Mathematical Problems and Puzzles from the Polish Mathematical Olympiads

Stefan Straszewicz, "Mathematical Problems and Puzzles from the Polish Mathematical Olympiads"
Pergamon Press 1965 ASIN: B0000CMPWZ 367 pages PDF 29,3 MB

This book is a translation of the second Polish edition, published in 1960, in which various improvements were made.

The contest for secondary school pupils known as the Mathematical Olympiad has been held in Poland every year since 1949/50.

The problems set at the contests require only a knowledge of school mathematics (i.e., elementary algebra, geometry and trigonometry) but are on the whole more difficult than the usual school exercises.

COMMENT:

Although long out of print and hard to find, this is MUST read for aspiring contestants in the AMC/AIME/USAME mathematics contests. If you only have time for a couple of books to review and study, this should be one of them.

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Mathematical Analysis I

Elias Zakon, "Mathematical Analysis I"
The Trillia Group | 2004 | ISBN: 193170502X | 336 pages | PDF | 2,4 MB

This text carefully leads the student through the basic topics of Real Analysis. Topics include metric spaces, open and closed sets, convergent sequences, function limits and continuity, compact sets, sequences and series of functions, power series, differentiation and integration, Taylor's theorem, total variation, rectifiable arcs, and sufficient conditions of integrability. Well over 500 exercises (many with extensive hints) assist students through the material.

For students who need a review of basic mathematical concepts before beginning "epsilon-delta"-style proofs, the text begins with material on set theory (sets, quantifiers, relations and mappings, countable sets), the real numbers (axioms, natural numbers, induction, consequences of the completeness axiom), and Euclidean and vector spaces; this material is condensed from the author's Basic Concepts of Mathematics, the complete version of which can be used as supplementary background material for the present text.

This text is designed to be used as early as possible in the undergraduate mathematics curriculum; indeed, it was used for many years as the text for a two-semester class for second-year mathematics majors at the University of Windsor. If desired, the material can easily be specialized to n-dimensional (or even two-dimensional) Euclidean space.

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Mathematical Analysis I

Elias Zakon, "Mathematical Analysis I"
The Trillia Group | 2004 | ISBN: 193170502X | 336 pages | PDF | 2,4 MB

This text carefully leads the student through the basic topics of Real Analysis. Topics include metric spaces, open and closed sets, convergent sequences, function limits and continuity, compact sets, sequences and series of functions, power series, differentiation and integration, Taylor's theorem, total variation, rectifiable arcs, and sufficient conditions of integrability. Well over 500 exercises (many with extensive hints) assist students through the material.

For students who need a review of basic mathematical concepts before beginning "epsilon-delta"-style proofs, the text begins with material on set theory (sets, quantifiers, relations and mappings, countable sets), the real numbers (axioms, natural numbers, induction, consequences of the completeness axiom), and Euclidean and vector spaces; this material is condensed from the author's Basic Concepts of Mathematics, the complete version of which can be used as supplementary background material for the present text.

This text is designed to be used as early as possible in the undergraduate mathematics curriculum; indeed, it was used for many years as the text for a two-semester class for second-year mathematics majors at the University of Windsor. If desired, the material can easily be specialized to n-dimensional (or even two-dimensional) Euclidean space.

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Mathematical Analysis: Linear and Metric Structures and Continuity(repost)

Mariano Giaquinta, Giuseppe Modica , "Mathematical Analysis: Linear and Metric Structures and Continuity"
Birkhäuser Boston | 2007 | ISBN: 0817643745 | 465 pages | Djvu | 6,2 MB

This self-contained work on linear and metric structures focuses on studying continuity and its applications to finite- and infinite-dimensional spaces.

The book is divided into three parts. The first part introduces the basic ideas of linear and metric spaces, including the Jordan canonical form of matrices and the spectral theorem for self-adjoint and normal operators. The second part examines the role of general topology in the context of metric spaces and includes the notions of homotopy and degree. The third and final part is a discussion on Banach spaces of continuous functions, Hilbert spaces and the spectral theory of compact operators.

