This post collects the top 5 most popular posts according to Google search console.

Read moreThis post collects the top 5 most popular posts according to Google search console.

Read morePicard's Little Theorem and Twice-Punctured Plane

We show that the range of a non-constant entire function's range cannot be a twice-punctured plane.

Read moreSL(2,R) As a Topological Space and Topological Group

In this post we show that $SL(2,\mathbb{R})$ can be identified as the inside of a solid torus and see what we can learn from it.

Read moreArtin's Theorem of Induced Characters

We give a relatively more detailed proof of Artin's theorem in representation theory of finite groups as well as an example of dihedral group.

Read moreChinese Remainder Theorem in Several Scenarios of Ring Theory

We study the Chinese remainder theorem in various contexts and abstract levels.

Read moreProjective Representations of SO(3)

In this post we study projective representations of $SO(3)$, although we will make more use of $SU(2)$. At the end of this post we reach the conclusion that one will think about polynomials with odd or even terms. Projective representations have its own significance in physics although the room of this post is too small to contain it. Nevertheless, the reader is invited to use linear algebra much more extensively with a taste of modern physics in this post.

Read moreIn this post we deliver the basic computation of the quadratic reciprocity law and see its importance in algebraic number theory.

Read moreVague Convergence in Measure-theoretic Probability Theory - Equivalent Conditions

We give an introduction to vague convergence and see several equivalent conditions of it.

Read moreThe Pontryagin Dual group of Q_p

In this post we show that the Pontryagin dual group of $\mathbb{Q}_p$ is isomorphic to itself.

Read moreThe Haar Measure on the Field of p-Adic Numbers

In this post we study the canonical Haar measure on $Q_p$, and give a explicit definition just as the Lebesgue measure.

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