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Author: Ross G. Pinsky
Publisher: Springer
ISBN: 3319079654
Category : Mathematics
Languages : en
Pages : 165
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Book Description
The primary intent of the book is to introduce an array of beautiful problems in a variety of subjects quickly, pithily and completely rigorously to graduate students and advanced undergraduates. The book takes a number of specific problems and solves them, the needed tools developed along the way in the context of the particular problems. It treats a melange of topics from combinatorial probability theory, number theory, random graph theory and combinatorics. The problems in this book involve the asymptotic analysis of a discrete construct, as some natural parameter of the system tends to infinity. Besides bridging discrete mathematics and mathematical analysis, the book makes a modest attempt at bridging disciplines. The problems were selected with an eye toward accessibility to a wide audience, including advanced undergraduate students. The book could be used for a seminar course in which students present the lectures.
Author: Ross G. Pinsky
Publisher: Springer
ISBN: 3319079654
Category : Mathematics
Languages : en
Pages : 165
Get Book
Book Description
The primary intent of the book is to introduce an array of beautiful problems in a variety of subjects quickly, pithily and completely rigorously to graduate students and advanced undergraduates. The book takes a number of specific problems and solves them, the needed tools developed along the way in the context of the particular problems. It treats a melange of topics from combinatorial probability theory, number theory, random graph theory and combinatorics. The problems in this book involve the asymptotic analysis of a discrete construct, as some natural parameter of the system tends to infinity. Besides bridging discrete mathematics and mathematical analysis, the book makes a modest attempt at bridging disciplines. The problems were selected with an eye toward accessibility to a wide audience, including advanced undergraduate students. The book could be used for a seminar course in which students present the lectures.
Author: Ross Pinsky
Publisher: Springer
ISBN: 9783319079660
Category : Mathematics
Languages : en
Pages : 154
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Book Description
The primary intent of the book is to introduce an array of beautiful problems in a variety of subjects quickly, pithily and completely rigorously to graduate students and advanced undergraduates. The book takes a number of specific problems and solves them, the needed tools developed along the way in the context of the particular problems. It treats a melange of topics from combinatorial probability theory, number theory, random graph theory and combinatorics. The problems in this book involve the asymptotic analysis of a discrete construct, as some natural parameter of the system tends to infinity. Besides bridging discrete mathematics and mathematical analysis, the book makes a modest attempt at bridging disciplines. The problems were selected with an eye toward accessibility to a wide audience, including advanced undergraduate students. The book could be used for a seminar course in which students present the lectures.
Author: Atle Seierstad
Publisher: Springer Science & Business Media
ISBN: 0387766170
Category : Mathematics
Languages : en
Pages : 299
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Book Description
This book contains an introduction to three topics in stochastic control: discrete time stochastic control, i. e. , stochastic dynamic programming (Chapter 1), piecewise - terministic control problems (Chapter 3), and control of Ito diffusions (Chapter 4). The chapters include treatments of optimal stopping problems. An Appendix - calls material from elementary probability theory and gives heuristic explanations of certain more advanced tools in probability theory. The book will hopefully be of interest to students in several ?elds: economics, engineering, operations research, ?nance, business, mathematics. In economics and business administration, graduate students should readily be able to read it, and the mathematical level can be suitable for advanced undergraduates in mathem- ics and science. The prerequisites for reading the book are only a calculus course and a course in elementary probability. (Certain technical comments may demand a slightly better background. ) As this book perhaps (and hopefully) will be read by readers with widely diff- ing backgrounds, some general advice may be useful: Don’t be put off if paragraphs, comments, or remarks contain material of a seemingly more technical nature that you don’t understand. Just skip such material and continue reading, it will surely not be needed in order to understand the main ideas and results. The presentation avoids the use of measure theory.
