2nd Edition of Sage for Undergraduates

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Gregory Bard

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May 28, 2020, 2:49:42 PM5/28/20
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Dear sage-edu,

I'm embarking on an exciting project over the next six weeks. I'm updating
my book, Sage for Undergraduates, to be compatible with the new Python3
syntax. In this 2nd edition, I'll also add a few projects from macroeconomics,
epidemiology, and differential equations.

I'm curious if anyone has any requests for me? Was there a topic that I left
out in the 1st edition, that you think I should have included? Was there a
topic or concept that I covered badly? Don't be afraid to criticize---I don't
mind at all.

If there is something that I can add, which will be useful to your teaching,
to your students, or to your research, then please let me know as soon
as possible.
---Greg

p.s. Like the 1st edition, the 2nd edition will be available for free in
electronic form. The printed edition will be published by The American
Mathematical Society.

Steve Coleman

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May 29, 2020, 1:47:12 AM5/29/20
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I have not seen your book yet but its been on my Amazon wish list for a while. I have been hesitant to buy too many 'old version' books and was hoping for some updated syntax examples for me to cut my teeth on.

While as a newcomer I obviously cannot comment on your first edition,  but I can mention what specifically I have been looking for but have not found yet. 

Symbolic manipulation, substitutions, simplification for basic physics formulas. I have done some limited symbolics with Mathematica, but I just had to retire for medical reasons and can't personally justify the cost. I have heard good things about Sage symbolic manipulation capabilities, but so far I have not seen any really good discussion on it, particularly for the newest version. I apparently tried to join the Sage bandwagon right when so many changes took place, and many older code examples just don't seem to work right. If you had a discussion on symbolics it would be a no-brainer to buy your latest edition.

Thanks for your work on documenting Sage. I look forward to your new book. 



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Furkan Semih Dündar

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May 29, 2020, 1:47:13 AM5/29/20
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Dear Bard,

Recently I have written 3 physics related tutorials licensed under GPL 3. The topics are 1) Lorentz force (i.e. electromagnetic force on a charged particle) 2) Lagrangian mechanics 3) Hamiltonian mechanics.

If you would like to include them, you can find them on https://github.com/fsdundar/phys-tutorial-sage

Best wishes,
Furkan.

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kcrisman

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May 29, 2020, 8:37:43 AM5/29/20
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I'm embarking on an exciting project over the next six weeks. I'm updating
my book, Sage for Undergraduates, to be compatible with the new Python3
syntax. In this 2nd edition, I'll also add a few projects from macroeconomics,
epidemiology, and differential equations.

Greg, that is great news!  Thanks to AMS for supporting this, and to you for wanting to embark on a second edition (huge amount of work). 
 

I'm curious if anyone has any requests for me? Was there a topic that I left
out in the 1st edition, that you think I should have included? Was there a
topic or concept that I covered badly? Don't be afraid to criticize---I don't
mind at all.

 
Live code examples, perhaps Jupyter/CoCalc worksheets for each chapter?   Particularly as I assume you won't be using PreTeXt to have a "live" version :-) I think that would be very helpful for practical usage.  I know I am always demotivated when I have to try to copy and paste from pdfs for code, it's very tiresome to get the cursor to go exactly where you want, etc.  But beginners will be doing a lot of copying.  A monolithic pdf as the only option makes it harder to disseminate individual examples/projects easily.  

kcrisman

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May 29, 2020, 11:51:02 AM5/29/20
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Symbolic manipulation, substitutions, simplification for basic physics formulas. I have done some limited symbolics with Mathematica, but I just had to retire for medical reasons and can't personally justify the cost. I have heard good things about Sage symbolic manipulation capabilities, but so far I have not seen any really good discussion on it, particularly for the newest version. I apparently tried to join the Sage bandwagon right when so many changes took place, and many older code examples just don't seem to work right. If you had a discussion on symbolics it would be a no-brainer to buy your latest edition.


