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Difference between revisions of "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.  
 
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:
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Books:
*''[[Topology Illustrated]]'', published in 2016
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*''Topology Illustrated''
*''[[Calculus Illustrated|Calculus Illustrated. Volume 1 Precalculus]], published in 2019
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*''Calculus Illustrated''
*''[[Calculus Illustrated|Calculus Illustrated. Volume 2 Differential Calculus]], published in 2020
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**''Volume 1 Precalculus  
*''[[Calculus Illustrated|Calculus Illustrated. Volume 3 Integral Calculus]], published in 2020
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**''Volume 2 Differential Calculus''
*''How Swords Cut'', published in 2020
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**''Volume 3 Integral Calculus''
*''Linear Algebra Illustrated'', published in 2020
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**''Volume 4 Calculus in Higher Dimensions ''
*''[[Calculus Illustrated|Calculus Illustrated. Volume 4 Calculus in Higher Dimensions]], to be published in 2021
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**''Volume 5 Differential Equations''
*''[[Calculus Illustrated|Calculus Illustrated. Volume 5 Differential Equations]], to be published in 2021
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*''How Swords Cut''
 
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*''Linear Algebra Illustrated''
  
 
The calculus series includes parts of ''Discrete Calculus'', which is based on a simple idea:
 
The calculus series includes parts of ''Discrete Calculus'', which is based on a simple idea:

Revision as of 13:13, 20 August 2020

PeterSaveliev.jpg

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

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:

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


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:
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:

  • (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.
Mirror image of man.png
  • - 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