If I Were a Professor

I occasionally exchange long emails in the form of writing prompts with a friend of mine. I finally got around to completing my latest challenge from a few weeks ago. My prompt and response are below.

Your institution has just started offering online courses, and they are testing the program out by offering special topics courses. It can be any topic for any academic level, but you must be able to fill a whole course on that subject (although online courses usually have less content than a classroom lecture course). Assume you have all the prerequisite qualifications to teach. Qualifications be damned! You don’t need to know the entire content of the course. This is just a pitch to your department chair.

Make a course outline/description and any other materials you like to go along with it (maybe a rough schedule, list of resources/texts, that sort of thing). Bonus points for fascinating or outlandish topics, crossing disciplines, plot twists.

Revolutions in Modern Science

Paradigm shifts in math and science which marked the transition of culture from Modernism to Postmodernism

Description

Case studies of the development of discoveries in physics and mathematics from the early 20th century which revolutionized their fields. Analysis of theorems, experiments, and their historical, philosophical, and cultural context and ramifications. Special attention will be given to how these discoveries disrupted the modernist world view. For each, a relevant non-technical literary work will accompany technical reference material.

Prerequisites

Physics II and (Introduction to Philosophy or any Literature) and (Proof Structures or Symbolic Logic)

Recommended: Modern Physics, (Modern Literature or Late Modern Philosophy)

Outline

Part 1 - Gödel’s Incompleteness Theorems

Result:

No set of axioms can be both consistent and complete. Mathematics cannot be derived through logic alone.

Timeline:

Reading:

• Principa Mathematica, Alfred North Whitehead and Bertrand Russell (selected sections)
• Logicomix: An Epic Search for Truth, Apostolos Doxiadis and Christos H. Papadimitriou

Part 2 - Quantum Mechanics

Result:

The universe is not continuous but is actually composed of discrete elements, and position and motion of these elements is not absolute but probabilistic. 

Timeline:

Reading:

• Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles, Robert Eisberg and Robert Resnick (selected chapters)
• Copenhagen, Michael Frayn (play)

Part 3 - Special Relativity

Result:

Time and space are not absolute but relative to observer's frame of reference.

Timeline:

Reading:

• The Evolution of Physics, Albert Einstein and Leopold Infeld
• Spacetime Physics, Edwin F. Taylor and John Archibald Wheeler (selected chapters)
• Mostly Harmless, Douglas Adams

Schedule

• Introduction - Modernism and Postmodernism

• Principia Mathematica and ZF Set Theory
• Selected Proofs
• Infinite Sets and the Barber’s paradox
• Completeness Theorem

• Incompleteness theorems

• Greek Atomism through the plum pudding model
• Double slit experiment
• Millikan and Rutherford
• The Schrödinger equation
• Heisenberg Uncertainty

• The Manhattan Project and the atomic bomb

• Aristotle’s elements through the luminiferous aether
• Maxwell’s Equations
• Michaelson-Morely experiment
• Lorentz transformations
• The Twin Paradox
• Special Relativity
• General Relativity (as time permits)