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Preface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
1. Basic Math and Calculus Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Number Theory
Order of Operations
Variables
Functions
Summations
Exponents
Logarithms
Euler’s Number and Natural Logarithms
Euler’s Number
Natural Logarithms
Limits
Derivatives
Partial Derivatives
The Chain Rule
Integrals
Conclusion
Exercises
2
3
5
6
11
13
16
18
18
21
22
24
28
31
33
39
39
2. Probability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Understanding Probability
Probability Versus Statistics
Probability Math
Joint Probabilities
Union Probabilities
Conditional Probability and Bayes’ Theorem
Joint and Union Conditional Probabilities
42
43
44
44
45
47
49
v
Binomial Distribution
Beta Distribution
Conclusion
Exercises
51
53
60
61
3. Descriptive and Inferential Statistics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
What Is Data?
Descriptive Versus Inferential Statistics
Populations, Samples, and Bias
Descriptive Statistics
Mean and Weighted Mean
Median
Mode
Variance and Standard Deviation
The Normal Distribution
The Inverse CDF
Z-Scores
Inferential Statistics
The Central Limit Theorem
Confidence Intervals
Understanding P-Values
Hypothesis Testing
The T-Distribution: Dealing with Small Samples
Big Data Considerations and the Texas Sharpshooter Fallacy
Conclusion
Exercises
63
65
66
69
70
71
73
73
78
85
87
89
89
92
95
96
104
105
107
107
4. Linear Algebra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
What Is a Vector?
Adding and Combining Vectors
Scaling Vectors
Span and Linear Dependence
Linear Transformations
Basis Vectors
Matrix Vector Multiplication
Matrix Multiplication
Determinants
Special Types of Matrices
Square Matrix
Identity Matrix
Inverse Matrix
Diagonal Matrix
Triangular Matrix
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110
114
116
119
121
121
124
129
131
136
136
136
136
137
137
Sparse Matrix
Systems of Equations and Inverse Matrices
Eigenvectors and Eigenvalues
Conclusion
Exercises
138
138
142
145
146
5. Linear Regression. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
A Basic Linear Regression
Residuals and Squared Errors
Finding the Best Fit Line
Closed Form Equation
Inverse Matrix Techniques
Gradient Descent
Overfitting and Variance
Stochastic Gradient Descent
The Correlation Coefficient
Statistical Significance
Coefficient of Determination
Standard Error of the Estimate
Prediction Intervals
Train/Test Splits
Multiple Linear Regression
Conclusion
Exercises
149
153
157
157
158
161
167
169
171
174
179
180
181
185
191
191
192
6. Logistic Regression and Classification. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
Understanding Logistic Regression
Performing a Logistic Regression
Logistic Function
Fitting the Logistic Curve
Multivariable Logistic Regression
Understanding the Log-Odds
R-Squared
P-Values
Train/Test Splits
Confusion Matrices
Bayes’ Theorem and Classification
Receiver Operator Characteristics/Area Under Curve
Class Imbalance
Conclusion
Exercises
193
196
196
198
204
208
211
216
218
219
222
223
225
226
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7. Neural Networks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
When to Use Neural Networks and Deep Learning
A Simple Neural Network
Activation Functions
Forward Propagation
Backpropagation
Calculating the Weight and Bias Derivatives
Stochastic Gradient Descent
Using scikit-learn
Limitations of Neural Networks and Deep Learning
Conclusion
Exercise
228
229
231
237
243
243
248
251
253
256
256
8. Career Advice and the Path Forward. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
Redefining Data Science
A Brief History of Data Science
Finding Your Edge
SQL Proficiency
Programming Proficiency
Data Visualization
Knowing Your Industry
Productive Learning
Practitioner Versus Advisor
What to Watch Out For in Data Science Jobs
Role Definition
Organizational Focus and Buy-In
Adequate Resources
Reasonable Objectives
Competing with Existing Systems
A Role Is Not What You Expected
Does Your Dream Job Not Exist?
Where Do I Go Now?
Conclusion
258
260
263
263
266
269
270
272
272
275
275
276
278
279
280
282
283
284
285
A. Supplemental Topics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
B. Exercise Answers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
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