> PDF Ebook Number Theory: Structures, Examples, and Problems, by Titu Andreescu, Dorin Andrica

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This introductory textbook takes a problem-solving approach to number theory, situating each concept within the framework of an example or a problem for solving. Starting with the essentials, the text covers divisibility, unique factorization, modular arithmetic and the Chinese Remainder Theorem, Diophantine equations, binomial coefficients, Fermat and Mersenne primes and other special numbers, and special sequences. Included are sections on mathematical induction and the pigeonhole principle, as well as a discussion of other number systems. By emphasizing examples and applications the authors motivate and engage readers.

• Sales Rank: #1452704 in Books
• Published on: 2009-03-11
• Original language: English
• Number of items: 1
• Dimensions: 9.40" h x 1.20" w x 6.50" l, 1.50 pounds
• Binding: Hardcover
• 384 pages

Review

From the reviews:

“Number theory is a very important field in mathematics, with many applications in theoretical physics, cryptography and so on. The present book of problems with solutions is a wonderful selection of the basic ideas in this field. … Both authors are outstanding specialists in this field … . This textbook contains eleven chapters with problems and solutions. … This material is very useful for high school students, undergraduate and graduate students, teachers and all lovers of mathematics.” (Carnelia Bejan, IASI Polytechnic Magazine, Vol. 22 (1/4), March-December, 2010)

“This is a collection of elementary number theory problems taken mainly from mathematical olympiads and other contests held in different countries, mainly in recent years. … This makes the book a useful source of material for tests, homeworks, projects, and classroom discussion. … The book is a welcome addition to the library of Problem Books, and will undoubtedly prove valuable to coaches and teams involved in mathematical competitions as well as to university instructors and students.” (Mowaffaq Hajja, Zentralblatt MATH, Vol. 1182, 2010)

"The book is a collection of number theory problems chosen from various national and international Mathematical Olympiads. … Each chapter of this book starts a brief … review of concepts, with various solved examples, mainly selected from Olympiad exams. … The book could be used as a text for undergraduates … . The main audience will consist of Olympiad-level students … . I recommend this friendly volume for students looking for challenging problems in number theory and teachers of number theory for undergraduates … ." (Mehdi Hassani, The Mathematical Association of America, June, 2009)

From the Back Cover

Number theory, an ongoing rich area of mathematical exploration, is noted for its theoretical depth, with connections and applications to other fields from representation theory, to physics, cryptography, and more. While the forefront of number theory is replete with sophisticated and famous open problems, at its foundation are basic, elementary ideas that can stimulate and challenge beginning students. This lively introductory text focuses on a problem-solving approach to the subject.

Key features of Number Theory: Structures, Examples, and Problems:

* A rigorous exposition starts with the natural numbers and the basics.

* Important concepts are presented with an example, which may also emphasize an application. The exposition moves systematically and intuitively to uncover deeper properties.

* Topics include divisibility, unique factorization, modular arithmetic and the Chinese Remainder Theorem, Diophantine equations, quadratic residues, binomial coefficients, Fermat and Mersenne primes and other special numbers, and special sequences. Sections on mathematical induction and the pigeonhole principle, as well as a discussion of other number systems are covered.

* Unique exercises reinforce and motivate the reader, with selected solutions to some of the problems.

* Glossary, bibliography, and comprehensive index round out the text.

Written by distinguished research mathematicians and renowned teachers, this text is a clear, accessible introduction to the subject and a source of fascinating problems and puzzles, from advanced high school students to undergraduates, their instructors, and general readers at all levels.

About the Author

Titu Andreescu received his Ph.D. from the West University of Timisoara, Romania. The topic of his dissertation was "Research on Diophantine Analysis and Applications." Professor Andreescu currently teaches at The University of Texas at Dallas. He is past chairman of the USA Mathematical Olympiad, served as director of the MAA American Mathematics Competitions (1998–2003), coach of the USA International Mathematical Olympiad Team (IMO) for 10 years (1993–2002), director of the Mathematical Olympiad Summer Program (1995–2002), and leader of the USA IMO Team (1995–2002). In 2002 Titu was elected member of the IMO Advisory Board, the governing body of the world’s most prestigious mathematics competition. Titu co-founded in 2006 and continues as director of the AwesomeMath Summer Program (AMSP). He received the Edyth May Sliffe Award for Distinguished High School Mathematics Teaching from the MAA in 1994 and a "Certificate of Appreciation" from the president of the MAA in 1995 for his outstanding service as coach of the Mathematical Olympiad Summer Program in preparing the US team for its perfect performance in Hong Kong at the 1994 IMO. Titu’s contributions to numerous textbooks and problem books are recognized worldwide.

