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Difference between revisions of "Peter Saveliev"
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*''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] | *''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] | ||
$$\lim_{\Delta x\to 0}\left( \begin{array}{cc}\text{ discrete }\\ \text{ calculus }\end{array} \right)= \text{ calculus }$$ | $$\lim_{\Delta x\to 0}\left( \begin{array}{cc}\text{ discrete }\\ \text{ calculus }\end{array} \right)= \text{ calculus }$$ | ||
− | *''One-Semester Calculus'', lecture notes. | + | *''One-Semester Calculus'' (abbreviated, streamlined, simplified), lecture notes. |
**Chapter 1 Calculus of Sequences [https://www.dropbox.com/s/p8hxmgaygbb7i7j/ch1.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 2 Discrete Calculus of Functions [https://www.dropbox.com/s/jjgfkn1kauyjqbb/ch2.pdf pdf] | ||
− | **Chapter | + | **Chapter 3 Limits and Continuity [https://www.dropbox.com/s/djhsgnycvvillo9/ch3.pdf?dl=0 pdf] |
These are sold on Amazon: | These are sold on Amazon: |
Revision as of 01:58, 26 February 2022
Hello! My name is Peter Saveliev (rhymes with “leave”). I am a professor of mathematics at Marshall University, Huntington WV, USA.
Books:
- Topology Illustrated (Note: Because of the employment situation, the second edition is postponed until 2024+.)
- 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 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 (abbreviated, streamlined, simplified), lecture notes.
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.