Chapter 1: Calculating Pi and Beyond: Searching Order in Disorder with Simulation [30]
Description: The beginning chapter will use Monte Carlo simulation as a topic to introduce some fundamental concepts in simulation.
Topics to be covered:
1. Simulating Pi
2. The goat problem and uniform sampling
3. How to properly set a simulation environment
Chapter 2: Markov Chain: A Peek into the Future [20]
Description: Markov chain simulation will be introduced from both probabilistic perspective and matrix multiplication perspective.
Topics to be covered:
1. How to predict weather?
2. The transition matrix and stability states
3. Markov chain Monte Carlo simulation
Chapter 3: Multi-Armed Bandits: Probability Simulation and Bayesian Statistics [30]
Description: Classical multi-armed bandits' model will be introduced to continue the probabilistic perspective of the previous chapter. In addition, Bayesian statistics will be introduced.
Topics to be covered:
1. Introduction to multi-armed bandit
2. Greedy versus explorative strategies
3. The interpretation of a Bayesian statistician.
Chapter 4: Balls in 2D Box: A Simplest Physics Engine [20]
Description: This chapter is mainly about event-driven simulation. It is not about simulation in the time space but in the event space.
Topics to be covered:
1. Introduce the physics laws that govern motion
2. Use event-driven paradigm to build a physics engine
3. More realistic simulation with friction
Chapter 5: Percolation: Threshold and Phase Change [25]
Description: Phase changing is an important physics behavior for systems near critical boundaries. We are going to simulate critical behaviors using percolation as examples.
Topics to be covered:
1. The concept of percolation and
2. Why dimension matters: 1D percolation and 2D percolation
3. 3D percolation and even higher dimensions
Chapter 6: Queuing System: How Stock Trades are Made [30]
Description: As the first example in the business world, concepts in queuing systems are introduced and the simulation using basic data structures like queue and deque will be carried out.
Topics to be covered:
1. Basic data structures in Python
2. Microstructure of trading
3. Simulating trading
Chapter 7: Rock, Scissor and Paper: Multi-Agent Simulation
[30]
Description: Sometimes we want to simulate a system with multiple agents acting on their own behalf. In this chapter, we are going to run a multi-agent simulation and test the performance of different competing strategies in such a scenario.
Topics to be covered:
1. Characteristics of multi-agent system
2. Baseline strategies
3. Analyzing nontrivial strategies
Chapter 8: Matthew Effect and Tax Policy: Why the Rich Keeps Getting Richer
[30]
Description: Differential equation is an important field of study that governs a big group of phenomena. In this chapter, we are going to study it with a very relevant topic: wealth distribution in modern society.
Topics to be covered:
1. Introduction of differential equations
2. Matthew effect and ROI
3. How tax policy can gauge social wealth distribution
Chapter 9: Misinformation Spreading: Simulation on a Graph (Centrality, Networkx)[30]
Description: Network simulation is another important domain. Nowadays social media like Twitter, Facebook and reddit can be easily modelled as a network. We will cover a simple simulation to study how misinformation can spread in a network and how we can fight against it.
Topics to be covered:
1. Concepts of a network
2. Simulate misinformation spreading in a directed network
3. How to fight misinformation (or suppress freedom of expression)
Chapter 10: Simulated Annealing and Genetic Algorithm [30]
Description: There are two simulation algorithms widely used in research and industry that mimic natural phenomena. We are going to use them to solve two real world problems and explain the origin of their power.
Topics to be covered:
4. Simulated Annealing Basics
5. Use Simulated Annealing to solve an optimization problem
6. Genetic Algorithm
7. Use Genetic algorithm to solve an optimization problem
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