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. | + | 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 2016 | + | *''[[Topology Illustrated]]'', published in 2016 |

− | *''[[Calculus Illustrated]]'', | + | *''[[Calculus Illustrated|Calculus Illustrated. Volume 1 Precalculus]], published in 2019 |

− | + | *''[[Calculus Illustrated|Calculus Illustrated. Volume 2 Differential Calculus]], published in 2020 | |

− | $$\lim_{\Delta x\to 0}\left( \begin{array}{cc}\text{ discrete }\\ \text{ calculus }\end{array} \right)= \text{ calculus }.$$ | + | *''[[Calculus Illustrated|Calculus Illustrated. Volume 3 Integral Calculus]], published in 2020 |

+ | *''How Swords Cut'', published in 2020 | ||

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+ | The calculus series includes parts of ''Discrete Calculus'', which is based on a simple idea: | ||

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

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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]]$\quad$ [[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]] | ||

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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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*[[Current classes]] | *[[Current classes]] | ||

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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! |

− | * | + | * - 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]] | ||

− | *[[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. |

[[image:Political_spectrum_as_circle_distorted_D.png| center]] | [[image:Political_spectrum_as_circle_distorted_D.png| center]] | ||

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*[http://users.marshall.edu/~saveliev/vita.pdf Vita] | *[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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[[category: Mathematics]] | [[category: Mathematics]] |

## Latest revision as of 13:44, 5 July 2020

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 Precalculus, published in 2019**Calculus Illustrated. Volume 2 Differential Calculus, published in 2020**Calculus Illustrated. Volume 3 Integral Calculus, published in 2020**How Swords Cut*, published in 2020

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:

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.