Mathematics Cheat Sheet [pdf]

https://ourway.keybase.pub/mathematics_cheat_sheet.pdf

by weatherlight • 5 years ago

225 67 5 years ago

ourway.keybase.pub

analog31• 5 years ago

I noticed that the physical constants might be outdated. As I understand it, the Planck constant is now considered to be a defined quantity.

https://en.wikipedia.org/wiki/Planck_constant#Understanding_...

exporectomy2• 5 years ago

Indeed. Avogadro's number too now has an exact value and all that stuff that depends on it has changed with it.

pixelpoet• 5 years ago

Typo on page 56, "Laprange" instead of "Lagrange". Also I find it strange that logarithms are part 10 / page 121, after Newtonian mechanics.

meigwilym• 5 years ago

Also

PART 2: MATHEMTAICAL SYMBOLS

neatze• 5 years ago

My first thought what an outstanding pdf, my second though;

this should be in latex on github/gitlab, so people can contribute and maintain, I would love to add numerical psedo code to as much equations as I possibly can with my primitive comprehension of mathematics.

timeinput2• 5 years ago

Yeah that was my first thought too. I want the LaTeX so I can re-typeset it.

exporectomy2• 5 years ago

Might be some copyright issues. I see non-attributed images in the Moments of Inertia section that are licensed CC BY-SA on Wikipedia. Also apparently some text book scans.

accacio3• 5 years ago

Let's do this; I just created https://github.com/Accacio/math-cheatsheet, When I get time I will implement CI/CD to genereate the pdfs

app4soft4• 5 years ago

When I get time I will implement CI/CD to genereate the pdfs

You may take a look on `.travis.yml`[0] used for MetaPost + ConTeXt rendition of Oliver Byrne's "The first six books of the Elements of Euclid".[1]

[0] https://github.com/jemmybutton/byrne-euclid/blob/master/.tra...

[1] https://github.com/jemmybutton/byrne-euclid/releases/tag/Cur...

alister• 5 years ago

This came up 2 years ago on Hacker News[1] and I wrote the following:

/QUOTE

I think the author's page (Alex Spartalis) deserves to be mentioned:

https://www.alexspartalis.com/cheat-sheet.html

He has the same version (v2.10) there and mentions that, "The Web version does not include the distribution functions due to file size restrictions. Email me if you would like a copy of these." That explains why pages 213-330 are missing. Someone should offer to upload the full copy to keybase.pub (or someplace) since his personal site can't handle the load.

People sometimes do tremendous work creating a program/book/artwork, and want the world to see it, but don't get around to really share it or promote it.

ENDQUOTE/

However, now it appears that Alex's site no longer exists and nobody (including me) ever did upload the full copy to keybase.pub.

[1] https://news.ycombinator.com/item?id=20048205

app4soft4• 5 years ago

Also, here is backup of Alexander Spartalis' 640-pages "The Mathematics Handbook", v4.1, June 2nd, 2019.[0,1,2]

However, now it appears that Alex's site no longer exists

In 2019 Alex moved to new site, which also is not availabale anymore, BUT there are backups of both sites.[0,3]

JFTR, You may try contact with Alex Spartails via Facebook & Instagram.[4,5]

[0] http://web.archive.org/web/20200127012510/http://mathscheats...

[1] https://drive.google.com/file/d/1MM2Hu5qlptkg8dNLM9QibeXHErL...

[2] https://www.scribd.com/document/412167295/the-mathematics-ha...

[3] http://web.archive.org/web/20190530065518/https://www.alexsp...

[4] https://m.facebook.com/alexspartails

[5] https://instagram.com/alexspartails

kwanbix3• 5 years ago

Isn't it here? http://mathscheats.weebly.com/2019-downloads.html

HelloNurse• 5 years ago

That is "The Mathematics Handbook", v4.1

timeinput2• 5 years ago

This site might have an alternative copy that's been updated more recently: http://mathscheats.weebly.com/2019-downloads.html

I still wish there was LaTeX for it.

app4soft4• 5 years ago

I still wish there was LaTeX for it.

As email probably unavailable, there are Alex's Facebook/Instagram.[0]

[0] https://news.ycombinator.com/item?id=27468908#27469861

_448• 5 years ago

Well, this[0] takes the cake for the way Maths is promoted on that website :)

Stumbled upon the website while searching for the complete version of the OP link.

[0] http://nanar.com

vim-guru• 5 years ago

Wow. What a treasure trove Thanks for posting!

danbruc3• 5 years ago

What is this useful for, page 45?

