Course Chapters - Table of Contents

This course provides a comprehensive introduction to data science using Python, progressing from foundational concepts to advanced machine learning techniques. Each chapter includes interactive MicroSims to reinforce learning through hands-on experience.

Course Structure Overview

Duration: 10 weeks
Target Audience: Advanced high school students and college freshmen
Prerequisites: Basic algebra and introductory programming experience

Chapter Progression

Foundation Phase (Weeks 1-3)

Chapter 0: Setup

Python environment and Jupyter notebooks setup
Conda virtual environment configuration
Required package installation
Development environment best practices

Chapter 1: Foundations of Data Science

Introduction to data science and its applications
Setting up Python environment and Jupyter notebooks
First MicroSim: Exploring sample datasets
Basic data types and structures in Python
Understanding the data science workflow
Data science roles and career paths
Ethics and best practices in data science

Chapter 2: Data Exploration and Visualization

Loading and examining datasets with pandas
Creating basic plots with matplotlib
MicroSim: Interactive data visualization
Identifying patterns in data through visual exploration
Data profiling and quality assessment
Handling missing values and outliers
Exploratory data analysis techniques

Chapter 3: Data Visualization Techniques

Principles of effective data visualization
Matplotlib fundamentals and customization
Plotly for interactive visualizations
Statistical plots and distributions
Time series visualization
Multi-dimensional data representation
MicroSim: Visualization parameter explorer

Statistical Foundation Phase (Weeks 4-5)

Chapter 4: Statistical Foundations

Descriptive statistics and summary measures
Understanding distributions and variability
MicroSim: Statistical parameter exploration
Introduction to probability concepts
Central limit theorem and sampling distributions
Hypothesis testing fundamentals
Correlation vs. causation

Chapter 5: Simple Linear Regression

Mathematical foundations of linear regression
Implementing regression from scratch
MicroSim: Interactive regression line fitting
Interpreting coefficients and model output
Assumptions of linear regression
Residual analysis and diagnostics
Making predictions with linear models

Model Development Phase (Weeks 6-8)

Chapter 6: Model Evaluation and Validation

Measuring model performance (R², MSE, MAE)
Training and testing data splits
MicroSim: Cross-validation simulation
Understanding overfitting and underfitting
Bias-variance trade-off
Model selection criteria
Performance metrics for different problem types

Chapter 7: Multiple Linear Regression

Extending to multiple predictor variables
Feature selection and engineering
MicroSim: Multi-dimensional regression explorer
Handling categorical variables
Interaction effects and polynomial terms
Multicollinearity detection and treatment
Model interpretation in multiple dimensions

Chapter 8: Introduction to NumPy and Advanced Computation

NumPy arrays and vectorized operations
Matrix operations for regression
MicroSim: Linear algebra visualization
Computational efficiency in data science
Broadcasting and array manipulation
Mathematical functions and statistics
Integration with pandas and matplotlib

Advanced Modeling Phase (Weeks 9-10)

Chapter 9: Non-linear Models and Feature Engineering

Polynomial regression and feature transformation
Understanding non-linear relationships
MicroSim: Polynomial degree explorer
Feature engineering techniques
Basis functions and kernel methods
Model complexity and interpretation trade-offs
When to use non-linear approaches

Chapter 10: Regularization Techniques

Ridge and Lasso regularization
MicroSim: Bias-variance trade-off explorer
Model selection strategies
Cross-validation for hyperparameter tuning
Elastic Net and other regularization methods
Feature selection through regularization
Preventing overfitting in complex models

Machine Learning Phase (Advanced Topics)

Chapter 11: Introduction to Machine Learning

Supervised vs. unsupervised learning
Classification and regression problems
Decision trees and ensemble methods
MicroSim: Algorithm comparison explorer
Feature importance and selection
Model interpretability techniques
Introduction to scikit-learn

Chapter 12: Neural Networks and Deep Learning

Neural networks and deep learning concepts
Perceptrons and multi-layer networks
Activation functions and backpropagation
MicroSim: Neural network playground
Training neural networks
Common architectures and applications
When to use neural networks vs. traditional methods

Chapter 13: Introduction to Machine Learning with PyTorch

Building simple networks with PyTorch
Tensors and automatic differentiation
Creating and training models
MicroSim: PyTorch model builder
Comparing traditional and deep learning approaches
GPU acceleration and optimization
Model saving and deployment

Chapter 14: Advanced Model Evaluation

Comprehensive performance metrics
ROC curves and AUC analysis
Confusion matrices and classification reports
MicroSim: Metric comparison explorer
Statistical significance testing
Model comparison techniques
Reporting and communicating results

Chapter 15: Capstone Project and Model Deployment

End-to-end data science project planning
Model interpretation and communication
MicroSim: Model comparison dashboard
Best practices and ethical considerations
Model deployment strategies
Documentation and reproducibility
Presenting data science findings

Special Topics

Matplotlib vs Plotly Comparison

Detailed comparison of visualization libraries for AI-generated plots and animations, including pros and cons for different use cases.

Learning Methodology

Each chapter incorporates: - Interactive MicroSims for hands-on parameter exploration - Real-world datasets and practical applications - Progressive complexity building from simple to advanced concepts - Explainable AI focus emphasizing model interpretability - Code examples with complete implementations

Course Philosophy

This course emphasizes the balance between model explainability and predictive accuracy, guiding students to identify the simplest effective solutions to data-driven problems. The integration of interactive simulations ensures abstract mathematical concepts become concrete and intuitive.