Author: Atkinson
Publisher: Academic Press
ISBN: 0080955169
Category : Computers
Languages : en
Pages : 586
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Book Description
Discrete and Continuous Boundary Problems
Author: Matthias Beck
Publisher: Springer
ISBN: 1493929690
Category : Mathematics
Languages : en
Pages : 285
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Book Description
This richly illustrated textbook explores the amazing interaction between combinatorics, geometry, number theory, and analysis which arises in the interplay between polyhedra and lattices. Highly accessible to advanced undergraduates, as well as beginning graduate students, this second edition is perfect for a capstone course, and adds two new chapters, many new exercises, and updated open problems. For scientists, this text can be utilized as a self-contained tooling device. The topics include a friendly invitation to Ehrhart’s theory of counting lattice points in polytopes, finite Fourier analysis, the Frobenius coin-exchange problem, Dedekind sums, solid angles, Euler–Maclaurin summation for polytopes, computational geometry, magic squares, zonotopes, and more. With more than 300 exercises and open research problems, the reader is an active participant, carried through diverse but tightly woven mathematical fields that are inspired by an innocently elementary question: What are the relationships between the continuous volume of a polytope and its discrete volume? Reviews of the first edition: “You owe it to yourself to pick up a copy of Computing the Continuous Discretely to read about a number of interesting problems in geometry, number theory, and combinatorics.” — MAA Reviews “The book is written as an accessible and engaging textbook, with many examples, historical notes, pithy quotes, commentary integrating the mate rial, exercises, open problems and an extensive bibliography.” — Zentralblatt MATH “This beautiful book presents, at a level suitable for advanced undergraduates, a fairly complete introduction to the problem of counting lattice points inside a convex polyhedron.” — Mathematical Reviews “Many departments recognize the need for capstone courses in which graduating students can see the tools they have acquired come together in some satisfying way. Beck and Robins have written the perfect text for such a course.” — CHOICE
Author: Robert M. Young
Publisher: American Mathematical Soc.
ISBN: 1470457202
Category : Mathematics
Languages : en
Pages : 429
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Book Description
This book explores the rich and elegant interplay between the two main currents of mathematics, the continuous and the discrete. Such fundamental notions in discrete mathematics as induction, recursion, combinatorics, number theory, discrete probability, and the algorithmic point of view as a unifying principle are continually explored as they interact with traditional calculus.
Author: Hanif D. Sherali
Publisher: Springer Science & Business Media
ISBN: 1475743882
Category : Mathematics
Languages : en
Pages : 529
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Book Description
This book deals with the theory and applications of the Reformulation- Linearization/Convexification Technique (RL T) for solving nonconvex optimization problems. A unified treatment of discrete and continuous nonconvex programming problems is presented using this approach. In essence, the bridge between these two types of nonconvexities is made via a polynomial representation of discrete constraints. For example, the binariness on a 0-1 variable x . can be equivalently J expressed as the polynomial constraint x . (1-x . ) = 0. The motivation for this book is J J the role of tight linear/convex programming representations or relaxations in solving such discrete and continuous nonconvex programming problems. The principal thrust is to commence with a model that affords a useful representation and structure, and then to further strengthen this representation through automatic reformulation and constraint generation techniques. As mentioned above, the focal point of this book is the development and application of RL T for use as an automatic reformulation procedure, and also, to generate strong valid inequalities. The RLT operates in two phases. In the Reformulation Phase, certain types of additional implied polynomial constraints, that include the aforementioned constraints in the case of binary variables, are appended to the problem. The resulting problem is subsequently linearized, except that certain convex constraints are sometimes retained in XV particular special cases, in the Linearization/Convexijication Phase. This is done via the definition of suitable new variables to replace each distinct variable-product term. The higher dimensional representation yields a linear (or convex) programming relaxation.
Author: Boris M. Miller
Publisher: Springer Science & Business Media
ISBN: 1461500958
Category : Mathematics
Languages : en
Pages : 454
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Book Description
Impulsive Control in Continuous and Discrete-Continuous Systems is an up-to-date introduction to the theory of impulsive control in nonlinear systems. This is a new branch of the Optimal Control Theory, which is tightly connected to the Theory of Hybrid Systems. The text introduces the reader to the interesting area of optimal control problems with discontinuous solutions, discussing the application of a new and effective method of discontinuous time-transformation. With a large number of examples, illustrations, and applied problems arising in the area of observation control, this book is excellent as a textbook or reference for a senior or graduate-level course on the subject, as well as a reference for researchers in related fields.
Author: Ewa Ratajczak-Ropel
Publisher: Springer
ISBN: 3319628933
Category : Technology & Engineering
Languages : en
Pages : 236
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Book Description
This book addresses two of the most difficult and computationally intractable classes of problems: discrete resource constrained scheduling, and discrete-continuous scheduling. The first part of the book discusses problems belonging to the first class, while the second part deals with problems belonging to the second class. Both parts together offer valuable insights into the possibility of implementing modern techniques and tools with a view to obtaining high-quality solutions to practical and, at the same time, computationally difficult problems. It offers a valuable source of information for practitioners dealing with the real-world scheduling problems in industry, management and administration. The authors have been working on the respective problems for the last decade, gaining scientific recognition through publications and active participation in the international scientific conferences, and their results are obtained using population-based methods. Dr E. Ratajczk-Ropel explores multiple agent and A-Team concepts, while Dr A. Skakovski focuses on evolutionary algorithms with a particular focus on the population learning paradigm.
Author: H. Joseph Weaver
Publisher:
ISBN: 9780894647352
Category : Mathematics
Languages : en
Pages : 375
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Book Description
