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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. | ||
| − | + | 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: | ||
$$\lim_{\Delta x\to 0}\left( \begin{array}{cc}\text{ discrete }\\ \text{ calculus }\end{array} \right)= \text{ calculus }$$ | $$\lim_{\Delta x\to 0}\left( \begin{array}{cc}\text{ discrete }\\ \text{ calculus }\end{array} \right)= \text{ calculus }$$ | ||
They are sold on Amazon: | They are sold on Amazon: | ||
| − | [[image:front cover.png|x150px|link=http://www.amazon.com/dp/1495188752]] | + | [[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|]] $\ $ [[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. | 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]] | *[[Current classes]] | ||
Revision as of 13:13, 20 August 2020
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:
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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.
- 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:
- (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.
- - 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.
