Revisiting calculus from algebra, coalgebra, module and topology, category theory, group theory,algebraic topology...

Sequence and Continuous function

 Representable functor in Calculus

Proving Homeomorphism with Yoneda Lemma: The Unification of epsilon-delta and epsilon-N Formulation

A Higher Perspective on Basic Problems in Calculus

Limit in Analysis and Category Theory

Derivation and Differential Algebra

Differential Algebra

Coalgebras and the Leibniz Rule for Higher-Order Derivatives

Taylor series

Module over a Noncommutative Algebra and Taylor series

Differentail neighbourhood and Taylor series

ODEs

From Commutative Algebra to Linear Constant Coefficient Ordinary Differential Equation

Why the Smooth Function Module Is Injective over Real Polynomials but the Polynomial Module Is Not

Integration

The Residue Theorem via Fundamental Groups and Homology Group: Integration as a Group Homomorphism

Wednesday, November 20, 2024 A New Proof of King’s Rule Using Involution

Statistic

Normal Distribution as Orbit of Standard Normal Distribution under Affine Group Action

Topological Method

Beyond Sequences: A Topological Approach to Density Arguments

Stone–Weierstrass Theorem