Essential Math for Data Science E-Learning

Mathematics form the foundation for Machine Learning algorithms and Data Science, necessary for working and research in the Data Science field. Many Data Science elements depend on mathematical concepts such as probability, statistics, calculus, linear algebra, and so on. Hence, it is important for data scientists, to under-stand the principles of these concepts and how these principles might affect their models and day-to-day tasks.

In this Essential Math for Data Science Learning Kit, you will explore important concepts of mathematics that form the foundation for Machine Learning algorithms, Data Science and Artificial Intelligence..

Learning Kits are structured learning paths, mainly within the Emerging Tech area. A Learning Kit keeps
the student working toward an overall goal, helping them to achieve your career aspirations. Each part takes the student step by step through a diverse set of topic areas. Learning Kits are made up of required tracks, which contain all of the learning resources available such as Assessments (Final Exams), Mentor, Practice Labs and of course E learning. And all resources with a 365 days access from first activation.

This Learning Kit, with more than 45 hours of online content, is divided into the following tracks:

Course content

Track 1: Introduction to Math

In this track, you will focus on the fundamentals of linear algebra and calculus. This includes discrete math concepts and their implementations, theoretical and practical guide to calculus, exploring linear algebra, and matrix operations.
Courses (12 hours +):

Math & Optimizations: Introducing Sets & Set Operations

Course: 1 Hour

• Course Overview
• Comparing Discrete Data and Discrete Mathematics
• Sets and Set Operations
• Creating and Working with Sets
• Performing Union and Intersection
• Computing Difference and Symmetric Difference
• Understanding Subsets and Supersets
• Course Summary

Math & Optimizations: Introducing Graphs & Graph Operations

Course: 1 Hour, 34 Minutes

• Course Overview
• Components of Graphs
• Types of Graphs
• Creating Undirected Graphs Using NetworkX
• Adding Attributes to Graphs Nodes and Edges
• Creating Directed Graphs Using NetworkX
• Computing Degree of a Node
• Understanding Predecessors and Successors
• Computing Simple Cycles, Triangles, and Edge Covers
• Performing Topological Sort
• Computing Shortest Path and Minimum Spanning Tree
• Course Summary

Math & Optimizations: Solving Optimization Problems Using Linear Programming

Course: 1 Hour, 32 Minutes

• Course Overview
• Understanding the Importance of Optimization
• Objectives, Decision Variables, and Constraints
• Optimal Solution and Feasible Solutions6
• Linear Programming
• Case Study: Happy Pet Food
• Solving the Problem Formulation Graphically
• An Overview of the Simplex Method
• Using the SciPy Library to Minimize Cost
• Using the SciPy Library to Maximize Profit
• Solving Linear Programming Problems
• Course Summary

Math & Optimizations: Solving Optimization Problems Using Integer Programming

Course: 57 Minutes

• Course Overview
• Understanding the Importance of Optimization
• Objectives, Decision Variables, and Constraints
• Optimal Solution and Feasible Solutions
• Linear Programming
• Case Study: Happy Pet Food
• Solving the Problem Formulation Graphically
• An Overview of the Simplex Method
• Using the SciPy Library to Minimize Cost
• Using the SciPy Library to Maximize Profit
• Solving Linear Programming Problems
• Course Summary

Calculus: Getting Started with Derivatives

Course: 1 Hour, 13 Minutes

• Course Overview
• Differentiation and Derivatives
• Calculating the Slope between Two Points
• Calculating the Slope at a Point
• Applying Derivatives
• Understanding Differential Equations and Differences
• Computing Derivatives of Constant Functions
• Computing Derivatives of Linear Functions
• Calculating Derivatives with Built-in Functions
• Course Summary

Calculus: Derivatives with Linear and Quadratic Functions & Partial Derivatives

Course: 1 Hour, 26 Minutes

• Course Overview
• Calculating Derivatives on Linear Functions with Built-in Functions
• Interpreting the Derivative as the Slope of a Tangent Line
• Interpreting the Velocity of an Accelerating Particle
• Modeling Velocity and Trajectory
• Partial Derivatives
• Computing Partial Derivatives
• Performing More Partial Derivative Computations
• Training Neural Networks with Partial Derivatives
• Course Summary

Calculus: Understanding Integration

Course: 1 Hour, 4 Minutes

• Course Overview
• Getting Familiar with Integration
• Differentiating Between Definite and Indefinite Integrals
• Comparing Derivatives and Integrals
• Computing Integrals
• Integrating Constant and Linear Functions
• Integrating Sine and Cosine Functions
• Integrating Quadratic and Polynomial Functions
• Course Summary

