The Cauchy-Schwarz Master Class

Author: J. Michael Steele
Publisher: Cambridge University Press
ISBN: 9780521546775
Category : Mathematics
Languages : en
Pages : 320

Book Description
This lively, problem-oriented text, first published in 2004, is designed to coach readers toward mastery of the most fundamental mathematical inequalities. With the Cauchy-Schwarz inequality as the initial guide, the reader is led through a sequence of fascinating problems whose solutions are presented as they might have been discovered - either by one of history's famous mathematicians or by the reader. The problems emphasize beauty and surprise, but along the way readers will find systematic coverage of the geometry of squares, convexity, the ladder of power means, majorization, Schur convexity, exponential sums, and the inequalities of Hölder, Hilbert, and Hardy. The text is accessible to anyone who knows calculus and who cares about solving problems. It is well suited to self-study, directed study, or as a supplement to courses in analysis, probability, and combinatorics.

The Cauchy-Schwarz Master Class

Author: J. Michael Steele
Publisher: Cambridge University Press
ISBN: 1139454560
Category : Mathematics
Languages : en
Pages : 317

Inequalities

Author: Zdravko Cvetkovski
Publisher: Springer Science & Business Media
ISBN: 3642237924
Category : Mathematics
Languages : en
Pages : 439

Book Description
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.

When Less is More

Author: Claudi Alsina
Publisher: American Mathematical Soc.
ISBN: 1614442029
Category : Mathematics
Languages : en
Pages : 181

Book Description
Introduces the richness and variety of inequalities in mathematics using illustration and visualisation.

Educative JEE Mathematics

Author: K.D. Joshi
Publisher: Universities Press
ISBN: 9788173714740
Category :
Languages : en
Pages : 992

Book Description

Probability Theory and Combinatorial Optimization

Author: J. Michael Steele
Publisher: SIAM
ISBN: 9781611970029
Category : Mathematics
Languages : en
Pages : 168

Book Description
This monograph provides an introduction to the state of the art of the probability theory that is most directly applicable to combinatorial optimization. The questions that receive the most attention are those that deal with discrete optimization problems for points in Euclidean space, such as the minimum spanning tree, the traveling-salesman tour, and minimal-length matchings. Still, there are several nongeometric optimization problems that receive full treatment, and these include the problems of the longest common subsequence and the longest increasing subsequence. The philosophy that guides the exposition is that analysis of concrete problems is the most effective way to explain even the most general methods or abstract principles. There are three fundamental probabilistic themes that are examined through our concrete investigations. First, there is a systematic exploitation of martingales. The second theme that is explored is the systematic use of subadditivity of several flavors, ranging from the naïve subadditivity of real sequences to the subtler subadditivity of stochastic processes. The third and deepest theme developed here concerns the application of Talagrand's isoperimetric theory of concentration inequalities.

Positive Polynomials

Author: Alexander Prestel
Publisher: Springer Science & Business Media
ISBN: 3662046482
Category : Mathematics
Languages : en
Pages : 269

Book Description
Positivity is one of the most basic mathematical concepts, involved in many areas of mathematics (analysis, real algebraic geometry, functional analysis, etc.). The main objective of the book is to give useful characterizations of polynomials. Beyond basic knowledge in algebra, only valuation theory as explained in the appendix is needed.

An Introduction to Inequalities

Author: Edwin F. Beckenbach
Publisher: Mathematical Assn of Amer
ISBN: 9780883856031
Category : Mathematics
Languages : en
Pages : 133

Book Description

Inequalities

Author: G. H. Hardy
Publisher: Cambridge University Press
ISBN: 9780521358804
Category : Mathematics
Languages : en
Pages : 344

Book Description
This classic of the mathematical literature forms a comprehensive study of the inequalities used throughout mathematics. First published in 1934, it presents clearly and lucidly both the statement and proof of all the standard inequalities of analysis. The authors were well-known for their powers of exposition and made this subject accessible to a wide audience of mathematicians.

Algebraic Inequalities

Author: Hayk Sedrakyan
Publisher: Springer
ISBN: 3319778366
Category : Mathematics
Languages : en
Pages : 244

Book Description
This unique collection of new and classical problems provides full coverage of algebraic inequalities. Many of the exercises are presented with detailed author-prepared-solutions, developing creativity and an arsenal of new approaches for solving mathematical problems. Algebraic Inequalities can be considered a continuation of the book Geometric Inequalities: Methods of Proving by the authors. This book can serve teachers, high-school students, and mathematical competitors. It may also be used as supplemental reading, providing readers with new and classical methods for proving algebraic inequalities.