That is true, as a more "advanced" section.  See e.g. https://math.stackexchange.com/questions/2383818/sagemath-replace-an-expression-in-a-formula-by-a-function-define-previously for one of the many widely scattered examples of where to find info on doing this well :-(

kcrisman

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May 29, 2020, 11:58:04 AM5/29/20
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I'm curious if anyone has any requests for me? Was there a topic that I left
out in the 1st edition, that you think I should have included? Was there a
topic or concept that I covered badly? Don't be afraid to criticize---I don't
mind at all.

The coverage for engineering-related is great, and linear/finite math is good too.  I wonder more about data analysis, and discrete math for computer science topics.  Get a little basic probability (of the type in such a course) in addition to the combinatorics.  Just thinking of this because CS/"data science" is burgeoning so much, and so it would widen the scope of who might be interested in using it.  Which would be good :-) 

Gregory Bard

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Jun 5, 2020, 2:52:38 PM6/5/20
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Dear Prof Crisman, Prof Coleman, and perhaps Prof Dündar,

On the specific issue of symbolic manipulation inside of physics formulas, there's a little bit of risk because I haven't taught a course that uses that. The last time I took such a course would have been the Summer of 1996 or 1997. (I'm not certain.) So, it has been a while! :) With that in mind, would you both please examine these two examples?

The first is pretty pedestrian, just converting Newton's Inverse-Square Law of Gravity to polar coordinates.


The second considers two electric charges of q_1 Coloumbs, located at (0, L) and (0, -L). Another charge of q_2 Coulombs is located at (x,y). The example computes the Coulomb's Law force, again in polar coordinates. Of course, if rho is fairly large, then this physical arrangement can be considered equivalent to an electric charge located at the origin, but with a charge of 2q_1 Coulumbs. I used a Taylor expansion of b=1/rho at b=0 (i.e. rho=infinity), of the sixth degree, and converted back from b's to rho's. Accordingly, we get some rho^4 and rho^6 terms, with and without even powers of either sin(theta) or cos(theta), depending on which simplify command is chosen.


It might be cool to make a plot of the coordinate plane, and see for which points this approximation is accurate to within +/-1%.

Is this the sort of thing that is desirable? Is it too easy? too hard? Is the physics correct? Perhaps you had something completely different in mind? Would degree 8 be better?

I can easily add this as a new section, late in Chapter 4.
---Greg

kcrisman

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Jun 6, 2020, 3:40:11 PM6/6/20
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I'll let others comment on correctness and interest, but at least the first one is a reasonable example of a question someone might have for such manipulation and, well commented, would serve well.  (I did not have time to look at the second, my apologies.)

Steve Coleman

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Jun 6, 2020, 10:55:03 PM6/6/20
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Thanks! You have actually exceeded my expectation, because both examples will be useful to work from for some graphic illustrations I need to redo in a paper I started writing more than years ago. That paper then got put on hold due to my worsening medical condition and having to retire, but maybe I'll be able to move forward using this example to work from.

I just need to change/add in a relativistic Lorentz component to your first example and graph the polar coordinate system as either a wireframe or energy heatmap to get my main point across.  Trying to illustrate some specific effects in the time domain while using static illustrations really leaves a lot to be desired, but these examples might give me a good path forward. So, there may be hope for that paper after all. I can't wait to play with this as it would make a dramatic improvement to that particular illustration and possibly several others.

I can't wait to be able to buy your book.

Steve

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Furkan Semih Dündar

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Jun 7, 2020, 2:43:34 AM6/7/20
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Dear Greg,

In case of Newton's force there should be a minus sign in front, since the force is attractive. I also checked the first few equations of the electromagnetic case, it looks OK though I haven't checked the equations that come afterwards.

Best wishes,
Furkan Semih.

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enthor

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Jun 2, 2021, 3:48:37 PMJun 2
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Hello Professor Bard,

I look forward to reading the new edition. 

