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My Notes
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Information Theory
Entropy
Intro to Real Analysis
1. The Real Numbers
2. Sequences
3. Series
4. Topology
5. Function Limits & Continuity
6. The Derivative
7. Sequence of Functions
8. Series of Functions
9. Power Series
10. Integral
Linear Algebra
Sections
Basis
Coordinate Representation
Diagonalizability
fdvs
Inner Product Space
Internal Direct Sums
Isometry
Isomorphisms
Linear Combination and Span
Linear Independence
Linear Transformations
Norm
Projection
Subspace test
Vector Space Axioms
Vector Space Properties
Linear Algebra
Numerical Analysis
1.1 Accuracy
1.2 Taylor Polynomials
1.3 Speed
2.1 Bisection Method
2.2 Fixed Point Iteration
2.3 Fixed Point Iteration Convergence
2.4 Newton's Method
2.7 Bracketing
3.2 Lagrange Polynomials
3.3 Newton Polynomials
4.1 Rudiments of Numerical Calculus
4.2 Undetermined Coefficients
5.1 Osculating Polynomials
Numerical Analysis
Statistics
Bayesian Statistics
1. Logic Probability and Uncertainty
2. Bayes Inference for Discrete Random Variables
3. Bayesian Inference on Binomial Proportion
4. Bayesian Inference on Poisson
5. Bayesian Inference on Normal Distribution
6. Hypothesis Testing
7. Bayesian Simple Linear Regression
8. Bayesian Analysis of Variance from Normal Likelihood
10. Jeffreys' Prior
11. Posterior Using Gibbs' Sampler
Bayesian Statistics
Regression Analysis
1. Simple Linear Regression
2. MLE in Simple Regression Model
3 Non-central Chi-Squared Theorems
4. Centred Model & Anova Derivations
5. SLR Confidence & Prediction Intervals
6. SLR Matrix Representation
7. Correlation and Hypothesis Testing
8. Intro to Multiple Linear Regression
9. MLR Hypothesis Testing
Anova Steps
Least Squares Vectorization
Regression Analysis
Vector Calc
Sections
Arc Length
Basic Topology in Euclidean Spaces
Change of Variables
Differentiation
Double Integral Over a Rectangle
Double Integral Over Elementary Regions
Green's Theorem
Implicit Function Theorem
Limits and Continuity
Line Integral
Local Extremums of Real-Valued Functions
Path Integral
Surfaces and Stokes Theorem
Types of Functions
Vector Fields
Vector Calc
Welcome
Least Squares Vectorization
Idea:
4
b
1
+
3
b
2
=
92
5
b
1
+
2
b
2
=
80
8
b
1
+
4
b
2
=
144
(
4
3
5
2
8
4
)
(
b
1
b
2
)
=
(
92
80
144
)
X
b
=
y
X
T
X
b
=
X
T
y
(
X
T
X
)
−
1
(
X
T
X
)
b
=
(
X
T
X
)
−
1
X
T
y
(least squares estimator)
b
=
(
X
T
X
)
−
1
X
T
y