This schedule will be periodically updated as we go along. It is subject to change. For the syllabus, click here. Library reserves can be accessed directly through Blackboard.
Introduction + Arithmetic
We set up the thought experiment, then construct the natural numbers out of emptiness. These numbers lead to various other families of numbers.
HW for 8/31 (1) Read Introduction (2) Submit ReadIntro on Blackboard (can be submitted until midnight, this time only).
Wed 8/31 (1) New York Times opinion piece on math (PDF on Blackboard) (2) Philosophy behind thought experiments (3) Schrodinger’s Cat (4) Xeno’s Paradox (5) Unreasonable effectiveness of mathematics. (6) Emotional impact of mathematics (7) Show film clip if ready.
HW for 9/7: (1) Submit ReadChap1 (submit by classtime) (2) Read “Levels of Nothing” by Robert Lawrence Kuhn (available under “Course Materials” on Bbd).
Wed 9/7 (1) Set up groups, introductions (2) Creatio ex nihilo (3) Creation myths (4) Physics creation theories (5) Intelligent Design (6) Set theory constructions of natural numbers and implicit axioms (7) Platonic view of math (8) For more on the concept of “nothing,” students can optionally watch episode 1212 of the show “Closer than Truth.”
HW for 9/12: (1) Submit ReadChap2 (submit by classtime) (2) Read sections 19, 20, 21 (starting on page 115) of “A Mathematician’s Apology” by G. H. Hardy. (Alternative link to this text is here starting on page 44.)
Mon 9/12 (1) Synesthesia (2) Genders of numbers (3) Number sense in colloquial speech (4) Russell’s paradox (5) Game of addition – is the diagram correct? (6) Representation of numbers in different bases (7) Naturals are “closed” under addition and multiplication (8) Equation: 100/3 = 40 (why is this correct?) (9) G. H. Hardy and attitudes to math
HW for 9/14: (1) Submit ReadChap3
Wed 9/14 (1) Negative numbers, historically (2) Defining sets for negatives and for fractions (3) Abstraction (4) Mathematics as a game (more on Hardy).
HW for 9/19: (1) Submit ReadChap4, ReadChap5 (2) Read “The Library of Babel.”
Mon 9/19 (1) Pythagoras history (2) Do all fractions have repeating expansions? (3) Algebraic vs transcendental numbers (4) Crystal Ball number (5) Library of Babel and exploration of website (6) Normal numbers (7) Randomness (see “Why Computers can’t generate randomness” in Slate magazine).
HW for 9/21: (1) Submit ReadChap6 (2) Watch a video on irrationals (3) Another video: How pi shows up in strange places
Wed 9/21 (1) Imaginary and complex numbers (2) Uses and properties (3) Recap of Day 1 (4) Optional: Wason Selection Task experiment in class. (Share article on math making you smarter in “Instructor’s notes” folder under “course materials” afterwards.)
Geometry
We use the numbers we have already created, along with the basic ingredient of the “point” to build empty space, then all of geometry.
HW for 9/26: (1) Submit ReadChap7 (2) Get the gist about Kandinsky and his color theories from this piece. Also, read about a psychological experiment based on such theories in this article (again, get the gist, rather than worrying too much about the details). Additional reference.
Mon 9/26 (1) Nothing vs emptiness (2) What religion and physics have to say about empty space (3) Euclid (4) Kandinsky (5) “Order” relation (6) length and distance (7) Axioms
HW for 9/28: (1) Submit ReadChap8 (2) Read about Euclid’s influence on political discourse in this article (3) Watch movie clip.
Wed 9/28 (1) Different constructions of the plane (2) Angles and parallel lines (3) Euclid’s axioms (4) The theory of formal discipline (reference)
HW for 10/3: (1) Submit ReadChap9, ReadChap10 (2) Think of topics for essay (3) Read Does Math Make You Smarter? (also available under “Course Materials as PDF).
Mon 10/3 (1) Hierarchy of shapes (2) Circle and other constructions (3) Trisecting an angle (4) What is meant by a “straight” line (5) What “plane” would be generated (if any) if the original line segment was curved? If it had a kink in it? (6) difference between complex plane and R^2
HW for 10/5: (1) Submit ReadChap11, ReadChap12
Wed 10/5 (1) Creation of 3-D using previous algorithm (2) Coordinates vs Complexes (3) Sphere and 3-D objects (4) Sphere vs plane (5) Geodesics and Two-Point Axiom (6) Geodesics on cylinder (7) Geodesic dome
HW for 10/10: (1) Submit ReadChap13 (2) Read “Euclid alone has looked on beauty bare.” Think about each line to analyze the poem. (3) Watch video on Daina Taimina’s crocheted hyperbolic geometry TEDx talk (optional).
Mon 10/10 (1) Angles and areas on different surfaces (2) hyperbolic geometry including Beltrami-Klein model and Poincare’ disc (3) parallel axiom variations (4) Non-Euclidean geometry (5) Analysis of Millay’s poem (6) More on essay topics
HW for 10/12: (1) Submit ReadChap14 (2) Watch video that explains 4-D: https://www.youtube.com/watch?v=j-ixGKZlLVc (3) Read about crochet coral reef.
