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

Difference between revisions of "Peter Saveliev"

From Mathematics Is A Science
Jump to navigationJump to search
Line 18: Line 18:
 
They are sold on Amazon:
 
They are sold on Amazon:
  
[[image:front cover.png|x150px|link=http://www.amazon.com/dp/1495188752]] $\ $ [[image:Calculus Illustrated v1.png|x150px|link=https://www.amazon.com/dp/B082WKCYHY]] $\ $ [[image:Calculus Illustrated v2.png|x150px|link=https://www.amazon.com/dp/B0848P8WKF]] $\ $ [[image:Calculus Illustrated v3.png|x150px|link=https://www.amazon.com/gp/product/B08BQXW9XJ]] $\ $ [[image:HSCcover.png|x150px|link=https://www.amazon.com/dp/B08CCHRHFC]] $\ $ [[image:LAcover.png|x150px|link=https://www.amazon.com/dp/B08CL4H9M2]]
+
[[image:front cover.png|x150px|link=http://www.amazon.com/dp/1495188752]] $\ $ [[image:Calculus Illustrated v1.png|x150px|link=https://www.amazon.com/dp/B082WKCYHY]] $\ $ [[image:Calculus Illustrated v2.png|x150px|link=https://www.amazon.com/dp/B0848P8WKF]] $\ $ [[image:Calculus Illustrated v3.png|x150px|link=https://www.amazon.com/gp/product/B08BQXW9XJ]] $\ $ [[image:HSCcover.png|x150px|link=https://www.amazon.com/dp/B08CCHRHFC]] $\ $ [[image:LAcover.png|x150px|link=https://www.amazon.com/dp/B08CL4H9M2]]$\ $[[image:v4.png|x150px|link=https://www.amazon.com/dp/B08FGQFXMX/]] $\ $ [[image:v5.png|x150px|link=https://www.amazon.com/dp/B08FJH5XLS]]  
$\ $[[image:v4.png|x150px|]] $\ $ [[image:v5.png|x150px|]]
 
 
 
 
 
 
 
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.
 
 
 
*[[Current classes]]
 
 
 
  
  
Line 34: Line 26:
  
 
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. But then pen draws pen. No!
*(b) Two $-1$'s: $180$ degrees rotation, the we have two right (or two left) hands. 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!
+
#(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.
  
* - 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.
+
[[image:mirror image of man.png| center]]
  
[[image:mirror image of man.png| center]]
+
* 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.
 
* - 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.
Line 48: Line 41:
  
  
*[http://users.marshall.edu/~saveliev/vita.pdf Vita]
 
 
*[mailto:saveliev@marshall.edu Email]
 
*[mailto:saveliev@marshall.edu Email]
*[https://twitter.com/PeterSaveliev Twitter](MATH ONLY)
+
*[https://twitter.com/PeterSaveliev Twitter]
  
  
 
[[category: Mathematics]]
 
[[category: Mathematics]]

Revision as of 15:05, 25 June 2021

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
  • 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