Related papers: A primer on Fourier Series
The convergence of double Fourier series of functions of bounded partial $\Lambda$-variation is investigated. The sufficient and necessary conditions on the sequence $\Lambda=\{\lambda_n\}$ are found for the convergence of Fourier series of…
Over 300 sequences and many unsolved problems and conjectures related to them are presented herein together with theorems corollaries, formulae, examples, mathematical criteria, etc. (about integer sequences, numbers, quotients, residues,…
An introduction to applied mathematics written for students in engineering and science. Focus is on a rigorous presentation that also builds understanding by discussion, analogy, and examples. Discussion of concepts involved in modeling…
This article is written with the hope to draw attention to a method that uses integral transforms to find exact values for a large class of convergent series (and, in particular, series of rational terms). We apply the method to some series…
A new family of error-correcting codes, called Fourier codes, is introduced. The code parity-check matrix, dimension and an upper bound on its minimum distance are obtained from the eigenstructure of the Fourier number theoretic transform.…
The Fourier transform is naturally defined for integrable functrions. Otherwise, it should be stipulated in which sense the Fourier transform is understood. We consider some class of radial and, generally saying, nonintegrable functions.…
The aim of this textbook is to bridge in regard of quantum computation what proves to be a considerable threshold even to the usual science trained readership between the level of science popularization, and on the other hand, the presently…
In this paper, we have proved four theorems on the degree of approximation of continuous functions by matrix means of their Fourier series which is expressed in terms of the modulus of continuity and a non-negative mediate function.
This book is written to offer a humble, but unified, treatment of e-values in hypothesis testing. It is organized into three parts: Fundamental Concepts, Core Ideas, and Advanced Topics. The first part includes four chapters that introduce…
We introduce a newly designed undergraduate-level interdisciplinary course in scientific computing that aims to prepare students as the next generation of research-oriented computational scientists and engineers. The course offers students…
The present paper presents some reflections of the author on divergent series and their role and place in mathematics over the centuries. The point of view presented here is limited to differential equations and dynamical systems.
An introduction to the On-Line Encyclopedia of Integer Sequences (or OEIS, https://oeis.org) for graduate students in mathematics
An elementary introduction to functional methods and the Schwinger-Dyson equations is presented. Emphasis is placed on practical topics not normally covered in textbooks, such as a diagrammatic method for generating equations at high order,…
This is a book on elementary mathematics suitable to use in courses for first-year students of science and engineering. Students often find the formal approach to math courses rather discouraging, and demand 'rel-life applications' in order…
This is the first in a series of three papers on Algebraic Set Theory. Its main purpose is to lay the necessary groundwork for the next two parts, one on Realisability and the other on Sheaf Models in Algebraic Set Theory.
This is an expository talk on a topic of classical analysis, arising from the VMO theory of the topological degree due to Br\'ezis and Nirenberg (1995). We sketch the history of the subject and some of its recent developments. The paper is…
This textbook is an introduction to economic networks, intended for students and researchers in the fields of economics and applied mathematics. The textbook emphasizes quantitative modeling, with the main underlying tools being graph…
[Taken from the "README" in the book] My goal with this book is to provide some kind of bridge for mathematics between the high-school-level and college-level for physics students. From my perspective, our job as physicists is to observe…
This is the text for a one quarter or one semester undergraduate course on quantum computing that has been given at the University of California Santa Cruz. It is intended for students in the physical sciences who have already studied…
Complete residue systems play an integral role in abstract algebra and number theory, and a description is typically found in any number theory textbook. This note provides a concise overview of complete residue systems, including a robust…