/sci/ - Science & Math » Thread #14266020

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Anonymous Sun 27 Feb 01:34:27 2022 No.14266020 View Reply Original Report

Quoted By: >>14266035 >>14266038 >>14266044 >>14266091 >>14266095 >>14266112 >>14266496 >>14266512 >>14266599 >>14269960 >>14270859 >>14270903 >>14270915 >>14272187 >>14274115 >>14276195

How successful would a Complete Undergraduate and Graduate Mathematics Textbook be? Sort of like Picrelated but comprehensive and covering the total university curriculum for Mathematics. I may work on one after I finish my Ph.D. Thoughts? I think it'd be kinda nice to have the whole formal field in one text (set?) because works like Picrelated don't cover it in depth.

Anonymous

Anonymous Sun 27 Feb 2022 01:36:20 No.14266024 Report

Quoted By: >>14266711

Okay there Bourbaki Jr.

Anonymous

Anonymous Sun 27 Feb 2022 01:40:07 No.14266031 Report

Quoted By:

unless it's several people writing, it will be mediocre.

Anonymous

Anonymous Sun 27 Feb 2022 01:41:27 No.14266035 Report

Quoted By: >>14266047

>>14266020
I don't see how you can make a manageable sized textbook. What topic do you think you'd include? Would you also have a part that introduces proof writing or assume that about the reader?
I assuming you would at least try to cover topology, abstract algebra, and analysis.

Anonymous

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Anonymous Sun 27 Feb 2022 01:42:04 No.14266037 Report

Quoted By: >>14268219

it's pretty good.

Anonymous

Anonymous Sun 27 Feb 2022 01:42:42 No.14266038 Report

Quoted By: >>14266047

>>14266020
Seems like a pretty interdasting idea.

How in depth will it be? Will it be an introductory text, or a reference book? Will you be including practice problems as well?

Anonymous

Anonymous Sun 27 Feb 2022 01:44:56 No.14266044 Report

Quoted By: >>14266091

>>14266020
It would be shit. Far too inflexible.

Anonymous

Anonymous Sun 27 Feb 2022 01:46:36 No.14266047 Report

Quoted By: >>14266064

>>14266035
>>14266038

It would be quite large. Yes, proof is a very important part of the university curriculum. It would be included.

Anonymous

Anonymous Sun 27 Feb 2022 01:50:28 No.14266064 Report

Quoted By:

>>14266047
There are roughly a total of 32 topics in the university curriculum (undegrad + graduate). If the book covered 100 pages for each topic, the textbook would be ~3000 to ~4000 pages. Two times bigger than the Aleksandrov books. I think it will sell, it's quite handy. Imagine spending $200 on one set for 8 years, compared to ~$2,000 otherwise.

Anonymous

Anonymous Sun 27 Feb 2022 02:06:04 No.14266091 Report

Quoted By:

>>14266020
You'd need a book series.
Also you'd probably have to limit it to core subjects.

For example, there is the three series Analysis book by Amann Escher that touches the core of undergraduate analysis and covers some abstract algebra in Volume I. An algebra book like Rotman 3E is probably a fine followup. Together I think these 5 books would give a significant coverage of the core of undergraduate mathematics. That's a total of 2.5k pages which isn't horrible for a book series. Certainly missing PDEs and probability and some other stuff though.

I think there can be some interesting organizational benefits like how Amann and Escher are able to use the language of algebra freely as they explore analysis. But as >>14266044 said the pedagogical benefit of doing so comes at the loss of flexibility. As in, you kind of have to use it as your primary source in order to be able to follow along.

Another similar effort for Analysis is Jacob and Evans A Course in Analysis series which much like Stein Shakarchi tries to show the unified picture of Analysis.

Anonymous

Anonymous Sun 27 Feb 2022 02:09:36 No.14266095 Report

Quoted By: >>14266106

>>14266020
Will you be writing it so that anyone who picks it up-given the right level of determination-can learn Mathematics, or will it act as more of a supplementary text for Mathematics majors?

