Related papers: Mathematics for theoretical physics
This book is based on notes compiled over the many years I have been teaching the course "Applied Functional Analysis" in the first year of the Master programme at Delft University of Technology, for students with previous exposure to the…
These notes offer a basic introduction to the primary mathematical concepts of quantum physics, and their physical significance, from the operator and Hilbert space point of view, highlighting more what are essentially the abstract…
This is a tutorial introduction to the functional analysis mathematics needed in many physical problems, such as in waves in continuous media. Functional analysis takes us beyond finite matrices, allowing us to work with infinite sets of…
We lay the groundwork for a formal framework that studies scientific theories and can serve as a unified foundation for the different theories within physics. We define a scientific theory as a set of verifiable statements, assertions that…
An expository hitchhikers guide to some theorems in mathematics.
This is an introduction to calculus, and its applications to basic questions from physics. We first discuss the theory of functions $f:\mathbb R\to\mathbb R$, with the notion of continuity, and the construction of the derivative $f'(x)$ and…
This is the introduction I wrote for the multi-authored book "From Riemann to differential geometry and relativity", edited by L. Ji, A. Papadopoulos and S. Yamada (Berlin, Springer verlag, 2017). The book consists of twenty chapters,…
The purpose of this paper is to expound and clarify the mathematics and explanations commonly employed in certain notable areas of astronomy and astrophysics. The first section concentrates upon the mathematics employed to represent and…
This book is a textbook for the course of foundations of geometry. It is addressed to mathematics students in Universities and to High School students for deeper learning the elementary geometry. It can also be used in mathematics coteries…
In the footsteps of the book \textit{Measure Theory and Integration By and For the Learner} of our series in Probability Theory and Statistics, we intended to devote a special volume of the very probabilistic aspects of the first cited…
[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…
The foundations of mathematics have long been considered settled by the Zermelo-Fraenkel-Choice axioms. But set theory abounds in models with different truths and even classical questions such as the measurability of projective sets can…
A pedagogical but concise overview of Riemannian geometry is provided, in the context of usage in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions,…
This is a chapter for a planned collective volume entitled "New spaces in mathematics and physics" (M. Anel, G. Catren Eds.). The first part contains a short formal exposition of supergeometry as it is understood by mathematicians. The…
Mathematical software systems are becoming more and more important in pure and applied mathematics in order to deal with the complexity and scalability issues inherent in mathematics. In the last decades we have seen a cambric explosion of…
We give detailed exposition of modern differential geometry from global coordinate independent point of view as well as local coordinate description suited for actual computations. In introduction, we consider Euclidean spaces and different…
These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.
A description of physical reality in which wholeness is the foundation is discussed along with the motivation for such an attempt. As a possible mathematical framework within which a physical theory based on wholeness may be expressed,…
The parts contributed by the author in recent discussions with several physicists and mathematicians are reviewed, as they have been occasioned by the 2006 book "The Trouble with Physics", of Lee Smolin. Some of the issues addressed are the…
Many have wondered how mathematics, which appears to be the result of both human creativity and human discovery, can possibly exhibit the degree of success and seemingly-universal applicability to quantifying the physical world as…