motivating diagonalization of a matrix [duplicate]

This question already has answers here: Why do we need a diagonal matrix? (2 answers) Closed 7 years ago. I have to teach about diagonalization of a matrix to a first year undergrad student and I was wondering what would be a good way to motivate this concept. I would appreciate any suggestions. Thanks! Answer … Read more

Why Cantor set removes one third?

I found the derivation of Cantor-like set in Understanding Analysis by Abbott. There he removes one fourth, and most properties (length, cardinality, compactness, uncountableness) are preserved (except dimension). That’s why I wonder: why we remove one third to build Cantor set? Is it because Cantor himself did this? Or is there some property that would … Read more

What was the original purpose for the binary system?

Obviously computers weren’t around when binary was first created… was there a particular use for binary back then or was it just developed as another number system? Answer From “Herrn von Leibnitz Rechnung mit null und eins” (Mister Leibnitz’ computation with 0 and 1): Diese Art zu rechnen wird nicht zu dem Ende angezeigt, daß … Read more

Origin/Etymology of the term Homology

Does anyone know who was the first person to invent the term homology and what their motivation was? All I could find was that Emmie Noether is accredited with inventing the homology group, and that Poincare made essential contributions to the nascent concept. Although I thought Poincare called topology “analysis situs”, so I doubt he … Read more

Who coined the term “crystallographic root system”?

Who coined the term “crystallographic root system” and when? In particular is there a connection to applied 3D crystallography? It does not seem to be Killing or Cartan’s terms (so presumably after 1900), and before Humphrey in 1990. Answer I contacted Dr. Humphreys, his take: No, I definitely didn’t invent this usage. The notion of … Read more

What are amazing results concerning Euler totient function? [closed]

Closed. This question needs to be more focused. It is not currently accepting answers. Want to improve this question? Update the question so it focuses on one problem only by editing this post. Closed 3 years ago. Improve this question What are important or amazing results involving the Euler totient function? I am aware of … Read more

How is it shown that the definition of the Euler-Mascheroni constant is finite? [closed]

Closed. This question is off-topic. It is not currently accepting answers. Want to improve this question? Update the question so it’s on-topic for Mathematics Stack Exchange. Closed 3 years ago. Improve this question Sorry if it’s trivial – but I would really like to know. Also, how were the hand-calculated approximations derived? A link to … Read more

Why does math work if there are too many paradoxes?

I’m a newbie that studies applied maths and I have been learning about measure theory for the past few weeks and I came across things like Banach–Tarski paradox, Gödel’s incompleteness theorems, axiom of choice.. Which made me feel super uncomfortable and confused so my question is why is maths seem to be working if the … Read more

Mathematical logic and foundations of mathematics in the 20th century

I would like some references regarding the foundations of mathematics in the 20th century, and mathematical logic, e.g. (1) I want to understand what happened to the foundation, what originated the transition from Russell’s logicism to the ZFC system, and other aspects that characterize modern mathematics; (2) When does logic start to became formal in … Read more

What is an ordinary differential equation equation that is yet to be solved?

In another word, the ODE i am talking about is very special that an special method must be developed in order to solve solely that ODE approximately in infinite series. An standard method mean it could solve an class of general ODEs. I am wondering are there any, You could just give one example and … Read more