Wed 10/12 (1) How to tell which surface you are on (2) Curved space (3) Four and higher dimensions (4) watch animations for tesseract (5) geometry of the universe (6) More discussion of essay topics
Algebra
To actually build the universe, we need a “contractor,” which will be Nature. We use algebra to communicate with her.
HW for 10/17: (1) Submit ReadChap15, ReadChap16 (2) What is Nature? Bring to class an answer which could be your own, or could follow some myth, religion, physics, etc.
Mon 10/17 (1) Discussion of “designing” the universe vs. “building” it (2) Different perceptions of Nature and answer to “What is Nature?” (3) Drawing straight lines (4) The power of x (5) Guessing games for kids (6) Brief history of algebra
HW for 10/19: (1) Submit ReadChap17 (2) Submit Essay Draft
Wed 10/19 (1) Polynomials on Desmos (2) Designing a roller coaster (3) Can one follow the curve of a butternut squash? (4) Experiments with interpolation and approximation on Online Polynomial Tool (5) Essay draft due
HW for 10/24: (1) Submit ReadChap18, ReadChap19 (2) Read article on climate change and the Keeling Curve and also article on carbon concentration prediction for the year 2100 by Trump administration (Wash Post article is also available under “Course Materials”).
Mon 10/24 (1) Experimental method for equation of a circle (2) Piecewise interpolation (smoothing property of cubics) (3) Different distance formulas (optional: parabola in taxicab norm) (4) Value of pi for different metrics (5) 3-D equations (6) Keeling curve and climate change
Patterns
Exploring the construction of patterns in the universe and how they relate to fundamental notions like symmetry and beauty.
HW for 10/26: (1) Submit ReadChap20, ReadChap21
Wed 10/26 (1) Do triangles exist, or are they like unicorns? (2) Symmetry (3) Group Theory (4) Peer review on essays
HW for 10/31: (1) Submit ReadChap22, ReadChap23 (2) Read Chapter 1 of Mario Livio’s “Is God a Mathematician?” (Use “Look Inside” link at Amazon)
Mon 10/31 (1) Fibonacci and other sequences (2) Rabbit reproduction rates (3) Exponential growth (4) Logistic growth and experiments (Read entry on logistic growth under “Course Materials” including PowerPoint) (5) Essay draft returned
HW for 11/2: (1) Submit ReadChap24, ReadChap25
Wed 11/2 (1) Mona Lisa (Trump and Biden as well) (2) Julia and Mandelbrot sets (3) Fractal explorations (Use http://usefuljs.net/fractals/)
HW for 11/7: (1) Submit ReadChap26 (2) Final Essay due
Mon 11/7 (1) Geometric fractals (2) Occurrence in nature (3) Chaos (4) Bacteria “Lab” (Do cellular automata next time.) (5) Final Essay due
Physics
Setting down rules for the universe.
HW for 11/9: (1) Submit ReadChap27
Wed 11/9 (1) Arbitrariness of rules (2) Associativity and other properties (3) Inverse square law (4) Cellular automata experiments (Use https://devinacker.github.io/celldemo/)
HW for 11/14: (1) Submit ReadChap28 (2) Read entries for 14, 16 and 19 April, 1905 of Einstein’s Dreams.
Mon 11/14 (1) Theories of time (2) Newton’s view of spacetime (3) Curved vs straight paths through spacetime (4) Noether’s symmetry laws
Mon 11/14 Special Lecture (optional): AOK Library Gallery 5:30-7 “Dissertation” defense of book.
HW for 11/16: (1) Submit ReadChap29 (2) Read and digest up to and including “Relativistic Train Robbery” of this reference.
Wed 11/16 (1) Geodesics (2) Simplified example of gravitation curving space (3) Special and general relativity (4) Brief idea of Minkowski space
Infinity
The silent presence that exerts control over our universe, even if it doesn’t exist in our universe.
HW for 11/21 (1) Submit ReadChap30, ReadChap31 (2) Bring an idea for a project to class.
Mon 11/21 (1) Floating point number systems (2) Planck’s constant (3) Continuous vs discrete (4) Potential infinity and actual infinity (5) Enumerating instants of time (6) Project coming up!
Wed 11/23 No class.
HW for 11/28: (1) Submit ReadChap32, ReadChap33 (2) Submit proposal for project
Wed 11/28 (1) Cardinality (2) Aleph vs Cee (3) Integers and rationals (4) Hilbert Hotel (5) Discuss ideas/proposals for project
HW for 11/30 (1) Submit ReadChap34, ReadChap35
Mon 11/30 (1) Cardinality of reals and the power set of reals (2) Continuum Hypothesis (3) Incompleteness and undecidability
Emergence
Complexity from simple rules – how the universe might emerge.
HW for 12/5 (1) Submit ReadChap36
Mon 12/6 (1) Odds of universe forming (2) Feedback loops and complexity (3) Turing patterns (4) Nature of mathematics (5) Experiments using NetLogo Web: http://www.netlogoweb.org/launch#http://www.netlogoweb.org/assets/modelslib/Sample%20Models/Biology/Ant%20Lines.nlogo
HW for 12/7 Discussion of projects
Wed 12/7 (1) Wrap-up (2) Discussion of projects
HW for 12/12 Final projects due
Mon 12/12 Student presentations for project
Project Presentations 12/16
Fri 12/16 from 1-3 pm Student presentations for project, attendance mandatory