Invitation to Discrete Mathematics PDF Download

Author: Jiří Matoušek
Publisher: Oxford University Press
ISBN: 0198570430
Category : Mathematics
Languages : en
Pages : 462

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Book Description
A clear and self-contained introduction to discrete mathematics for undergraduates and early graduates.

Author: Jiří Matoušek
Publisher: OUP Oxford
ISBN: 0191524670
Category : Mathematics
Languages : en
Pages : 462

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Book Description
This book is a clear and self-contained introduction to discrete mathematics. Aimed mainly at undergraduate and early graduate students of mathematics and computer science, it is written with the goal of stimulating interest in mathematics and an active, problem-solving approach to the presented material. The reader is led to an understanding of the basic principles and methods of actually doing mathematics (and having fun at that). Being more narrowly focused than many discrete mathematics textbooks and treating selected topics in an unusual depth and from several points of view, the book reflects the conviction of the authors, active and internationally renowned mathematicians, that the most important gain from studying mathematics is the cultivation of clear and logical thinking and habits useful for attacking new problems. More than 400 enclosed exercises with a wide range of difficulty, many of them accompanied by hints for solution, support this approach to teaching. The readers will appreciate the lively and informal style of the text accompanied by more than 200 drawings and diagrams. Specialists in various parts of science with a basic mathematical education wishing to apply discrete mathematics in their field can use the book as a useful source, and even experts in combinatorics may occasionally learn from pointers to research literature or from presentations of recent results. Invitation to Discrete Mathematics should make a delightful reading both for beginners and for mathematical professionals. The main topics include: elementary counting problems, asymptotic estimates, partially ordered sets, basic graph theory and graph algorithms, finite projective planes, elementary probability and the probabilistic method, generating functions, Ramsey's theorem, and combinatorial applications of linear algebra. General mathematical notions going beyond the high-school level are thoroughly explained in the introductory chapter. An appendix summarizes the undergraduate algebra needed in some of the more advanced sections of the book.

Author: Konrad Jacobs
Publisher: Princeton University Press
ISBN: 9780691025285
Category : Mathematics
Languages : en
Pages : 264

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Book Description
Based on a well-received course designed for philosophy students, this book is an informal introduction to mathematical thinking. The work will be rewarding not only for philosophers concerned with mathematical questions but also for serious amateur mathematicians with an interest in the "frontiers" as well as the foundations of mathematics. In what might be termed a sampler of the discipline, Konrad Jacobs discusses an unusually wide range of topics, including such items of contemporary interest as knot theory, optimization theory, and dynamical systems. Using Euclidean geometry and algebra to introduce the mathematical mode of thought, the author then turns to recent developments. In the process he offers what he calls a "Smithsonian of mathematical showpieces": the five Platonic Solids, the Mbius Strip, the Cantor Discontinuum, the Peano Curve, Reidemeister's Knot Table, the plane ornaments, Alexander's Horned Sphere, and Antoine's Necklace. The treatments of geometry and algebra are followed by a chapter on induction and one on optimization, game theory, and mathematical economics. The chapter on topology includes a discussion of topological spaces and continuous mappings, curves and knots, Euler's polyhedral formula for surfaces, and the fundamental group. The last chapter deals with dynamics and contains material on the Game of Life, circle rotation, Smale's "horseshoe," and stability and instability, among other topics.

Author:
Publisher:
ISBN:
Category : Computer science
Languages : en
Pages : 410

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Book Description

Author: Oscar Levin
Publisher: Createspace Independent Publishing Platform
ISBN: 9781724572639
Category :
Languages : en
Pages : 238

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Book Description
Note: This is a custom edition of Levin's full Discrete Mathematics text, arranged specifically for use in a discrete math course for future elementary and middle school teachers. (It is NOT a new and updated edition of the main text.)This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this.Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs.While there are many fine discrete math textbooks available, this text has the following advantages: - It is written to be used in an inquiry rich course.- It is written to be used in a course for future math teachers.- It is open source, with low cost print editions and free electronic editions.

Author: Edward R. Scheinerman
Publisher: Courier Corporation
ISBN: 0486275329
Category : Mathematics
Languages : en
Pages : 408

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Book Description
This text is designed for those who wish to study mathematics beyond linear algebra but are unready for abstract material. Rather than a theorem-proof-corollary exposition, it stresses geometry, intuition, and dynamical systems. 1996 edition.

Author: Vašek Chvátal
Publisher: Cambridge University Press
ISBN: 1108934919
Category : Mathematics
Languages : en
Pages : 270

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Book Description
Paul Erdős published more papers during his lifetime than any other mathematician, especially in discrete mathematics. He had a nose for beautiful, simply-stated problems with solutions that have far-reaching consequences across mathematics. This captivating book, written for students, provides an easy-to-understand introduction to discrete mathematics by presenting questions that intrigued Erdős, along with his brilliant ways of working toward their answers. It includes young Erdős's proof of Bertrand's postulate, the Erdős-Szekeres Happy End Theorem, De Bruijn-Erdős theorem, Erdős-Rado delta-systems, Erdős-Ko-Rado theorem, Erdős-Stone theorem, the Erdős-Rényi-Sós Friendship Theorem, Erdős-Rényi random graphs, the Chvátal-Erdős theorem on Hamilton cycles, and other results of Erdős, as well as results related to his work, such as Ramsey's theorem or Deza's theorem on weak delta-systems. Its appendix covers topics normally missing from introductory courses. Filled with personal anecdotes about Erdős, this book offers a behind-the-scenes look at interactions with the legendary collaborator.

Author: Andrew V. Sills
Publisher: CRC Press
ISBN: 1351647962
Category : Mathematics
Languages : en
Pages : 257

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Book Description
The Rogers--Ramanujan identities are a pair of infinite series—infinite product identities that were first discovered in 1894. Over the past several decades these identities, and identities of similar type, have found applications in number theory, combinatorics, Lie algebra and vertex operator algebra theory, physics (especially statistical mechanics), and computer science (especially algorithmic proof theory). Presented in a coherant and clear way, this will be the first book entirely devoted to the Rogers—Ramanujan identities and will include related historical material that is unavailable elsewhere.

Author: Shahriar Shahriari
Publisher: Cambridge University Press
ISBN: 1108476546
Category : MATHEMATICS
Languages : en
Pages : 631

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Book Description
A conversational introduction to combinatorics for upper undergraduates, emphasizing problem solving and active student participation.

Author: Rod Haggarty
Publisher: Addison Wesley Publishing Company
ISBN: 9780201730470
Category : Computer science
Languages : en
Pages : 0

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Book Description
A concise introduction to key mathematical ideas for computing students which develops their understanding of discrete mathematics and its application in computing. The topics are presented in a logical order that build upon each other and are constantly reinforced by worked examples. Reliance on students' previous mathematical experience is kept to a minimum, though some basic algebraic manipulation is required.