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Course Syllabus
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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 self-contained.
Note the
Student Resource Page
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Week |
Topic
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Suggested Readings
Chapter/Section
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Homework/Lab Assignment
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Homework Due Date |
| 1 January 8 |
Introduction: Exploring
Fractals and Chaos |
Peak & Frame
Chapter 1, pg 5-17
Schroeder
Chapter 1, 1-25
Course Flyer
The Santa Fe Institute
Pattern Shells
Patterns in Game of Life
Dow Jones Industrials
Treasury Yield Curve
Parkfield Earthquake Prediction
Climate Change
Early History of SFI I (Murray Gell-Mann :48)
Early History of SFI II (Murray Gell-Mann 1:28)
Early History of SFI III (Murray Gell-Mann 3:38)
Complex Adaptive Systems (10:22)
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 Cities-I (7:17)
Geoff West on Cities-II (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 I (9:33)
Stock Trading with Fibonacci Numbers II (2:37)
Stock Trading with Fibonacci Numbers and Eliott Waves (2:47)
What is a Fractal Pattern? (2:00)
Emergence in Complexity Theory (9:12)
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Explore the Links on the Syllabus page
Homework:
Write a paragraph about your previous experience with fractals and chaos
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Friday January 12
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| 2 January 15 |
Fractals and Fractal Generators & Iterated Function Sets
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Peak & Frame
Chapter 1, pg 18-40
Schroeder
Chapter 1, 25-49
Optional: Feldman Chapters 14-15
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 Self-Similar (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)
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| 3 January 22 |
Fractals - Cont.
Introduction to Chaos and the Mandelbrot Set
Lorenz Equations
Iterated Maps
Attractors & Fixed Points
Logistic & Other Maps
Fractal Boundaries
Newton's Method
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Peak & Frame
Chapter 2, All
Begin Chapter 3
Schroeder
Chapter 9
Optional: Feldman Chapter 17
Atmospheric Modes
Lorenz Equations (Wikipedia)
Lorenz Equations: Sensitive Dependence
NY Times Article:
"In Natures Casino"
M Set Morphology
Julia Set Morphology
Fractal Basin Boundaries
M Set: Wikipedia
Logistic Map Explorable with Widgets
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
Logistic Map - Mandelbrot Set Video (18:38)
Benoit Mandelbrot TED Talk (17:09)
Holly Krieger on M Set Introduction (9:10)
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)
Holly Krieger on Filled Julia Set (6:47)
Newton's Fractal (26:05)
Julia & Fatou Sets, Holomorphic Dynamics (27:42)
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| 4 January 29 |
Dynamical Systems
Atmospheric Modes: Nonlinear Dynamics in the Real World
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Peak & Frame
Chapter 3, All
Begin Chapter 4
Schroeder
Chapter 3
Chapter 10, 211-225
Optional: Feldman Chapter 18
Intro to Dynamical Systems I (6:40)
Intro to Dynamical Systems II (4:51)
Systems Theory of Organizations (10:53)
Synchronization of Metronomes (4:00)
Veritasium: Synchronization (20:57)
Met Office: Global Climate System (3:51)
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)
PBS on Chaos and Weather Prediction (6:13)
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)
Is the Gulf Stream Collapsing? (13:32)
What if Gulf Stream Shut Down?
Lecture on Slowing Down of Gulf Stream, by Dr. Stefan Rahmstorf (U. Potsdam, 27:00, includes movie clips from Day After Tomorrow - start at 12:00)
Principal Component Analysis (6:27)
Principal Component Analysis Details
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| 5 February 5 |
Time Series and Probability
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Peak and Frame
Chapter 4, 5
Schroeder Chapter 12
pp 268-286
pp 89-102
Optional: Feldman Chapters 1-7
Probability (Wikipedia)
Probability (StatTrek)
Example: Monte Hall Problem
Example: Secretary Problem
Example: 100 Prisoners Problem
Market Probabilities
Introduction to Fourier Series (8:24)
Introduction to Time Series Analysis (2:59)
What is Time Series Analysis (7:28)
Introduction to Fourier Transforms (20:56)
Fourier Transform, Fourier Series, and Frequency Spectrum (15:44)
Fourier Transforms (Technical)
Basic Probability (7:50)
Independent and Dependent Events (6:43)
Marilyn vos Savant: Monty Hall (7:05)
Mutually Exclusive vs. Independent Events (4:01)
Probability Densities (9:36)
Simple Introduction to Probability (11:28)
Simple Introduction to Statistics (4:49)
Histograms and Other Charts (7:34)
Mean, Mode, Standard Deviation (7:34)