I wonder what you think about writing a version geared towards younger students. For the last couple of years I have concerned myself with the woeful state of student preparation for college-level STEM majors as evidenced by the standardized test scores ... in math and everything else. I haven't come up with any hopeful answers yet except for a) increasing interest and motivation (somehow); b) attention-focusing mental disciplines (e.g. "Flow"); and c) math counselors / coaches assigned to each student for their entire academic career. I think SageMath could be pretty great. 

Best wishes!

Gregory Bard

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Jun 2, 2021, 4:56:20 PMJun 2
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I think that this idea is superb.

There is a huge opportunity for products aimed at families, where someone roughly of age 13-19, feels drawn towards STEM, and wishes to voluntarily "play" with STEM concepts in the summer---a time when schools (at least in the USA) are closed. This is analogous to someone of the same age who feels attracted to soccer or swimming, and who voluntarily devotes a few weeks in the summer to go to a camp dedicated around that sport. The young person would instead go online, and engage with Sage, math, physics, Python, chemistry, and perhaps some economics too (e.g. linear programming).

Many schools for that age group have a "math and science club" or a "STEM club" that could point young people toward these activities. These activities could also be enjoyed by young people on weekends during the school year.

The computer gives a lot to such an enterprise, as compared to a textbook without the use of a computer. There can be graphics, animations, and even encouraging sounds when a "challenge" is successfully completed. We can have videos from university (or school) faculty who have authored any particular lesson, introducing the concepts. Due to the pandemic, vastly more teachers and professors know how to make videos now, compared to 2018.

Of course, I won't be able to devote any time towards this while the 2nd edition is still in progress. The 2nd edition "owns" my time this summer. I can contribute time starting in September of 2021.

I think the key to success would be to have a medium-sized group of authors, a diverse mix of high-school teachers and university professors, making mini-projects and challenges in many subjects, perhaps with some peer-review (but not too much). The teachers and professors who volunteer their time should not be micromanaged on things like fonts and indentation. That sort of nit-picking about typesetting is a wet blanket that smoothers and asphyxiates creativity.
---Greg

p.s. In case someone wants something right away, for an eager teenager bubbling with early-June energy and enthusiasm, I recommend:
  • B. Averbach and O. Chein, Problem Solving Through Recreational Mathematics, published by Dover Publications in 1999. [Originally published by W. H. Freeman & Co. in 1980.] (400 pg.)
  • J. Beissinger and V. Pless, The Cryptoclub: Using Mathematics to Make and Break Secret Codes, published by CRC Press in 2006. (215 pg.)
  • G. Ellison. Hard Math for Middle School, self-published in 2010, but really good. (238 pg.)
  • S. Gordon, F. Gordon, A. Tucker, and M. Seigel, Functioning in the Real World---a Pre-Calculus Experience, published by Pearson, 2nd edition in 2003. (800 pg.) Note: this is more suited to the classroom than to recreation.
  • B. Kastner, Space Mathematics---Math Problems Based on Space Science, published by Dover Publications in 2012. [Reprint of Space Mathematics: A Resource for Secondary School Teachers, published by NASA in 1985.] (192 pg.)
  • ... and since employers and universities alike are decrying the lack of "soft skills" (organizational and communications skills) in today's "under 25" generation, I would be doing a teenager a disservice if I did not also recommend: D. Allen, M. Williams, and M. Wallace, Getting Things Done for Teens---Take Control of Your Life in a Distracting World, published by Penguin Books in 2018. (288 pp, many of which are cartoons.)

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enthor

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Jun 2, 2021, 5:38:33 PMJun 2
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Professor,

Thank you for the enthusiastic response! 

I am not an educator. I write programs sometimes.

I wrote something about attention focusing, see
github, user enthor. Perhaps useful! 

Anyone who wishes may contact me via gmail
user id b252t11q. 

I would love it if we could solve this problem.

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