Rational Numbers: Every rational number can be written as r = [(r - 1) + (r + 1)] / 2

I would have expected p / q with p and q integers or some variation of this.

gspr2• 5 years ago

That is indeed strange. And why restrict it to rationals, when it's true for every real (or every complex, whatever)? It's even true for integers, under a suitable interpretation of what is meant by dividing by 2 in that case.

bidirectional• 5 years ago

It's also totally trivial when you rewrite it slightly: (r + r + 1 - 1) / 2. So basically adding r to itself to get 2r then dividing by 2 gives you back r, with a pointless plus and minus 1 thrown in.

nabla9• 5 years ago

It's trivial only if you are simplifying mathematical expression.

When you have to go the opposite direction, you start with r and must turn it something that fits some other expression, there are infinite ways to proceed. Right ones rarely just pop up into your mind.

Remembering trivial identities things like that are useful as small intermediate steps when manipulating expressions.

gspr2• 5 years ago

Sorry if I sound exclusively negative about someone else's hard work – that is not the intention.

I find people's obsession over memorizing mathematical symbols (part 2) really strange. If you understand what the concepts involved in a symbol mean, you won't have a problem recognizing the commonly used symbols. And if you don't understand what the concepts involved mean, then having memorized the symbol does you no good.

Am I missing something?

Edit, since I'm apparently in a very critical mood today: It seems very strange for a document to barely scratch the absolute essentials for something as important and broadly applicable as linear algebra, yet go on and on and on with quite esoteric lists of special primes that surely concern at most researchers in specialized parts of number theory? Of all the lists of primes that the author chooses to focus on, I must say I had only heard of three (Fibonacci, Mersenne and Gaussian). Granted, my PhD is in a very different part of math, but this seems a bit… crazy… in such a document. (Also, are the lists "even primes: 2", and "odd primes [insert list of all other primes here]" meant as jokes?)

Edit 2: Same goes with the obsession with pi. The amount of effort and space spent on features of primes and pi that are incredibly unimportant except to very specialized researchers is… a bit insane in a document like this.

danbruc3• 5 years ago

I don't think this is supposed to be a serious attempt to write a math reference book, this looks much more like the result of personal interests. That would very well explain why a lot of room is allocated to niche topics while on the other hand entire areas areas of mathematics are missing.

bryanrasmussen• 5 years ago

If you understand what the concepts involved in a symbol mean, you won't have a problem recognizing the commonly used symbols. And if you don't understand what the concepts involved mean, then having memorized the symbol does you no good.

this would imply in learning a new language if you know what the concepts a word refers to means that you won't have any difficulty recognizing the word - no matter how many words there are, how long the statement you are reading is, and how similar various words are to each other?

When learning something it is nice to have a reference.

mannykannot• 5 years ago

Indeed - formal symbols have no intrinsic meaning, and one must learn their meaning as a separate step from learning their form and how to recognize them.

One's chances of finding out what an unfamiliar symbol means in context (or a familiar symbol in unfamiliar usage) is greatly helped (though not completed) if you can get a name or one or more précis of its uses.

stonemetal12• 5 years ago

If it is about memorizing then yeah, I don't get it. If it is a handy reference for I found a weird symbol what does it mean, then I do. When I was 14, I found a 1960s era electrical engineering text book. Being rather nerdy I bought it and read most of it. The only problem was I didn't understand the math because it had this weird S symbol in it. I didn't know what it was called or what it was about so I couldn't even formulate the question to find out more.

beforeolives• 5 years ago

Do people really use this or any other of the cheatsheets you find online?

In my experience, any cheat sheet that I didn't make myself is useless to me. Going directly to the sheet without having done the synthesis of information yourself skips the most important part of the process.

kwanbix3• 5 years ago

Same for me. I need to start with the bulk of the info and start to compress it to be helpful to me.

parenthesis• 5 years ago

Yes, you make your own sheets of the things you can never quite remember.

Often going through that process leaves you remembering them.

nebulous12• 5 years ago

I do. Mainly for things I don't really intend to memorize. It's just an easier reference than, say, a man page.

overcast• 5 years ago

Pretty much anything is easier to reference than a man page :) I wish the standard for man, would be to include examples. But maybe I'm in the minority of people who learn by example.

kokanator• 5 years ago

They tend to be a great resource for rarely used knowledge.

The key is remembering you have a cheatsheet for that rarely used knowledge.

HWR_14• 5 years ago

These cheetsheets aren't meant to be printed off and carried into your open book tests. They are meant to be greppable formula lookups. They're useful if you can define the problem but don't know the equation off your head to solve it. Think something like differentiating a trig function after you haven't used it in a while or looking up some statistical approximation.

