-06
- Released on: 2012-01-06
- Original language: English
- Number of items: 1
- Dimensions: 9.25" h x 1.03" w x 6.10" l, 1.35 pounds
- Binding: Paperback
- 444 pages
- Used Book in Good Condition
Review
From the reviews:
“The book is aimed at the more advanced students about to enter university and is particularly useful to candidates, and their trainers, for mathematical competitions such as the Olympiads. The themes and methods are introduced in 19 chapters of the book, which include exercises and their solutions.” (Peter Shiu, The Mathematical Gazette, Vol. 98 (541), March, 2014)
“This volume collects problems of various degrees of difficulty in the field of elementary inequalities. This book is intended as a valuable source for the training of high-school students in view of mathematical Olympiads. School teachers will also gain benefit from this book. … It would be a particularly valuable resource for those who participate in mathematics competitions at the high school or college level. … this book is a ‘must have’ for a university’s library, and I recommend it highly to its ‘ideal audience’.” (Teodora-Liliana Radulescu, Zentralblatt MATH, Vol. 1233, 2012) From the Back Cover
This work is about inequalities which play an important role in mathematical Olympiads. It contains 175 solved problems in the form of exercises and, in addition, 310 solved problems. The book also covers the theoretical background of the most important theorems and techniques required for solving inequalities. It is written for all middle and high-school students, as well as for graduate and undergraduate students. School teachers and trainers for mathematical competitions will also gain benefit from this book.
About the Author
Dipl. Math. Zdravko Cvetkovski, European University-Skopje, R. Macedonia, Informatics Department.
Most helpful customer reviews
0 of 0 people found the following review helpful.
Very useful book for Mathematics Competitions
By Dr S Muralidharan
This is a wonderful book. The book provides a comprehensive treatment of inequalities. It also contains a wealth of examples and exercises with full solutions. This will be a treasure trove for any student planning to participate in Mathematics competitions and also to their trainers The author has done a good service by collecting all the important inequalities in one volume.
0 of 0 people found the following review helpful.
A helpful introduction, but contains errors
By Andrew E. Pennebaker
In the 2012 edition, exercise 1.8 has a critical typo. "R" should be "R+", as 3abc(a+b+c) is not actually >= 3(abc)^2 when a=1, b=1, c=-1.
3 of 8 people found the following review helpful.
Wonderfully Up to Date Book on a Key Math Topic
By Let's Compare Options Preptorial
It's interesting how different disciplines look differently at inequalities. In education, they are most often associated with the math Olympiads as some of the most difficult problems for K-12 students, as well as undergrads. In these fields, the boundaries are stated algebraically. In business, economics, physics, engineering and many other areas of applied math, they are associated with optimization, boundary values, symmetry and many other solutions. Those advanced applications involve calculus, ODEs and PDEs.
The "other" outstanding book on inequalities explicitly mentions the Olympiads, but also is filled with other practical applications, proofs and theories: Inequalities: A Mathematical Olympiad Approach.
If you love math in general, you'll love this book for it's beauty and many astonishing insights about how important inequalities are. Life, whether balancing your checkbook or watching a movie, is most exciting when the "keep it close" rule is followed-- like a close game being more nail biting than a blow out. "Almost" is the essence of inequalities, and they are found much more often in "real" life than a = b. After all, "boundaries" are the essence of duality, and reward is most amazing at the ragged brink of risk, since they are holistically inseparable when you consider boundary solutions, or zen, depending on your POV.
So, if you're into the Olympiads, this is a must. Even if not, you'll enjoy both the elegance of the proofs and the beauty of the underlying logic. For advanced readers, some proofs presented in this and the Olympiad book can be found nowhere else-- these are a couple of gems on a topic without a lot of recent coverage except in journals. Enjoy!
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