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Difference between revisions of "Peter Saveliev"

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[[Image:PeterSaveliev.jpg|right]]
 
[[Image:PeterSaveliev.jpg|right]]
  
Hello! My name is Peter Saveliev (rhymes with “leave”). 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”). Pronouns are available upon request.
  
My current projects are these two books:
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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.
*''[[Topology Illustrated]]'', published in 2016
 
*''[[Calculus Illustrated|Calculus Illustrated. Volume 1 Precalculus]], published in 2019
 
*''[[Calculus Illustrated|Calculus Illustrated. Volume 2 Differential Calculus]], published in 2020
 
*''[[Calculus Illustrated|Calculus Illustrated. Volume 3 Integral Calculus]], published in 2020
 
*''How Swords Cut'', published in 2020
 
*''Linear Algebra Illustrated'', published in 2020
 
*''[[Calculus Illustrated|Calculus Illustrated. Volume 4 Calculus in Higher Dimensions]], to be published in 2021
 
*''[[Calculus Illustrated|Calculus Illustrated. Volume 5 Differential Equations]], to be published in 2021
 
  
 +
Classes:
 +
*MATH 132 Precalculus with Science Applications -- [https://teams.microsoft.com/l/meetup-join/19%3anmPyUkGoJ08mIfLW5Cbzc5Rnn7ZqjfzsVg56B7dOZy41%40thread.tacv2/1704037706916?context=%7b%22Tid%22%3a%22239ab278-3bba-4c78-b41d-8508a541e025%22%2c%22Oid%22%3a%2259940c89-a887-47a9-ae01-81da7e4f27b9%22%7d Watch]
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*MATH 140 Applied Calculus -- [https://teams.microsoft.com/l/meetup-join/19%3aosuyB1ZR4g1WkfDJYGuM80tFHK9jVex6PuInovJUfew1%40thread.tacv2/1704038234149?context=%7b%22Tid%22%3a%22239ab278-3bba-4c78-b41d-8508a541e025%22%2c%22Oid%22%3a%2259940c89-a887-47a9-ae01-81da7e4f27b9%22%7d Watch]
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*MATH 335 Ordinary Differential Equations -- [https://teams.microsoft.com/l/meetup-join/19%3az8Cfp4DXL8ZiDmHG9WR2cw85lZM4Etem2FVObDWQfGQ1%40thread.tacv2/1704038373961?context=%7b%22Tid%22%3a%22239ab278-3bba-4c78-b41d-8508a541e025%22%2c%22Oid%22%3a%2259940c89-a887-47a9-ae01-81da7e4f27b9%22%7d Watch]
  
The calculus series includes parts of ''Discrete Calculus'', which is based on a simple idea:
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Books:
 +
*''Topology Illustrated'' (Note: Due to my day job, the second edition is postponed indefinitely.)
 +
*''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 enough material for these three chapters from the first 3 volumes of Calculus Illustrated.  [https://www.dropbox.com/s/k4hdqqixming8ls/EDC.pdf pdf]
 
$$\lim_{\Delta x\to 0}\left( \begin{array}{cc}\text{ discrete }\\ \text{ calculus }\end{array} \right)= \text{ calculus }$$
 
$$\lim_{\Delta x\to 0}\left( \begin{array}{cc}\text{ discrete }\\ \text{ calculus }\end{array} \right)= \text{ calculus }$$
 +
*''One-Semester Calculus'' (calculus abbreviated/streamlined/simplified/trivialized), lecture notes [https://www.dropbox.com/s/jlkk8osm0ms5lqe/OSC.pdf?dl=0 pdf]
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<!-- **Chapter 1 Calculus of Sequences [https://www.dropbox.com/s/p8hxmgaygbb7i7j/ch1.pdf?dl=0 pdf]
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**Chapter 2 Discrete Calculus of Functions [https://www.dropbox.com/s/jjgfkn1kauyjqbb/ch2.pdf pdf]
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**Chapter 3 Limits and Continuity [https://www.dropbox.com/s/djhsgnycvvillo9/ch3.pdf?dl=0 pdf]
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**Chapter 4 The Derivative [https://www.dropbox.com/s/q7ur2pmy259popd/ch4.pdf?dl=0 pdf]
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**Chapter 5 Differentiation and Integration [https://www.dropbox.com/s/zt1n4x1mninvndi/ch5.pdf?dl=0 pdf]
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**Chapter 6 Applications [https://www.dropbox.com/s/dkj8lkjo9uojawi/ch6.pdf?dl=0 pdf]-->
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*''PROOFS and Other Math for Grownups'', lecture notes [https://www.dropbox.com/s/zhd061yjp15yr4h/PMG.pdf?dl=0 pdf]
  
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]] $\
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These are sold on Amazon:
[[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|]] $\ $ [[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]]
 
  
 +
[[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]]
  
  
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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!
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#(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!  
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#(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!
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#(c) Three $\ -1$'s: central symmetry. Yes!
  
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* - 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.
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[[image:mirror image of man.png| center]]
  
[[image:mirror image of man.png| center]]
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* 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.
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[[image:Political_spectrum_as_circle_distorted_D.png| center]]
 
[[image:Political_spectrum_as_circle_distorted_D.png| center]]
  
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This page is being phased out.
  
*[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)
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*[https://twitter.com/PeterSaveliev Twitter]
  
  
 
[[category: Mathematics]]
 
[[category: Mathematics]]

Latest revision as of 19:53, 26 January 2024

PeterSaveliev.jpg

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.

Classes:

  • MATH 132 Precalculus with Science Applications -- Watch
  • MATH 140 Applied Calculus -- Watch
  • MATH 335 Ordinary Differential Equations -- Watch

Books:

  • Topology Illustrated (Note: Due to my day job, the second edition is postponed indefinitely.)
  • 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 enough material for these three chapters from the first 3 volumes of Calculus Illustrated. pdf

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

  • One-Semester Calculus (calculus abbreviated/streamlined/simplified/trivialized), lecture notes pdf
  • PROOFS and Other Math for Grownups, lecture notes pdf


These 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

This page is being phased out.