The Mathematical Bridge
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| Author | : Stephen Fletcher Hewson |
| Publisher | : World Scientific |
| Total Pages | : 672 |
| Release | : 2009 |
| Genre | : Education |
| ISBN | : 9812834079 |
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.
| Author | : Titu Andreescu |
| Publisher | : Birkhäuser |
| Total Pages | : 308 |
| Release | : 2017-02-17 |
| Genre | : Mathematics |
| ISBN | : 0817646299 |
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.
| Author | : Jim Kelly |
| Publisher | : Allison & Busby Ltd |
| Total Pages | : 329 |
| Release | : 2019-02-21 |
| Genre | : Fiction |
| ISBN | : 0749022620 |
Cambridge, 1940. It is the first winter of the war, and snow is falling. When an evacuee drowns in the river, his body swept away, Detective Inspector Eden Brooke sets out to investigate what seems to be a deliberate attack. The following night, a local electronics factory is attacked, and an Irish republican slogan is left at the scene. The IRA are campaigning to win freedom for Ulster, but why has Cambridge been chosen as a target? And when Brooke learns that the drowned boy was part of the close-knit local Irish Catholic community, he begins to question whether there may be a connection between the boy's death and the attack at the factory. As more riddles come to light, can Brooke solve the mystery before a second attack claims a famous victim?
| Author | : Ralph W. Oberste-Vorth |
| Publisher | : American Mathematical Society |
| Total Pages | : 254 |
| Release | : 2020-02-20 |
| Genre | : Mathematics |
| ISBN | : 1470453029 |
A Bridge to Abstract Mathematics will prepare the mathematical novice to explore the universe of abstract mathematics. Mathematics is a science that concerns theorems that must be proved within the constraints of a logical system of axioms and definitions rather than theories that must be tested, revised, and retested. Readers will learn how to read mathematics beyond popular computational calculus courses. Moreover, readers will learn how to construct their own proofs. The book is intended as the primary text for an introductory course in proving theorems, as well as for self-study or as a reference. Throughout the text, some pieces (usually proofs) are left as exercises. Part V gives hints to help students find good approaches to the exercises. Part I introduces the language of mathematics and the methods of proof. The mathematical content of Parts II through IV were chosen so as not to seriously overlap the standard mathematics major. In Part II, students study sets, functions, equivalence and order relations, and cardinality. Part III concerns algebra. The goal is to prove that the real numbers form the unique, up to isomorphism, ordered field with the least upper bound. In the process, we construct the real numbers starting with the natural numbers. Students will be prepared for an abstract linear algebra or modern algebra course. Part IV studies analysis. Continuity and differentiation are considered in the context of time scales (nonempty, closed subsets of the real numbers). Students will be prepared for advanced calculus and general topology courses. There is a lot of room for instructors to skip and choose topics from among those that are presented.
| Author | : Dennis Sentilles |
| Publisher | : Courier Corporation |
| Total Pages | : 418 |
| Release | : 2013-05-20 |
| Genre | : Mathematics |
| ISBN | : 0486277585 |
This helpful "bridge" book offers students the foundations they need to understand advanced mathematics. The two-part treatment provides basic tools and covers sets, relations, functions, mathematical proofs and reasoning, more. 1975 edition.
| Author | : Emile Borel |
| Publisher | : Master Point Press |
| Total Pages | : 536 |
| Release | : 2017-11-20 |
| Genre | : Games & Activities |
| ISBN | : 9781771401814 |
134 Probability tables, their uses, simple formulas, applications & 4000 probabilities Originally published in 1940, and revised in 1954, this classic work on mathematics and probability as applied to Bridge first appeared in English translation in 1974, but has been unavailable for many years. This new edition corrects numerical errors found in earlier texts; it revises the previous English translation where needed and corrects a number of textual and typographical errors in the 1974 edition. Tables have been included again in the text, as they were in the original edition. The chapter on Contract and Plafond scoring has been retained as continuing to serve its intended purpose. The chapters on shuffling, although no longer applicable to Duplicate Bridge, are included for the benefit of those interested in the mathematics of all card games. All, it is hoped, without too many new errors being introduced.
| Author | : Valentin Deaconu |
| Publisher | : CRC Press |
| Total Pages | : 213 |
| Release | : 2016-12-19 |
| Genre | : Mathematics |
| ISBN | : 1498775276 |
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.
| Author | : Filippo Gazzola |
| Publisher | : Springer |
| Total Pages | : 274 |
| Release | : 2015-05-29 |
| Genre | : Mathematics |
| ISBN | : 3319154346 |
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.
| Author | : Raven Deerwater |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 9781602620070 |
| Author | : Sam Vandervelde |
| Publisher | : Lulu.com |
| Total Pages | : 258 |
| Release | : 2010 |
| Genre | : Education |
| ISBN | : 055750337X |
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.
