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Some mathematical inequalities among various weighted means are studied. Inequalities on weighted logarithmic mean are given. Besides, the gap in Jensen's inequality is studied as a convex function approach. Consequently, some non-trivial…
Some class of sums which naturally include the sums of powers of integers is considered. A number of conjectures concerning a representation of these sums is made.
This PhD thesis deals with a number of different problems in mathematical physics with the common thread that they have probabilistic aspects. The problems all stem from mathematical studies of lattice systems in statistical and quantum…
Constructivists (and intuitionists in general) asked what kind of mental construction is needed to convince ourselves (and others) that some mathematical statement is true. This question has a much more practical (and even cynical)…
We comment on the fact that certain mathematical models that have been proposed in the quantum gravity literature, may not be subject to experimental checks, even if they turn out to be mathematically well defined. This means that they…
Mathematical maturity is a key concept for the professional life of a mathematician. This paper is not only a brief discussion of the importance of mathematical maturity but also presents some unusual ways we can use the concept to help our…
The article gives a survey of mathematical proofs that rely on computer calculations and formal proofs.
This article seeks to encourage a mathematical dialog regarding a possible solution to Beals Conjecture. It breaks down one of the worlds most difficult math problems into laymans terms and encourages people to question some of the most…
In this paper I present a kind of proof for classical Euclidean geometric problems which relies on both synthetic and analytic geometry. Using the elementary tools of polynomial algebra and multivariate calculus we manage to reduce the…
There is a problem with the foundations of classical mathematics, and potentially even with the foundations of computer science, that mathematicians have by-and-large ignored. This essay is a call for practicing mathematicians who have been…
The role of mathematical models in physics has for longer been well established. The issue of their proper building and use appears to be less clear. Examples in this regard from relativity and quantum mechanics are mentioned. Comments…
Since ancient times, mathematics has proven unreasonably effective in its description of physical phenomena. As humankind enters a period of advancement where the completion of the much coveted theory of quantum gravity is at hand, there is…
These are notes on discrete mathematics for computer scientists. The presentation is somewhat unconventional. Indeed I begin with a discussion of the basic rules of mathematical reasoning and of the notion of proof formalized in a natural…
Research universities in the United States have larger mathematics faculties outside their mathematics departments than inside. Members of this "extensive" faculty conduct most mathematics research, their interests are the most heavily…
We present a review of data types and statistical methods often encountered in astronomy. The aim is to provide an introduction to statistical applications in astronomy for statisticians and computer scientists. We highlight the complex,…
This article of mathematical education reflects author's experience with job applications and teaching methods and procedures to employ in the American Higher Education. It is organized as a standard questionnaire.
Mathematical ideas and approaches common in complexity-related fields have been fruitfully applied in experimental high energy physics also. We briefly review some of the cross-pollination that is occurring.
This is a philosophy paper rather than mathematical physics work. I will publish it in some other place.
We give a definition for Obstacle Problems with measure data and general obstacles. For such problems we prove existence and uniqueness of solutions and consistency with the classical theory of Variational Inequalities. Continuous…
Herein we present one hundred inequalities culled from various corners of the probability, statistics, and combinatorics literature. We welcome new suggestions.