This site is being phased out.
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”). | + | 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. | |
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− | The | ||
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− | + | Classes: | |
+ | *MATH 132 Precalculus with Science Applications | ||
+ | *MATH 140 Applied Calculus | ||
+ | *MATH 335 Ordinary Differential Equations | ||
− | + | 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'' | ||
+ | *''PROOFS. Welcome to Mathematics'' | ||
+ | *''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] | ||
+ | $$\lim_{\Delta x\to 0}\left( \begin{array}{cc}\text{ discrete }\\ \text{ calculus }\end{array} \right)= \text{ calculus }$$ | ||
+ | *''One-Semester Calculus'' (calculus abbreviated/streamlined/simplified/trivialized), lecture notes [https://www.dropbox.com/s/jlkk8osm0ms5lqe/OSC.pdf?dl=0 pdf] | ||
+ | <!-- **Chapter 1 Calculus of Sequences [https://www.dropbox.com/s/p8hxmgaygbb7i7j/ch1.pdf?dl=0 pdf] | ||
+ | **Chapter 2 Discrete Calculus of Functions [https://www.dropbox.com/s/jjgfkn1kauyjqbb/ch2.pdf pdf] | ||
+ | **Chapter 3 Limits and Continuity [https://www.dropbox.com/s/djhsgnycvvillo9/ch3.pdf?dl=0 pdf] | ||
+ | **Chapter 4 The Derivative [https://www.dropbox.com/s/q7ur2pmy259popd/ch4.pdf?dl=0 pdf] | ||
+ | **Chapter 5 Differentiation and Integration [https://www.dropbox.com/s/zt1n4x1mninvndi/ch5.pdf?dl=0 pdf] | ||
+ | **Chapter 6 Applications [https://www.dropbox.com/s/dkj8lkjo9uojawi/ch6.pdf?dl=0 pdf]--> | ||
− | + | These 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:v4.png|x150px|link=https://www.amazon.com/dp/B08FGQFXMX/]] $\ $ [[image:v5.png|x150px|link=https://www.amazon.com/dp/B08FJH5XLS]] $\ $ [[image:proofs1.png|x150px|link=https://www.amazon.com/dp/B0D1QPD84M]] | ||
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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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[[image:Political_spectrum_as_circle_distorted_D.png| center]] | [[image:Political_spectrum_as_circle_distorted_D.png| center]] | ||
+ | This page is being phased out. | ||
− | |||
*[mailto:saveliev@marshall.edu Email] | *[mailto:saveliev@marshall.edu Email] | ||
− | *[https://twitter.com/PeterSaveliev Twitter] | + | *[https://twitter.com/PeterSaveliev Twitter] |
[[category: Mathematics]] | [[category: Mathematics]] |
Latest revision as of 14:02, 15 April 2024
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
- MATH 140 Applied Calculus
- MATH 335 Ordinary Differential Equations
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
- PROOFS. Welcome to Mathematics
- 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
These 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.
This page is being phased out.