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3169 results in Mathematical Methods

Page 1 of 159

Tensors
  • Basics and Applications with Scilab Problems
  • Pushpa Bindal, Vandna Luthra
  • Coming soon
  • Expected online publication date:
    October 2025
    Print publication:
    01 December 2026

Probability Theory for Quantitative Scientists
  • Luca Leuzzi, Enzo Marinari, Giorgio Parisi
  • Coming soon
  • Expected online publication date:
    July 2025
    Print publication:
    31 July 2025
  • Based on the long-running Probability Theory course at the Sapienza University of Rome, this book offers a fresh and in-depth approach to probability and statistics, while remaining intuitive and accessible in style. The fundamentals of probability theory are elegantly presented, supported by numerous examples and illustrations, and modern applications are later introduced giving readers an appreciation of current research topics. The text covers distribution functions, statistical inference and data analysis, and more advanced methods including Markov chains and Poisson processes, widely used in dynamical systems and data science research. The concluding section, 'Entropy, Probability and Statistical Mechanics' unites key concepts from the text with the authors' impressive research experience, to provide a clear illustration of these powerful statistical tools in action. Ideal for students and researchers in the quantitative sciences this book provides an authoritative account of probability theory, written by leading researchers in the field.

  • 1 - Origins

  • Veit Elser, Cornell University, New York
  • Book:
    Solving Problems with Projections
    Published online:
    05 June 2025
    Print publication:
    19 June 2025, pp 1-22

  • Summary

    The main ideas are introduced in a historical context. Beginning with phase retrieval and ending with neural networks, the reader will get a sense of the book’s broad scope.

  • 4 - Projections

  • Veit Elser, Cornell University, New York
  • Book:
    Solving Problems with Projections
    Published online:
    05 June 2025
    Print publication:
    19 June 2025, pp 116-186

  • Summary

    Projecting to sets and are the elementary operations used by the RRR algorithm to find solutions in their intersection. This chapter covers all the projections that arise in this book.

  • 7 - Jordan Decomposition

  • Yisong Yang, New York University
  • Book:
    Advanced Linear Algebra
    Published online:
    27 May 2025
    Print publication:
    12 June 2025, pp 210-229

  • Summary

    In this chapter, we establish the celebrated Jordan decomposition theorem which allows us to reduce a linear mapping over the complex numbers into a canonical form in terms of its eigenspectrum. As a preparation we first recall some facts regarding factorization of polynomials. Then we show how to reduce a linear mapping over a set of its invariant subspaces determined by a prime factorization of the characteristic polynomial of the mapping. Next we reduce a linear mapping over its generalized eigenspaces. Finally, we prove the Jordan decomposition theorem by understanding how a mapping behaves itself over each of its generalized eigenspaces.

Page 1 of 159