Will I ever learn my lesson? Probably not. I suspect most people in math have the same problem: you buy a new book and have all sorts of grand plans about going through it and mastering all its theorems, etc. etc. That was me in February, when I ordered a copy of Differential Geometry of Curves and Surfaces by Kristopher Tapp. Read more...

I was reading the Wikipedia page for the famous Lorenz system of differential equations, and saw a nice animated plot of the phase space written in the Julia language. Among the other code examples on that page is a solution for Maxima, which outputs the following when run: It's not a bad plot, but I thought it could be improved. Read more...

Despite the "unreasonable effectiveness"1 of mathematics applied to physics, I think it is important to remember that there is an awful lot we cannot calculate exactly. In general, except for the simplest of problems, numerical computations or some other type of approximation are the only way to get answers. Read more...

Title: How to Succeed in College Mathematics, by Richard M. Dahlke, PhD. ISBN: 978-0-615-16803-6 An excellent guidebook of interest to anyone studying mathematics at the post-secondary level. Written by Professor Richard M. Dahlke, a U.S.-based professor of mathematics, How to Succeed in College Mathematics gives useful advice on topics such as improving academic performance, keeping a healthy attitude towards studying, and how to improve problem-solving skills. Read more...

An integral equation is one that contains an unknown function under the integral sign. When that integral is over an interval varying with \(x\), it is more specifically classified as a Volterra integral equation. I came across this interesting, relatively simple Volterra equation in Stewart's Calculus and thought it would be interesting to try out. Read more...

Proposition: A matrix with a row consisting of all zeroes cannot be inverted, nor can one with a column of all zeroes. Proof Let A denote some \(n\times n\) matrix where one of its rows has only zeroes — let us refer to this as row r. Then take another \(n \times n\) matrix B and suppose toward contradiction that \(B = A^{-1}\). Read more...

Universal Wave Equation Example According to r/EngineeringStudents, the speed of sound in mayonnaise is 2613 \(\textrm{ms}^{-1}\). According to Scientific American, a soprano's frequency range could be between 250 and 1500 Hz, so let's see what the wavelength of a 1200 Hz soprano tone would be as it passes through mayonnaise. Read more...