Format: Hardback, 250 pages
Series: Mathematical Olympiad Series 17
Pub. Date: 12-May-2022
ISBN-13: 9789811250712
In China, lots of excellent maths students takes an active part in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad. In the past ten years China's IMO Team has achieved outstanding results ? they won the first place almost every year.
The materials of this book come from a series of two books (in Chinese) on Forward to IMO: A Collection of Mathematical Olympiad Problems (2015?2016). It is a collection of problems and solutions of the major mathematical competitions in China. It provides a glimpse of how the China national team is selected and formed.
China Mathematical Competition
China Mathematical Competition (Complementary Test)
China Mathematical Olympaid
China National Team Selection Test
China Girls' Mathematical Olympiad
China Western Mathematical Invitation
China Southeastern Mathematical Olympiad
International Mathematical Olympiad
Mathematics students, school teachers, college lecturers, university professors; mathematics enthusiasts.
https://doi.org/10.1142/12455 | January 2023
Pages: 150
ISBN: 978-981-124-380-6 (hardcover)
ISBN: 978-981-124-399-8 (softcover)
The book has two chapters. The first chapter is a modern or contemporary account of stability theory. After a preliminary section on some of the basic techniques of model theory, the focus is on local (formula-by-formula) stability theory, treated a little differently from in the author's Geometric Stability Theory book. There is also a survey of general and geometric stability theory, as well as detailed applications to combinatorics (regularity lemma) using pseudofinite methods.
The second chapter is an introduction to "continuous logic" or "continuous model theory", where truth values are real numbers, drawing on the main texts and papers, but with an independent point of view. This chapter also includes some historical background, a discussion of hyperimaginaries in classical first order model theory, as well as an introduction to local stability in the continuous framework making use of some functional analysis results from Grothendieck's thesis.
These chapters are based on notes, written by students, from a couple of advanced graduate courses in Notre Dame, in Autumn 2018, and Spring 2021.
Stability Theory
Continuous Logic
Graduate students and researchers in mathematics and related subjects interested in model theory and its applications.
https://doi.org/10.1142/12301 | August 2022
Pages: 2000
The Collected Works of Anatole Katok : Volume 1
The Collected Works of Anatole Katok : Volume 2
ISBN: 978-981-123-806-2 (hardcover)
These volumes collect most of the papers of Anatole Katok, one of the founders of the modern theory of dynamical systems. Katok's work reflects half a century of research in mathematics and includes ergodic theory, hyperbolic, elliptic, and parabolic smooth dynamics, as well as higher-rank actions. Katok's papers cover an extremely broad range of topics in dynamics, and they contain many seminal contributions that had great impact on later developments and are now widely recognized as classical.
Katok also authored numerous historical and biographical papers, and these contain accounts of crucial developments from the point of view of one of the main protagonists.
Besides papers which have already appeared in academic journals, this collection includes several previously unpublished papers as well as some whose English translation appears here for the first time.
These collected works are organized by topic into six chapters, each featuring an introduction written by respective leading specialists. Volume I focuses on following topics: Hyperbolicity, Entropy, Geodesic Flows, Interval Exchange Transformations, Billiards, Twist Maps, Spectral Theory, Approximations, Combinatorial Constructions, and History of Dynamics. Volume II focuses on these topics: Cohomology and Geometric Rigidity, Measure Rigidity.
Volume I:
Hyperbolicity, Entropy, Geodesic Flows
Interval Exchange Transformations, Billiards, Twist Maps
Spectral Theory, Approximations, Combinatorial Constructions
History of Dynamics, Surveys, Unpublished Preprints
Volume II:
Cohomology and Geometric Rigidity
Measure Rigidity
Graduates, researchers in the fields of dynamical systems and ergodic theory.
https://doi.org/10.1142/12673 | August 2022
Pages: 250
ISBN: 978-981-125-049-1 (hardcover)
This volume presents a pedagogical review of the functional distribution of anomalous and nonergodic diffusion and its numerical simulations, starting from the studied stochastic processes to the deterministic partial differential equations governing the probability density function of the functionals. Since the remarkable theory of Brownian motion was proposed by Einstein in 1905, it had a sustained and broad impact on diverse fields, such as physics, chemistry, biology, economics, and mathematics. The functionals of Brownian motion are later widely attractive for their extensive applications. It was Kac, who firstly realized the statistical properties of these functionals can be studied by using Feynman's path integrals.
In recent decades, anomalous and nonergodic diffusions which are non-Brownian become topical issues, such as fractional Brownian motion, Levy process, Levy walk, among others. This volume examines the statistical properties of the non-Brownian functionals, derives the governing equations of their distributions, and shows some algorithms for solving these equations numerically.
Probability Theory
Anomalous and Nonergodic Diffusion
Functional Distributions
Algorithms for the Models Governing Functional Distribution
Appendix A: Fractional Calculus and Related Space
Graduate and postgraduate students, as well as researchers in mathematics, physics and chemistry.