Mathematical Analysis: Linear and Metric Structures and Continuity motivates the study of linear and metric structures with examples, observations, exercises, and illustrations. It may be used in the classroom setting or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering.

Other books recently published by the authors include: Mathematical Analysis: Functions of One Variable, and Mathematical Analysis: Approximation and Discrete Processes. This book builds upon the discussion in these books to provide the reader with a strong foundation in modern-day analysis.

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Mathematical Analysis: Linear and Metric Structures and Continuity(repost)

Mariano Giaquinta, Giuseppe Modica , "Mathematical Analysis: Linear and Metric Structures and Continuity"
Birkhäuser Boston | 2007 | ISBN: 0817643745 | 465 pages | Djvu | 6,2 MB

This self-contained work on linear and metric structures focuses on studying continuity and its applications to finite- and infinite-dimensional spaces.

The book is divided into three parts. The first part introduces the basic ideas of linear and metric spaces, including the Jordan canonical form of matrices and the spectral theorem for self-adjoint and normal operators. The second part examines the role of general topology in the context of metric spaces and includes the notions of homotopy and degree. The third and final part is a discussion on Banach spaces of continuous functions, Hilbert spaces and the spectral theory of compact operators.

Mathematical Analysis: Linear and Metric Structures and Continuity motivates the study of linear and metric structures with examples, observations, exercises, and illustrations. It may be used in the classroom setting or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering.

Other books recently published by the authors include: Mathematical Analysis: Functions of One Variable, and Mathematical Analysis: Approximation and Discrete Processes. This book builds upon the discussion in these books to provide the reader with a strong foundation in modern-day analysis.

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Mathematical Analysis II

Elias Zakon, "Mathematical Analysis II"
The Trillia Group | 2009 | ISBN: 1931705038 | 424 pages | PDF | 2,5 MB

This final text in the Zakon Series on Mathematics Analysis follows the release of the author's Basic Concepts of Mathematics and Mathematical Analysis I and completes the material on Real Analysis that is the foundation for later courses in functional analysis, harmonic analysis, probability theory, etc. The first chapter extends calculus to n-dimensional Euclidean space and, more generally, Banach spaces, covering the inverse function theorem, the implicit function theorem, Taylor expansions, etc. Some basic theorems in functional analysis, including the open mapping theorem and the Banach-Steinhaus uniform boundedness principle, are also proved. The text then moves to measure theory, with a complete discussion of outer measures, Lebesgue measure, Lebesgue-Stieltjes measures, and differentiation of set functions. The discussion of measurable functions and integration in the following chapter follows an innovative approach, carefully choosing one of the equivalent definitions of measurable functions that allows the most intuitive development of the material. Fubini's theorem, the Radon-Nikodym theorem, and the basic convergence theorems (Fatou's lemma, the monotone convergence theorem, dominated convergence theorem) are covered. Finally, a chapter relates antidifferentiation to Lebesgue theory, Cauchy integrals, and convergence of parametrized integrals. Nearly 500 exercises allow students to develop their skills in the area

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Mathematical Analysis II

Elias Zakon, "Mathematical Analysis II"
The Trillia Group | 2009 | ISBN: 1931705038 | 424 pages | PDF | 2,5 MB

This final text in the Zakon Series on Mathematics Analysis follows the release of the author's Basic Concepts of Mathematics and Mathematical Analysis I and completes the material on Real Analysis that is the foundation for later courses in functional analysis, harmonic analysis, probability theory, etc. The first chapter extends calculus to n-dimensional Euclidean space and, more generally, Banach spaces, covering the inverse function theorem, the implicit function theorem, Taylor expansions, etc. Some basic theorems in functional analysis, including the open mapping theorem and the Banach-Steinhaus uniform boundedness principle, are also proved. The text then moves to measure theory, with a complete discussion of outer measures, Lebesgue measure, Lebesgue-Stieltjes measures, and differentiation of set functions. The discussion of measurable functions and integration in the following chapter follows an innovative approach, carefully choosing one of the equivalent definitions of measurable functions that allows the most intuitive development of the material. Fubini's theorem, the Radon-Nikodym theorem, and the basic convergence theorems (Fatou's lemma, the monotone convergence theorem, dominated convergence theorem) are covered. Finally, a chapter relates antidifferentiation to Lebesgue theory, Cauchy integrals, and convergence of parametrized integrals. Nearly 500 exercises allow students to develop their skills in the area

