Computer Algebra

ALGEBRA , COMPUTER ALGEBRA , AND MATHEMATICAL THINKING Paul

Mathematical symbolism generally—and symbolic algebra in particular—is among mathematics’ most powerful intellectual and practical tools. Knowing mathematics well enough to use it effectively requires a degree of comfort and ease with basic symbolics. Helping students acquire symbolic fluency and intuition has traditionally been an important, and sometimes daunting, goal of mathematics educatio...

Algebra , Computer Algebra , and Mathematical Thinking

Mathematical symbolism in general—and symbolic algebra in particular—is among mathematics’ most powerful intellectual and practical tools. Knowing mathematics well enough to use it effectively requires a degree of comfort and ease with basic symbolics. Helping students acquire symbolic fluency and intuition has traditionally been an important, but often daunting, goal of mathematics education. ...

Trigonometric Identities, Linear Algebra, and Computer Algebra

Computer Algebra for Microhydrodynamics

I describe a method for computer algebra that helps with laborious calculations typically encountered in theoretical microhydrodynamics. The program mimics how humans calculate by matching patterns and making replacements according to the rules of algebra and calculus. This note gives an overview and walks through an example, while the accompanying code repository contains the implementation de...

Certiied Computer Algebra

Computer algebra is about constructions and problems in algebra which can be ee-ciently computed or decided by mechanical procedures. A challenging point of importing computer algebra to type theory is that it require the formalisation of a considerable amount of non-trivial mathematics. The correctness of simple computer algebra algorithms can often depend on quite deep mathematical results, a...