Essential Maths: Exploring Linear Algebra

Course: 1 Hour, 51 Minutes

• Course Overview
• An Overview of Linear Algebra
• Vectors with Different Notations
• Vector Operations
• Matrices and Matrix Operations
• Adding Matrices Element-wise
• Performing Matrix Multiplication
• Computing Determinants and Transposing Matrices
• Defining and Identifying Diagonal Matrices
• Computing the Inverse of a Matrix
• Using SciPy to Work with Matrices
• Understanding Properties of Matrices
• Course Summary

Matrix Decomposition: Getting Started with Matrix Decomposition

Course: 1 Hour, 20 Minutes

• Course Overview
• Vectors and Notation
• Linear Transformations with Matrices
• Matrix Types
• Matrix Decomposition
• QR and Cholesky Decomposition
• Getting Set Up in Python
• Performing LU Decomposition in Python
• Performing QR Decomposition in Python
• Performing Cholesky Decomposition in Python
• Course Summary

Matrix Decomposition: Using Eigendecomposition & Singular Value Decomposition

Course: 1 Hour, 30 Minutes

• Course Overview
• The Purpose of Eigenvectors and Eigenvalues
• Applying a Change of Basis Vectors
• Visualizing Eigenvectors and Eigenvalues
• Deriving the Characteristic Equation
• Computing Eigenvectors and Eigenvalues
• Exploring Properties of Eigenvalues and Eigenvectors
• Diagonalizing Matrices
• Eigendecomposition vs. Singular Value Decomposition
• Using Singular Value Decomposition with a Matrix
• Importing an Image for Singular Value Decomposition
• Performing Singular Value Decomposition on an Image
• Course Summary
• Privacy and Cookie PolicyTerms of Use

Final Exam: Introduction to Math

This assessment will test your knowledge and application of the topics presented throughout the track.

Track 2: Statistics and Probability

In this track, you will acquire a deeper understanding of probability and statistical concepts including probability distributions, various types of statistical tests, and hypothesis testing. You will deep dive into understanding conditional probability concepts that forms the crux of naïve Bayes classification algorithms.
Courses (17 hours +)

Core Statistical Concepts: An Overview of Statistics & Sampling

Course: 50 Minutes

• Course Overview
• Working with Statistical Data
• Measures of Central Tendency
• Measures of Dispersion
• Sampling Techniques
• Working with Imbalanced Data
• Course Summary

Core Statistical Concepts: Statistics & Sampling with Python

Course: 1 Hour, 40 Minutes

• Course Overview
• Installing pandas and Data Visualization Modules
• Loading and Analyzing Data Using pandas
• Computing the Mean and Median of a Distribution
• Visualizing Distributions with Seaborn & Matplotlib
• Computing Variance and Standard Deviation
• Generating Random and Stratified Samples
• Implementing Cluster and Systematic Sampling
• Implementing Undersampling and Oversampling
• Oversampling with SMOTE
• Course Summary

Probability Theory: Getting Started with Probability

Course: 58 Minutes

• Course Overview
• Probability and Random Variables
• Events and Types of Events
• Installing Modules
• Simulating Trials to Flip a Coin
• Simulating Trials to Roll a Die
• Simulating Trials to Pick Marbles at Random
• Course Summary

Probability Theory: Understanding Joint, Marginal, & Conditional Probability

Course: 1 Hour, 42 Minutes

• Course Overview
• Joint, Marginal, and Conditional Probability
• Components of Marginal and Conditional Probability
• Chained Rule and Joint Probability of Events
• Calculating Marginal Probabilities
• Applying the Chain Rule to Conditional Probabilities
• Computing Joint Probabilities on Dice Rolls
• Exploring Joint Probability with Dependent Variables
• Computing Marginal and Conditional Probabilities with Dependent Variables
• Defining the Expected Value of a Random Variable
• Computing Expected Value of a Random Variable
• Computing Expected Value of a Dice Roll
• Course Summary

Probability Theory: Creating Bayesian Models

Course: 1 Hour, 50 Minutes

• Course Overview
• Bayes Theorem
• Bayesian Networks
• Using the Chain Rule with Bayesian Networks
• Creating a Bayesian Network Model
• Associating Probabilities with Bayesian Networks
• Computing Probabilities from Bayesian Networks
• Creating Bayesian Machine Learning Models
• Predicting Values Using a Bayesian Model
• Interpreting Probabilities Generated by Bayesian Models
• Understanding and Creating Naive Bayes Models
• Testing Naive Bayes Machine Learning Models
• Course Summary

Probability Distributions: Getting Started with Probability Distributions

Course: 1 Hour, 31 Minutes

• Course Overview
• Getting Familiar with Statistics
• Populations and Samples
• Types of Probability Distributions
• Statistical Terminology
• Installing Python Libraries to Analyze Data
• Visualizing Data with Box Plots
• Exploring Distributions with Charts
• Generating Confidence Intervals
• Measuring Parameters with Confidence Intervals
• Understanding Skewness and Kurtosis
• Computing Skewness and Kurtosis
• Course Summary