Dorin Andrica received his Ph.D in 1992 from "Babes¸-Bolyai" University in Cluj-Napoca, Romania; his thesis treated critical points and applications to the geometry of differentiable submanifolds. Professor Andrica has been chairman of the Department of Geometry at "Babes¸-Bolyai" since 1995. He has written and contributed to numerous mathematics textbooks, problem books, articles and scientific papers at various levels. He is an invited lecturer at university conferences around the world: Austria, Bulgaria, Czech Republic, Egypt, France, Germany, Greece, Italy, the Netherlands, Portugal, Serbia, Turkey, and the USA. Dorin is a member of the Romanian Committee for the Mathematics Olympiad and is a member on the editorial boards of several international journals. Also, he is well known for his conjecture about consecutive primes called "Andrica’s Conjecture." He has been a regular faculty member at the Canada–USA Mathcamps between 2001–2005 and at the AwesomeMath Summer Program (AMSP) since 2006.

Most helpful customer reviews

7 of 7 people found the following review helpful.
Number Theory: Structure, examples, and Problems
By Tae Su Chung
It's perfect to prefare math olympiad contest. It contains fundamental concepts
of elementary number theory and practical problems of math contests with original
solutions.

3 of 3 people found the following review helpful.
Very good book
By Luiz
It's not a book for beginners in number theory, it's perfect for people who're interest in study for mathematical olympiads and those who're interest in study deeper number theory. It's a fantastic book, like most books of titu and Dorin Andrica, i recomend !

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This book deals with the mathematical aspects of survival analysis and reliability as well as other topics, reflecting recent developments in the following areas: applications in epidemiology; probabilistic and statistical models and methods in reliability; models and methods in survival analysis, longevity, aging, and degradation; accelerated life models; quality of life; new statistical challenges in genomics.

The work will be useful to a broad interdisciplinary readership of researchers and practitioners in applied probability and statistics, industrial statistics, biomedicine, biostatistics, and engineering.

• Sales Rank: #6888994 in Books
• Published on: 2008-09-12
• Original language: English
• Number of items: 1
• Dimensions: 10.00" h x 1.25" w x 7.01" l, 2.55 pounds
• Binding: Hardcover
• 556 pages

Review

From the reviews:

“This edited volume, the outcome of the International Conference on Statistical Models for Biological and Technical Systems, showcases the current research interests in survival analysis and reliability. … The book’s style and format are fine. Its organization makes it useful for its target audience. … The volume includes 37 tables and 55 figures, a nice feature.” (Technometrics, Vol. 51 (2), May, 2009)

From the Back Cover

An outgrowth of the "International Conference on Statistical Models for Biomedical and Technical Systems," this book is comprised of contributions from renowned experts, demonstrating the significance of current research on theory, methods, and applications of the field. The contributions, which deal with the mathematical aspects of survival analysis and reliability as well as other topics, are a careful selection of invited and contributed chapters, reflecting recent developments in the following areas:

* Applications in epidemiology

* Estimation and testing for stochastic processes

* Generalizations of the Cox regression model

* Probabilistic and statistical models and methods in reliability

* Semi-parametric inference in survival analysis

* Models and methods in survival analysis, longevity, aging, and degradation

* Nonparametric estimation – Goodness-of-fit tests

* Accelerated life models

* Quality of life

* Analysis of censored data

* Adaptive and repeated measurements designs

* Measures of divergence, model selection, and survival models

* New statistical challenges in genomics

The book will be useful to a broad interdisciplinary readership of researchers and practitioners in applied probability and statistics, industrial statistics, biomedicine, biostatistics, and engineering. Practitioners and researchers in academia will gain insight and new ideas for exploring this fertile area of research.