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| 6 February 12 |
Physics of Computation and Information
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Peak and Frame
Chapter 7
Chapter 8
Schroeder
Chapter 11, 237-245
Chapter 12, 295-299
Optional: Feldman Chapters 20-22
Alan Turing
Turing Test
Finite State Machines (Wikipedia)
Video on Turing and Turing Machines (13:04)
Making of the Film "The Imitation Game" (14:15)
Best Scenes from the Film "The Imitation Game" (6:05)
Turing Machines (4:21)
A Real Turing Machine (5:08)
Information (Intro 3:25)
Information (Bits 9:52)
Information (Entropy 7:04)
Understanding Shannon Entropy (12:07)
Introduction to Information Theory (10:09)
Information (Markov Chains 7:14)
Information (Statistical Communication Theory 4:01)
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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 16
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Guidelines for Paper
Example Paper Format
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| 7 February 19 |
Cellular Automata, Neural Networks, Machine Learning and Artificial Intelligence (AI)
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Peak and Frame
Chapter 9
Schroeder
Chapter 17, 371-386
Optional: Feldman Chapters 23-25
Cellular Automata (Wikipedia)
Computation in CAs (Melanie Mitchell)
MitchellCAsandGAs (Melanie Mitchell)
Dan Shiffman on Nature of Code (E-Book)
A New Kind of Science (E-Book)
A New Kind of Finance (Paper)
Introduction to Machine Learning
Future of Data Science Education
(CAS) General Overview of CAs (7:51)
Daniel Shiffman on CAs I (6:02)
Dan Shiffman on CAs II (19:39)
Dan Shiffman on Game of Life (16:03)
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)
IBM Tech: What is Machine Learning? (8:22)
Google Cloud Tech: What is Machine Learning? (5:22)
Google Cloud Tech: The 7 Steps of Machine Learning (10:35)
Google Cloud Tech: Plain and Simple Estimators (Involves some coding; 5:46)
StatQuest - Neural Network Fundamentals Part I - Inside the Black Box (18:53)
Statquest - Neural Network Fundamentals Part II - Backpropagation (17:33)
StatQuest - Machine Learning Fundamentals: Bias and Variance (6:35)
Deep Learning in 6 Minutes (5:51)
Deep Learning: Structure, and What is a Neural Network? (19:13)
Deep Learning: How Machines Learn (21:00)
Deep Learning: Backpropagation (13:53)
What is Artificial Intelligence (or Machine Learning)? (6:14)
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| 8 February 26
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Landscapes, Networks, Adaptation, Statistical Models
Cluster Growth
Percolation
Pattern Formation
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Schroeder
Chapter 10, 232-236
Optional: Feldman
Chapters 26-27
SFI Complexity Course
Math of Sandpiles
What is a Fitness Landscape? (10:15)
Predicting Protein Folding with AI (7:54)
Revolutionizing Protein Folding with AI (12:06)
Self-Organized Criticality (SOC: 10:01)
Applications of Percolation Models in Finance (8:10)
Network Dynamics (6:47)
Network Robustness (18:32)
Diffusion Limited Aggregation (3:04)
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| 9 March 4 |
Cryptocurrencies and Econophysics
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Fractal Patterns in Stock Prices
NY Times Article on Investing Strategy: Buy at the Close, Sell on the Open
Buy Bitcoin Web Site
Tradeblock Web Site
Coindesk Web Site
What is Bitcoin? (5:32)
99Bitcoins The Role of Money, and What Led to Bitcoin? (12:48)
99Bitcoins Bitcoin Mining (16:00)
99Bitcoins Bitcoin Block Confirmations (2:02)
99Bitcoins What is a Hash? (1:53)
Kristine Cranley on What is Bitcoin? (3:45)
What is Bitcoin? History of Bitcoin (12:10)
A Brief History of Bitcoin (5:03)
How Bitcoin Works in 5 minutes (5:25)
How Cryptocurrency ACTUALLY works (13:54)
Bitcoin: How Cryptocurrencies Work (9:25)
How does a blockchain work - Simply Explained (5:59)
CNBC: Wall Street Adoption (12:50)
Valuing Bitcoin - Panel Discussion Crypto 2022 (31:35)
CNBC: President Biden's New Crypto Order (11:29)
Suzy Moat on Big Data (15:54)
Jim Simons on Quant Investing (23:07)
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| 10 March 11
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Data Science
Global Warming, Prediction in Complex Systems
Examples and
Applications
Summary & Discussion
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Niel Howe and William Straus on the Fourth Turning
The Fourth Turning
Neil Howe: The Fourth Turning: Why American 'Crisis' May Last Until 2030 (14:42)
Neil Howe: The 4th Turning (8:03)
PATREON: We Are In A "FOURTH TURNING," What Does That Mean? (10:20)
The Fourth Turning - How this crisis was predicted 30 years ago (10:04)
Conflict as Computation (2:29)
History and Inevitability (4:06)
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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 Friday March 15
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