Related papers: Hilbert's first and second problems and the founda…
An informal guide to the history of Heisenberg's matrix mechanics. It is designed for mathematicians with only a minimal background in either physics or geometry, and it is based upon Heisenberg's original arguments.
This paper is devoted to the study of reproducing kernel Hilbert spaces. We focus on multipliers of reproducing kernel Banach and Hilbert spaces. In particular we tried to extend this concept and prove some theorems.
Mixture models have been around for over 150 years, as an intuitively simple and practical tool for enriching the collection of probability distributions available for modelling data. In this chapter we describe the basic ideas of the…
In this book, there are five chapters: Systems of Linear Equations, Vector Spaces, Homogeneous Systems, Characteristic Equation of Matrix, and Matrix Dot Product. It has also exercises at the end of each chapter above to let students…
Several thoughts are presented on the long ongoing difficulties both students and academics face related to Calculus 101. Some of these thoughts may have a more general interest.
This paper deals with (1) the truncated matrix Hamburger moment problem from the point of view of reproducing kernel Hilbert spaces of vector valued entire functions of the kind introduced and extensively studied by Louis de Branges and (2)…
In this PhD thesis we propose an algorithmic approach to the study of the Hilbert scheme. Developing algorithmic methods, we also obtain general results about Hilbert schemes. In Chapter 1 we discuss the equations defining the Hilbert…
Lecture note topics: 1. Some tools from real and complex analysis, 2. Hilbert spaces, 3. Banach spaces, 4. Compact operators and their spectra, 5. Intermezzo: reproducing kernel Hilbert spaces, 6. Banach algebras ,7. Spectral theory of…
The problem of advancing coordinatization of mathematics is considered. The need to develop a theory for measuring value and complexity of mathematical implications and proofs is discussed including motivations, benefits and implementation…
There has been concern in the literature about the methodology of using secondary calibration timepoints when estimating evolutionary divergence dates. Such timepoints are divergence time estimates that have been derived from one molecular…
This is an expanded version of the notes by the second author of the lectures on Hitchin systems and their quantization given by the first author at the Beijing Summer Workshop in Mathematics and Mathematical Physics ``Integrable Systems…
This note is an expansion of three lectures given at the workshop "Topology, Complex Analysis and Arithmetic of Hyperbolic Spaces" held at Kyoto University in December of 2006 and will appear in the proceedings for this workshop.
An invited plenary given at the founding meeting of the Southern African Association for Research in Mathematics and Science Education in 1992.
This is an expanded and revised text for a fifteen minute talk given at the University of Queensland Physics Camp, September 2000. The focus is on the goals and motivations for studying quantum information theory, rather than on technical…
Lecture notes from a minicourse given at the ICTP in May 2002.
Gabor analysis which can be traced back to Dennis Gabor's influential 1946 paper \emph{Theory of communication}, is concerned with both the theory and the applications of the approximation properties of sets of time and frequency shifts of…
Reverse mathematics studies which subsystems of second order arithmetic are equivalent to key theorems of ordinary, non-set-theoretic mathematics. The main philosophical application of reverse mathematics proposed thus far is foundational…
The article attempts to demonstrate the rich history of one truly remarkable problem situated at the confluence of probability theory and theory of numbers - finding the probability of co-primality of two randomly selected natural numbers.…
This is a set of 288 questions written for a Moore-style course in Mathematical Logic. I have used these (or some variation) four times in a beginning graduate course. Topics covered are: propositional logic axioms of ZFC wellorderings and…
This is a non-standard paper, containing some problems, mainly in model theory, which I have, in various degrees, been interested in. Sometimes with a discussion on what I have to say; sometimes, of what makes them interesting to me,…