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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. 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: | My current projects are these two books: | ||
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*''[[Calculus Illustrated]]'', volume 1 published in 2019 | *''[[Calculus Illustrated]]'', volume 1 published in 2019 | ||
In part, the latter book is about ''Discrete Calculus'', which is based on a simple idea: | In part, the latter book is about ''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 }$$ |
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! | + | *(b) Two $-1$'s: $180$ degrees rotation, the we have two right (or two left) hands. No! |
− | *(c) Three $-1$s: central symmetry. Yes! | + | *(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) | ||
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[[category: Mathematics]] | [[category: Mathematics]] |
Revision as of 14:59, 17 November 2019
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:
- Topology Illustrated, published in 2016
- Calculus Illustrated, volume 1 published in 2019
In part, the latter book is about 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 }$$ 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.