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> Get Free Ebook Southern Exposure: Making the South Safe for Democracy, by Stetson Kennedy

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Using thorough and stark statistics, Kennedy describes a South emerging from World War II, coming to grips with the racism and feudalism that had held it back for generations. He includes an all-out Who’s Who, based on his own undercover investigations, of the "hate-mongers, race-racketeers, and terrorists who swore that apartheid must go on forever." The first paperback edition brings to a new generation of readers Kennedy’s searing profile of Dixie before the civil rights movement.

• Sales Rank: #3979223 in Books
• Published on: 2011-02-28
• Original language: English
• Number of items: 1
• Dimensions: 8.50" h x 1.70" w x 5.50" l, 1.00 pounds
• Binding: Paperback
• 286 pages

Review
 “[This book represents] a tradition that links analysis to action, that tells the truth and makes clear the imperative for change. Stetson Kennedy is the right person to follow. He is a freedom fighter, patriot and rebel, investigator and truth-teller, a foot soldier and leader in the larger movement for a more human planet.”—Bob Hall, editor of Southern Exposure Magazine

“A strong weapon against intolerance.”—Ellis Arnall, former governor of Georgia, in the New York Times

“A filing case bursting with documented evidence against almost every phase of southern life.” —Chicago Sun

About the Author

Stetson Kennedy is an award-winning author and human rights activist. Kennedy is also known as a pioneering folklorist, a labor activist, and environmentalist. He is the author of the books: Palmetto Country, Southern Exposure, The Jim Crow Guide, The Klan Unmasked, and After Appomattox.

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!! PDF Ebook Moment Maps and Combinatorial Invariants of Hamiltonian Tn-spaces (Progress in Mathematics), by Victor Guillemin

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The action of a compact Lie group, G, on a compact sympletic manifold gives rise to some remarkable combinatorial invariants. The simplest and most interesting of these is the moment polytopes, a convex polyhedron which sits inside the dual of the Lie algebra of G. One of the main goals of this monograph is to describe what kinds of geometric information are encoded in this polytope. This book is addressed to researchers and can be used as a semester text.

• Sales Rank: #5205250 in Books
• Brand: Brand: Birkhäuser
• Published on: 1994-12-01
• Original language: English
• Number of items: 1
• Dimensions: 9.21" h x .44" w x 6.14" l, .90 pounds
• Binding: Hardcover
• 152 pages

Features

• Used Book in Good Condition

Review

"...carefully written book [on] the so-called Delzant spaces... Many of the statements in the body of the book are left as exercises (with copious hints). At the end of each chapter there are very interesting bibliographical notes. The reader who works through this book will acquire a solid knowledge of this beautiful and elegant part of mathematics."

--Mathematical Reviews

From the Back Cover

The action of a compact Lie group, G, on a compact sympletic manifold gives rise to some remarkable combinatorial invariants. The simplest and most interesting of these is the moment polytope, a convex polyhedron which sits inside the dual of the Lie algebra of G. One of the main goals of this monograph is to describe what kinds of geometric information are encoded in this polytope. For instance, the first chapter is largely devoted to the Delzant theorem, which says that there is a one-one correspondence between certain types of moment polytopes and certain types of symplectic G-spaces. (One of the most challenging unsolved problems in symplectic geometry is to determine to what extent Delzant’s theorem is true of every compact symplectic G-Space.)

The moment polytope also encodes quantum information about the actions of G. Using the methods of geometric quantization, one can frequently convert this action into a representations, p , of G on a Hilbert space, and in some sense the moment polytope is a diagrammatic picture of the irreducible representations of G which occur as subrepresentations of p. Precise versions of this item of folklore are discussed in Chapters 3 and 4. Also, midway through Chapter 2 a more complicated object is discussed: the Duistermaat-Heckman measure, and the author explains in Chapter 4 how one can read off from this measure the approximate multiplicities with which the irreducible representations of G occur in p. This gives an excuse to touch on some results which are in themselves of great current interest: the Duistermaat-Heckman theorem, the localization theorems in equivariant cohomology of Atiyah-Bott and Berline-Vergne and the recent extremely exciting generalizations of these results by Witten, Jeffrey-Kirwan, Lalkman, and others.

