Lorenzo Sadun – författare
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4 produkter
4 produkter
Del 507 - London Mathematical Society Lecture Note Series
Emergence and Phase Transitions in Uniform Random Graphs
Häftad, Engelska, 2026
809 kr
Kommande
This book studies the emergence of large-scale structure from small structures in the context of random graphs. Typical large graphs with fixed edge density e and triangle density t are described by a 'graphon' that solves a constrained optimization problem. Proofs are provided of the existence of infinitely many open sets ('phases') in the (e,t) plane where the optimal graphon is unique and varies analytically with (e,t). The optimal graphons take a simple form, with symmetries that vary from phase to phase, indicating an emergent self-organization of the corresponding graphs. Besides being of independent interest in the theory of random graphs, extremal combinatorics and the calculus of variations, this provides a rigorous framework for studying ideas from statistical physics that have never been proven in their original setting. The techniques presented in this book can serve as a guide for optimization problems in other fields.
Häftad, Engelska, 2023
1 162 kr
Skickas inom 5-8 vardagar
The Six Pillars of Calculus: Business Edition is a conceptual and practical introduction to differential and integral calculus for use in a one- or two-semester course. By boiling calculus down to six common-sense ideas, the text invites students to make calculus an integral part of how they view the world. Each pillar is introduced by tackling and solving a challenging, realistic problem. This engaging process of discovery encourages students to wrestle with the material and understand the reasoning behind the techniques they are learning--to focus on when and why to use the tools of calculus, not just on how to apply formulas.Modeling and differential equations are front and center. Solutions begin with numerical approximations; derivatives and integrals emerge naturally as refinements of those approximations. Students use and modify computer programs to reinforce their understanding of each algorithm.The Business Edition of the Six Pillars series has been extensively field-tested at the University of Texas. It features hundreds of examples and problems designed specifically for business students. The core ideas are introduced by modeling market penetration of a new product, tracking changes in the national debt, and maximizing the profit of a business. Along the way, students learn about present value, consumer and producer surplus, amortization, and probability.
Häftad, Engelska, 2023
1 162 kr
Skickas inom 5-8 vardagar
The Six Pillars of Calculus: Biology Edition is a conceptual and practical introduction to differential and integral calculus for use in a one- or two-semester course. By boiling calculus down to six common-sense ideas, the text invites students to make calculus an integral part of how they view the world. Each pillar is introduced by tackling and solving a challenging, realistic problem. This engaging process of discovery encourages students to wrestle with the material and understand the reasoning behind the techniques they are learning--to focus on when and why to use the tools of calculus, not just on how to apply formulas.Modeling and differential equations are front and center. Solutions begin with numerical approximations; derivatives and integrals emerge naturally as refinements of those approximations. Students use and modify computer programs to reinforce their understanding of each algorithm.The Biology Edition of the Six Pillars series has been extensively field-tested at the University of Texas. It features hundreds of examples and problems specifically designed for students in the life sciences. The core ideas are introduced by modeling the spread of disease, tracking changes in the amount of $\mathrm{CO}_{2}$ in the atmosphere, and optimizing blood flow in the body. Along the way, students learn about optimal drug delivery, population dynamics, chemical equilibria, and probability.
Häftad, Engelska, 2008
809 kr
Skickas inom 5-8 vardagar
Linear algebra permeates mathematics, as well as physics and engineering. In this text for junior and senior undergraduates, Sadun treats diagonalization as a central tool in solving complicated problems in these subjects by reducing coupled linear evolution problems to a sequence of simpler decoupled problems. This is the Decoupling Principle. Traditionally, difference equations, Markov chains, coupled oscillators, Fourier series, the wave equation, the Schrodinger equation, and Fourier transforms are treated separately, often in different courses. Here, they are treated as particular instances of the decoupling principle, and their solutions are remarkably similar. By understanding this general principle and the many applications given in the book, students will be able to recognize it and to apply it in many other settings. Sadun includes some topics relating to infinite-dimensional spaces. He does not present a general theory, but enough so as to apply the decoupling principle to the wave equation, leading to Fourier series and the Fourier transform. The second edition contains a series of Explorations. Most are numerical labs in which the reader is asked to use standard computer software to look deeper into the subject. Some explorations are theoretical, for instance, relating linear algebra to quantum mechanics. There is also an appendix reviewing basic matrix operations and another with solutions to a third of the exercises.