Mathematics for Machine Learning and Data Science

  1. Statistics: From Data to Insights
    1. Descriptive Statistics
      1. Measures of Central Tendency
        1. Arithmetic Mean
          1. Median
            1. Mode
              1. Geometric Mean
                1. Harmonic Mean
                  1. Trimmed Mean
                  2. Measures of Dispersion
                    1. Range
                      1. Variance
                        1. Standard Deviation
                          1. Interquartile Range
                            1. Mean Absolute Deviation
                              1. Coefficient of Variation
                              2. Measures of Shape
                                1. Skewness
                                  1. Kurtosis
                                    1. Box Plots and Outlier Detection
                                    2. Quantiles and Percentiles
                                      1. Definition and Computation
                                        1. Five-Number Summary
                                          1. Quartiles and Deciles
                                          2. Data Visualization
                                            1. Histograms
                                              1. Box Plots
                                                1. Scatter Plots
                                                  1. Bar Charts
                                                    1. Pie Charts
                                                      1. Stem-and-Leaf Plots
                                                        1. Q-Q Plots
                                                      2. Sampling and Sampling Distributions
                                                        1. Population vs Sample
                                                          1. Sampling Methods
                                                            1. Simple Random Sampling
                                                              1. Stratified Sampling
                                                                1. Cluster Sampling
                                                                  1. Systematic Sampling
                                                                  2. Sampling Distribution of the Mean
                                                                    1. Properties and Characteristics
                                                                      1. Standard Error
                                                                      2. Sampling Distribution of Proportions
                                                                        1. Bootstrap Methods
                                                                          1. Bootstrap Sampling
                                                                            1. Bootstrap Confidence Intervals
                                                                          2. Point Estimation
                                                                            1. Estimators and Estimates
                                                                              1. Definition and Notation
                                                                                1. Sample Statistics as Estimators
                                                                                2. Properties of Estimators
                                                                                  1. Bias and Unbiasedness
                                                                                    1. Variance and Efficiency
                                                                                      1. Mean Squared Error
                                                                                        1. Consistency
                                                                                          1. Sufficiency
                                                                                          2. Method of Moments
                                                                                            1. Principle and Application
                                                                                            2. Maximum Likelihood Estimation
                                                                                              1. Likelihood Function
                                                                                                1. Log-Likelihood Function
                                                                                                  1. MLE Properties
                                                                                                    1. Computing MLEs
                                                                                                      1. Asymptotic Properties
                                                                                                      2. Bayesian Estimation
                                                                                                        1. Prior and Posterior Distributions
                                                                                                          1. Maximum A Posteriori Estimation
                                                                                                            1. Credible Intervals
                                                                                                          2. Interval Estimation
                                                                                                            1. Confidence Intervals
                                                                                                              1. Definition and Interpretation
                                                                                                                1. Confidence Level vs Confidence Coefficient
                                                                                                                  1. Construction Methods
                                                                                                                  2. Confidence Intervals for Means
                                                                                                                    1. Known Variance Case
                                                                                                                      1. Unknown Variance Case
                                                                                                                        1. Small Sample Sizes
                                                                                                                        2. Confidence Intervals for Proportions
                                                                                                                          1. Large Sample Approximation
                                                                                                                            1. Exact Methods
                                                                                                                            2. Confidence Intervals for Variance
                                                                                                                              1. Bootstrap Confidence Intervals
                                                                                                                              2. Hypothesis Testing
                                                                                                                                1. Fundamentals of Hypothesis Testing
                                                                                                                                  1. Null and Alternative Hypotheses
                                                                                                                                    1. Test Statistics
                                                                                                                                      1. Critical Regions
                                                                                                                                        1. Decision Rules
                                                                                                                                        2. Types of Errors
                                                                                                                                          1. Type I Error
                                                                                                                                            1. Type II Error
                                                                                                                                              1. Power of a Test
                                                                                                                                                1. Relationship Between Errors
                                                                                                                                                2. Significance Level and p-values
                                                                                                                                                  1. Definition of Significance Level
                                                                                                                                                    1. p-value Interpretation
                                                                                                                                                      1. Relationship Between p-values and Significance
                                                                                                                                                      2. One-Sample Tests
                                                                                                                                                        1. z-test for Mean
                                                                                                                                                          1. t-test for Mean
                                                                                                                                                            1. Test for Proportion
                                                                                                                                                              1. Chi-square Test for Variance
                                                                                                                                                              2. Two-Sample Tests
                                                                                                                                                                1. Two-Sample z-test
