Related papers: Lectures on the Epsilon Calculus
A Compact Introduction to Fractional Calculus is presented including basic definitions, fractional differential equations and special functions.
Under certain general conditions, an explicit formula to compute the greatest delta-epsilon function of a continuous function is given. From this formula, a new way to analyze the uniform continuity of a continuous function is given.…
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. Starting from ZFC, the exposition in this first part includes relation and order theory as well as a construction of…
There are versions of "calculus" in many settings, with various mixtures of algebra and analysis. In these informal notes we consider a few examples that suggest a lot of interesting questions.
The lecture notes document the mathematical theory of microwave and optical waveguides. We start with reviewing preliminary background from Maxwell's equations. Then we discuss hollow waveguides, and inhomogeneously-filled waveguides,…
Strict-Tolerant Logic (ST) underpins naive theories of truth and vagueness (respectively including a fully disquotational truth predicate and an unrestricted tolerance principle) without jettisoning any classically valid laws. The classical…
These notes represent approximately one semester's worth of lectures on introductory general relativity for beginning graduate students in physics. Topics include manifolds, Riemannian geometry, Einstein's equations, and three applications:…
1 - Introduction 2 - Small-Angle Bhabha Scattering and the Luminosity Measurement 3 - Z^0 Physics 4 - Fits to Precision Data 5 - Physics at LEP2 6 - Conclusions
The ideas of the constraint-based statistics are introduced. The axiom and six theorems of the constraint-based statistics are established.
Short review article on quantum computation accepted for Supplement III, Encyclopaedia of Mathematics (publication expected Summer 2001). See also http://www.wkap.nl/series.htm/ENM
This document is an introduction to and review of two-dimensional mathematical physics. The reader is introduced to the subject matter primarily through problems, which are presented along with detailed worked solutions. For each chapter,…
In these lectures I will give an introduction to Feynman integrals. In the first part of the course I review the basics of the perturbative expansion in quantum field theories. In the second part of the course I will discuss more advanced…
A number of topics in analysis are discussed, with emphasis on basic principles. There is some overlap with "Elements of linear and real analysis" (arXiv:math/0108030), with numerous changes in content and presentation since then.
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
Computations in the cohomology of finite groups.
We discuss some aspects of the theory of subelliptic estimates.
The first lecture gives a colloquium-level overview of string theory and M-theory. The second lecture surveys various attempts to construct a viable model of particle physics. A recently proposed approach, based on F-theory, is emphasized.
In this series of lectures we review observational evidence for, and theoretical investigations into, cosmic acceleration and dark energy. The notes are in four sections. First I review the basic cosmological formalism to describe the…
Index: 1) Trajectories, distributions and path integrals. 2) Time-reversal and Equilibrium 3) Separation of timescales 4) Large Deviations 5) Metastability and dynamical phase transitions 6) Fluctuation Theorems and Jarzynski equality
We briefly describe each of the four topics: Schubert Calculus, Schubert Cell, Schubert Cycle, and Schubert Polynomials.