Quantitative Mathematics Study Path
This study path is organized for learners who want a practical foundation in quantitative mathematics. Each topic combines explanation, worked examples, Python code, visual intuition, and short checks for understanding.
How to Use These Lessons
- Read each lesson in order the first time.
- Run the Python examples in a local Python environment when possible.
- Use the interactive browser widgets when studying from the rendered site.
- Attempt the practice questions before reading the explanation.
- Return to earlier algebra and Python topics whenever later lessons feel mechanical or confusing.
Topics
Python Fundamentals
Variables, control flow, functions, NumPy arrays, and plotting for quantitative Python work.
College Algebra
Expressions, equations, functions, graphs, polynomials, exponentials, logarithms, and systems.
Trigonometry
Unit circle, sine and cosine, angle measures, graph transformations, and identity practice.
Calculus
Limits, derivatives, optimization, integrals, and applications.
Linear Algebra
Vectors, matrices, linear systems, transformations, and eigenvalues.
Probability and Statistics
Random variables, distributions, estimation, testing, and regression.
Differential Equations
Change rules, symbolic solution methods, slope fields, numerical approximation, and systems.
Discrete Mathematics
Logic, sets, relations, sequences, induction, and graph basics.
Learning Pattern
Most lessons follow this sequence:
- Motivation: why the topic matters.
- Concept: intuitive explanation.
- Definition: formal notation.
- Visual model: graph or interactive diagram.
- Worked example: step-by-step solution.
- Common mistakes: errors to avoid.
- Practice: short exercises or quizzes.
- Python connection: reusable code for Python environments.