Posts tagged: math

Last night Ehssan sent me a post from a math professor that has been making the rounds. The professor loves research and hates grading. Who doesn't? But lately, he wrote, his research has started to...

There are a few people in my life (mostly in the role of an advisor/mentor) that have given me a feeling that I haven't experienced anywhere else. These are people who are well accomplished and well...

I asked Hadi, half-jokingly, whether Bach was the Justin Bieber of his time. Are we just listening to the most "popular" artists of the 1700s and calling it high culture? And the flip side: will...

I recently got introduced to this game called Can't Stop and it got me thinking about probabilities. You know how it is - you start playing a dice game and suddenly you're knee-deep in combinatorics...

There's a mathematical insight that explains why some people consistently end up with better outcomes than others, and it has nothing to do with talent, luck, or even the quality of their choices.

Here's a fun paper to read: Real numbers, data science and chaos: How to fit any dataset with a single parameter. The premise of the paper is that "all the samples of any arbitrary data set can be...

A frequentist vs Bayesian case

James Tanton is full of seemingly innocent and amusing questions. One of the questions that kept me busy one night is this one:

Since first time I that have encountered a statistical "paradox" I have this feeling that my explanations for what is the "right" answer might not be correct and it might be the case that I'm just...

Disclaimer: I'm not a statistician, and no, correlation does not mean causation. Also, I'm not a seismologist. And none of the followings are necessarily true. I'm just stretching my thoughts here!

What is the minimum number of links that you need to connect 4 computers in a wired network? 3.

Let's say we have a graph (i.e. network), and we want to cluster the vertices (nodes).  Here, think of the nodes as people, agents, oscillators, some dynamic being, and the edges... the edges tell...

It always excites me when I see a combinatorial matrix theory problem, and this is no exception, though it is so basic that it shows up in all forms and shapes. Let me start with a combinatorial...

In the neuroscience community there's a divide on whether there are functional connectivity networks in the brain. This is a very vaguely defined concept, although, one can think of it this way:

My friend asked me this: Put balls into $n$ buckets uniformly at random and count $h$ the number of buckets with at least one ball in them. What is the expected value of number of balls $k$?

This past summer I was given a course in introductory linear algebra to teach. The topics of the course, as usual, start from solving systems of linear equations, and then matrices, determinant and...

So, bored in a math talk Ulam starts writing integers in a spiral and circling primes. He soon notices something weird:

I recently participated at the Fields Medal Symposium held at the Fields Institute in Toronto, in honour of Martin Hairer, one of the recipients of the medal in 2014. His work revolves around...

این کوزه‌گر دهر چنین جام لطیف می‌سازد و باز بر زمین می‌زندش

In a huge graph, it is hard to determine a bottleneck by just looking at it, or doing any type of search. And by a bottleneck, I mean part of graph that is not very much connected to the other part....

My first solo paper "Existence of a Not Necessarily Symmetric Matrix with Given Distinct Eigenvalues and Graph" got published in Journal of Linear Algebra and its Applications, yesterday. It took it...

Today I started my linear algebra class by motivating the determinant using a little bit of history and applications. In particular I talked about determinant appearing in the change of variables in...

One of the things that I always tell my students is to check their solutions when they are done solving a problem. That by itself can mean several things, depending on what the problems is. Of course...

I've been using sage for a while now. I've also been teaching linear algebra for a few years. One of the problems in teaching linear algebra is coming up with a handful of examples of matrices that...

Gershgorin circle theorem roughly states that the eigenvalues of an $n \times n$ matrix lie inside $n$ circles where $i$-th circle is centred at $A{i,i}$ and its radius is the sum of the absolute...

For a given function $f(x)$ around a point $a$, if you zoom in close enough on the graph of the function, you can't tell the difference between the curve and the tangent line to the graph of the...

We started the project in Graduate Research Workshop in Combinatorics (Rocky Mountain Great Plains GRWC) in summer 2014, hosted by University of Denver and University of Colorado Denver. Two weeks of...

In Theorem 3.1 of "The combinatorial inverse eigenvalue problems: complete graphs and small graphs with strict inequality, W. Barrett, A. Lazenby, N. Malloy, C. Nelson, W. Sexton, Electronic Journal...

If you know about my work, you know that for the past several years I've been working on a special type of problems called structured inverse eigenvalue problems (or SIEP's for short). Well, I mainly...

If you have a prime number $p$ (other than two and five) then the last digit of $p$ is 1, 3, 7, or 9. If for some reason we believe that prime numbers are randomly distributed (after all, the last...

I went to several talks and meetings in the past few days, and I am going to talk about some of them, but first let me start with some predicting game:

Officially, I first learned about randomized algorithms and derandomizing them in a course called Randomness in Computations, offered by John Hitchcock at University of Wyoming. It wasn't until then...

Ehssan Khanmohammadi and I just submitted a paper on inverse eigenvalue problems for infinite graphs. Essentially we proved that for a given bounded set $\Lambda$ and an infinite graph $G$ on...

I was watching this random video on youtube (which by the way is not the best video) that I thought maybe I can do the same thing. So, I started coding in Sage. Here is a what I want to do:

Today I read a lot of random mathematics and many of them led to places outside math, and among them is this one: Parkinson's Law. One of them that at this last hour of work day is still related to...

I have used several geogebra applets in my calculus class, but there's always things that you wanna do that there's no applet out there for, or you can't modify them etc. So, I decided to write my...

Dmitry Ryabogin from Kent State University gave two talks today here at UCalgray. The first talk was about convex bodies with congruent projections. You can read about it here: PDF. And their recent...

For the past several months my Saturdays consist of two meetings, each of which about 4 hours long, with two of my colleagues working on various problems. Clearly we've hit a lot of dead ends, and...

We (Sudipta Mallik and I) just submitted our paper on the "Spectral characterization of matchings in graphs". It is based on our previous work on "Construction of real skew-symmetric matrices from...

> Mathematics has a reputation for objectivity. But without real-world infinite objects upon which to base abstractions, mathematical truth becomes, to some extent, a matter of opinion. The choice...

Yesterday I gave a colloquium talk at WIU and as a tradition the department head gave me a book. The book is called The Ph$\gamma$sics Book: From the Big Bang to Quantum Resurrection, 250 Milestones...

I just read a book called "Fermat's last theorem" by Simon Singh, and I think it was awesome. I actually listened to the audio version of it. The book does not assume any prior knowledge of...

Today, I'm going to Snowbird, UT, to participate in an Mathematics Research Communities 2014 workshop, where I'll learn about algebraic and geometric approaches in neuroscience. Here is the link:...

It's been almost three weeks (5 days a week, 75 minutes a day) that I am teaching elementary linear algebra, and I can already talk mathematics with my students. It's been very rewarding. I am...

30 pages for the new paper. Almost done.

https://www.youtube.com/watch?v=6ybd5rbQ5rU

These days I'm working hard to finish writing my dissertation. I put an average of 12 hours a day in. It's started looking nice. One more chapter to write, then doing final edits, putting codes in,...

Gilbert Strang talking about his favorite topic at the Joint Math Meeting 2014, Baltimore, MD.

A gift from a good friend :)

History of Mathematics

The case of the missing fractals

> Permanent & Determinant: Non-identical Twins > Tuesday, May 20, 2014 > > The determinant is undoubtedly the most important polynomial function in mathematics. Its lesser known sibling, the...

Algebra, Combinatorics, and Number Theory Seminar Ross Hall 247 3:10pm, Tuesday, 29 April 2014