### Lecture 1

• Given a collection of samples from a real-world distribution, describe how you would generate additional samples with a similar distribution.
• What is the relationship between the median and the mean of a typical income distribution.
• What is the Lorenz curve?
• What is the Gini coefficient?
• Name a reasonably good parametric approximation to income distributions.
• Describe possible sources of income inequality in an economy in which all workers are treated identically.
• Explain how competition in an economy can amplify inequality.

### Lecture 2

• What is the purpose of an auction?
• What is a common value auction? What is a private value auction?
• What is an English / Dutch / first price sealed bid / second price sealed bid auction?
• What other auction is a Dutch auction equivalent to? Why?
• What other auction is an English auction equivalent to? Why?
• What are revenue and efficiency of auctions?
• Explain common assumptions in auction theory: independence, risk neutrality, no budget constraints, symmetry, rationality
• Explain how you simulate auctions in a discrete event simulation. How do you represent strategies? What kinds of strategies are possible?
• What is the Nash equilibrium?
• What is a repeated auction and how does it differ from a simple auction?

### Lecture 3

• Explain and discuss the paper "Markets as a substitute for rationality".
• Explain how markets select for efficiency. Describe a simple simulation demonstrating this phenomenon.
• Explain how private investment selects for efficiency and how bad investors are punished by the market.
• Explain attacks that public investment schemes may be subject to.

### Lecture 4

• What is a cellular automaton?
• How are 1D, 1-NN cellular automata numbered?
• What is Rule 110 and what is special about it?
• What is the 2D parity cellular automaton?
• What are the rules for Conway's game of life?
• What is the "gossip model"? What does it model?
• How does the gossip model relate to diffusion and relaxation models?
• What is the Greenberg-Hastings cellular automaton?
• What is the "majority model"?
• What is Schelling's model of segregation and what does it show? Why is it important?

### Lecture 5

• Generally, what is a cellular automaton? How does it differ from other kinds of computational models?
• What classes of cellular automata do we distinguish?
• What is Hashlife?
• What is WireWorld?
• What is Langton's Ant?
• What are self-replicating loops? What is Evoloop?
• What is LargerThanLife?
• How can you implement Conway's Life and its generalizations using FFT?
• What is a lattice gas cellular automaton?

### Lecture 6

• Describe how differential equations can be used to model bacterial population growth.
• Describe the relationship between differential equation models and the underlying discrete, stochastic processes.
• What is logistic growth?
• For a 1D first order differential equation, what are the criteria for stability of solutions?
• Given systems of first order equations, what are the nullclines?
• What is a limit cycle?
• What are the equations for the harmonic oscillator?
• What are the equations for a real physical pendulum? What does the phase space look like?
• What does the phase space for the Lotka-Volterra equations look like?
• Describe the FitzHugh-Nagumo and the van der Pol models.
• What is a chaotic solution to a differential equation?
• Given examples of differential equations with chaotic behavior.
• What is the logistic map?
• What is the minimum dimensionality for a chaotic solution of a differential equation? difference equation?

### Lecture 7

• Describe the structure of epidemic disease models using differential equations.
• What are the SIR, SIS, SIR-with-birth models?
• What is a hypercycle model?
• What is a delay differential equation? What properties do such equations commonly have?
• What is a diffusion model? How is it expressed as a partial differential equation?
• How do diffusion models relate to random walks?
• What is the relationship between the diffusion equation and the Poisson equation?

### Lecture 8

• What is morphogenesis?
• What are the first stages of the morphogenesis of higher animals?
• What are the first stages of the embryogenesis of Drosophila?
• What patterns in the Drosophila embryo are laid down maternally?
• What is a reaction-diffusion network?
• Explain how reaction-diffusion reactions create equally sized segments.
• What is a Turing system?
• What is a Gray-Scott system?
• How can you quickly explore the parameter space of systems like Gray Scott systems?

### Lecture 9

• What is a social network, and what are its components?
• What are examples of social networks? (Not just the electronic kind.)
• What is the relationship between social networks and graphs?
• What is the star graph? hypercube graph? line graph? wheel graph? barbell graph? complete graph? empty graph?
• What are walks, trails, and paths?
• What are closed walks, cycles, and tours?
• What is are geodesics, the geodesic distance, the diameter of a graph, and the eccentricity of a node?
• When is a graph connected? What are cut-points and bridges?
• What does it mean for two graphs to be isomorphic? What is subgraph isomorphism? What is the complexity of solving these problems?
• What is a tree? a bipartite graph? a complement of a graph? a clique?
• What idea does the notion of "centrality" try to capture in a social network?
• What measures of centrality are there?
• What is structural balance?
• What is a cohesive subgroup? How can they be defined?
• What is the clustering coefficient of a node/graph?

### Lecture 10

• What is a random binomial graph?
• What is the Erdös-Renyi model?
• What is the model of randomly citing scientists?
• How is the Barabasi-Albert model generated?
• What is the key property of the Barabasi-Albert model?
• What kind of graphs is the Barabasi-Albert model supposed to generate?
• What is a power law?
• Does the Erdös-Renyi model follow a power law?
• How is the Watts-Strogatz graph generated?
• What is a small world graph?

### Lecture 11

• What is the difference between correlation and causation?
• Define causation.
• Give an example where correlation between two variables exists, even though there is no causal relationship.
• Describe the steps for developing a frequentist statistical test.
• What is the difference between a Bayesian probability of a hypothesis and a frequentist p-value?
• What is a confidence interval?
• What is 95% confidence interval for the binomial distribution? Where does this occur frequently?
• What is the t-test used for?
• What assumptions does the t-test rely on?
• What happens when the assumptions of the t-test are violated?
• What is the null hypothesis in a two-sided t-test?
• What is the difference between a one-sample and a two-sample t-test?
• What is the Mann-Whitney U Test?
• Since the U Test is non-parametric, why don't we always use it?
• Explain the parts of a box plot.
• How are the notches in a box plot computed? What do they mean?
• Explain the concept of publication bias and how it affects the interpretation of published results.
• What are bootstrap methods? When are they used?
• What is a permutation test? When is it used?
• What is cross-validation and when is it used?