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

# Peter Saveliev

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

Books:

*Topology Illustrated*(Note: Because of the employment situation, the second edition is postponed until 2024+.)*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:

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- 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. But then pen draws pen. No!
- (b) Two $\ -1$'s: $180$ degrees rotation. But then 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 our universe is non-orientable! Read Integer-valued calculus, an essay that makes a case for discrete calculus by appealing to topology and physics.

- 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.