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

Difference between revisions of "Peter Saveliev"

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[[Image:PeterSaveliev.jpg|right]]
 
[[Image:PeterSaveliev.jpg|right]]
  
Hello! My name is Peter Saveliev. I am a professor of mathematics at Marshall University, Huntington WV, USA.  
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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.  
  
 
My current projects are these two books:
 
My current projects are these two books:
 
*''[[Topology Illustrated]]'', published in 2016
 
*''[[Topology Illustrated]]'', published in 2016
*''[[Calculus Illustrated]]'', volume 1 published in 2019  
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*''[[Calculus Illustrated]]'', Volume 1 ''Precalculus'' published in 2019  
In part, the latter book is about ''Discrete Calculus'', which is based on a simple idea:
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Both books include parts of ''Discrete Calculus'', which is based on a simple idea:
$$\lim_{\Delta x\to 0}\left( \begin{array}{cc}\text{ discrete }\\ \text{ calculus }\end{array} \right)= \text{ calculus }.$$
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$$\lim_{\Delta x\to 0}\left( \begin{array}{cc}\text{ discrete }\\ \text{ calculus }\end{array} \right)= \text{ calculus }$$
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They are sold on Amazon:
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[[image:front cover.png|x150px|link=http://www.amazon.com/dp/1495188752]]  [[image:Calculus Illustrated.png|x150px|link=https://www.amazon.com/dp/B082WKCYHY]]
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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.
 
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.
  
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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:
 
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!
 
*(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!  
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*(b) Two $-1$'s: $180$ degrees rotation, the we have two right (or two left) hands. No!  
*(c) Three $-1$s: central symmetry. Yes!
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*(c) Three $-1$'s: central symmetry. Yes!
  
  
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*[https://twitter.com/PeterSaveliev Twitter](MATH ONLY)
 
*[https://twitter.com/PeterSaveliev Twitter](MATH ONLY)
  
Note: I am frequently asked, what should "[[Sabellius|Saveliev]]" sound like? I used to care about that but got over that years ago. The one I endorse is the most popular: "Sav-leeeeeev". Or, simply call me ''Peter''.
 
  
 
[[category: Mathematics]]
 
[[category: Mathematics]]

Revision as of 19:24, 19 December 2019

PeterSaveliev.jpg

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:

Both books include 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.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