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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.
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.
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