Introduction to Data Science for Mechanical Engineers (Lecture Book)
Preface
Lecture 1: Introduction
What is data science?
Some cool appliations of data science in mechanical engineering
Why Python?
Python expressions
Python variables and types
Homework 1
Lecture 2: Data arrays
Python tuples
Python lists
Numerical Python
Homework 2
Lecture 3: Data loading and selection
Matrices
Comma-separated values file format
The Python data analysis library
Homework 3
Lecture 4: Data visualization
Plotting simple functions
Plotting noisy measurements
Scatter plots
Histograms
Homework 4
Lecture 5: Functions, data manipulation, and models
Basics of strings
The print function
Python functions
Applying functions to dataframes
Models are functions
Homework 5
Lecture 6: Conditionals and loops
Python conditionals
Python loops
Selecting dataframe rows that satisfy a boolean expression
Homework 6
Lecture 7: Probability as a measure of uncertainty
Probability as a representation of our state of knowledge
The common sense assumptions that give rise to the basic probability rules.
The principle of insufficient reason
Estimating probabilities by simulation
Estimating probabilities from data - Bootstrapping
Homework 7
Lecture 8: The basic rules of probability
The basic rules of probability
Example - Drawing balls from a box without replacement
Probability of logical disjunctions
The sum rule
Example - Drawing balls from a box without replacement (sum rule)
Example - Drawing balls from a box without replacement (information flow)
Homework 8
Lecture 9: Discrete random variables
Discrete Random variables
The probability mass function
The Bernoulli distribution
Properties of the probability mass function
The Categorical distribution
The Binomial Distribution
The Poisson distribution
Homework 9
Lecture 10: Continuous random variables
Continuous random variables
Example: Uncertainties in steel ball manufacturing
The cumulative distribution function
The probability density function
The uniform distribution
Homework 10
Lecture 11: Expectations, variances, and their properties
Expectation of discrete random variables
Examples of expectations of discrete random variables
Expectation of a continuous random variable
Simplifying our notation about expectations
Properties of expectations
Variance of a random variable
Properties of variance
Examples of variances of random variables
Homework 11
Lecture 12: The Normal distribution, quantiles, and credible intervals
The standard Normal distribution
Quantiles of the standard Normal
The Normal distribution
Quantiles of the Normal
Fitting Normal distributions to data
Homework 12
Lecture 13: Fitting models with the principle of maximum likelihood
The joint probability density function
Repeated independent experiments
The maximum likelihood principle
Fitting the parameters of a Normal using the maximum likelihood principle
Fitting the Bernoulli with maximum likelihood
Predictive checking
Homework 13
Lecture 14: Covariance, correlation, and linear regression with one variable
Covariance between two random variables
Correlation between two random variables
Correlation is not causation
Two uncorrelated random variables are not necessarily independent
Linear regression with one variable
Homework 14
Lecture 15: Linear regression
Regression with one variable revisited
Example: Linear regression with a single variable
Polynomial Regression
The generalized linear model
Measures of Predictive Accuracy
Cross validation for selecting the number of basis functions
Maximum likelihood interpretation of least squares
Example: Regression with estimated measurement noise
Homework 15
Lecture 16: Classification via logistic regression
Logistic regression
Example: Logistic regression with one variable (High melting explosives)
Logistic regression with many features
Diagnostics for Classification
Homework 16
Bibliography
Index