Intuitive dyadic calculus: The basics

Intuitive dyadic calculus: the basics

This article is divided into two parts. In the first part we present a general theory of the dyadic lattices. In the second part we show several applications of this theory to harmonic analysis: a decomposition of an arbitrary measurable function in terms of its local mean oscillations, and a pointwise bound of CalderónZygmund operators by sparse operators. Table of

Basics of Algebra, Topology, and Differential Calculus

Internal Set Theory and an Intuitive Development of the Calculus

In this paper, we present Internal Set Theory (IST) as a means to more intuitively develop mathematics while still maintaining complete rigor. We begin by stating the axioms of IST and demonstrating several of their central consequences. We then use these results to rigorously introduce the notions of infinitesimal numbers and infinite closeness. Lastly, we develop the calculus in a nonstandard...

Study on the Intuitive Introduction in Calculus Teaching

In the popularization course of higher education, students entering into the higher colleges are not those excellent students with excellent achievements in the senior school, so the teaching of college mathematics in higher colleges should transform from the learning emphasis to popularization emphasis for traditional excellent higher education. In the transformation process, as a main basic c...

Basics of Algebra, Topology, and Di↵erential Calculus