Scholarship

The Algebra Of Two’s Complements – May 14, 2024.→ [preprint] ←
Explaining the mathematics behind the standard way of representing negative numbers in binary.  #binary-representation #twos-complements #modular-arithmetic

Material Implication – June 22, 2024.→ [preprint] ←
A brief note explaining why the logical connective “implication” is defined the way it is.  #implication #material-implication #logical-connective #induction #proof-by-contradiction

The Algebra Of Two’s Complements – May 14, 2024.→ [preprint] ←
Explaining the mathematics behind the standard way of representing negative numbers in binary. #binary-representation #twos-complements #modular-arithmetic

Exponentials and logarithms – April 10, 2024.→ [preprint] ←
A narrative-style introduction to exponentials and logarithms… #math #reals #exponentiation

Exponentiation rules in \(\mathbb{R}\) – March 22, 2024.[preprint]
This is something one usually learns in a piece-wise fashion, because it is information that is usually scattered among all sorts of different books (analysis, algebra, etc.). Well, here I round it all up in one place. #math #reals #exponentiation

On sine and cosine – August 28, 2023.[preprint]
Relating the geometric intuitions of sine and cosine, to their formal expressions in terms of Taylor series. #trigonometry #sine #cosine #differentiation #taylor #series