Anonymous

Anonymous Sun 27 Feb 2022 02:20:00 No.14266106 Report

Quoted By:

>>14266095
The first and the second, sort of. It would start at Calculus, peak at graduate Algebra and end with graduate Probability/Stochastic Equations.

Anonymous

Anonymous Sun 27 Feb 2022 02:22:51 No.14266112 Report

Quoted By:

>>14266020
I don't think it is possible in a single volume if you want a comprehensive treatment unless you leave most theorems as exercises.

Anonymous

Anonymous Sun 27 Feb 2022 06:07:49 No.14266496 Report

Quoted By: >>14266497

>>14266020
The closest current example is James Stewart's calculus, since it comfortably covers 3 classes and is used by 70% of calc classes. That book fucking blows. I seriously hate it

Anonymous

Anonymous Sun 27 Feb 2022 06:09:25 No.14266497 Report

Quoted By:

>>14266496
Yeah it's sort of an eyesore.

Anonymous

Anonymous Sun 27 Feb 2022 06:25:32 No.14266512 Report

Quoted By: >>14266514 >>14268247 >>14268341 >>14270901 >>14270915

>>14266020
What it would need:
Calc 1-3
Differential equations
Linear algebra
Complex analysis
Numerical Analysis
It can be done. (Don't say probability, this isn't high school. Don't say topology, you aren't special. Don't say real analysis, this is for undergrad)

Anonymous

Anonymous Sun 27 Feb 2022 06:28:04 No.14266514 Report

Quoted By: >>14266606

>>14266512
Stupid list.

Anonymous

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Anonymous Sun 27 Feb 2022 08:41:41 No.14266599 Report

Quoted By: >>14270936

>>14266020
They have one for undergrad engineering

Anonymous

Anonymous Sun 27 Feb 2022 08:47:34 No.14266606 Report

Quoted By: >>14266611

>>14266514
Whats your major?

Anonymous

Anonymous Sun 27 Feb 2022 08:50:13 No.14266611 Report

Quoted By: >>14266623

>>14266606
gender study

Anonymous

Anonymous Sun 27 Feb 2022 08:59:46 No.14266623 Report

Quoted By:

>>14266611
Lol

Anonymous

Anonymous Sun 27 Feb 2022 10:24:52 No.14266711 Report

Quoted By: >>14266733

>>14266024
/thread
They really are useless books for learning but if you already know, they're really fucking fun.

Anonymous

Anonymous Sun 27 Feb 2022 10:58:22 No.14266733 Report

Quoted By:

>>14266711
Got any suggestions for books that break down learning specific maths

Anonymous

Anonymous Sun 27 Feb 2022 21:48:57 No.14268219 Report

Quoted By: >>14268302 >>14270924

>>14266037
Is it proof based?

Anonymous

Anonymous Sun 27 Feb 2022 21:58:06 No.14268247 Report

Quoted By:

>>14266512
Terrible, terrible list.
The real one should be:
Analysis (single variable)
Linear algebra and geometry
Analysis (multivariable)
Differential geometry in R^3
Linear algebra from an abstract perspective
Differential equations
Complex analysis
PDE's
Topology

Anonymous

Anonymous Sun 27 Feb 2022 22:14:41 No.14268302 Report

Quoted By:

>>14268219
Mathematical methods usually implies it ain't (as does physics and engineering which are not Knowledge such as Axiom of Choice, but misguided attempts at using the Divine to understand the world).

What I'm saying is physicists are stuck in the Cave of Plato. At least engineers are part of the real world since they get jobs, while physicists live in some weird limbo between sense data and some ideal ivory tower. Physicists literally have another cave within their cave.

