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This book aims to convey the theory and techniques involved in proving algebraic inequalities. Each chapter begins with a theoretical part, in which several classical theorems are stated and proven. These include the fundamental Arithmetic-Geometric Mean and Cauchy-Schwarz inequalities, as well as the Nesbitt, Schur, Hölder, Rearrangement, and Chebyshev inequalities. Numerous examples are provided to illustrate the subtleties involved in applying these inequalities. Problems range from relatively easy to extremely challenging, benefiting both beginners and veteran problem solvers alike. To help the reader hone their skills, 109 inequality problems are provided, of which 54 are introductory and 55 are advanced. Detailed solutions to all of these problems are given, in which an eclectic medley of ideas are employed.
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About the Author:
Titu Andreescu, University of Texas at Dallas, Richardson, TX, USA.Adithya Ganesh, Massachusetts Institute of Technology, Cambridge, MA, USA.
Review:
"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
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- PublisherXyz Pr
- Publication date2015
- ISBN 10 0988562286
- ISBN 13 9780988562288
- BindingHardcover
- Edition number1
- Number of pages203
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