Essential Math For Data Science Table Of Contents (CloudMonk.io)

Essential Math for Data Science by Thomas Nield Table of Contents



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Essential Math for Data Science by Thomas Nield Preface

1. Basic Math And Calculus Review


1. Basic Math And Calculus Review (EsMthDS 2022)
* Basic Math And Calculus Review

* Number Theory
* Order of Operations
* Variables
* Functions
* Summations
* Exponents
* Logarithms
* Euler’s Number and Natural Logarithms
* Natural Logarithms
* Limits
* Derivatives
* Partial Derivatives
* The Chain Rule
* Integrals
* Conclusion
* Exercises

2. Probability


2. Probability (EsMthDS 2022)

* Understanding Probability
* Probability versus Statistics
* Probability Math
* Joint Probabilities
* Union Probabilities
* Conditional Probability and Bayes Theorem
* Joint and Union Conditional Probabilities
* Binomial Distribution
* Beta Distribution
* Conclusion
* Exercises

3. Descriptive And Inferential Statistics


3. Descriptive And Inferential Statistics (EsMthDS 2022)
* Descriptive Statistics and Inferential Statistics

* 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 Cumulative Density Function (CDF)
* Inferential Statistics
* The Central Limit Theorem
* Confidence Intervals
* Understanding P-Values
* Hypothesis Testing
* The T-Distribution - Dealing with Small Samples
* Big Data Considerations and Texas Sharpshooter Fallacy
* Conclusions
* Exercises

4. Linear Algebra


4. Linear Algebra (EsMthDS 2022)

* 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
* Sparse Matrix
* Systems of Equations and Inverse Matrices
* Eigenvectors and Eigenvalues
* Conclusion
* Exercises


5. Linear Regression


5. Linear Regression (EsMthDS 2022)

* 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
* Conclusions
* Exercises


6. Logistic Regression And Classification


6. Logistic Regression And Classification (EsMthDS 2022)
* Logistic Regression and Classification

* 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 the Confusion Matrix
* Reciever Operator Characteristics (ROC)/Area Under Curve (AUC)
* Class Imbalance
* Conclusions
* Exercises


7. Neural Networks


7. Neural Networks (EsMthDS 2022)

* When to Use Neural Networks and Deep Learning
* A Simple Neural Network
* Activation Functions
* Forward Propogation
* Backpropogation
* Calculating the Weight and Bias Derivatives
* Stochastic Gradient Descent
* Using Scikit-learn
* Limitations of Neural Networks and Deep Learning
* Conclusions
* Exercise


8. Career Advice And The Path Forward


8. Career Advice And The Path Forward (EsMthDS 2022)
* Data Science and Machine Learning Career Advice And The Path Forward

* 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 Adviser
* 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


A. Appendix


A. Appendix (EsMthDS 2022)

* Using Latex Rendering with SymPy
* Binomial Distribution from Scratch
* Beta Distribution from Scratch
* Deriving Bayes Theorem
* CDF and Inverse CDF from Scratch
* Use e to Predict Event Probability Over Time
* Hill Climbing and Linear Regression
* Hill Climbing and Logistic Regression
* A Brief Intro to Linear Programming
* MNIST Classifier Using Scikit-learn
* B. Exercise Answers

About The Author


Thomas Nield

Fair Use Sources


Fair Use Source:
* 1098102932 (EsMthDS 2022)

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