Mathematical Problems And Proofs

Author: Branislav Kisacanin
Publisher: Springer Science & Business Media
ISBN: 0306469634
Size: 71.40 MB
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A gentle introduction to the highly sophisticated world of discrete mathematics, Mathematical Problems and Proofs presents topics ranging from elementary definitions and theorems to advanced topics -- such as cardinal numbers, generating functions, properties of Fibonacci numbers, and Euclidean algorithm. This excellent primer illustrates more than 150 solutions and proofs, thoroughly explained in clear language. The generous historical references and anecdotes interspersed throughout the text create interesting intermissions that will fuel readers' eagerness to inquire further about the topics and some of our greatest mathematicians. The author guides readers through the process of solving enigmatic proofs and problems, and assists them in making the transition from problem solving to theorem proving. At once a requisite text and an enjoyable read, Mathematical Problems and Proofs is an excellent entrée to discrete mathematics for advanced students interested in mathematics, engineering, and science.

Problems In Set Theory Mathematical Logic And The Theory Of Algorithms

Author: Igor Lavrov
Publisher: Springer Science & Business Media
ISBN: 9780306477126
Size: 27.59 MB
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Problems in Set Theory, Mathematical Logic and the Theory of Algorithms by I. Lavrov & L. Maksimova is an English translation of the fourth edition of the most popular student problem book in mathematical logic in Russian. It covers major classical topics in proof theory and the semantics of propositional and predicate logic as well as set theory and computation theory. Each chapter begins with 1-2 pages of terminology and definitions that make the book self-contained. Solutions are provided. The book is likely to become an essential part of curricula in logic.

Linear Control Systems

Author: Branislav Kisačanin
Publisher: Springer Science & Business Media
ISBN: 9780306467431
Size: 58.49 MB
Format: PDF, Kindle
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Anyone seeking a gentle introduction to the methods of modern control theory and engineering, written at the level of a first-year graduate course, should consider this book seriously. It contains: A generous historical overview of automatic control, from Ancient Greece to the 1970s, when this discipline matured into an essential field for electrical, mechanical, aerospace, chemical, and biomedical engineers, as well as mathematicians, and more recently, computer scientists; A balanced presentation of the relevant theory: the main state-space methods for description, analysis, and design of linear control systems are derived, without overwhelming theoretical arguments; Over 250 solved and exercise problems for both continuous- and discrete-time systems, often including MATLAB simulations; and Appendixes on MATLAB, advanced matrix theory, and the history of mathematical tools such as differential calculus, transform methods, and linear algebra. Another noteworthy feature is the frequent use of an inverted pendulum on a cart to illustrate the most important concepts of automatic control, such as: Linearization and discretization; Stability, controllability, and observability; State feedback, controller design, and optimal control; and Observer design, reduced order observers, and Kalman filtering. Most of the problems are given with solutions or MATLAB simulations. Whether the book is used as a textbook or as a self-study guide, the knowledge gained from it will be an excellent platform for students and practising engineers to explore further the recent developments and applications of control theory.

Number Theory

Author: George E. Andrews
Publisher: Courier Corporation
ISBN: 0486135101
Size: 21.58 MB
Format: PDF
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Undergraduate text uses combinatorial approach to accommodate both math majors and liberal arts students. Covers the basics of number theory, offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more

Counting And Configurations

Author: Jiri Herman
Publisher: Springer Science & Business Media
ISBN: 1475739257
Size: 40.50 MB
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This book presents methods of solving problems in three areas of elementary combinatorial mathematics: classical combinatorics, combinatorial arithmetic, and combinatorial geometry. Brief theoretical discussions are immediately followed by carefully worked-out examples of increasing degrees of difficulty and by exercises that range from routine to rather challenging. The book features approximately 310 examples and 650 exercises.

Additive Number Theory Inverse Problems And The Geometry Of Sumsets

Author: Melvyn B. Nathanson
Publisher: Springer Science & Business Media
ISBN: 9780387946559
Size: 46.79 MB
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This book reviews results in inverse problems for finite sets of integers, culminating in Ruzsa's elegant proof of the deep theorem of Freiman that a finite set of integers with a small sumset must be a large subset of an n-dimensional arithmetic progression.

104 Number Theory Problems

Author: Titu Andreescu
Publisher: Springer Science & Business Media
ISBN: 9780817645618
Size: 12.97 MB
Format: PDF, Kindle
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This challenging problem book by renowned US Olympiad coaches, mathematics teachers, and researchers develops a multitude of problem-solving skills needed to excel in mathematical contests and in mathematical research in number theory. Offering inspiration and intellectual delight, the problems throughout the book encourage students to express their ideas in writing to explain how they conceive problems, what conjectures they make, and what conclusions they reach. Applying specific techniques and strategies, readers will acquire a solid understanding of the fundamental concepts and ideas of number theory.

Combinatorial And Additive Number Theory Ii

Author: Melvyn B. Nathanson
Publisher: Springer
ISBN: 3319680323
Size: 23.86 MB
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Based on talks from the 2015 and 2016 Combinatorial and Additive Number Theory (CANT) workshops at the City University of New York, these proceedings offer 19 peer-reviewed and edited papers on current topics in number theory. Held every year since 2003, the workshop series surveys state-of-the-art open problems in combinatorial and additive number theory and related parts of mathematics. Sumsets, partitions, convex polytopes and discrete geometry, Ramsey theory, primality testing, and cryptography are among the topics featured in this volume. Each contribution is dedicated to a specific topic that reflects the latest results by experts in the field. Researchers and graduate students interested in the current progress in number theory will find this selection of articles relevant and compelling.

Combinatorial Number Theory And Additive Group Theory

Author: Alfred Geroldinger
Publisher: Springer Science & Business Media
ISBN: 3764389613
Size: 41.61 MB
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This book begins with two seminars: Additive Cominatorics and non-unique factorizations; Sumsets and structure. The book then offers notes from those seminars to address the methods, techniques and problems of contemporary additive combinatorics.

Discrete Mathematics

Author: László Lovász
Publisher: Springer Science & Business Media
ISBN: 0387217770
Size: 14.69 MB
Format: PDF, ePub
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Aimed at undergraduate mathematics and computer science students, this book is an excellent introduction to a lot of problems of discrete mathematics. It discusses a number of selected results and methods, mostly from areas of combinatorics and graph theory, and it uses proofs and problem solving to help students understand the solutions to problems. Numerous examples, figures, and exercises are spread throughout the book.