Probability Distributions: Uniform, Binomial, & Poisson Distributions

Course: 1 Hour, 33 Minutes

• Course Overview
• Generating Uniform Distributions
• Exploring the CDF, PDF, and PPF Functions
• Generating and Sampling Uniform Data
• Generating Binomial Distributions
• Using Binomial Distributions
• Performing Computations on Binomial Distributions
• Using Poisson Distribution
• Exploring Functions for Poisson Distributions
• Applying Poisson Distributions
• Course Summary

Probability Distributions: Understanding Normal Distributions

Course: 1 Hour, 7 Minutes

• Course Overview
• Working with Normal Distributions
• Exploring Mean and SD of Normal Distributions
• Computing the CDF for Various Normal Distributions
• Analyzing the Symmetry of Normal Distributions
• Understanding the Law of Large Numbers
• Exploring the Central Limit Theorem
• Course Summary

Statistical & Hypothesis Tests: Getting Started with Hypothesis Testing

Course: 56 Minutes

• Course Overview
• Introducing Statistics
• Introducing Hypothesis Testing
• The Null Hypothesis and the Alternative Hypothesis
• P-values and Alpha Levels
• Introducing T-tests
• Errors in Hypothesis Testing
• Performing ANOVA Analysis
• Course Summary

Statistical & Hypothesis Tests: Using the One-sample T-test

Course: 1 Hour, 42 Minutes

• Course Overview
• Installing Modules
• Setting up a Manual One-sample T-test
• Performing T-tests Using Different Libraries
• Performing T-tests on Data with Different Distributions
• Testing for Normal Distributions Using Statistical Tests
• Exploring T-tests with Real-world Examples
• Using Single-sided T-tests
• Running the Wilcoxon Signed-rank Test
• Comparing Medians Using the Wilcoxon Signed-rank Test
• Course Summary

Statistical & Hypothesis Tests: Performing Two-sample T-tests & Paired T-tests

Course: 2 Hours, 12 Minutes

• Course Overview
• Introducing the Two-sample T-test
• Performing Levene's Test
• Comparing Means Using the Two-sample T-test9
• Understanding Welch's T-test
• Comparing Means Using Welch's T-test
• Understanding Type I and Type II Errors
• Exploring Type I Errors and Alpha Levels
• Exploring Type II Errors and Alpha Levels
• Introducing the Paired Difference T-test
• Preparing Data for the Paired T-test
• Using Paired T-tests
• Comparing Before and After Data with Paired T-tests
• Course Summary

Statistical & Hypothesis Tests: Using Non-parametric Tests & ANOVA Analysis

Course: 2 Hours, 18 Minutes

• Course Overview
• Understanding the Mann-Whitney U-test
• Comparing Categories with the Mann-Whitney U-test
• Using the Paired Wilcoxon Signed-rank Test
• Comparing Paired T-test & Wilcoxon Signed-rank Test
• Understanding Pairwise T-tests
• Comparing Values across Groups with Pairwise T-tests
• Understanding One-way ANOVA
• Performing One-way ANOVA and Linear Regression
• Performing the Post-hoc Tukey's HSD Test
• Checking ANOVA Residuals' Assumptions
• Using the Kruskal-Wallis Test
• Understanding Two-way ANOVA
• Performing Two-way ANOVA with Interaction
• Course Summary

Final Exam: Statistics and Probability
This assessment will test your knowledge and application of the topics presented throughout the track.

Track 3: Math Behind ML Algorithms

In this track, the focus will be on math applied in various machine learning algorithms. You will understand the intuition behind these algorithms along with math used in their optimization/loss/cost functions. You will understand the math behind regression algorithms, decision trees, distance-based models, kernel methods and SVM and neural networks.
Courses (12 hours +)

Regression Math: Getting Started with Linear Regression

Course: 1 Hour, 42 Minutes

• Course Overview
• Regression and Prediction
• Residuals in Regression
• The Computation of "The Best Fit"
• Partial Derivatives with Regression Models
• Calculating R-squared
• The Normal Equation
• Setting up Data and Viewing Correlations
• Splitting Data for Regression
• Defining the Slope and Intercept for Regression
• Creating a Regression Line and Predictions
• Viewing the Performance of a Regression Model
• Performing Regression with Built-in Modules
• Course Summary

Regression Math: Using Gradient Descent & Logistic Regression

Course: 1 Hour, 43 Minutes

• Course Overview
• How Gradient Descent Works
• What Gradients Are Used For
• Computing Gradient Descent
• Setting up Data for Gradient Descent
• Defining an Epoch Manually
• Performing Gradient Descent Manually
• How Logistic Regression Works
• Computing an S-curve
• Viewing Correlations for Logistic Regression
• Splitting and Shaping Data for Logistic Regression
• Performing Logistic Regression with Gradient Descent
• Course Summary