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Mathematical Analysis: Linear and Metric Structures and Continuity(repost)

Mariano Giaquinta, Giuseppe Modica , "Mathematical Analysis: Linear and Metric Structures and Continuity"
Birkhäuser Boston | 2007 | ISBN: 0817643745 | 465 pages | Djvu | 6,2 MB

This self-contained work on linear and metric structures focuses on studying continuity and its applications to finite- and infinite-dimensional spaces.

The book is divided into three parts. The first part introduces the basic ideas of linear and metric spaces, including the Jordan canonical form of matrices and the spectral theorem for self-adjoint and normal operators. The second part examines the role of general topology in the context of metric spaces and includes the notions of homotopy and degree. The third and final part is a discussion on Banach spaces of continuous functions, Hilbert spaces and the spectral theory of compact operators.

Mathematical Analysis: Linear and Metric Structures and Continuity motivates the study of linear and metric structures with examples, observations, exercises, and illustrations. It may be used in the classroom setting or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering.

Other books recently published by the authors include: Mathematical Analysis: Functions of One Variable, and Mathematical Analysis: Approximation and Discrete Processes. This book builds upon the discussion in these books to provide the reader with a strong foundation in modern-day analysis.

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Mathematical Analysis: Linear and Metric Structures and Continuity(repost)

Mariano Giaquinta, Giuseppe Modica , "Mathematical Analysis: Linear and Metric Structures and Continuity"
Birkhäuser Boston | 2007 | ISBN: 0817643745 | 465 pages | Djvu | 6,2 MB

This self-contained work on linear and metric structures focuses on studying continuity and its applications to finite- and infinite-dimensional spaces.

The book is divided into three parts. The first part introduces the basic ideas of linear and metric spaces, including the Jordan canonical form of matrices and the spectral theorem for self-adjoint and normal operators. The second part examines the role of general topology in the context of metric spaces and includes the notions of homotopy and degree. The third and final part is a discussion on Banach spaces of continuous functions, Hilbert spaces and the spectral theory of compact operators.

Mathematical Analysis: Linear and Metric Structures and Continuity motivates the study of linear and metric structures with examples, observations, exercises, and illustrations. It may be used in the classroom setting or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering.

Other books recently published by the authors include: Mathematical Analysis: Functions of One Variable, and Mathematical Analysis: Approximation and Discrete Processes. This book builds upon the discussion in these books to provide the reader with a strong foundation in modern-day analysis.

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Mathematical Analysis of Evolution, Information, and Complexity

Wolfgang Arendt, Wolfgang P. Schleich, "Mathematical Analysis of Evolution, Information, and Complexity"
Wiley-VCH | 2009 | ISBN: 3527408304 | 502 pages | PDF | 4 MB

Mathematical Analysis of Evolution, Information, and Complexity deals with the analysis of evolution, information and complexity. The time evolution of systems or processes is a central question in science, this text covers a broad range of problems including diffusion processes, neuronal networks, quantum theory and cosmology. Bringing together a wide collection of research in mathematics, information theory, physics and other scientific and technical areas, this new title offers elementary and thus easily accessible introductions to the various fields of research addressed in the book.


From the Back Cover
The present book is devoted to the mathematical analysis of evolution, information and complexity. The time evolution of systems or processes is a central question in science and covers a broad range of problems including diffusion processes, neuronal networks, quantum theory and cosmology. Analysis of information is needed in data compression, channel encoding, cryptography and often in the analysis of information processing in the computer or in the brain. Finally, the topic of analysis of complexity is important for theoretical informatics, in particular algorithms, but more generally for the investigation of complex and chaotic systems.

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