Course Syllabus
Get Adobe
Acrobat Reader

The Lectures are Here.
Textbooks listed in the syllabus are suggested but not required. Note that readings listed below are not required, but students can find much interesting information related to topics in the course. The lecture slides contain many references to URLs where further information can be found, but the lecture slides are intended to be for the most part selfcontained.

Week 
Topic

Suggested Readings
Chapter/Section

Homework/Lab Assignment

Homework Due Date 
1 January 3 
Introduction  Exploring
Fractals and Chaos 
Peak & Frame
Chapter 1, pg 517
Schroeder
Chapter 1, 125
Course Flyer
The Santa Fe Institute
Pattern Shells
Patterns in Game of Life
Dow Jones Industrials
Treasury Yield Curve
Parkfield Earthquake Prediction
Climate Change
Overview of Complexity (3:34)
Complexity Theory Overview(10:51)
SFI Big Questions (5:06)
SFI: Searching for Order in the Complexity of Evolving Worlds (4:38)
Jennifer Dunne on Interactions (4:40)
SFI: Evolution of Complex Societies (6:00)
SFI: Evolution of Life and Intelligence (7:15)
Geoff West on CitiesI (7:17)
Geoff West on CitiesII (17:33)
Jared Diamond on Why Societies Collapse (19:48)
Duncan Watts on Common Sense and Complex Systems (10:54)
Forecasting Disasters in the Complex Earth (JBR 1:09:25)
Video Feedback: Setting it Up (6:49)
Video Feedback 1 (3:19)
Video Feedback 2 (1:56)
Video Feedback Crutchfield (15:33)
Art Benjamin on Fibonacci Numbers (6:24)
Stock Trading with Fibonacci Numbers (9:33)
What is a Fractal Pattern? (2:00)
Emergence in Complexity Theory (9:12)

Explore the Links on the Syllabus page
Homework:
Write a paragraph about your previous experience with fractals and chaos

Tuesday January 11

2 January 10 
Fractals  Fractal Generators & Iterated Function Sets

Peak & Frame
Chapter 1, pg 1840
Schroeder
Chapter 1, 2549
Optional: Feldman Chapters 1415
Gaussian Normal Statistics
Scaling Laws
Fractal Antennas
Romanesco
The Fractal Explorer Web Site
Chaos_Game (Using Excel)
What is a Fractal? (4:13)
Fun with Fractals (5:04)
BBC: How Fractals can help you Understand the Universe (3:09)
Fractals are Often not Completely SelfSimilar (19:54)
Understanding the Universe with Fractals (3:09)
Sierpinski Tetrahedron
Hilbert Curve
Cantor Set
Koch Snowflake
Fractals Wikipedia
How Long are Coastlines?? (6:00)
SFI: Fractal Dimensions I (5:30)
SFI: Fractal Dimensions II (5:30)
SFI: Fractal Dimensions III (2:30)
SFI: Fractal Dimensions IV (7:13)
SFI: Fractal Dimensions V, Box Counting (4:42)
SFI: Fractal Dimensions VI, Box Counting(3:38)
SFI: Fractal Dimensions VII Examples from the real World (3:45)
Numberphile: Measuring Coastlines (8:03)



3 January 17 
Fractals  Cont.
Introduction to Chaos and the Mandelbrot Set
Lorenz Equations
Iterated Maps
Attractors & Fixed Points
Logistic & Other Maps
Fractal Boundaries
Newton's Method

Peak & Frame
Chapter 2, All
Begin Chapter 3
Schroeder
Chapter 9
Optional: Feldman Chapter 17
Synchronization of Metronomes (4:00)
Atmospheric Modes
Lorenz Equations (Wikipedia)
Lorenz Equations Sensitive Dependence
Story of the Lorenz Equations (11:50)
Science of the Butterfly Effect (12:50)
Lorenz Attractor  I (13:21)
Lorenz Attractor  II (1:34)
Jack Wisdom: Chaos in the Solar System (3:33)
Uncertainty in Weather Forecasting
NY Times Article:
"In Natures Casino"
Logistic Map  Mandelbrot Set Video (18:38)
Holly Krieger on M Set Introduction (9:10)
M Set: Wikipedia
M Set Morphology
Tour of M Set (5:11)
Fractals, A World in a Grain of Sand (15:00)
Holly Krieger on M Set and Fibonacci Numbers (9:59)
Julia Set Morphology
Holly Krieger on Filled Julia Set (6:47)
Fractal Basin Boundaries
Logistic Map Explorable with Widgets