The Math Behind Decision Trees: An Exploration of Decision Trees

Course: 2 Hours, 8 Minutes

• Course Overview
• How Classification Is Used
• Comparing Rule-based and ML-based Models
• How Decision Trees Work
• Building a Rule-based Decision Tree
• How Entropy Works
• How Entropy and Information Gain Work Together
• How GINI Impurity Works
• Deciding Splits Based on GINI Impurity
• Setting up Datasets
• Imagine a Rule-based Decision Tree
• Creating a Basic Decision Tree
• Working with Decision Trees and Continuous Data
• Plotting a Decision Tree in a Tree Diagram
• Defining the Rules for a Rule-based Decision Tree
• Training an ML-based Decision Tree
• Testing an ML-based Decision Tree9 MinutesCompletedActions
• Course Summary

Distance-based Models: Overview of Distance-based Metrics & Algorithms

Course: 1 Hour, 13 Minutes

• Course Overview
• How Distance-based Models Work
• Specialized Distance Metrics
• Algorithms Based on Distance Metrics
• Plotting Points in Two Dimensions
• Computing Euclidean and Manhattan Distances
• Calculating Minkowski and Hamming Distances
• Measuring Cosine Distances
• Course Summary

Distance-based Models: Implementing Distance-based Algorithms

Course: 1 Hour, 13 Minutes

• Course Overview
• Analyzing Data to be Classified
• Building a KNN Classifier
• Testing and Evaluating a KNN Classifier
• Building a KNN Regressor
• Testing and Evaluating a KNN Regressor
• Computing Centroids and Clusters
• Building and Evaluating a K-Means Model
• Course Summary

Support Vector Machine (SVM) Math: A Conceptual Look at Support Vector Machines

Course: 59 Minutes

• Course Overview
• Support Vector Machines (SVMs) in Machine Learning
• SVMs, Data Classification, and Hyperplanes
• SVMs, Scaling, and Soft and Hard Margins
• Working with Non-linear Data
• The Optimization Problem for SVMs
• Optimizing a Soft-margin Classifier
• Course Summary

Support Vector Machine (SVM) Math: Building & Applying SVM Models in Python

Course: 1 Hour, 34 Minutes

• Course Overview
• Generating Data for Binary Classification
• Preparing Data for an SVM Classifier
• Training and Evaluating an SVM Model
• Analyzing a Dataset for a Binary Classifier
• Visualizing the Relationships between Features
• Training and Evaluating the LIBSVM Classifier
• Analyzing the Data for Support Vector Regression
• Building a Support Vector Regressor
• Course Summary

Neural Network Mathematics: Understanding the Mathematics of a Neuron

Course: 53 Minutes

• Course Overview
• The Architecture and Components of Neural Networks
• The Math behind Neurons
• Installing Python Modules
• Performing Linear Transformation
• Processing Data in Batches
• Course Summary

Neural Network Mathematics: Exploring the Math behind Gradient Descent

Course: 1 Hour, 54 Minutes

• Course Overview
• The Intuition behind Gradient Descent
• Computing Gradients
• Activation Functions
• Visualizing Common Activation Functions
• Visualizing the ReLU Function and Its Variants
• Mitigating Issues in Neural Network Training
• Simple Regression Using TensorFlow
• Learning Rate and Number of Epochs
• Exploring Datasets and Setting up Utilities
• Training a Simple Neural Network from Scratch
• Course Summary

Final Exam: Math Behind ML Algorithms

This assessment will test your knowledge and application of the topics presented throughout the track.

Track 4: Advanced Math

In this module, the focus will be on statistical analysis and modeling in R. Explore probability distributions, statistical tests, regression analysis, clustering, and regularized models.
Courses (2 hours +)

ML & Dimensionality Reduction: Performing Principal Component Analysis

Course: 1 Hour, 16 Minutes

• Course Overview
• Linear Transformations of Vectors
• Change of Basis, The Intuition behind PCA
• An Explanation of Principal Components
• A Quick Exploration of Eigenvectors and Eigenvalues
• Computing Principal Components
• Computing Eigenvectors and Eigenvalues
• Calculating Principal Components
• Building a Baseline Classification Model
• Training a Model Using Principal Components
• Course Summary

Recommender Systems: Under the Hood of Recommendation Systems

Course: 1 Hour, 23 Minutes

• Course Overview
• Uses and Categories of Recommendation Systems
• The Collaborative Filtering Technique
• How to Work with Matrix Factorization
• Using Matrix Factorization with Gradient Descent
• Introducing a Regularization Term to Matrices
• Preparing the Ratings Matrix
• Decomposing a Ratings Matrix
• Estimating Ratings Using Gradient Descent
• Course Summary

Final Exam: Advanced Math

This assessment will test your knowledge and application of the topics presented throughout the track.