Related papers: Lectures on the Epsilon Calculus
We survey the classical results on the prime number theorem
These lectures contain an introduction to supersymmetric theories and the minimal supersymmetric standard model. Phenomenological and cosmological consequences of supersymmetry are also discussed.
We provide a simple reformulation of the $\epsilon$-$\delta$ limit definition introduced in undergraduate calculus courses that enhances its pedagogical value for conceptual understanding and computational skill.
The basic notions of logic-predicate logic, Peano arithmetic, incompleteness theorems, etc.-have for long been an advanced topic. In the last decades, they became more widely taught, inphilosophy, mathematics, and computer science…
These lecture notes introduce the reader to the hot big bang model, cosmological perturbations, gravitational waves, the cosmic microwave background, inflation, the singularity problem, the cosmological constant problem and the cosmology of…
Expository notes on the Schwarz lemma born out of some lectures given on the subject.
We present a detailed proof of the prime number theorem suitable for a typical undergraduate- or graduate-level complex analysis course. Our presentation is particularly useful for any instructor who seeks to use the prime number theorem…
These Lecture Notes are a brief introduction to the Malliavin calculus. In particular, different notions of Malliavin derivative found in the literature are considered and compared.
Lectures on quantum computing. Contents: Algorithms. Quantum circuits. Quantum Fourier transform. Elements of number theory. Modular exponentiation. Shor`s algorithm for finding the order. Computational complexity of Schor`s algorithm.…
This introduction begins with a section on fundamental notions of mathematical logic, including propositional logic, predicate or first-order logic, completeness, compactness, the L\"owenheim-Skolem theorem, Craig interpolation, Beth's…
Planning to explore the beginning of the Universe? A lightweight introductory guide to the theory of Inflation.
Lecture script of a one-semester course that aims to develop an understanding and appreciation of fundemental concepts in modern physics for students who are comfortable with calculus. This document contains the first six lessons that will…
In this set of lectures, we give a pedagogical introduction to the subject of anyons. We discuss 1) basic concepts in anyon physics, 2) quantum mechanics of two anyon systems, 3) statistical mechanics of many anyon systems, 4) mean field…
A series of lecture notes on the elementary theory of algebraic numbers, using only knowledge of a first-semester graduate course in algebra (primarily groups and rings). No prerequisite knowledge of fields is required. Based primarily on…
This is a pedagogical article cited in the foregoing research note, quant-ph/9911050
The $\epsilon$-expansion of several two-loop self-energy diagrams with different thresholds and one mass are calculated. On-shell results are reduced to multiple binomial sums which values are presented in analytical form.
Recently delivered lectures on Self-Referential Mathematics, [2], at the Department of Mathematics and Applied Mathematics, University of Pretoria, are briefly presented. Comments follow on the subject, as well as on Inconsistent…
We explain the notion of the {\em entropy} of a discrete random variable, and derive some of its basic properties. We then show through examples how entropy can be useful as a combinatorial enumeration tool. We end with a few open…
We discuss a version of the fundamental theorem of calculus in several variables and some applications, of potential interest as a teaching material in undergraduate courses.
These lecture notes aim to provide a clear and comprehensive introduction to using open quantum system theory for quantum algorithms. The main arguments are Variational Quantum Algorithms, Quantum Error Correction, Dynamical Decoupling and…