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: Mandelbrot’s 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.