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A set of open-source notes for learning calculus using the Julia programming language, emphasizing graphical, numerical, and algebraic approaches with self-graded exercises.
This article provides a visual introduction to tree calculus, a minimal, modular, Turing-complete, and reflective calculus system in theoretical computer science, emphasizing its simplicity and teachability.
The author shares his reflections on Stephen Wolfram's A New Kind of Science, arguing that continuous calculus is only an engineering compromise made for a discrete universe in an era of scarce computing power, and discusses how computational irreducibility challenges the traditional paradigm of prediction.
This blog post contrasts differential calculus (analysis) as algorithmic and easy with integral calculus (synthesis) as non-algorithmic and difficult, drawing parallels to broader themes in mathematics, computer science, and AI training via automatic differentiation.
MIT has launched the MIT4America Calculus Project to provide remote calculus tutoring to students in underresourced US high schools, addressing the lack of calculus access in nearly half of American high schools.
A curated GitHub collection (Mathematics for Machine Learning) that organizes books, papers, video lectures, and math basics for learning the math behind machine learning, covering linear algebra, calculus, probability, statistics, and more.
Explains the mathematical concepts of gradient, Jacobian, and Hessian as fundamental tools in AI model training, describing how they measure change and their roles in optimization.
A paper proves that all elementary functions like sin, exp, log, sqrt can be generated from a single binary operator eml(x,y)=exp(x)-ln(y), similar to how NAND gates unify digital logic. This could simplify AI architectures by enabling a single trainable node for continuous mathematics.
This paper presents a calculus-based framework that uses first and second derivative tests to estimate the optimal vocabulary size hyper-parameter for end-to-end ASR systems, improving performance on the Librispeech corpus.
A personal blog post rigorously introducing the Riemann integral and proving the Fundamental Theorem of Calculus, including supporting theorems like Rolle’s and the Mean Value Theorem.