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Study Notes and Blog

Math Study Notes

The following are study notes I made when I was studying mathematics in my undergraduate career.

Math Tutorial Notes

A list of tutorial notes I made when I was a teaching assistant in HKUST.

Note 01

Linear Systems; Echelon and Reduced Echelon Forms; Basic and Free Variables

Note 02

Vector Spaces, Linear Span and Linear Independence

Note 03

Linear Transformations

Note 04

Matrix Operations; Inverse, Transpose and Elementary Matrices; Determinants

Note 05

Vector Spaces Again, Bases and Dimensions

Note 06

Important Subspaces of

$\mathbb R^n$ , Row, Column Spaces; Rank-Nullity Theorem

Note 07

Coordinates and Matrix Representations of Linear Transformations; Generalized Nullity-Rank Theorem

Note 08

Eigenvalues and Eigenvectors for Square Matrices; Algebraic and Geometric Multiplicity of Eigenvalues; Diagonalization

Note 09

Inner Product, "Norm" (i.e., "Length"); Orthogonal and Orthonormal Sets, Orthogonal Complement; Gram-Schmidt Orthogonalization Process

Note 10

Orthogonal Projection onto Finite Dimensional Subspaces; Minimizer Obtained by Orthogonal Projections

Note 01

Mathematical Induction and Inequalities

Note 02

Informal Logic, Sets and Functions

Note 03

Note 04

Infimum and Supremum

Note 05

Note 06

Note 07

Continuous Functions

Note 08

Differentiation (Part I): L'Hopital's Rule & Mean-Value Theorem

Note 09

Differentiation (Part II): Taylor Series (Skipped in this course)

Note 10

Riemann Integral (Part I): Riemannn Integrability

Note 11

Riemann Integral (Part II): Miscellaneous

Note 12

Riemann Integral (Part III): Improper Integral (Skipped in this course)

Note 01

Review of Linear Algebra and Multivariable Calculus

Note 02

Differentiability and

Note 03

Inverse and Implicit Function Theorem

Note 04

Basic Concept and Properties of Limit Inferior and Limit Superior

Note 05

More Examples of Limit Superior and Limit Inferior

Note 06

Midterm Review on

$\limsup$ and $\liminf$

Note 07

Sequence and Series of Functions; Uniform and Nonuniform Convergence

Note 08

Consequence of Uniform Convergence

Note 09

Set Operations with Functions; Topology on $\mathbb{R}$ Openness, Closedness and Compactness

Note 10

Lebesgue Inner, Outer Measures and Lebesgue Measure

Note 11

Lebesgue Measurable Functions

Note 12

Lebesgue Integration and Convergence Theorems

Old Blog

https://checkerlee.blogspot.com/