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Nine Mathematical Challenges: An Elucidation

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Release : 2021-09-24
Genre : Education
Kind : eBook
Book Rating : 904/5 ( reviews)

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Book Synopsis Nine Mathematical Challenges: An Elucidation by : A. Kechris

Download or read book Nine Mathematical Challenges: An Elucidation written by A. Kechris. This book was released on 2021-09-24. Available in PDF, EPUB and Kindle. Book excerpt: This volume stems from the Linde Hall Inaugural Math Symposium, held from February 22–24, 2019, at California Institute of Technology, Pasadena, California. The content isolates and discusses nine mathematical problems, or sets of problems, in a deep way, but starting from scratch. Included among them are the well-known problems of the classification of finite groups, the Navier-Stokes equations, the Birch and Swinnerton-Dyer conjecture, and the continuum hypothesis. The other five problems, also of substantial importance, concern the Lieb–Thirring inequalities, the equidistribution problems in number theory, surface bundles, ramification in covers and curves, and the gap and type problems in Fourier analysis. The problems are explained succinctly, with a discussion of what is known and an elucidation of the outstanding issues. An attempt is made to appeal to a wide audience, both in terms of the field of expertise and the level of the reader.

Nine Mathematical Challenges

Download Nine Mathematical Challenges PDF Online Free

Author :
Release : 2021
Genre : Education
Kind : eBook
Book Rating : 906/5 ( reviews)

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Book Synopsis Nine Mathematical Challenges by : A. S. Kechris

Download or read book Nine Mathematical Challenges written by A. S. Kechris. This book was released on 2021. Available in PDF, EPUB and Kindle. Book excerpt: The finite simple groups and their classification / Michael Aschbacher -- Recent progress on the Birch and Swinnerton-Dyer conjecture / Ashay Burungale, Christopher Skinner and Ye Tian -- Bounding ramification by covers and curves / Hélène Esnault and Vasudevan Srinivas -- The Lieb-Thirring inequalities : recent results and open problems / Rupert Frank -- Some topological properties of surface bundles / Ursula Hämenstadt -- Some recent advances on Duke's equidistribution theorems / Philippe Michel -- Gap and type problems in Fourier analysis / Alex Poltoratski -- Quantitative bounds for critically bounded solutions to the Navier-Stokes equations / Terry Tao -- The continuum hypothesis / W. Hugh Woodin.

From Complex Analysis to Operator Theory: A Panorama

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Release : 2023-09-21
Genre : Mathematics
Kind : eBook
Book Rating : 396/5 ( reviews)

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Book Synopsis From Complex Analysis to Operator Theory: A Panorama by : Malcolm Brown

Download or read book From Complex Analysis to Operator Theory: A Panorama written by Malcolm Brown. This book was released on 2023-09-21. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to the memory of Sergey Naboko (1950-2020). In addition to original research contributions covering the vast areas of interest of Sergey Naboko, it includes personal reminiscences and comments on the works and legacy of Sergey Naboko’s scientific achievements. Areas from complex analysis to operator theory, especially, spectral theory, are covered, and the papers will inspire current and future researchers in these areas.

The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations

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Release : 2022-09-21
Genre : Mathematics
Kind : eBook
Book Rating : 497/5 ( reviews)

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Book Synopsis The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations by : Jacob Bedrossian

Download or read book The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations written by Jacob Bedrossian. This book was released on 2022-09-21. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to provide beginning graduate students who completed the first two semesters of graduate-level analysis and PDE courses with a first exposure to the mathematical analysis of the incompressible Euler and Navier-Stokes equations. The book gives a concise introduction to the fundamental results in the well-posedness theory of these PDEs, leaving aside some of the technical challenges presented by bounded domains or by intricate functional spaces. Chapters 1 and 2 cover the fundamentals of the Euler theory: derivation, Eulerian and Lagrangian perspectives, vorticity, special solutions, existence theory for smooth solutions, and blowup criteria. Chapters 3, 4, and 5 cover the fundamentals of the Navier-Stokes theory: derivation, special solutions, existence theory for strong solutions, Leray theory of weak solutions, weak-strong uniqueness, existence theory of mild solutions, and Prodi-Serrin regularity criteria. Chapter 6 provides a short guide to the must-read topics, including active research directions, for an advanced graduate student working in incompressible fluids. It may be used as a roadmap for a topics course in a subsequent semester. The appendix recalls basic results from real, harmonic, and functional analysis. Each chapter concludes with exercises, making the text suitable for a one-semester graduate course. Prerequisites to this book are the first two semesters of graduate-level analysis and PDE courses.

Topics in Applied Mathematics and Modeling

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Release : 2022-12-05
Genre : Mathematics
Kind : eBook
Book Rating : 91X/5 ( reviews)

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Book Synopsis Topics in Applied Mathematics and Modeling by : Oscar Gonzalez

Download or read book Topics in Applied Mathematics and Modeling written by Oscar Gonzalez. This book was released on 2022-12-05. Available in PDF, EPUB and Kindle. Book excerpt: The analysis and interpretation of mathematical models is an essential part of the modern scientific process. Topics in Applied Mathematics and Modeling is designed for a one-semester course in this area aimed at a wide undergraduate audience in the mathematical sciences. The prerequisite for access is exposure to the central ideas of linear algebra and ordinary differential equations. The subjects explored in the book are dimensional analysis and scaling, dynamical systems, perturbation methods, and calculus of variations. These are immense subjects of wide applicability and a fertile ground for critical thinking and quantitative reasoning, in which every student of mathematics should have some experience. Students who use this book will enhance their understanding of mathematics, acquire tools to explore meaningful scientific problems, and increase their preparedness for future research and advanced studies. The highlights of the book are case studies and mini-projects, which illustrate the mathematics in action. The book also contains a wealth of examples, figures, and regular exercises to support teaching and learning. The book includes opportunities for computer-aided explorations, and each chapter contains a bibliography with references covering further details of the material.

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