Convex Polytopes and Polyhedra by Peter Mcmullen
A valuable resource for researchers in discrete and combinatorial geometry, this book offers comprehensive coverage of several modern developments on algebraic and combinatorial properties of polytopes. The introductory chapters provide a new approach to the basic properties of convex polyhedra and how they are connected; for instance, fibre operations are treated early on. Finite tilings and polyhedral convex functions play an important role, and lead to the new technique of tiling diagrams. Special classes of polytopes such as zonotopes also have corresponding diagrams. A central result is the complete characterization of the possible face-numbers of simple polytopes. Tools used for this are representations and the weight algebra of mixed volumes. An unexpected consequence of the proof is an algebraic treatment of Brunn-Minkowski theory as applied to polytopes. Valuations also provide a thread running through the book, and the abstract theory and related tensor algebras are treated in detail.-
The Theory of Partitions
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The Banach–Tarski Paradox
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Special Functions
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Equivalents of the Riemann Hypothesis: Volume 1, Arithmetic Equivalents
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Non-Associative Normed Algebras
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Finite Precision Number Systems and Arithmetic
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The Classical Fields
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Handbook of Constructive Mathematics
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Aperiodic Order: Volume 2, Crystallography and Almost Periodicity
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Polynomials with Special Regard to Reducibility
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Boolean Functions
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Categorical Foundations
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Introduction to the Network Approximation Method for Materials Modeling
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Proof Complexity
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Asymptotic Analysis of Random Walks
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Contact Geometry and Nonlinear Differential Equations
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Lie's Structural Approach to PDE Systems
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Sub-Riemannian Geometry
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Combinatorics, Automata and Number Theory
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Variational Methods for Nonlocal Fractional Problems
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Ergodic Control of Diffusion Processes
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Algorithmic Aspects of Graph Connectivity
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Topics in Algorithmic Graph Theory
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Exact and Approximate Controllability for Distributed Parameter Systems
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Mathematics of the Bond Market
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Orthogonal Polynomials in the Spectral Analysis of Markov Processes
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Real Analysis through Modern Infinitesimals
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Introduction to Radon Transforms
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Lattice Sums Then and Now
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The Racah-Wigner Algebra in Quantum Theory
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Boolean Models and Methods in Mathematics, Computer Science, and Engineering
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Exact Constants in Approximation Theory
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An Algebraic Introduction to K-Theory
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Solving Polynomial Equation Systems IV: Volume 4, Buchberger Theory and Beyond
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Infinite Dimensional Optimization and Control Theory
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Banach Algebras and the General Theory of *-Algebras: Volume 1, Algebras and Banach Algebras
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Geometry of Sporadic Groups: Volume 2, Representations and Amalgams
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Ultrametric Pseudodifferential Equations and Applications
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Compound Renewal Processes
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General Orthogonal Polynomials
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The Theory of Information and Coding
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Stopping Times and Directed Processes
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Nonnegative Matrices and Applications
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Random Graphs
Peter McMullen is Professor Emeritus of Mathematics at University College London. He was elected a foreign member of the Austrian Academy of Sciences in 2006, and a fellow of the American Mathematical Society in 2012. He is also a member of the London and European Mathematical Societies. He has co-edited several books, has co-authored 'Abstract Regular Polytopes' (Cambridge, 2002) and written 'Geometric Regular Polytopes' (Cambridge, 2020). His work has been discussed in the 'Encyclopaedia Britannica', and he was an invited speaker at the International Congress of Mathematicians in 1974.
| SKU | Unavailable |
| ISBN 13 | 9781009699983 |
| ISBN 10 | 1009699989 |
| Title | Convex Polytopes and Polyhedra |
| Author | Peter Mcmullen |
| Series | Encyclopedia Of Mathematics And Its Applications |
| Condition | Unavailable |
| Binding Type | Hardback |
| Publisher | Cambridge University Press |
| Year published | 2026-02-28 |
| Number of pages | 650 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |