mathematical bridges

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Mathematical Bridges

Author : Titu Andreescu
ISBN : 9780817646295
Genre : Mathematics
File Size : 71. 89 MB
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Building bridges between classical results and contemporary nonstandard problems, this highly relevant work embraces important topics in analysis and algebra from a problem-solving perspective. The book is structured to assist the reader in formulating and proving conjectures, as well as devising solutions to important mathematical problems by making connections between various concepts and ideas from different areas of mathematics. Instructors and motivated mathematics students from high school juniors to college seniors will find the work a useful resource in calculus, linear and abstract algebra, analysis and differential equations. Students with an interest in mathematics competitions must have this book in their personal libraries.

Mathematical Bridges

Author : TITU. MORTICI ANDREESCU (CRISTINEL. TETIVA, MARIAN.)
ISBN : 1493979183
Genre : Mathematics
File Size : 38. 83 MB
Format : PDF, Kindle
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Bridging classical results and contemporary nonstandard problems, this book covers important topics in analysis and algebra from a problem-solving perspective. The text offers numerous mathematical "gems" that help illustrate the inherent beauty of the topic.

Mathematical Bridges

Author : Titu Andreescu
ISBN : 081764394X
Genre : Mathematics
File Size : 52. 8 MB
Format : PDF, Kindle
Download : 489
Read : 915

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Building bridges between classical results and contemporary nonstandard problems, this highly relevant work embraces important topics in analysis and algebra from a problem-solving perspective. The book is structured to assist the reader in formulating and proving conjectures, as well as devising solutions to important mathematical problems by making connections between various concepts and ideas from different areas of mathematics. Instructors and motivated mathematics students from high school juniors to college seniors will find the work a useful resource in calculus, linear and abstract algebra, analysis and differential equations. Students with an interest in mathematics competitions must have this book in their personal libraries.

A Mathematical Bridge

Author : Stephen Fletcher Hewson
ISBN : 9789812834072
Genre : Education
File Size : 43. 45 MB
Format : PDF
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Although higher mathematics is beautiful, natural and interconnected, to the uninitiated it can feel like an arbitrary mass of disconnected technical definitions, symbols, theorems and methods. An intellectual gulf needs to be crossed before a true, deep appreciation of mathematics can develop. This book bridges this mathematical gap. It focuses on the process of discovery as much as the content, leading the reader to a clear, intuitive understanding of how and why mathematics exists in the way it does.The narrative does not evolve along traditional subject lines: each topic develops from its simplest, intuitive starting point; complexity develops naturally via questions and extensions. Throughout, the book includes levels of explanation, discussion and passion rarely seen in traditional textbooks. The choice of material is similarly rich, ranging from number theory and the nature of mathematical thought to quantum mechanics and the history of mathematics. It rounds off with a selection of thought-provoking and stimulating exercises for the reader.

Bridges To Infinity

Author : Michael Guillen
ISBN : 0874773458
Genre : Mathematics
File Size : 84. 18 MB
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Explains important mathematical concepts, such as probability and statistics, set theory, paradoxes, symmetries, dimensions, game theory, randomness, and irrational numbers

Varieties Of Constructive Mathematics

Author : Douglas Bridges
ISBN : 0521318025
Genre : Mathematics
File Size : 81. 93 MB
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A survey of constructive approaches to pure mathematics emphasizing the viewpoint of Errett Bishop's school. Considers intuitionism, Russian constructivism, and recursive analysis, with comparisons among the various approaches included where appropriate.

Bridge To Higher Mathematics

Author : Sam Vandervelde
ISBN : 055750337X
Genre : Mathematics
File Size : 68. 64 MB
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This engaging math textbook is designed to equip students who have completed a standard high school math curriculum with the tools and techniques that they will need to succeed in upper level math courses. Topics covered include logic and set theory, proof techniques, number theory, counting, induction, relations, functions, and cardinality.

Computability

Author : Douglas S. Bridges
ISBN : 9781461208631
Genre : Mathematics
File Size : 27. 98 MB
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Aimed at mathematicians and computer scientists who will only be exposed to one course in this area, Computability: A Mathematical Sketchbook provides a brief but rigorous introduction to the abstract theory of computation, sometimes also referred to as recursion theory. It develops major themes in computability theory, such as Rice's theorem and the recursion theorem, and provides a systematic account of Blum's complexity theory as well as an introduction to the theory of computable real numbers and functions. The book is intended as a university text, but it may also be used for self-study; appropriate exercises and solutions are included.

Mathematical Models For Suspension Bridges

Author : Filippo Gazzola
ISBN : 9783319154343
Genre : Mathematics
File Size : 71. 50 MB
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This work provides a detailed and up-to-the-minute survey of the various stability problems that can affect suspension bridges. In order to deduce some experimental data and rules on the behavior of suspension bridges, a number of historical events are first described, in the course of which several questions concerning their stability naturally arise. The book then surveys conventional mathematical models for suspension bridges and suggests new nonlinear alternatives, which can potentially supply answers to some stability questions. New explanations are also provided, based on the nonlinear structural behavior of bridges. All the models and responses presented in the book employ the theory of differential equations and dynamical systems in the broader sense, demonstrating that methods from nonlinear analysis can allow us to determine the thresholds of instability.

A Bridge To Higher Mathematics

Author : Valentin Deaconu
ISBN : 9781498775267
Genre : Mathematics
File Size : 25. 33 MB
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A Bridge to Higher Mathematics is more than simply another book to aid the transition to advanced mathematics. The authors intend to assist students in developing a deeper understanding of mathematics and mathematical thought. The only way to understand mathematics is by doing mathematics. The reader will learn the language of axioms and theorems and will write convincing and cogent proofs using quantifiers. Students will solve many puzzles and encounter some mysteries and challenging problems. The emphasis is on proof. To progress towards mathematical maturity, it is necessary to be trained in two aspects: the ability to read and understand a proof and the ability to write a proof. The journey begins with elements of logic and techniques of proof, then with elementary set theory, relations and functions. Peano axioms for positive integers and for natural numbers follow, in particular mathematical and other forms of induction. Next is the construction of integers including some elementary number theory. The notions of finite and infinite sets, cardinality of counting techniques and combinatorics illustrate more techniques of proof. For more advanced readers, the text concludes with sets of rational numbers, the set of reals and the set of complex numbers. Topics, like Zorn’s lemma and the axiom of choice are included. More challenging problems are marked with a star. All these materials are optional, depending on the instructor and the goals of the course.

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