Programmer Mind vs Mathematician Mind (Humility)
In the past I thought so: Common money-earning programmers just have the skill to comprehend with their egg-heads how program flow moves between multiple levels of functions and classes calling each other in a “perverted”, unpredictable, messy fashion. While I am a programmer, too, I am different: I am a mathematician, I comprehend abstraction, generalization, […]
What is Calculus and How Might AGT Change it?
Differential and integral calculus are two of the most important mathematical discoveries of the last few centuries. Since the work of Isaac Newton in 1665, through Lagrange and Cauchy, to formalize this branch of mathematics—calculus has served a crucial role in most fields of human inquiry. Anyone who’s done even basic geometry and algebra would […]
Impact Of AGT On Calculus
Calculus has served a crucial role in most fields of human inquiry. Anyone who’s done even basic geometry and algebra would appreciate the importance of calculus. Learn more about calculus here:
The Potential Role of AGT in Economic Analysis
One of the fields of human inquiry that make extensive use of mathematics and calculus is economics. Contemporary economic theory relies heavily on mathematical concepts and ideas to make sense or and theorize about economic phenomenon to devise economic models/policies. Anyone who doesn’t know the basics of calculus and mathematical analysis can’t hope to become […]
Differentiating between Topological and Discrete Continuity
Topological continuity is a key concept within mathematical theory. Topological analysis has opened paths to a deeper understanding of continuity at a more abstract level. However, topological continuity isn’t the only form of continuity mathematicians study—discrete continuity is one type of continuity that is separate from topological continuity. Algebraic General Topology is one way of […]
An infinitely big structure in the center of a black hole?
I remind that I defined generalized limit of arbitrary function. The limit may be an infinitely big value. It allows to define derivative and integral of an arbitrary function. I also defined what are solutions of partial differential equations where such infinities (instead of e.g. real numbers or complex numbers) are defined. You may see […]
Filters An Introduction
We apply filters to existing sets to express otherwise inexpressible statements.They effectively allow us to refer to infinitely small or infinitely large sets and conduct mathematical analysis to develop valuable insights.
Continuity as Convergence of Sequences—Expanding Our Definition of Continuity
I feel that continuity is best understood when we consider convergence at different levels of abstraction. While it’s fairly easy to understand the continuity of functions when they’re defined in spaces like R2, with standards like: The left hand limit must equal the right hand limit. The function should have a finite value at each […]
New Edition of the Book “Algebraic General Topology. Book 1: Basics”
I’ve published a new edition of my book Algebraic General Topology. The new edition features “unfixed morphisms” a way to turn a category into a semigroup. (Certain additional structure on the category is needed.) The book features a wide generalization of general topology done in an algebraic way. Now we can operate on general topological […]
Understanding Functional Discontinuities – The Building Blocks Of AGT
A discontinuity is any point on a function where one of the three possibilities arise: The right-side limit is unequal to left-side limit The function jumps suddenly The function goes to infinity at a certain point in the domain.