                                                                                                                                                                  1. Two-Sample t-test
                                                                                                                                                                    1. Paired t-test
                                                                                                                                                                      1. Two-Sample Test for Proportions
                                                                                                                                                                        1. F-test for Equality of Variances
                                                                                                                                                                        2. Goodness-of-Fit Tests
                                                                                                                                                                          1. Chi-square Goodness-of-Fit Test
                                                                                                                                                                            1. Kolmogorov-Smirnov Test
                                                                                                                                                                            2. Tests of Independence
                                                                                                                                                                              1. Chi-square Test of Independence
                                                                                                                                                                                1. Fisher's Exact Test
                                                                                                                                                                                2. Multiple Testing
                                                                                                                                                                                  1. Multiple Comparisons Problem
                                                                                                                                                                                    1. Bonferroni Correction
                                                                                                                                                                                      1. False Discovery Rate
                                                                                                                                                                                    2. Regression Analysis
                                                                                                                                                                                      1. Simple Linear Regression
                                                                                                                                                                                        1. Model Assumptions
                                                                                                                                                                                          1. Least Squares Estimation
                                                                                                                                                                                            1. Properties of Estimators
                                                                                                                                                                                              1. Inference for Regression Parameters
                                                                                                                                                                                              2. Multiple Linear Regression
                                                                                                                                                                                                1. Model Specification
                                                                                                                                                                                                  1. Matrix Formulation
                                                                                                                                                                                                    1. Estimation and Inference
                                                                                                                                                                                                      1. Model Diagnostics
                                                                                                                                                                                                      2. Logistic Regression
                                                                                                                                                                                                        1. Logit Model
                                                                                                                                                                                                          1. Maximum Likelihood Estimation
                                                                                                                                                                                                            1. Interpretation of Coefficients
                                                                                                                                                                                                          2. Analysis of Variance
                                                                                                                                                                                                            1. One-Way ANOVA
                                                                                                                                                                                                              1. Model and Assumptions
                                                                                                                                                                                                                1. F-test for Equality of Means
                                                                                                                                                                                                                  1. Post-hoc Comparisons
                                                                                                                                                                                                                  2. Two-Way ANOVA
                                                                                                                                                                                                                    1. Main Effects and Interactions
                                                                                                                                                                                                                      1. Model Specification
                                                                                                                                                                                                                    2. Nonparametric Statistics
                                                                                                                                                                                                                      1. Sign Test
                                                                                                                                                                                                                        1. Wilcoxon Signed-Rank Test
                                                                                                                                                                                                                          1. Mann-Whitney U Test
                                                                                                                                                                                                                            1. Kruskal-Wallis Test
                                                                                                                                                                                                                              1. Spearman Rank Correlation
                                                                                                                                                                                                                              2. Bayesian vs Frequentist Approaches
                                                                                                                                                                                                                                1. Philosophical Differences
                                                                                                                                                                                                                                  1. Interpretation of Probability
                                                                                                                                                                                                                                    1. Parameter Estimation Approaches
                                                                                                                                                                                                                                      1. Hypothesis Testing Approaches
                                                                                                                                                                                                                                        1. Practical Considerations

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                                                                                                                                                                                                                                      6. Optimization Techniques for Machine Learning