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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.
List of contents
1 Number Theory.- 2 Combinatorics.- 3 Analysis.- 4 Algebra.- 5 Geometry and Topology.- 6 Probability and Statistics.- 7 Algorithms and Complexity.- 8 Logic and Set Theory.- References.- Index.
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.
