This repository contains interactive Jupyter notebooks exploring fundamental concepts in statistics, probability theory, and related mathematical foundations.
notebooks/
├── intro/
│ ├── calculus/
│ │ ├── 01_calculus_overview.ipynb
│ │ ├── 02_integration.ipynb
│ │ └── 03_differentiation.ipynb
│ ├── combinatorics/
│ │ ├── 01_counting.ipynb
│ │ ├── 02_permutations.ipynb
│ │ ├── 03_selections.ipynb
│ │ ├── 04_pigenhole_principle.ipynb
│ │ └── 05_overview.ipynb
│ ├── probability/
│ │ ├── decision_theory/
│ │ │ ├── 01_weighted_average.ipynb
│ │ │ └── 02_expected_value.ipynb
│ │ ├── distributions/
│ │ │ ├── geometric_distribution.ipynb
│ │ │ ├── poisson_distribution.ipynb
│ │ │ └── uniform_distribution.ipynb
│ │ ├── measures/
│ │ │ └── 01_intro_to_measures.ipynb
│ │ └── rules/
│ │ ├── 01_basics.ipynb
│ │ ├── 02_bayes.ipynb
│ │ └── 03_random_variables.ipynb
│ ├── set-theory/
│ └── statistics/
- Calculus: Essential calculus concepts
- Set Theory: Foundation for probability spaces
- Combinatorics: Counting principles and methods
- Fundamental Rules: Basic probability axioms and rules
- Random Variables: Properties and transformations
- Bayes' Theorem: Conditional probability and applications
- Uniform Distribution
- Geometric Distribution
- Poisson Distribution
- Measure Theory: Mathematical foundations
- Decision Theory:
- Weighted averages
- Expected value calculations
- Descriptive statistics
- Inferential statistics
- Hypothesis testing
- Confidence intervals
- Regression analysis
- Interactive visualizations using ipywidgets
- Real-world examples and applications
- Theoretical foundations and proofs
- Practice problems and solutions
- Links to additional resources
- Create Conda environment:
conda create --name stats_notebooks python=3.x
conda activate stats_notebooks- Install required packages:
conda install jupyter numpy scipy matplotlib ipywidgets- Register the kernel:
python -m ipykernel install --user --name=stats_notebooksStart JupyterLab:
jupyter labnote You may need to run jupyter lab --allow-root
Navigate to the desired notebook in the notebooks/ directory. It's recommended to start with foundational topics in calculus and set theory before progressing to probability concepts.
- Basic calculus understanding
- Familiarity with set notation
- Basic Python programming skills
Feel free to:
- Report issues or bugs
- Suggest improvements
- Submit pull requests
- Request additional topics
- [Add recommended textbooks]
- [Add online courses]
- [Add reference materials]
- [Add helpful links]
- [Add documentation links]
- [Add tutorial links]
MIT
Nathan Ormond
This repository is actively developed. Topics and structure will evolve as the collection grows.