The last two chapters of this book are a self-contained and somewhat unorthodox treatment of the theory of toric varieties in which the usual hierarchal relation of complex to symplectic is reversed. This book is addressed to researchers and can be used as a semester text.

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? PDF Download Singularity Theory and Gravitational Lensing, by Arlie O. Petters, Harold Levine, Joachim Wambsganss

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This monograph is the first to develop a mathematical theory of gravitational lensing. The theory applies to any finite number of deflector planes and highlights the distinctions between single and multiple plane lensing. Introductory material in Parts I and II present historical highlights and the astrophysical aspects of the subject. Part III employs the ideas and results of singularity theory to put gravitational lensing on a rigorous mathematical foundation.

• Sales Rank: #3413724 in Books
• Brand: Brand: Birkhäuser
• Published on: 2001-06-15
• Original language: English
• Number of items: 1
• Dimensions: 9.72" h x 1.38" w x 7.06" l, 2.76 pounds
• Binding: Hardcover
• 604 pages

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• Used Book in Good Condition

Review

"The time is ripe for a comprehensive volume explaining gravitational lensing to mathematicians and reviewing relevant singularity theory for astrophysicists. This is such a book. [It] . . . is accessible and attractive, . . . ranging widely through the history, physics and mathematics to paint a full picture of this . . . theory. This most attractively presented book summarizes current mathematical methods in the field and sets the stage for further exciting developments . . . A collaboration between a mathematical physicist, a mathematician, and a physicist, it has something for everybody."

―Mathematical Reviews

"This is a well-developed monograph on gravitational lensing both from the observational and from the mathematical points of view. However, also independent of the present interest in gravitational lensing, this book is a good source for several types of singularity theories . . . index and bibliography are very well done."

―Zentralblatt Math

 "The rather voluminous monograph to be reviewed here covers both astrophysical and mathematicsl aspects of gravitational lensing. The scientific backgrohnd of the three authors guarantees that they are the right persons for such an enterprise.  Arlie Petters is one of very few scientists who are competent in mathematics as well as in astrophysics.  His coauthors are a pure astrophysicist and a pure matheamtician: Joachim Wambsganss is aleading expert on gravitational lensing as a tool in astrophysics and Harold Levine has made important contributions to the theory of signularities of maps in the 1960s. . . "It is not much of an exaggeration to say that large parts of this monograph can serve as a self-contained matheamtics text-book on the theory of singularites of maps and related subjects, and even a particularly well-written one.  So I would not hesitate to recommend it to pure matheamticians who will find a fine exposistion of a subject from their field, along with applicaions to astrophysics which should be very well readable for them.  I also recommend the book to pure astrophysicists, because it contains a lot of material which has a high atrophysical relevance. . .  If one compares to tbook by Petters, Leven and Wambsganss with the earlier mongraph on gravtiational lenses by Schneider, Ehlers and Falco, one finds that there is not very much overlap.  The two books rather complement each other."

---Gen. Relativ. Gravit.

From the Back Cover

This monograph, unique in the literature, is the first to develop a mathematical theory of gravitational lensing. The theory applies to any finite number of deflector planes and highlights the distinctions between single and multiple plane lensing.

Introductory material in Parts I and II present historical highlights and the astrophysical aspects of the subject. Among the lensing topics discussed are multiple quasars, giant luminous arcs, Einstein rings, the detection of dark matter and planets with lensing, time delays and the age of the universe (Hubble’s constant), microlensing of stars and quasars.

The main part of the book---Part III---employs the ideas and results of singularity theory to put gravitational lensing on a rigorous mathematical foundation and solve certain key lensing problems. Results are published here for the first time.

Mathematical topics discussed: Morse theory, Whitney singularity theory, Thom catastrophe theory, Mather stability theory, Arnold singularity theory, and the Euler characteristic via projectivized rotation numbers. These tools are applied to the study of stable lens systems, local and global geometry of caustics, caustic metamorphoses, multiple lens images, lensed image magnification, magnification cross sections, and lensing by singular and nonsingular deflectors.

