Peter Saveliev

Hello! My name is Peter Saveliev (rhymes with “leave”). Pronouns are available upon request.

I am a professor of mathematics at Marshall University, Huntington WV, USA. But that's just my day job. The projects below are entirely my own.

Books:

• Topology Illustrated (This is a new edition, corrected and updated. I had to split the paper version into two volumes because of Amazon's page limits. There is no solution manual in the works at this time.)
• Calculus Illustrated (constantly updated)
  • 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
• PROOFS. Welcome to Mathematics
• Calculus in Motion: From Incremental to Continuous
• Elementary Discrete Calculus: How far we can go without limits? pdf

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

These are sold on Amazon (Warning: Color printing is expensive!):

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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:

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.

• 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.

This page is being phased out.

• Email
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• Lectures on College Mathematics on YouTube