Anonymous

Anonymous Sun 27 Feb 2022 22:29:08 No.14268341 Report

Quoted By: >>14269937

>>14266512
>What it would need:
Intro to Proofs
Number Theory
Calc 1-3
Physics 1-3 (no reason why not)
Linear Algebra
Differential Equations
Complex Analysis
Abstract Algebra
Probability and Statistics (yes, fuck you)
Numerical Methods and Analysis
Linear Programming
Geometry and Differential Geometry
Analysis

Anonymous

Anonymous Mon 28 Feb 2022 15:58:48 No.14269937 Report

Quoted By: >>14270236

>>14268341
>Number Theory
???
>Abstract Algebra
???

Anonymous

Anonymous Mon 28 Feb 2022 16:10:46 No.14269960 Report

Quoted By:

>>14266020
It would not work since universities tend to switch around their curriculum a lot.
Most courses dont have books but lecture notes which are often preprinted versions of books the professors are writing currently.

Since a book is not easily changed not tailored to the students needs, the book becomes an monolithic obstacle.
For every change in each course would require a reprint. (you expect the students to purchase a new "good for your entire education" book each year??)

It does *seem* convenient to have all ideas at your disposal in a single source.
However, ideas are fluid and collecting them in a single printed source thus solidifies them beyond repair.
This idea is not suited to the need of education, but to the need of a retailer.

Anonymous

Anonymous Mon 28 Feb 2022 18:23:50 No.14270236 Report

Quoted By: >>14270837

>>14269937
theyre different courses

Anonymous

Anonymous Mon 28 Feb 2022 22:00:35 No.14270837 Report

Quoted By: >>14270940

>>14270236
Yes but why would a physicist take them?

Anonymous

Anonymous Mon 28 Feb 2022 22:08:14 No.14270859 Report

Quoted By:

>>14266020
https://web.evanchen.cc/napkin.html

Anonymous

Anonymous Mon 28 Feb 2022 22:29:46 No.14270901 Report

Quoted By:

>>14266512
>Don't say probability
Oh okay, so a useless book for any real applications then? Why not just aim it at graduate level pure mathematicians to wank off to and get nothing of import done as per usual?

Anonymous

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Anonymous Mon 28 Feb 2022 22:31:40 No.14270903 Report

Quoted By:

>>14266020
Basic coverage of everything but unironically based as 2 month revision crammer or a quick overview of everything

Anonymous

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Anonymous Mon 28 Feb 2022 22:35:53 No.14270915 Report

Quoted By:

>>14266020
>Complete Undergraduate and Graduate
>graduate
You're delirious.

The Handbook of Mathematics covers a lot but I still wouldn't say it covers a full undergrad.
>>14266512
You have no standards.

Anonymous

Anonymous Mon 28 Feb 2022 22:39:11 No.14270924 Report

Quoted By:

>>14268219
Look, do you want a comprehensive text that is useful as a reference or a comprehensive text that is so godawfully large that it is almost useless?

I would say a methodology text is EXACTLY what would be desired. Those who want the formal proofs can get them in dedicated texts.

If you want something to actually learn from, why constrain yourself to a text? Develop and record a full end-to-end curriculum at that point. That's what we're moving towards anyway.

Anonymous

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Anonymous Mon 28 Feb 2022 22:44:31 No.14270936 Report

Quoted By: >>14271735

>>14266599
>blocks your path

Anonymous

Anonymous Mon 28 Feb 2022 22:46:54 No.14270940 Report

Quoted By: >>14272448

>>14270837
i thought we were aiming a book for math majors
but number theory and abstract algebra are quire fun and rewarding

Anonymous

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Anonymous Tue 01 Mar 2022 07:13:42 No.14271735 Report

Quoted By: >>14272808

>>14270936
>that book
>written 1941
Lol
Lmao

Anonymous

Anonymous Tue 01 Mar 2022 14:26:26 No.14272187 Report

Quoted By:

>>14266020
Heavy.

