anantha wrote a new post, Welcome!, on the site Infinity 2 weeks, 1 day ago

Welcome to the blog Infinity!

soupless wrote a new post, Solving Antiderivative of a Function using Table of Integrals, on the site notes 1 month ago

Before anything else, we will start with definitions.

– **Antiderivative**

> Given a well-defined function $f$ on an interval $[a,b]$, the antiderivative of $f$, which we denote as $F$, is also a function […]kasrastanimaths wrote a new post, Introducing Homeomorphisms with a meme, on the site Kasrastani Maths 3 months, 1 week ago

# Notes

This was a beamer slideshow that [badly] converted into a more text like format. This was also meant for a “maths talk” I did on how to introduce homeomorphisms in a more interesting way.

# […]

kasrastanimaths wrote a new post, Point Set Topology Notes:Defining the Topology and Basis, on the site Kasrastani Maths 3 months, 1 week ago

# Initial Notes

These notes were also written in December 2020 just as I started to figure out how to use $LaTeX$, and started to write things related to math. This was actually used in a Youtube video I […]

kasrastanimaths wrote a new post, Prime:Factorization and Uniqueness of Factorization, on the site Kasrastani Maths 3 months, 1 week ago

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montessiel wrote a new post, Plenty of room at the Hotel Hilbert, on the site Climbing the holy mountain of mathematics 3 months, 1 week ago

>There she stood in the doorway

>I heard the mission bell

>And I was thinking to myself

>”This could be Heaven or this could be Hell”

$tiny{text{The Eagles – Hotel California}}$Infinity in […]

Paul VanKoughnett created the site Simpleton Symposium 3 months, 1 week ago

Andy's profile was updated 3 months, 1 week ago

Andy wrote a new post, First Post, on the site Category Theory for the Unemployed Mathematician 3 months, 1 week ago

So I’m going to try this out as a way of writing down things I’m thinking about/working on. I’m a part-time lecturer with 2 kids so the amount of research I do is basically negligible, but I do sometimes […]

montessiel wrote a new post, About this blog, on the site Climbing the holy mountain of mathematics 3 months, 1 week ago

I am a mathematics PhD student at Vilnius university. I care about arithmetic geometry and isogeny based cryptography.

This blog is intended as an online journal for my learnings and research. I also intend add […]

Jonathan wrote a new post, On the relationship between ABGHR orientations and "classical orientations" of Thom spectra, on the site noncommutativespecter 3 months, 1 week ago

I’ve been playing around with orientations of Thom spectra lately and I realized that I kept getting tripped up by the difference between the notion of an $E$-orientation given in [ABGHR] and the “classical” […]

montessiel changed their profile picture 3 months, 1 week ago

Jonathan's profile was updated 3 months, 1 week ago

shubhrajit et al. wrote a new post, First Blog, on the site Combinatorics Saga 3 months, 1 week ago

shubhrajit et al. changed their profile picture 3 months, 1 week ago

shubhrajit et al.'s profile was updated 3 months, 1 week ago

C. Ding wrote a new post, Half exactness of $K_0$ functor, on the site C. Ding's blog 4 months, 1 week ago

**Theorem**. Let $require{amscd}$ $begin{CD}

0 @> >> A @>i>> [email protected]>pi>>[email protected]>>>0

end{CD}$ be an exact sequence of $mathbb{C}$-algebras, then

$begin{CD}K_0(A)@>{i_*}>>K_0(B)@>{pi_*}>>K_0(C)end{CD}$

is exact […]C. Ding wrote a new post, elements of $K_0$ group, on the site C. Ding's blog 4 months, 3 weeks ago

Let $e$ be an idempotent in a unital algebra $A$ and $u=begin{pmatrix}1-e & e e & 1-eend{pmatrix}$, then $u$ is invertible and $ubegin{pmatrix}1-e & 0 0 & eend{pmatrix}=begin{pmatrix}1 & 0 0 & […]

C. Ding wrote a new post, On Homotopy, on the site C. Ding's blog 5 months ago

**Lemma**. Suppose $A$ is a unital Banach algebra and $gamma$ is a continuous path in the idempotents of $A$. Then there is a continuous path $u$ in invertible elements of $A$ such that $u(t)gamma(t) […]

C. Ding wrote a new post, Examples of Idempotents, on the site C. Ding's blog 5 months, 3 weeks ago

If $e$ is an idempotent in an algebra, so is $ueu^{-1}$ whenever $u$ is invertible.

So, if $e$ and $f$ are homotopic in $M_infty(A)$ if they are homtopic in some $M_n(A)$ where $A$ is a C*-algebra. Note that […]- Load More