itpmblog wrote a new post, Intro to Visualizing Topology: Quotient, on the site ITPM Blog 3 weeks, 6 days ago

In topology we often think about what things look like. But fundamentally, these are mathematical objects and the jump to visualization is not trivial.

We often think in topology of gluing two different points […]

itpmblog wrote a new post, Topology & Calculus, on the site ITPM Blog 4 weeks, 1 day ago

If one is familiar with line integrals from calculus, one may have encountered vocabulary used in theorems to describe regions such as **open** and **closed**, **connected** , and **simply connected**. These all […]

itpmblog wrote a new post, (Mathematically) Making a 2×2 Rubik’s Cube, on the site ITPM Blog 2 months ago

Almost everyone has, at some point, played with the deceptively simple puzzle that is a Rubik’s cube. Even before studying pure maths, we had heard about the idea of Group Theory through an interest in Rubik’s Cub […]

itpmblog wrote a new post, 关于我们, on the site ITPM Blog 2 months ago

Chúng tôi là sinh viên năm thứ mười hai ở trường học viên quốc gia quận Morris. Chúng tôi học toán thuần túy. Brendan Halstead là thày giáo của chúng tôi.

itpmblog wrote a new post, Universal Property: How can we define mathematical objects?, on the site ITPM Blog 2 months, 2 weeks ago

In algebra we are interested in thinking about objects. Objects can be many things including numbers, sets, and many more complicated constructions. Category theory is a powerful tool which analyzes these objects […]

itpmblog wrote a new post, Bigger Infinities Than Infinity, on the site ITPM Blog 2 months, 3 weeks ago

Can you get a room in an infinitely large, yet fully booked, hotel? There are a lot of rooms to count in Hilbert’s Grand Hotel, an infinite number of them to be exact. A common understanding of infinity is that i […]