Anonymous

Anonymous Tue 01 Mar 2022 17:04:47 No.14272448 Report

Quoted By:

>>14270940
Oh yeah nevermind I'm retarded

Anonymous

Anonymous Tue 01 Mar 2022 19:50:27 No.14272808 Report

Quoted By: >>14272809 >>14273143

>>14271735
Literally nothing has changed at the undergraduate level except the introduction of numerical solutions by computers.

Anonymous

Anonymous Tue 01 Mar 2022 19:52:03 No.14272809 Report

Quoted By: >>14273149 >>14276172

>>14272808
>except the introduction of numerical solutions by computers.
Which mind you, are discouraged as it bypasses the learning objectives of finding analytical solutions to problems.

Anonymous

Anonymous Tue 01 Mar 2022 22:20:14 No.14273143 Report

Quoted By: >>14273437

>>14272808
Of course the knowledge and techniques were developed long ago anon. But have you ever read a math or physics book from that era? Talk about a dry read, I've got a prentice hall strength of materials book from 1937, man did it read like sandpaper.

Anonymous

Anonymous Tue 01 Mar 2022 22:21:56 No.14273149 Report

Quoted By:

>>14272809
>discouraged as it bypasses the learning objectives of finding analytical solutions to problems.
Seems like as time goes by more and more schools will encourage it if for nothing else but out of convenience

Anonymous

Anonymous Wed 02 Mar 2022 00:20:21 No.14273437 Report

Quoted By: >>14273871

>>14273143
S&S was a livelier read than Stewart by a mile

Anonymous

Anonymous Wed 02 Mar 2022 05:30:11 No.14273871 Report

Quoted By: >>14274501

>>14273437
There is a antique bookstore near me and I like to check out engineering, math and physics books by their decade, so far the easiest one to understand is from the year 1902 on thermodynamics. Straight to the point, filled with just the right amount of practice problems, graphs and problem solving advice

Anonymous

Anonymous Wed 02 Mar 2022 09:35:32 No.14274115 Report

Quoted By:

>>14266020

You could take all the free Oxford University undergrad notes and bind them.
It wouldn't flow nor be compact, but it's equivalent in content alone to what you want.

It's something I've wanted for a while.
"The one-stop undergrad book."
It's why I was enamored with Bourbaki and the napkin project.

Anyway, some handbooks that throw in exercises come close.
Best example I've seen so far:

Handbook of Mathematics by Vialar Thierry

If not that, then the one by Bronshtein et al.

Anonymous

Anonymous Wed 02 Mar 2022 14:56:14 No.14274501 Report

Quoted By: >>14276074

>>14273871
Not gonna leave us without the title.

Anonymous

Anonymous Thu 03 Mar 2022 06:19:26 No.14276074 Report

Quoted By:

>>14274501
Don't kbow where I placed it in my reading area anon. I'll try and find it

Anonymous

Anonymous Thu 03 Mar 2022 08:10:31 No.14276172 Report

Quoted By: >>14276286 >>14276309

>>14272809
>Which mind you, are discouraged as it bypasses the learning objectives of finding analytical solutions to problems.

lol the world is nonlinear. existing problems of any import will be non-linear in nature as all closed form solutions have already found applications. you act as if the two are mutually exclusive. in fact the numerical scientist will have the closed form solutions as his starting point.

Anonymous

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Anonymous Thu 03 Mar 2022 08:30:20 No.14276195 Report

Quoted By:

>>14266020
You really want to go with the one piece at a time. Now say you want to do Calculus you are going to do a little bit of Algebra, and your skills will be chiseled. You can even backtrack and do linear algebra and that whole thing just gets a lot more developed.

Anonymous

Anonymous Thu 03 Mar 2022 09:43:40 No.14276286 Report

Quoted By:

>>14276172
It's a Nonlinear World - enns
https://libgen.rs/book/index.php?md5=6FB6EA5DBC1B9768E6137C2BECCD1953

Anonymous

Anonymous Thu 03 Mar 2022 10:02:03 No.14276309 Report

Quoted By:

>>14276172
and the computationally trained scientist will have far more and higher quality sense making experiences.

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