This book explores the theory and techniques involved in
proving algebraic inequalities. To expand the reader's mathematical
toolkit, the authors present problems from journals and contests from
around the world.
Inequalities are an essential topic in Olympiad
problem solving, and 109 Inequalities will serve as an
instructive resource for students striving for success at national and
international competitions. Inequalities are also of great
theoretical interest and pave the way towards advanced topics such as
analysis, probability theory, and measure theory. Most of all, the
authors hope that the reader finds inspiration in both the struggle
and beauty of proving algebraic inequalities.
A publication of XYZ Press. Distributed in North America by the American Mathematical Society.
Middle and high school students interested in mathematics competition preparation.
"109 Inequalities from the AwesomeMath Summer Program" lives up to its promise as an instructive resource for students striving for success at national and international competitions...[T]he problems form an excellent training regimen for mathematical inequalities and will help readers master the subject...It is an excellent resource and would be a valuable addition to a problem solver's library.
-- Jack Chen, MAA Reviews
The book covers many classical topics in elementary algebra,
including factoring, quadratic functions, irrational expressions,
Vieta's relations, equations and systems of equations, inequalities,
sums and products, and polynomials. Expanding upon the previous work
in the series, 105 Problems in Algebra from the AwesomeMath Summer
Program, this book features additional more advanced topics,
including exponents and logarithms, complex numbers, and
trigonometry.
The special section on trigonometric substitutions and more
explores seemingly algebraic problems with natural geometric and
trigonometric interpretations. To give the reader practice with the
strategies and techniques discussed in each of the chapters, the
authors have included 108 diverse problems, of which 54 are
introductory and 54 are advanced. Solutions to all of these problems
are provided, in which different approaches are compared.
A publication of XYZ Press. Distributed in North America by the American Mathematical Society.
Middle and high school students interested in mathematics competition preparation.