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Math Tools for Research (updating)

2025-02-06
Yalin

  1. Gradshteyn I S, Ryzhik I M. Table of integrals, series, and products[M]. Academic press, 2014. (Available )

The book is valued by users of previous editions of the work both for its comprehensive coverage of integrals and special functions, and also for its accuracy and valuable updates. Since the first edition, published in 1965, the mathematical content of this book has significantly increased due to the addition of new material, though the size of the book has remained almost unchanged.

  1. Chiu S N, Stoyan D, Kendall W S, et al. Stochastic geometry and its applications[M]. John Wiley & Sons, 2013.(Available)

Stochastic Geometry and its Applications is ideally suited for researchers in physics, materials science, biology and ecological sciences as well as mathematicians and statisticians. It should also serve as a valuable introduction to the subject for students of mathematics and statistics.

  1. Daley D J, Vere-Jones D. An introduction to the theory of point processes: volume I: elementary theory and methods[M]. Springer New York, 2003. (Available)

  2. Another version: Daley D J, Vere-Jones D. An introduction to the theory of point processes: volume II: general theory and structure[M]. Springer Science & Business Media, 2007.

  3. Kallenberg O. Random measures, theory and applications[M]. Cham: Springer, 2017. (Available)

Offering the first comprehensive treatment of the theory of random measures, this book has a very broad scope, ranging from basic properties of Poisson and related processes to the modern theories of convergence, stationarity, Palm measures, conditioning, and compensation. The three large final chapters focus on applications within the areas of stochastic geometry, excursion theory, and branching processes.

  1. Boyd S. Convex optimization[J]. Cambridge UP, 2004. (Available)

“Convex Optimization” by Stephen Boyd and Lieven Vandenberghe is a highly valuable resource that provides a comprehensive and accessible introduction to the field. It combines theoretical rigor with practical insights, making it an essential reference for students, researchers, and practitioners interested in convex optimization and its applications.

  1. Byrd P F, Friedman M D. Handbook of elliptic integrals for engineers and physicists[M]. Springer, 1971. (Available)

“Handbook of Elliptic Integrals for Engineers and Physicists” by Byrd and Friedman is a comprehensive and authoritative reference that provides essential information on elliptic integrals. It combines theoretical insights with practical tools, making it an invaluable resource for engineers, physicists, and mathematicians who work with elliptic integrals in their research and applications.


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