Welcome to my Intuitive Advanced Math wiki

Math does not have to be frustrating and hard to learn. Actually, it is fun to learn if you understand the ideas behind the formulas. Unfortunately, the run for brevity became an obsession for most mathematicians, especially in University circles. They forgot that formulas should clarify things and not the opposite. But the worst part is the examples that are harder to understand than the theory itself, and the notation which is … undefined. The authors presuppose that you should remember all the definitions and notation from X pages back, and use it freely. Wiki type hyper-linking should improve the situation.

This site is supposed to help with my research in Computer Vision. I will collect any relevant information along with my own learning of advanced mathematical tools. The best method to learn something is to teach that to someone else (method of Lewis Carroll).As a visual learner, I use visual tools to understand and remember. As an engineer, I don't need formality and rigorous proofs. For me it is much more important to understand the idea than to know/remember it. You can benefit from my knowledge too.

This Wiki is for:

  • Myself - I'm concerned with the question of preserving my memory on important facts and theories
  • Engineers - I suppose that you know matrices and integrals already
  • Scientists, especially in computer vision area

This wiki is not recommended for:

  • Students who want to learn the principles and proofs in depth
  • People who afraid of formulas
  • Mathematicians
  • Physicists - you will NOT find Maxwell and wave equation solutions here, or any perplexing physical reasoning.

The reason for one more math source (this wiki):

I believe that math is only a simplified asymptotic approximation of the real World, and it should be treated as such.
The sources on engineering math include books (of at least 500 pages) of two types: cookbooks for "dummies", or physics based books filled with chapters on analytic computation of integrals. Well, when did you compute the integral analytically with elementary functions?! Even if you did, it was probably done by some computer algebra system like Mathematica, or Matlab. Cookbooks are not appropriate for a research. I just want to say that the explanations should be short and useful for further engineering research.

How the information is presented:

  • General idea and definition - if the idea is clear, it can be used in different context and situations
  • Algorithm for computation or problem solution - you don't really understand it until you know how to implement it (it is true not only in computer science)
  • Analogies - how the defined term or theory can be used in further research
  • Examples and visual interpretations - regular things from different viewpoints
  • Proof - only if constructive, or adds to the understanding (no formal rigorousness whatsoever, e.g., I don't see a point for engineer to work hard on the proof of Jordan's theorem that roughly states: "The closed non-crossing curve divides the plane to interior and exterior", which is intuitively obvious).

Dr. Arie Nakhmani - about me

I'm a computer vision and control systems scientist. More information about me can be found on my personal site:
http://labs.uab.edu/anry/
and here is my Mendeley account:

Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License