This site is devoted to mathematics and its applications. Created and run by Peter Saveliev.

# Difference between revisions of "Peter Saveliev"

Hello! My name is Peter Saveliev (rhymes with “leave”). I am a professor of mathematics at Marshall University, Huntington WV, USA.

My current projects are these two books:

The calculus series includes parts of Discrete Calculus, which is based on a simple idea: $$\lim_{\Delta x\to 0}\left( \begin{array}{cc}\text{ discrete }\\ \text{ calculus }\end{array} \right)= \text{ calculus }$$

They are sold on Amazon:

$\$ $\$ $\$ $\ $\ $$\ \ $I have been involved in research in algebraic topology and several other fields but nowadays I think this is a pointless activity. My non-academic projects have been: digital image analysis, automated fingerprint identification, and image matching for missile navigation/guidance. • Once upon a time, I took a better look at the poster of Drawing Hands by Escher hanging in my office and realized that what is shown isn't symmetric! To fix the problem I made my own picture called Painting Hands: Such a symmetry is supposed to be an involution of the$3$-space,$A^2=I$; therefore, its diagonalized matrix has only$\pm 1$on the diagonal. These are the three cases: • (a) One$-1$: mirror symmetry, then pen draws pen. No! • (b) Two$-1$'s:$180$degrees rotation, the we have two right (or two left) hands. No! • (c) Three$-1\$'s: central symmetry. Yes!

• - Why is discrete calculus better than infinitesimal calculus? - Why? - Because it can be integer-valued! - And? - And the integer-valued calculus can detect if the space is non-orientable! Read Integer-valued calculus, an essay that makes a case for discrete calculus by appealing to topology and physics.
• - The political “spectrum” might be a circle! - So? - Then there can be no fair decision-making system! Read The political spectrum is a circle, an essay based on the very last section of the topology book.