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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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]] |

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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. But then pen draws pen. 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! | |

+ | * - 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. | ||

− | + | [[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. | ||

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*[mailto:saveliev@marshall.edu Email] | *[mailto:saveliev@marshall.edu Email] | ||

− | *[https://twitter.com/PeterSaveliev Twitter] | + | *[https://twitter.com/PeterSaveliev Twitter] |

[[category: Mathematics]] | [[category: Mathematics]] |

## Revision as of 15:05, 25 June 2021

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:

$\ $ $\ $ $\ $ $\ $ $\ $ $\ $ $\ $

- 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. But then pen draws pen. 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!

- - 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.

- 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.