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Inequalities
This book discusses about the basic topics on inequalities and their applications. These include the arithmetic mean–geometric mean inequality, Cauchy–Schwarz inequality, Chebyshev inequality, rearrangement inequality, convex and concave functions and Muirhead's theorem. The book contains over 400 problems with their solutions. A chapter on geometric inequalities is a special feature of this book. Most of these problems are from International Mathematical Olympiads and from many national mathematical Olympiads. The book is intended to help students who are preparing for various mathematical competitions. It is also a good source book for graduate students who are consolidating their knowledge of inequalities and their applications.
Inequalities
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Challenge and Thrill of Pre-College Mathematics
Challenge And Thrill Of Pre-College Mathematics Is An Unusual Enrichment Text For Mathematics Of Classes 9, 10, 11 And 12 For Use By Students And Teachers Who Are Not Content With The Average Level That Routine Text Dare Not Transcend In View Of Their Mass Clientele. It Covers Geometry, Algebra And Trigonometry Plus A Little Of Combinatorics. Number Theory And Probability. It Is Written Specifically For The Top Half Whose Ambition Is To Excel And Rise To The Peak Without Finding The Journey A Forced Uphill Task.The Undercurrent Of The Book Is To Motivate The Student To Enjoy The Pleasures Of A Mathematical Pursuit And Of Problem Solving. More Than 300 Worked Out Problems (Several Of Them Fro...
Mathematical Olympiad Challenges
Hundreds of beautiful, challenging, and instructive problems from algebra, geometry, trigonometry, combinatorics, and number theory Historical insights and asides are presented to stimulate further inquiry Emphasis is on creative solutions to open-ended problems Many examples, problems and solutions, with a user-friendly and accessible style Enhanced motivatio References
The IMO Compendium
"The IMO Compendium" is the ultimate collection of challenging high-school-level mathematics problems and is an invaluable resource not only for high-school students preparing for mathematics competitions, but for anyone who loves and appreciates mathematics. The International Mathematical Olympiad (IMO), nearing its 50th anniversary, has become the most popular and prestigious competition for high-school students interested in mathematics. Only six students from each participating country are given the honor of participating in this competition every year. The IMO represents not only a great opportunity to tackle interesting and challenging mathematics problems, it also offers a way for hig...
Introduction to the Theory of Standard Monomials
The book is a reproduction of a course of lectures delivered by the author in 1983-84 which appeared in the Brandeis Lecture Notes series. The aim of this course was to give an introduction to the series of papers by concentrating on the case of the full linear group. In recent years, there has been great progress in standard monomial theory due to the work of Peter Littelmann. The author’s lectures (reproduced in this book) remain an excellent introduction to standard monomial theory. Standard monomial theory deals with the construction of nice bases of finite dimensional irreducible representations of semi-simple algebraic groups or, in geometric terms, nice bases of coordinate rings of ...
Partial Differential Equations
This book provides a basic introductory course in partial differential equations, in which theory and applications are interrelated and developed side by side. Emphasis is on proofs, which are not only mathematically rigorous, but also constructive, where the structure and properties of the solution are investigated in detail. The authors feel that it is no longer necessary to follow the tradition of introducing the subject by deriving various partial differential equations of continuum mechanics and theoretical physics. Therefore, the subject has been introduced by mathematical analysis of the simplest, yet one of the most useful (from the point of view of applications), class of partial differential equations, namely the equations of first order, for which existence, uniqueness and stability of the solution of the relevant problem (Cauchy problem) is easy to discuss. Throughout the book, attempt has been made to introduce the important ideas from relatively simple cases, some times by referring to physical processes, and then extending them to more general systems.
