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The following presentation builds on previous posts on linear algebra to establish the use of linear algebra in engineering. Building on the previous articles, this presentation includes a general summary of […]

Proofs are, indeed, a difficult thing in mathematics. But mathematics is at its core *just* proofs, and less importantly calculations.

To prove requires a certain ingenuity to construct the right object or […]

Apparently we have some readers in the community of folks with whom Mr. Tetra Halstead associates. Good morning to you all.

Every other school day from 1:30–3:00, the four of us (J. Brewster, B. Halstead, D. S […]

In order to any kind of analysis we create a metric space. A metric space is a set equipped with a distance function $d(a,b)to [0,infty)$. We read this as “the distance between $a$ and $b$”. This must satisfy […]

Examples are a very important tool in understanding mathematics, including linear maps and matrices. Common examples of linear maps include differentiation and integration where c = 0 as maps between vector spaces […]

Matrices are everywhere – computer science, engineering, movies, and, of course, linear algebra.

Before we can understand why matrices are such a useful tool in many fields, it is important to understand what […]

Classical logic is used (by *some* mathematicians) to establish the basis of mathematics — but sets of statements in classical logic are also special cases of a variety of mathematical objects. One such object w […]

An understanding of quotients is an important prerequisite for creating various surfaces in Euclidean spaces with topology.

As a review, a quotient formalizes the idea of “gluing” points together by any poi […]

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 […]

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 […]

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 […]

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

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 […]

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 […]

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I’ve decided to migrate the content of the blog [here](https://rmehtany.github.io/notes/AlgebraicGeometry/) as I wasn’t particularly happy with the styling and features of the site. Be sure to check it out!

Basic Special Functions are Absolute Value Function, Signum Function, Floor and Ceiling Functions, Fractional Part Function and Integer Function.

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