Learning Paths

Use these paths as reading orders, not as rigid courses. Each finished note should name its prerequisites near the top, point to next steps near the bottom, and cite sources with Markdown footnotes.^[1]

Foundations

1. README
2. CONTRIBUTING
3. LaTeX Examples
4. Pre-Calculus
5. Trigonometry
6. Analytic Geometry
7. Linear Algebra

Pre-Calculus

1. Pre-Calculus
2. Functions
3. Polynomials and Rational Functions
4. Exponentials and Logarithms
5. Trigonometry

Analytic Geometry

1. Analytic Geometry
2. Distance and Midpoint
3. Vectors and Dot Product
4. Lines and Planes
5. Completing the Square
6. Conic Sections

Probability

1. Sigma-Algebra
2. Borel Sigma-Algebra
3. Probability
4. De Morgan Laws
5. Random Variable
6. Expectation of a Random Variable
7. Variance of a Random Variable
8. Moment Generating Functions

Statistical Inference

1. Point Estimation
2. Maximum Likelihood Estimation
3. Confidence Intervals
4. Hypothesis Testing
5. p-values
6. Type I and Type II Errors
7. Simple Linear Regression
8. One-Way ANOVA

Distributions

1. Distributions
2. Discrete
3. Bernoulli Distribution
4. Binomial Distribution
5. Geometric Distribution
6. Poisson Distribution
7. Continuous
8. Probability Density
9. Cumulative Distribution Function
10. Uniform Distribution
11. Exponential Distribution
12. Normal Distribution
13. Chi-Square Distribution
14. Student t Distribution
15. F Distribution

Calculus (single variable)

1. Calculus
2. Limits
3. Fundamental Limits of Calculus
4. Squeeze Theorem
5. Derivatives
6. Chain Rules
7. Implicit Differentiation
8. Higher-Order Derivatives
9. Integrals
10. Riemann Sum
11. Integration by Parts
12. Fundamental Theorem of Calculus

Sequences and Series

1. Sequences
2. Infinite Series
3. Series Sums by Partial Sums
4. Geometric Series
5. Harmonic Series
6. P Series
7. Telescoping Series
8. Comparison Tests
9. Integral Test
10. Ratio Test
11. Root Test
12. Alternating Series
13. Absolute Convergence
14. Power Series
15. Taylor Series
16. Maclaurin Series
17. Binomial Series

Multivariable Calculus

1. Multivariable Functions
2. Limits and Continuity of Two-Variable Functions
3. Partial Derivatives
4. Clairaut's Theorem
5. Differentiability of a Function
6. Differential of a Function
7. Tangent Plane
8. Directional Derivative
9. Maximum Rate of Directional Derivative
10. Maxima and Minima
11. Lagrange Multipliers
12. Polar Coordinates
13. Cylindrical Coordinates
14. Spherical Coordinates
15. Double Integrals
16. Double Integrals over General Regions
17. Double Integrals in Polar Coordinates
18. Fubini's Theorem
19. Triple Integrals

Linear Algebra

1. Linear Algebra
2. Systems of Linear Equations
3. Matrices and Row Reduction
4. Vector Spaces and Bases
5. Determinants
6. Eigenvalues and Eigenvectors
7. Orthogonality and Projections
8. Least Squares and QR

Numerical Methods

1. Numerical Methods
2. Root Finding
3. Bolzano's Theorem
4. Graphical Method
5. Bisection Method
6. False Position Method
7. Secant Method
8. Newton-Raphson Method
9. Numerical Methods/Linear Systems/Solving Linear Systems
10. Direct Methods - Triangular System
11. Gaussian Elimination
12. LU Factorization
13. Iterative Methods
14. Gauss-Jacobi Method
15. Gauss-Seidel Method
16. Sufficient Convergence Condition for Gauss-Jacobi
17. Polynomial Interpolation
18. Existence and Uniqueness of Interpolating Polynomial
19. Polynomial Interpolation by Definition
20. Lagrange Polynomial
21. Newton Polynomial
22. Midpoint Rule
23. Trapezoidal Rule
24. Simpson 1-3 Rule
25. Simpson 3-8 Rule
26. Curve Fitting
27. Least Squares

Statistical Inference

1. Estimação Pontual
2. Máxima Verossimilhança
3. Intervalos de Confiança
4. Teste de Hipóteses
5. p-valor
6. Erros Tipo I e II
7. Regressão Linear
8. ANOVA

Statistical Process Control

1. Statistical Process Control
2. What is SPC
3. Quality Tools
4. Control Charts
5. Common-Cause and Special-Cause Variation
6. Control Limits and Specification Limits
7. I-MR Chart
8. Xbar-R Chart
9. Xbar-S Chart
10. p Chart
11. np Chart
12. c Chart
13. Defects per Unit
14. Autocorrelated Data
15. Process Capability
16. Quadratic Loss Function

DSA / Asymptotic Analysis

1. Asymptotic Analysis