Infinitesimal Calculus with Finite Fields - Famous Math Problems

Explore infinitesimal calculus over finite fields in this 34-minute video lecture. Discover how to apply calculus concepts to the semi-cubical parabola in the finite field F_7, challenging traditional notions of real number analysis. Learn about the importance of polynumbers, de Casteljau Bezier curves, and a more computational approach to mathematics. Examine the geometric properties of a hexagon inscribed and circumscribed to the semi-cubical parabola in F_7, gaining insights into algebraic calculus and its applications in undergraduate education and research.

Syllabus

Introduction
Retreat from the 'functional' POV.
A symmetrical POV. It makes 'at a glance' sense of the table of powers.
Polynumbers are elemental "primary", functions are not.
Polynumber formalism of Derivatives over [point-to-point] 'secantism'
Switch from 't ' 'variable' parameter to a polynumber 'α' := '| 0 , 1.. ' parameter dependence
Shift from a 'α' := '| 0, 1.. ' to 'α' := '| 1 , 0.. + 'ε' := '| 0 , 0.. bipolynumber parameter
'point' plus 'vector' Derivative description
31:10 see