Josh Laison
Math 130: Contemporary Mathematics


(Back: Masha, Meg, Ashlee, Thomas, Gretal, Conner, Terry, Ty, Colleen, Katherine, Gabe, Annalise, Arianna, Zach, Jae, Kevin, David, Jacob, Genevieve)
                               (Front: Josh, Mona, Josh, Jessie, Mady, Gwen)
Course Procedures
Possible topics
Class Project Timeline
Class Project Guidelines

Course calendar:
Monday Wednesday Friday
Week 1 Jan 18: First day of class.
Math Puzzles Handout
Jan 20: Reading: Lockhart's Lament.
Reading assignment 1: Write a few sentences in response to each of these questions.
1. How is your experience of school mathematics similar to or different from Lockhart's?
2. In particular, do you have the same negative impression of mathematics he says students get from their school mathematics experience?
3. What do you hope to get out of this course?
Jan 22: Martin Luther King, Jr. Day Celebration
No class today!
Week 2 Jan 25: Reading: Sixth Book of Mathematical Diversions: 9. Patterns and Primes.
Reading assignment 2:
1. Explain something in the reading you thought was particularly thought-provoking or beautiful.
2. Explain something in the reading you thought was confusing or difficult to understand.
3. Ask a question related to the reading but not asked by the author.
Jan 27: Problem assignment 1. Jan 29: Reading: Mathematical Circus: 13. Fibonacci and Lucas Numbers.
Reading assignment 3:
1. Explain something in the reading you thought was particularly thought-provoking or beautiful.
2. Explain something in the reading you thought was confusing or difficult to understand.
3. Ask a question related to the reading but not asked by the author.
Week 3 Feb 1: No assignments. Feb 3: Problem assignment 2. Feb 5: Reading: The Unexpected Hanging: 10. Rotations and Reflections
and New Mathematical Diversions: 2. Group Theory and Braids
Reading assignment 4: Same questions.
Week 4 Feb 8: No assignments. Feb 10: Problem assignment 3. Feb 12: Quiz #1 today.
Week 5 Feb 15: Reading: Time Travel and Other Mathematical Bewilderments:
13. Tiling with Convex Polygons and 14. Tiling with Polyominoes, Polyiamonds, and Polyhexes
Reading assignment 5: Same questions.
Feb 17: Feb 19: Reading: The Second Book of Mathematical Puzzles and Diversions: 1. The Five Platonic Solids
Reading assignment 6: Same questions.
Week 6 Feb 22: Problem assignment 4. Feb 24: No assignments. Feb 26: Reading: Mathematical Carnival Chapter 4: Hypercubes, and the first two pages of The Unexpected Hanging Chapter 12: Flatlands
Reading assignment 7: Same questions.
Week 6 Feb 29: Problem assignment 5. Mar 2: Group project stage 2 due today. Mar 4: No assignments.
Week 7 Mar 7: Reading: Sixth Book of Mathematical Diversions 10: Graph Theory
Reading assignment 8: Same questions.
Mar 9: Quiz #2 today. Mar 11: Problem assignment 6.
Week 8 Mar 14: Pi Day Extravaganza!
Reading: New Mathematical Diversions 8: The Transcendental Number Pi
Reading assignment 9: Same questions.
Mar 16: No assignments. Mar 18: No assignments.
SPRING BREAK! SPRING BREAK! SPRING BREAK!
Week 10 Mar 28: No assignments. Mar 30: No class today! Meet with your group to work on your project. Apr 1: No class today! Meet with your group to work on your project.
Week 11 Apr 4: Reading: Sixth Book of Mathematical Diversions: Klein Bottle and Other Surfaces
and Knotted Doughnuts and Other Mathematical Entertainments: Doughnuts: Linked and Knotted
Reading assignment 10: Same questions.
Apr 6: Group project stage 4 due today. Bring a typed copy of your presentation notes to turn in. Apr 8: Problem assignment 7.
Week 12 Apr 11: No assignments. Apr 13: No assignments. Apr 15: Reading: Penrose Tiles to Trapdoor Ciphers: Mandelbrotís Fractals
and Wheels, Life and Other Mathematical Amusements: The Game of Life, Part I.
Reading assignment 11: Same questions.
Week 13 Apr 18: No assignments. Apr 20: SSRD, no class today! Apr 22: Problem assignment 8.
Week 14 Apr 25: Quiz #3 today. Apr 27: Final project presentations! Apr 29: Final project presentations!
Week 15 May 2: Final project presentations! Last day of class!

Intro links:
wolframalpha
The Nature of Things documentary about Martin Gardner
Die Hard Jug Puzzle
Prime number links:
Large prime numbers from the Great Internet Mersenne Prime Search.
Numberphile video of the new largest prime
The Prime Number Theorem chart and graphs
The Clay Millenium Problems
Fermat's Last Theorem
Twin primes and the The Bounded Gaps Between Primes Polymath project
Primality tests and the AKS Primality test
RSA
Prime cicada life cycles
Fibonacci number links:
The Fibonacci Association and Fibonacci Quarterly
Vi Hart's videos on Fibonacci numbers, part 1, part 2, and part 3.
Symmetry and group theory links:
Molecular chirality
Galois theory
The Classification of Finite Simple Groups
The Monster Group
Tiling links:
Pentagonal tilings and the newly discovered 15th tiling
MC Escher tilings
Design your own Escher tilings here and here.
Penrose tilings
Pinwheel tiling and Federation Square architecture
Crystals and more examples.
Parquet deformations
Polyhedron links:
Kepler's cosmological theory
Unusual dice from the Dice Lab
A cube through a cube of the same size
Platonic solid duals
Geodesic domes
Spherical cameras
Proofs of Euler's formula
Slicing a cake to get polygons
4D links:
Unfolding a 4D cube
All unfoldings of a 4D cube
Slicing a 4D cube
4D Rubik's cube
The regular polychora
Polychoron Patterns
The book Flatland
Graph theory links:
The Konigsberg bridge problem
The number of graphs
The Icosian Game
The Planarity game
The Four-Color Theorem
The proof of the four color theorem part 1 and part 2
The Strong Perfect Graph Theorem
Mathsgear Utilities puzzle mug
Some applications of graph theory in a talk I gave
The Erdos Number project
Pi links:
My Pi Day youtube playlist!
Buffon's needle simulation
Find your Pi Day app
Pi art
/
G4G links:
Hypernom game
Patterns of the Universe book
Artwork of Bjarne Jespersen
Designs of Gwen Fisher
Topology links:
Coffee cups and donuts
Coffee cups and donuts 2
Two-holed torus trick
Turning a torus inside out
Vi Hart's Wind and Mr. Ug
Unzipping a Klein bottle
Minesweeper on a torus
Torus and Klein bottle games
Klein bottle video
Projective plane video
Buy a Klein bottle here, and impress people at parties.
Mobius bands in biology, industry, knitting, ...
Colbert on the Poincare Conjexture
Dynamical Systems links:
A fractal generator.
Another fractal generator.
Fractal images: Koch snowflake, Sierpinski triangle, Barnsley's fern, Menger sponge
Examples of Julia sets
Movies of different Julia sets and zooming into a Julia set and Mandelbrot set
Mandelbrot set song
Mandelbrot set and Julia set investigator, and some Mandelbrot movies, and more movies.
Play the game of life.
Some neat starting patterns: this, this, this, this, this, and this.