The definitive account of the recent computer solution of the oldest problem in discrete geometry.
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Discrete calculus: methods for counting
by Mariconda, Carlo, Tonolo, Alberto
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Type: Book
This book provides an introduction to combinatorics, finite calculus, formal series, recurrences, and approximations of sums. Readers will find not only coverage of the basic elements of the subjects but also deep insights into a range of less common topics rarely considered wit…
This completely self-contained text is intended either for a course in honors calculus or for an introduction to analysis. Beginning with the real number axioms, and involving rigorous analysis, computational dexterity, and a breadth of applications, it is ideal for undergraduat…
This text presents the Eulerian numbers in the context of modern enumerative, algebraic, and geometric combinatorics. The book first studies Eulerian numbers from a purely combinatorial point of view, then embarks on a tour of how these numbers arise in the study of hyperplane a…
This textbook provides an introduction to the Catalan numbers and their remarkable properties, along with their various applications in combinatorics. Intended to be accessible to students new to the subject, the book begins with more elementary topics before progressing to more…
This book is the very first one in the English language entirely dedicated to the Lambert W function, its generalizations, and its applications. One goal is to promote future research on the topic. The book contains all the information one needs when trying to find a result. The…
The tool for visualization is Microsoft Visual C++. This popular software has the standard C++ combined with the Microsoft Foundation Classes (MFC) libraries for Windows visualization. This book explains how to create a graph interactively, solve problems in graph theory with mi…
Featuring up-to-date coverage of three topics lying at the intersection of combinatorics and commutative algebra, namely Koszul algebras, primary decompositions and subdivision operations in simplicial complexes, this book has its focus on computations. "Computations and combina…
Christos H. Papadimitriou and Kenneth Steiglitz have combined the theory of computational complexity developed by computer scientists, and the foundations of mathematical programming developed by the operations research community. This text will be useful to students with a wide…
This text explores the geometry and analysis of higher rank analogues of the symmetric spaces introduced in volume one. To illuminate both the parallels and differences of the higher rank theory, the space of positive matrices is treated in a manner mirroring that of the upper-h…
This unique treatise presents an integrated perspective on the relationship and interplay of set theory and graph theory, providing an extensive selection of examples that highlight how methods from one theory can be used to better solve problems originated in the other. This co…
Esercizi scelti di Algebra
by Del Corso, Ilaria, Dvornicich, Roberto, Chirivì, Rocco
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Type: Book
Questo libro - primo di due volumi - presenta oltre 250 esercizi scelti di algebra ricavati dai compiti d'esame dei corsi di Aritmetica tenuti dagli autori all'Università di Pisa. Ogni esercizio viene presentato con una o più soluzioni accuratamente redatte con linguaggio e nota…
"Preface: Since its inception in the 1960s, evolutionary game theory has become increasingly influential in the modelling of biology, both in terms of mathematical developments and especially in the range of applications. Important biological phenomena, such as the fact that the…
This is the first in a series of volumes, which provide an extensive overview of conjectures and open problems in graph theory. The readership of each volume is geared toward graduate students who may be searching for research ideas. However, the well-established mathematician w…