Examples, illustrations, bibliography and index make this a suitable text for an undergraduate/graduate course, seminar, or independent these project on gravitational lensing. The book is also an excellent reference text for professional mathematicians, mathematical physicists, astrophysicists, and physicists.

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Singularity Theory and Gravitational Lensing by Petters
By W. Simmons
The book addresses the subject on two levels. The first part of the book is oriented toward physicists and the second half toward mathematicians. I think this is excellent.

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? Download Minimax Theorems (Progress in Nonlinear Differential Equations and Their Applications), by Michel Willem

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Many boundary value problems are equivalent to Au=O (1) where A: X ---+ Y is a mapping between two Banach spaces. When the problem is variational, there exists a differentiable functional 0 and e E X such that lIell > rand inf

• Sales Rank: #4287227 in Books
• Published on: 1997-02-01
• Original language: English
• Number of items: 1
• Dimensions: 9.21" h x .44" w x 6.14" l, .94 pounds
• Binding: Hardcover
• 200 pages

Review

"The material is presented in a unified way, and the proofs are concise and elegant... Essentially self-contained."

--Mathematical Reviews

From the Back Cover
Willem's book is devoted to minimax theorems and their applications to partial differential equations. Presenting basic minimax theorems in a simple and unified way, this book may serve as a textbook for advanced graduate students in partial differential equations.

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A gripping story of the cultural resilience of the descendants of Geronimo and Cochise.             This book reveals the conflicting meanings of power held by the federal government and the Chiricahua Apaches throughout their history of interaction. When Geronimo and Naiche, son of Cochise, surrendered in 1886, their wartime exploits came to an end, but their real battle for survival was only beginning. Throughout their captivity in Florida, Alabama, and Oklahoma, Naiche kept alive Chiricahua spiritual power by embodying it in his beautiful hide paintings of the Girl’s Puberty Ceremony—a ritual at the very heart of tribal cultural life and spiritual strength.            This narrative is a tribute to the Chiricahua people, who survive today, despite military efforts to annihilate them, government efforts to subjugate them, and social efforts to destroy their language and culture. Although federal policy makers brought to bear all the power at their command, they failed to eradicate Chiricahua spirit and identity nor to convince them that their lower status was just part of the natural social order. Naiche, along with many other Chiricahuas, believed in another kind of power. Although not known to have Power of his own in the Apache sense, Naiche’s paintings show that he believed in a vital source of spiritual strength. In a very real sense, his paintings were visual prayers for the continuation of the Chiricahua people. Accessible to individuals for many purposes, Power helped the Chiricahuas survive throughout their history.            In this book, Griffin-Pierce explores Naiche’s artwork through the lens of current anthropological theory on power, hegemony, resistance, and subordination. As she retraces the Chiricahua odyssey during 27 years of incarceration and exile by visiting their internment sites, she reveals how the Power was with them throughout their dark period. As it was when the Chiricahua warriors and their families struggled to stay alive, Power remains the centering focus for contemporary Chiricahua Apaches. Although never allowed to return to their beloved homeland, not only are the Chiricahua Apaches surviving today, they are keeping their traditions alive and their culture strong and vital.

• Sales Rank: #2693684 in Books
• Brand: Brand: University Alabama Press
• Published on: 2006-12-17
• Original language: English
• Number of items: 1
• Dimensions: 9.00" h x .50" w x 6.13" l, .80 pounds
• Binding: Paperback
• 240 pages

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• Used Book in Good Condition

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“It was with great pleasure that I read Chiricahua Apache Enduring Power and endorse the publication of this book with the highest praise. The scholarship is impeccable and it will provide a much needed addition to the growing literature on Indian hide paintings”—JoAllyn Archambault, Director, American Indian Program, Smithsonian Institution

About the Author
Trudy Griffin-Pierce and author of several books about American Indians, including Native Peoples of the Southwest. She is of Catawba Indian descent and was born in South Carolina, although Arizona has been her home since 1971.

 

 

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The book as written is excellent; however the final pages were missing from the ...
By Tekatsitsiakwa
The book as written is excellent;however the final pages were missing from the book itself.

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