Course curriculum

This ten part series explores the first book of Euclid's Elements, culminating in the proof of the Pythagorean Theorem. The last two thousand years of carefully studying Euclid has revolutionized logic. We explore the ideas of axiomatic systems, proof techniques, dependence diagrams, logical independence, model theory, and decidability.

    1. How to Use This Course

    2. GOALS OF THE COURSE

      FREE PREVIEW

    3. Class Resources

    1. Lesson 1 Video

      FREE PREVIEW

    2. Lesson 1 Quiz (Multiple Choice)

    3. Lesson 1 Video Notes

    1. Lesson 2 Video

    2. Lesson 2 Quiz (Multiple Choice)

    3. Lesson 2 Video Notes

    4. Euclid: The 13 books and their contents

    1. Lesson 3 Video

    2. Lesson 3 Quiz (Multiple Choice)

    3. Lesson 3 Video Notes

    1. Lesson 4 Video

    2. Lesson 4 Quiz (Multiple Choice)

    3. Lesson 4 Video Notes

    1. Statements of the Axioms & Propositions

    2. Lesson 5 Video - INTRO

    3. Proposition 1

    4. Proposition 2

    5. Proposition 3

    6. Proposition 4

    7. Proposition 5

    8. Proposition 6

    9. Proposition 7

    10. Proposition 8

    11. Proposition 9

    12. Proposition 10

    13. Final remarks

About this course

  • $100.00
  • 47 lessons
  • 7 hours of video content
  • Part 1 of a 4 part series
  • Course available for free with Membership in The Academy

About the Course

This is part one of a four part series called Introduction to Modern Mathematics. The intention of this series is to bring the un-initiated up to speed with what the modern mathematical methodologies, paradigms, and objects of study are as quickly as possible by using the two most important mathematical texts of all time Euclid's Elements & Gauss' Disquitiones Arithmeticae.

This course, Part 1: Euclid, is mostly expository and historical. Modern math texts have a specific methodology that was invented by Euclid. The studying of this textbook and the philosophical and logical controversies surrounding it have transformed the way mathematicians think, discover, and communicate mathematics. 

               Core Objectives:

  1. Teach the Definition-Theorem-Proof style of mathematics
  2. Learn basic proof styles (Direct & Contradiction)
  3. Prove the first 10 propositions & Pythagorean Theorem.
  4. Learn the "black box" method of proof.
  5. Learn about “dependence diagrams” and axiom systems.
  6. Understand the difference between Syntax and Semantics.
  7. The “independence” of the Parallel Postulate via Model Theory.
  8. Be introduced to Non-Euclidean Geometry.