Rutgers Math Corps 2025

Formal Euclidean Geometry, Prof. Kontorovich

Course Schedule

Lecture Date	Video	Notes	Topics/Comments/Further Links
Lecture 1 7/07		Lecture 1 Notes	Engineering vs Mathematics Truth + Proof Truth + Proof + Axioms Euclid's Elements The Parallel Postulate
Lecture 2 7/08		Lecture 2 Notes	Proposition I.1 Platonic Solids Parallel Postulate
Lecture 3 7/09		Lecture 3 Notes	In Non-Euclidean Geometry, AAA Implies Congruence Undefined Terms Beginning Structure
Lecture 4 7/10		Lecture 4 Notes	Setting up Formal Euclidean Plane Equilateral Triangle Developing Axioms
Lecture 5 7/14		Lecture 5 Notes	More Axioms Continuing to Prove Prop I.1
Lecture 6 7/15		Lecture 6 Notes	Continuing to Prove Prop I.1
Lecture 7 7/16		Lecture 7 Notes	Lean Syntax
Lecture 8 7/16		Lecture 8 Notes	Nearing end of proof of Prop I.1
Lecture 9 7/21		Lecture 9 Notes	Nearing end of proof of Prop I.1
Lecture 10 7/22		Lecture 10 Notes	Radii are positive
Lecture 11 7/22		Lecture 11 Notes	Proof of the Riemann Hypothesis Proof of Prop I.1
Lecture 12 7/22		Lecture 12 Notes	Proof of Prop I.2 More missing axioms!
Lecture 13 7/28		Lecture 13 Notes	Finale: All Axioms Euclid's Proof of Pythagorean Theorem