Rutgers Math Corps 2025

Formal Euclidean Geometry, Prof. Kontorovich

Course Schedule

| Lecture Date | Video | Notes | Topics/Comments/Further Links | |---------|-------|-------|-------------------------------| | Lecture 1<br>7/07 | <a href="https://youtu.be/JAIN7FQwr_8" target="_blank"> <img src="https://img.youtube.com/vi/JAIN7FQwr_8/maxresdefault.jpg" width="300"> </a> | Lecture 1 Notes | Engineering vs Mathematics <br> Truth + Proof <br> Truth + Proof + Axioms <br> Euclid's Elements <br> The Parallel Postulate | | Lecture 2<br>7/08 | <a href="https://youtu.be/4wDJfuPr-Yo" target="_blank"> <img src="https://img.youtube.com/vi/4wDJfuPr-Yo/maxresdefault.jpg" width="300"> </a> | Lecture 2 Notes | Proposition I.1 <br> Platonic Solids <br> Parallel Postulate | | Lecture 3<br>7/09 | <a href="https://youtu.be/lFlu60qs7_4" target="_blank"> <img src="https://img.youtube.com/vi/lFlu60qs7_4/maxresdefault.jpg" width="300"><br><a href="https://youtu.be/wN4vNqoeUMM" target="_blank"> <img src="https://img.youtube.com/vi/wN4vNqoeUMM/maxresdefault.jpg" width="300"> </a> | Lecture 3 Notes | In Non-Euclidean Geometry, AAA Implies Congruence <br> Undefined Terms <br> Beginning Structure | | Lecture 4<br>7/10 | <a href="https://youtu.be/3F6bvkSSWOw" target="_blank"> <img src="https://img.youtube.com/vi/3F6bvkSSWOw/maxresdefault.jpg" width="300"> </a> | Lecture 4 Notes | Setting up Formal Euclidean Plane <br> Equilateral Triangle <br> Developing Axioms | | Lecture 5<br>7/14 | <a href="https://youtu.be/ttOv_C1Y1Go" target="_blank"> <img src="https://img.youtube.com/vi/ttOv_C1Y1Go/maxresdefault.jpg" width="300"> </a> | Lecture 5 Notes | More Axioms <br> Continuing to Prove Prop I.1 | | Lecture 6<br>7/15 | <a href="https://youtu.be/Q1cvVf2_n_o" target="_blank"> <img src="https://img.youtube.com/vi/Q1cvVf2_n_o/maxresdefault.jpg" width="300"> </a> | Lecture 6 Notes | Continuing to Prove Prop I.1 | | Lecture 7<br>7/16 | <a href="https://youtu.be/lJ5bYWbPtC4" target="_blank"> <img src="https://img.youtube.com/vi/lJ5bYWbPtC4/maxresdefault.jpg" width="300"> </a> | Lecture 7 Notes | Lean Syntax | | Lecture 8<br>7/16 | <a href="https://youtu.be/96vvPooTLko" target="_blank"> <img src="https://img.youtube.com/vi/96vvPooTLko/maxresdefault.jpg" width="300"> </a> | Lecture 8 Notes | Nearing end of proof of Prop I.1 | | Lecture 9<br>7/21 | <a href="https://youtu.be/5BXcxqCIQas" target="_blank"> <img src="https://img.youtube.com/vi/5BXcxqCIQas/maxresdefault.jpg" width="300"> </a> | Lecture 9 Notes | Nearing end of proof of Prop I.1 | | Lecture 10<br>7/22 | <a href="https://youtu.be/ea25ud96mQc" target="_blank"> <img src="https://img.youtube.com/vi/ea25ud96mQc/maxresdefault.jpg" width="300"> </a> | Lecture 10 Notes | Radii are positive | | Lecture 11<br>7/22 | <a href="https://youtu.be/H-1oSCpF6ZM" target="_blank"> <img src="https://img.youtube.com/vi/H-1oSCpF6ZM/maxresdefault.jpg" width="300"> </a> | Lecture 11 Notes | Proof of the Riemann Hypothesis <br> Proof of Prop I.1 | | Lecture 12<br>7/22 | <a href="https://youtu.be/ZmySB_0JN8k" target="_blank"> <img src="https://img.youtube.com/vi/ZmySB_0JN8k/maxresdefault.jpg" width="300"> </a> | Lecture 12 Notes | Proof of Prop I.2 <br> More missing axioms! | | Lecture 13<br>7/28 | <a href="https://youtu.be/m8WB87OFRic" target="_blank"> <img src="https://img.youtube.com/vi/m8WB87OFRic/maxresdefault.jpg" width="300"> </a> | Lecture 13 Notes | Finale: All Axioms <br> Euclid's Proof of Pythagorean Theorem |