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Landscape of 21st Century Mathematics

Selected Advances, 2001–2020

  • Book
  • © 2021

Overview

Authors:
  1. Bogdan Grechuk

    1. Department of Mathematics, University of Leicester, Leicester, UK

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  • Includes over 400 great theorems from all areas of mathematics
  • Presents current mathematics research directions and results
  • Accessible to advanced undergraduates and above

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Number Theory

    • Bogdan Grechuk
    Pages 1-49

  3. Combinatorics

    • Bogdan Grechuk
    Pages 51-102

  4. Analysis

    • Bogdan Grechuk
    Pages 103-171

  5. Algebra

    • Bogdan Grechuk
    Pages 173-206

  6. Geometry and Topology

    • Bogdan Grechuk
    Pages 207-254

  7. Probability and Statistics

    • Bogdan Grechuk
    Pages 255-301

  8. Algorithms and Complexity

    • Bogdan Grechuk
    Pages 303-342

  9. Logic and Set Theory

    • Bogdan Grechuk
    Pages 343-348

  10. Back Matter

    Pages 349-429
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Keywords

About this book

Landscape of 21st Century Mathematics offers a detailed cross section of contemporary mathematics. Important results of the 21st century are motivated and formulated, providing an overview of recent progress in the discipline.


The theorems presented in this book have been selected among recent achievements whose statements can be fully appreciated without extensive background. Grouped by subject, the selected theorems represent all major areas of mathematics: number theory, combinatorics, analysis, algebra, geometry and topology, probability and statistics, algorithms and complexity, and logic and set theory. The presentation is self-contained with context, background and necessary definitions provided for each theorem, all without sacrificing mathematical rigour. Where feasible, brief indications of the main ideas of a proof are given.


Rigorous yet accessible, this book presents an array of breathtaking recent advances in mathematics. It is written for everyone with a background in mathematics, from inquisitive university students to mathematicians curious about recent achievements in areas beyond their own.

Authors and Affiliations

  • Department of Mathematics, University of Leicester, Leicester, UK

    Bogdan Grechuk

About the author

Bogdan Grechuk fell in love with mathematics as a child, taking part in various mathematics competitions, including the International Mathematical Olympiad where he won a gold medal in 1997. He's been lecturing at the University of Leicester (UK) since 2011.

Bibliographic Information

  • Book Title: Landscape of 21st Century Mathematics

  • Book Subtitle: Selected Advances, 2001–2020

  • Authors: Bogdan Grechuk

  • DOI: https://doi.org/10.1007/978-3-030-80627-9

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

  • Hardcover ISBN: 978-3-030-80626-2Published: 22 September 2021

  • Softcover ISBN: 978-3-030-80629-3Published: 23 September 2022

  • eBook ISBN: 978-3-030-80627-9Published: 21 September 2021

  • Edition Number: 1

  • Number of Pages: XIV, 429

  • Number of Illustrations: 8 b/w illustrations, 16 illustrations in colour

  • Topics: Mathematics, general

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