 
4 January 24 
Introduction to Dynamical Systems
Atmospheric Modes: Nonlinear Dynamics in the Real World

Peak & Frame
Chapter 3, All
Begin Chapter 4
Schroeder
Chapter 3
Chapter 10, 211225
Optional: Feldman Chapter 18
Intro to Dynamical Systems (1:53)
Systems Theory of Organizations (10:53)
Met Office: Coriolis Effect (1:53)
Met Office: Coriolis Effect & Winds (6:18)
AU Met: ENSO I (4:15)
Met Office: ENSO II (4:23)
Sengupta: ENSO Walker Circulation (6:19)
Nat GEO: ENSO (2:50)
AU Met: Understanding ENSO (4:13)
Met Office: North Atlantic Oscillation (2:13)
Met Office: Atlantic Multidecadal Oscillation (2:28)
Met Office: Pacific Decadal Oscillation (2:50)
Met Office: North Atlantic Oscillation (2:13)
Au Met: Madden Julian Oscillation (3:45)
United Nations: Milankovich Cycles (6:34)



5 January 31 
Time Series and Probability

Peak and Frame
Chapter 4, 5
Schroeder Chapter 12
pp 268286
pp 89102
Optional: Feldman Chapters 17
Probability (Wikipedia)
Probability (StatTrek)
Example: Monte Hall Problem
Example: Secretary Problem
Example: 100 Prisoners Problem
Market Probabilities
Introduction to Fourier Transforms (20:56)
Fourier Transform, Fourier Series, and Frequency Spectrum (15:44)
Fourier Transforms (Technical)



6 February 7 
Introduction to Computation, Information and Cellular Automata

Peak and Frame
Chapter 7 Chapter 8
Schroeder
Chapter 11, 237245
Chapter 12, 295299
Optional: Feldman Chapters 2022
Cellular Automata (Wikipedia)
Dan Shiffman on Nature of Code (Ebook)
Daniel Shiffman on CAs I (6:02)
Dan Shiffman on CAs II (19:39)
Dan Shiffman on Game of Life (16:03)
Information (Intro 3:25)
Information (Bits 9:52)
Information (Entropy 7:04)
Information (Markov Chains 7:14)
Information (Statistical Communication Theory 4:01)
Computation in CAs (Melanie Mitchell)
MitchellCAsandGAs (Melanie Mitchell)



7 February 14 
Introduction to Neural Networks and Machine Learning

Peak and Frame
Chapter 9
Schroeder
Chapter 17, 371386
Optional: Feldman Chapters 2325
Alan Turing
Turing Test
Finite State Machines (Wikipedia)
Video on Turing and Turing Machines (13:04)
Making of the Film "The Imitation Game"
NY Times Article on AI
Brittany Wenger on Neural Networks (8:23)
John Hopfield and Neural Networks (3:54)
Hopfield Paper on Spiking Neurons
Neural Networks (Wikipedia)
Deep Learning (Wikipedia)
Deep Learning: Structure (19:13)
Deep Learning: How Machines Learn (21:00)
Introduction to Machine Learning
Future of Data Science Education

First Paper: On a topic related to low dimensional systems, fractals, chaos, or other topic from the first half of the course:
Due Friday February 18

Guidelines for Paper
Example Paper Format

8 February 21

Landscapes, Networks, Adaptation, Statistical Models
Cluster Growth
Percolation
Pattern Formation

Schroeder
Chapter 10, 232236
Optional: Feldman
Chapters 2627
SFI Complexity Course
Math of Sandpiles
Percolation Theory (8:10)
Network Dynamics (6:47)
Network Robustness (18:32)
Diffusion Limited Aggregation (3:04)



9 February 28 
Introduction to Cryptocurrencies and Econophysics

Suzy Moat on Big Data (15:54)
Jim Simons on Quant Investing (23:07)
Fractal Patterns in Stock Prices
NY Times Article on Investing Strategy: Buy at the Close, Sell on the Open
What is Bitcoin? (12:48)



10 March 7

Data Science
Global Warming, Prediction in Complex Systems
Examples and
Applications
Summary & Discussion

Niel Howe and William Straus on the Fourth Turning
The Fourth Turning
Conflict as Computation (2:29)
History and Inevitability (4:06)




Second Paper/Project due describing and analyzing a high dimensional complex system of your choice, or other topic related to the second half of the course.
Due by 5:00 pm Monday March 14
