Further Information:
Algebraic Calculus One represents a major new rethink of this classical subject that makes it more algebraic and connects more strongly with modern computing, as infinite precision real numbers and associated limits no longer play a central role. The course is centred on YouTube videos by Prof N J Wildberger, which are hosted on the YouTube channel Wild Egg Maths, and the main focus is on developing the Integral Calculus for curves.
The YouTube videos are augmented with Notes, Worked Problems, Homework Questions, and a section on Links, Definitions and Notation. There are hundreds of worked problems and homework questions to strengthen your understanding.
We will be working in an affine geometry set up, building up carefully an affine notion of signed area, gradually leading to a powerful integration theory with applications to physics, geometry and analysis. This will be integration for geometrical curves, and it will be more powerful and general than the usual approach.
Along the way we will delve into historical aspects of the course, such as conic sections and cubic curves, lemniscates, Faulhaber polynomials, de Casteljau Bezier curves, Napier's logarithms, Bernoulli numbers, Pascal arrays, forward differences and summations, tangents, projective points atinfinityand many other lovelytopics, objects and identities.
Linear algebraic ideas will play a big role, and the Discrete Calculus will figure prominently. Computer science students may be excited by our concrete data-structure orientation. The course ends with the highlight of the Fundamental theorem, which is presented in a new light. Further courses in the series will develop more aspects of Calculus -- in particular the Differential Calculus will be highlighted in Algebraic Calculus Two, which is under preparation.
