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

Peter Saveliev

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

Books:

  • Topology Illustrated
  • Calculus Illustrated
    • Volume 1 Precalculus
    • Volume 2 Differential Calculus
    • Volume 3 Integral Calculus
    • Volume 4 Calculus in Higher Dimensions
    • Volume 5 Differential Equations
  • How Swords Cut
  • Linear Algebra Illustrated
  • Elementary Discrete Calculus: How far we can go without limits? For now, I just picked 3 chapters from the first 3 volumes of Calculus Illustrated. PDF

$$\lim_{\Delta x\to 0}\left( \begin{array}{cc}\text{ discrete }\\ \text{ calculus }\end{array} \right)= \text{ calculus }$$

They are sold on Amazon:

Front cover.png $\ $ Calculus Illustrated v1.png $\ $ Calculus Illustrated v2.png $\ $ Calculus Illustrated v3.png $\ $ HSCcover.png $\ $ LAcover.png$\ $V4.png $\ $ V5.png


  • 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:
Correcting Drawing Hands by Escher

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:

  1. (a) One $\ -1$: mirror symmetry. But then pen draws pen. No!
  2. (b) Two $\ -1$'s: $180$ degrees rotation. But then we have two right (or two left) hands. No!
  3. (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 our universe is non-orientable! Read Integer-valued calculus, an essay that makes a case for discrete calculus by appealing to topology and physics.
Mirror image of man.png
  • So, what would mathematics look like without fractions?
  • - 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.
Political spectrum as circle distorted D.png