✩ A Bridge To Advanced Mathematics ✩
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| ♥ Book Title : A Bridge to Advanced Mathematics ♣ Name Author : Dennis Sentilles ∞ Launching : 2013-05-20 ◊ Info ISBN Link : 9780486277585 ⊗ Detail ISBN code : 0486277585 ⊕ Number Pages : Total 416 sheet ♮ News id : MAPDAgAAQBAJ
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☯ Full Synopsis : "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."Article| Dennis Sentilles| Statement ..." |
| ♥ Book Title : Discrete Mathematics ♣ Name Author : Olympia Nicodemi ∞ Launching : 1987 ◊ Info ISBN Link : UCSC:32106012277627 ⊗ Detail ISBN code : ⊕ Number Pages : Total 491 sheet ♮ News id : hA0gAQAAIAAJ
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☯ Full Synopsis : ""Article| Olympia Nicodemi| Statement ..." |
| ♥ Book Title : The Elements of Advanced Mathematics, Second Edition ♣ Name Author : Steven G. Krantz ∞ Launching : 2002-01-18 ◊ Info ISBN Link : 1584883030 ⊗ Detail ISBN code : 9781584883036 ⊕ Number Pages : Total 232 sheet ♮ News id : dtusau3dpkAC
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☯ Full Synopsis : "The gap between the rote, calculational learning mode of calculus and ordinary differential equations and the more theoretical learning mode of analysis and abstract algebra grows ever wider and more distinct, and students' need for a well-guided transition grows with it. For more than six years, the bestselling first edition of this classic text has helped them cross the mathematical bridge to more advanced studies in topics such as topology, abstract algebra, and real analysis. Carefully revised, expanded, and brought thoroughly up to date, the Elements of Advanced Mathematics, Second Edition now does the job even better, building the background, tools, and skills students need to meet the challenges of mathematical rigor, axiomatics, and proofs. New in the Second Edition: Expanded explanations of propositional, predicate, and first-order logic, especially valuable in theoretical computer science A chapter that explores the deeper properties of the real numbers, including topological issues and the Cantor set Fuller treatment of proof techniques with expanded discussions on induction, counting arguments, enumeration, and dissection Streamlined treatment of non-Euclidean geometry Discussions on partial orderings, total ordering, and well orderings that fit naturally into the context of relations More thorough treatment of the Axiom of Choice and its equivalents Additional material on Russell's paradox and related ideas Expanded treatment of group theory that helps students grasp the axiomatic method A wealth of added exercises"Article| Steven G. Krantz| Statement ..." |
| ♥ Book Title : A Transition to Advanced Mathematics ♣ Name Author : Douglas Smith ∞ Launching : 2014-08-01 ◊ Info ISBN Link : 9781285463261 ⊗ Detail ISBN code : 1285463269 ⊕ Number Pages : Total 448 sheet ♮ News id : DOUbCgAAQBAJ
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☯ Full Synopsis : "A TRANSITION TO ADVANCED MATHEMATICS helps students to bridge the gap between calculus and advanced math courses. The most successful text of its kind, the 8th edition continues to provide a firm foundation in major concepts needed for continued study and guides students to think and express themselves mathematically—to analyze a situation, extract pertinent facts, and draw appropriate conclusions. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version."Article| Douglas Smith| Statement ..." |
| ♥ Book Title : A Bridge to Higher Mathematics ♣ Name Author : Valentin Deaconu ∞ Launching : 2016-12-19 ◊ Info ISBN Link : 9781498775267 ⊗ Detail ISBN code : 1498775268 ⊕ Number Pages : Total 204 sheet ♮ News id : KjINDgAAQBAJ
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☯ Full Synopsis : "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."Article| Valentin Deaconu| Statement ..." |
| ♥ Book Title : Bridge to Abstract Mathematics ♣ Name Author : Ralph W. Oberste-Vorth ∞ Launching : 2012 ◊ Info ISBN Link : 9780883857793 ⊗ Detail ISBN code : 0883857790 ⊕ Number Pages : Total 232 sheet ♮ News id : fO3tvd9qjLkC
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☯ Full Synopsis : "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."Article| Ralph W. Oberste-Vorth| Statement ..." |
| ♥ Book Title : Quantum Mathematical Physics ♣ Name Author : Felix Finster ∞ Launching : 2016-02-24 ◊ Info ISBN Link : 9783319269023 ⊗ Detail ISBN code : 331926902X ⊕ Number Pages : Total 518 sheet ♮ News id : AGShCwAAQBAJ
