Solve Math related questions with Python

Probability, Statistics and Machine Learning
References: 
Grinstead and Snell's Introduction to Probability; 
Advanced Data Analysis from an Elementary Point of View

Detailed class info can be found here

week 01 - introduction to Python, statists VS mathematics

• Lab01 Python installation
• Lec01 Introduction to Statistics and its mathematical aspects

week 02 - Basics in Python. Destributions.

• Lab02 numpy array, equations, loops, lists, strings, built-in functions
• Lec02 Random variables, expecations, variables, pdf, cdf

week 03 - numpy and matplotlib in Python. Central Limit Theorem and Law of Large Numbers.

• Lab03 numpy
• Lab03 matplotlib
• Lec03 Central Limit Theorem and Law of Large Numbers
• Lec03 Introduction to inverse_transform_method

week 04 - Inplement inverse sampling method; Plot "probability". The amazing Normal Distribution - everything is Normal.

• Lab04 density vs histogram; pdf and cdf
• Lab04 Inverse sampling by samples and by cdf
• Lec04 Normal distribution

week 05- Visualization of Central Limit and Law of Large Number. From central limit to normal, and to Hypothesis testing.

• Lab05 Visualization of Central Limit and Law of Large Number -- sampe methods are different!
• Lec05 Hypothesis Testing -- an application of central limit
• Lec05 Hypothesis Testing -- examples
• Lec04 How to use z-table

week 06 - ALL linear regressions you can build in Python. Intro to Naive Bayes == maximal likelihood estimation and Linear regression as its applicaiton (without proof, will prove later)

• Lec06 More Hypothesis Testing -- summarize double sided vs one sided p
• Lec06 Maximal Likelihood estimation -- Linear regression is a special example
• linear regression -- different descents methods
• linear regression using Theano
• linear regression with Cross Validation
• linear regression with Lasso
• linear regression with Ridge

week 07 - seaborn and Mixture model -- graphical representation of "Not so naive Bayes". Review

• Lab07 linespace vs arrange; Python plot "density" does not work
• Lab07 Frequency stats visualization and calculations
• Lab07 First mixture model and seaborn is a good plot tool

week 08 -- spring break

week 09 -- Monte Carlo, rejection sampling, importance sampling. More maximal likelihood estimation.

• lab09 Monte Carlo
• Lab09 An example to see variance and acceptance rate using: Monte Carlo, Rejection sampling (w/o Steroids), Importance sampling
• Lab09 Importance sampling -- use caution

week 10 -- Errors: Monte Carlo, Trapezoid Rule, Left integration. Detailed proof of linear regression as MLE.

• Lab10 Compare variance amount "Monte Carlo, Trapezoid Rule, Left integration"
• Lec10 Linear regression as MLE.

week 11 -- Timing code and Matrix operations in Python (numpy is faster). Markov Chain.

• Lab11 Matrices in Python
• Lab11 Tming your code
• Lec11 Markov Chain

week 12 -- properties of different states of Markov chains

• Lab12 Markov Chain Simulation and Recursion properties
• Lab12 When to round your answer for stable matrices?
• Lec12 Markov Chain: different states properties: transient, recurrent or absorbing

week 13 -- Determine Chain types by simulation in Python and by graph operation. Calculate time to absorption and probability.

• Lec13 Determine if a markov chain is an absorbing
• Lab13 A whole process of determining if a chain is absorbing, if so find time and probability of absorption

week 14 -- Ergodic Markov Chain

• Lec14 Ergodic Markov Chain, Random Walks