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 […]
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 […]
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.
Understanding Continuity from the Perspective of AGT
Continuity and limits, as understood in traditional calculus, rely on infinitesimally small sets to arrive at limits for arbitrary functions. This idea, when translated into other definitions of continuities, relies on ideas about convergence of sequences and the like.
What Is The Axiomatic Theory Of Formulas?
The methods or syntax to express mathematical truths are, obviously, essential to the study of mathematics. Without a taxonomy that highlights the correct use of mathematical symbols, rules which dictate the validity of mathematical statements and theory about how these statements are to be construed, you can’t do math.
Generalized Limit Expressed through Ultralimits
In my book Limit of a Discontinuous Function I defined the generalized limit defined for every (even discontinuous) function. The definition of my generalized limit uses the concept of funcoids. Funcoids are a little advanced topic, what somehow hinder understanding of generalized limit by other mathematicians. But in the special case of a function p […]