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Essential Math for Data Science: Take Control of Your Data with Fundamental Linear Algebra, Probability, and Statistics [Pehme köide]

  • Formaat: Paperback / softback, 350 pages
  • Ilmumisaeg: 10-Jun-2022
  • Kirjastus: O'Reilly Media
  • ISBN-10: 1098102932
  • ISBN-13: 9781098102937
  • Pehme köide
  • Hind: 63,19 €*
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  • Formaat: Paperback / softback, 350 pages
  • Ilmumisaeg: 10-Jun-2022
  • Kirjastus: O'Reilly Media
  • ISBN-10: 1098102932
  • ISBN-13: 9781098102937

Master the math needed to excel in data science, machine learning, and statistics. In this book author Thomas Nield guides you through areas like calculus, probability, linear algebra, and statistics and how they apply to techniques like linear regression, logistic regression, and neural networks. Along the way you'll also gain practical insights into the state of data science and how to use those insights to maximize your career.

Learn how to:

  • Use Python code and libraries like SymPy, NumPy, and scikit-learn to explore essential mathematical concepts like calculus, linear algebra, statistics, and machine learning
  • Understand techniques like linear regression, logistic regression, and neural networks in plain English, with minimal mathematical notation and jargon
  • Perform descriptive statistics and hypothesis testing on a dataset to interpret p-values and statistical significance
  • Manipulate vectors and matrices and perform matrix decomposition
  • Integrate and build upon incremental knowledge of calculus, probability, statistics, and linear algebra, and apply it to regression models including neural networks
  • Navigate practically through a data science career and avoid common pitfalls, assumptions, and biases while tuning your skill set to stand out in the job market

Preface ix
1 Bask Math and Calculus Review
1(40)
Number Theory
2(1)
Order of Operations
3(2)
Variables
5(1)
Functions
6(5)
Summations
11(2)
Exponents
13(3)
Logarithms
16(2)
Euler's Number and Natural Logarithms
18(1)
Euler's Number
18(3)
Natural Logarithms
21(1)
Limits
22(2)
Derivatives
24(4)
Partial Derivatives
28(3)
The Chain Rule
31(2)
Integrals
33(6)
Conclusion
39(1)
Exercises
39(2)
2 Probability
41(22)
Understanding Probability
42(1)
Probability Versus Statistics
43(1)
Probability Math
44(1)
Joint Probabilities
44(1)
Union Probabilities
45(2)
Conditional Probability and Bayes' Theorem
47(2)
Joint and Union Conditional Probabilities
49(2)
Binomial Distribution
51(2)
Beta Distribution
53(7)
Conclusion
60(1)
Exercises
61(2)
3 Descriptive and Inferential Statistics
63(46)
What Is Data?
63(2)
Descriptive Versus Inferential Statistics
65(1)
Populations, Samples, and Bias
66(3)
Descriptive Statistics
69(1)
Mean and Weighted Mean
70(1)
Median
71(2)
Mode
73(1)
Variance and Standard Deviation
73(5)
The Normal Distribution
78(7)
The Inverse CDF
85(2)
Z-Scores
87(2)
Inferential Statistics
89(1)
The Central Limit Theorem
89(3)
Confidence Intervals
92(3)
Understanding P-Values
95(1)
Hypothesis Testing
96(8)
The T-Distribution: Dealing with Small Samples
104(1)
Big Data Considerations and the Texas Sharpshooter Fallacy
105(2)
Conclusion
107(1)
Exercises
107(2)
4 Linear Algebra
109(38)
What Is a Vector?
110(4)
Adding and Combining Vectors
114(2)
Scaling Vectors
116(3)
Span and Linear Dependence
119(2)
Linear Transformations
121(1)
Basis Vectors
121(3)
Matrix Vector Multiplication
124(5)
Matrix Multiplication
129(2)
Determinants
131(5)
Special Types of Matrices
136(1)
Square Matrix
136(1)
Identity Matrix
136(1)
Inverse Matrix
136(1)
Diagonal Matrix
137(1)
Triangular Matrix
137(1)
Sparse Matrix
138(1)
Systems of Equations and Inverse Matrices
138(4)
Eigenvectors and Eigenvalues
142(3)
Conclusion
145(1)
Exercises
146(1)
5 Linear Regression
147(46)
A Basic Linear Regression
149(4)
Residuals and Squared Errors
153(4)
Finding the Best Fit Line
157(1)
Closed Form Equation
157(1)
Inverse Matrix Techniques
158(3)
Gradient Descent
161(6)
Overfitting and Variance
167(2)
Stochastic Gradient Descent
169(2)
The Correlation Coefficient
171(3)
Statistical Significance
174(5)
Coefficient of Determination
179(1)
Standard Error of the Estimate
180(1)
Prediction Intervals
181(4)
Train/Test Splits
185(6)
Multiple Linear Regression
191(1)
Conclusion
191(1)
Exercises
192(1)
6 Logistic Regression and Classification
193(34)
Understanding Logistic Regression
193(3)
Performing a Logistic Regression
196(1)
Logistic Function
196(2)
Fitting the Logistic Curve
198(6)
Multivariable Logistic Regression
204(4)
Understanding the Log-Odds
208(3)
R-Squared
211(5)
P-Values
216(2)
Train/Test Splits
218(1)
Confusion Matrices
219(3)
Bayes' Theorem and Classification
222(1)
Receiver Operator Characteristics/Area Under Curve
223(2)
Class Imbalance
225(1)
Conclusion
226(1)
Exercises
226(1)
7 Neural Networks
227(30)
When to Use Neural Networks and Deep Learning
228(1)
A Simple Neural Network
229(2)
Activation Functions
231(6)
Forward Propagation
237(6)
Backpropagation
243(1)
Calculating the Weight and Bias Derivatives
243(5)
Stochastic Gradient Descent
248(3)
Using scikit-learn
251(2)
Limitations of Neural Networks and Deep Learning
253(3)
Conclusion
256(1)
Exercise
256(1)
8 Career Advice and the Path Forward
257(30)
Redefining Data Science
258(2)
A Brief History of Data Science
260(3)
Finding Your Edge
263(1)
SQL Proficiency
263(3)
Programming Proficiency
266(3)
Data Visualization
269(1)
Knowing Your Industry
270(2)
Productive Learning
272(1)
Practitioner Versus Advisor
272(3)
What to Watch Out For in Data Science Jobs
275(1)
Role Definition
275(1)
Organizational Focus and Buy-In
276(2)
Adequate Resources
278(1)
Reasonable Objectives
279(1)
Competing with Existing Systems
280(2)
A Role Is Not What You Expected
282(1)
Does Your Dream Job Not Exist?
283(1)
Where Do I Go Now?
284(1)
Conclusion
285(2)
A Supplemental Topics 287(22)
B Exercise Answers 309(14)
Index 323
Thomas Nield is the founder of Nield Consulting Group as well as an instructor at O'Reilly Media and University of Southern California. He enjoys making technical content relatable and relevant to those unfamiliar or intimidated by it. Thomas regularly teaches classes on data analysis, machine learning, mathematical optimization, and practical artificial intelligence. He's authored two books, including Getting Started with SQL (O'Reilly) and Learning RxJava (Packt).