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Best Sets of Lecture Notes and Articles

Overview of basic results about images and preimages

Intuition of the meaning of homology groups

Are "if" and "iff" interchangeable in definitions?

Difference between gradient and Jacobian

$X$ is Hausdorff if and only if the diagonal of $X\times X$ is closed

Why do we use a Least Squares fit?

Cardinality of Borel sigma algebra

Dot Product Intuition

Is there really no way to integrate $e^{-x^2}$?

Lebesgue measurable but not Borel measurable

What is difference between cycle, path and circuit in Graph Theory

Difference between topology and sigma-algebra axioms.

What is the intuition for the point-set topology definition of continuity?

Lebesgue measurable set that is not a Borel measurable set

Interpretation of limsup-liminf of sets

Is there a $\sigma$-algebra on $\mathbb{R}$ strictly between the Borel and Lebesgue algebras?

Examples of uncountable sets with zero Lebesgue measure

Topologist's sine curve is not path-connected

An intuitive idea about fundamental group of $\mathbb{RP}^2$

Are Singleton sets in $\mathbb{R}$ both closed and open?

Is there any difference between $P$ and $\Pr$ to represent probabilities?

What is the difference between topological and metric spaces?

Constructing a subset not in $\mathcal{B}(\mathbb{R})$ explicitly

Rigorous proof that $dx dy=r\ dr\ d\theta$

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Why do we need (the abstract concept of) random variables (in discrete probability models)?

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Why do we use dummy variables in integrals?

Cantor set: Lebesgue measure and uncountability