Ceezy• 5 years ago

Math cheatsheet made by others are not very useful. When it's not about a large public API it doesn't really make sense. People also forget that most theorems/formulas have slight modifications that are very useful but make these kind of enterprise very difficult.

antegamisou2• 5 years ago

Theoretical Computer Science Cheat Sheet is a more elegant and concise actual math cheat sheet, compared to this handbook.

https://www.tug.org/texshowcase/cheat.pdf

belter2• 5 years ago

Some interesting constants and series but a lot of Trigonometry, Differentiation and Calculus formulas...More Math than Computer Science I would say.

helloworld11• 5 years ago

Nope, for someone who is almost completely ignorant of mathematics and especially tripped up in learning more because they don't know enough mathematical notation, the OP is much better because it actually explains the meaning of various notation symbols. Your link just jumps into formulas full of them without contextualizing these basics.

antegamisou2• 5 years ago

Would you call a two hundred page document a cheat sheet?

Humdeee• 5 years ago

I immediately went to save this file to my collection of ebooks/pdfs. I have the same file from mid 2019 apparently!

contravariant• 5 years ago

Going by the dates in the file and the listed values of the physical constants it also hasn't been updated in a while.

127• 5 years ago

Probably the best applied math "tutorial" without all the bullshit I've yet seen is the mathematical background appendix in Probabilistic Machine Learning: An Introduction by Kevin P. Murphy.

dzink• 5 years ago

In Bulgaria there is a little yellow book that carries all the rules in mathematics one would need through all of K-12 and then some. It has quadratic formulas, limits, trigonometry (including sin/cos conversion tables), not as many physics formulas though. Everything is explained succinctly as well. It is a commonly used and required book in all schools and it gives you a quick review of anything you need before math competitions, tests, or just brush up after a while. There absolutely needs to be a book like that for US kids and the baseline math levels here will rise up substantially.

belter2• 5 years ago

Is it in Cyrillic or Latin ? Do you know if its available online ?

aanastasov2• 5 years ago

It's in Cyrillic. The official title is "Четиризначни математически таблици и формули".

aanastasov2• 5 years ago

The small yellow book might have already fallen out of fashion. I graduated from a math high school in Bulgaria about 10 years ago, and I vaguely remember the yellow book being referred to as if it was popular during the stone age.

raninepaths• 5 years ago

Is it available in english? Or any other equivalent book in english?

CalChris• 5 years ago

The Art of Problem Solving series has this. The Basics, Vol. 1, and Beyond, Vol. 2, are a lot like that. They aren't course material. AOPS has that with Prealgebra thru Calculus. These are distillations for contest math with explanations and problems.

bernardv• 5 years ago

That’s quite a cheat sheet. Thank you.

swiley• 5 years ago

That's pretty great! Notation and shorthand seems to trip even the most capable mathematicians up. I remember making these all the time as a student to try an help. The probability section might be the most important IMO.

synergy20• 5 years ago

This is awesome, I use evince and okular to open the pdf and could not find the table-of-content on the left side of the pdf readers, which is an essential feature for PDFs, can the PDF re-generated to produce that?

shimonabi• 5 years ago

In my country every engineering or math student had a copy of a translation of a book by the Russian authors Bronshtein and Semendyayev.

https://en.wikipedia.org/wiki/Bronshtein_and_Semendyayev#Sem...

wirrbel• 5 years ago

+1 for Bronstein. I had classmates in my physics program who brought their family bronstein (later my father who majored in German philology told me he had a Bronstein himself for when he tried to study civil engineering, but gave it away to a friend after switching majors, I would have loved to have a family Bronstein :-) )

mmcgaha• 5 years ago

Eddie Shore's blog has a true cheat sheet sized "Big Font Math Reference".

https://drive.google.com/open?id=1h_B0QG2_xeki58q-Y2ubcmmwvr...

arh68• 5 years ago

Wait, what? Is this a rendering bug, or a typo?

γ = 0.527721566...

I think it's closer to 0.577 215 664 901 ... see https://en.wikipedia.org/wiki/Euler%E2%80%93Mascheroni_const...

fmajid• 5 years ago

Reminds me of the Schaum’s Outline Mathematical Handbook of Formulas and Tables by Murray Spiegel, which is more concise and better organized. My uncle gave me his copy when I was 12 years old and that got me started on my road to mathematics.

Mathematics Cheat Sheet [pdf]

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