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☯ Full Synopsis : "Quantum physics has been highly successful for more than 90 years. Nevertheless, a rigorous construction of interacting quantum field theory is still missing. Moreover, it is still unclear how to combine quantum physics and general relativity in a unified physical theory. Attacking these challenging problems of contemporary physics requires highly advanced mathematical methods as well as radically new physical concepts. This book presents different physical ideas and mathematical approaches in this direction. It contains a carefully selected cross-section of lectures which took place in autumn 2014 at the sixth conference ``Quantum Mathematical Physics - A Bridge between Mathematics and Physics'' in Regensburg, Germany. In the tradition of the other proceedings covering this series of conferences, a special feature of this book is the exposition of a wide variety of approaches, with the intention to facilitate a comparison. The book is mainly addressed to mathematicians and physicists who are interested in fundamental questions of mathematical physics. It allows the reader to obtain a broad and up-to-date overview of a fascinating active research area."Article| Felix Finster| Statement ..." |
| ♥ Book Title : A Transition to Advanced Mathematics ♣ Name Author : William Johnston ∞ Launching : 2009-07-27 ◊ Info ISBN Link : 9780195310764 ⊗ Detail ISBN code : 0195310764 ⊕ Number Pages : Total 745 sheet ♮ News id : -xQTDAAAQBAJ
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☯ Full Synopsis : "A Transition to Advanced Mathematics promotes the goals of a ``bridge'' course in mathematics, helping to lead students from courses in the calculus sequence to theoretical upper-level mathematics courses. The text simultaneously promotes the goals of a ``survey'' course, describing the intriguing questions and insights fundamental to many diverse areas of mathematics."Article| William Johnston| Statement ..." |
| ♥ Book Title : Structural understanding in advanced mathematical thinking ♣ Name Author : no defined ∞ Launching : 2004 ◊ Info ISBN Link : 9788072901722 ⊗ Detail ISBN code : 8072901729 ⊕ Number Pages : Total 236 sheet ♮ News id : 2_mBAojQ7-UC
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| ♥ Book Title : A Transition to Advanced Mathematics ♣ Name Author : Douglas Smith ∞ Launching : 2010-06-01 ◊ Info ISBN Link : 9780495562023 ⊗ Detail ISBN code : 0495562025 ⊕ Number Pages : Total 416 sheet ♮ News id : jJUs0ZDOOHoC
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☯ Full Synopsis : "A TRANSITION TO ADVANCED MATHEMATICS helps students make the transition from calculus to more proofs-oriented mathematical study. The most successful text of its kind, the 7th edition continues to provide a firm foundation in major concepts needed for continued study and guides students to think and express themselves mathematically to analyze a situation, extract pertinent facts, and draw appropriate conclusions. The authors place continuous emphasis throughout on improving students’ ability to read and write proofs, and on developing their critical awareness for spotting common errors in proofs. Concepts are clearly explained and supported with detailed examples, while abundant and diverse exercises provide thorough practice on both routine and more challenging problems. Students will come away with a solid intuition for the types of mathematical reasoning they’ll need to apply in later courses and a better understanding of how mathematicians of all kinds approach and solve problems. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version."Article| Douglas Smith| Statement ..." |
| ♥ Book Title : The Elements of Advanced Mathematics ♣ Name Author : Steven G. Krantz ∞ Launching : 1995-04-21 ◊ Info ISBN Link : 0849384915 ⊗ Detail ISBN code : 9780849384912 ⊕ Number Pages : Total 176 sheet ♮ News id : c55psIy0m5EC
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☯ Full Synopsis : "Clearly written and easy to understand, The Elements of Advanced Mathematics covers logic, set theory, methods of proof, and axiomatic structures, providing an excellent grounding in analytical thinking. It facilitates the transition from elementary mathematics, generally characterized by problem-solving techniques, to advanced mathematics, characterized by theory, rigor, and proofs. This text clearly identifies and explains the components and methods of advanced mathematics. Each chapter contains exercises designed to assist the reader in understanding the material."Article| Steven G. Krantz| Statement ..." |
| ♥ Book Title : Bridge to Abstract Mathematics ♣ Name Author : Ronald P. Morash ∞ Launching : 1991-01-01 ◊ Info ISBN Link : PSU:000030526686 ⊗ Detail ISBN code : ⊕ Number Pages : Total 389 sheet ♮ News id : fH9YAAAAYAAJ
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☯ Full Synopsis : "This text is designed for students who are preparing to take a post-calculus abstract algebra and analysis course. Morash concentrates on providing students with the basic tools (sets, logic and proof techniques) needed for advanced study in mathematics. The first six chapters of the text are devoted to these basics, and these topics are reinforced throughout the remainder of the text. Morash guides students through the transition from a calculus-level courses upper-level courses that have significant abstract mathematical content."Article| Ronald P. Morash| Statement ..." |