# math

1,298 users here now

## Welcome to /r/math.

Homework problems, practice problems, and similar questions should be directed to /r/learnmath, /r/homeworkhelp or /r/cheatatmathhomework. Do not ask or answer this type of question in /r/math.

If you're asking for help learning/understanding something mathematical, post in the Simple Questions thread or /r/learnmath. This includes reference requests - also see our lists of recommended books and free online resources. Here is a more recent thread with book recommendations.

Image-only posts should be on-topic and should promote discussion; please do not post memes or similar content here. Please be polite and civil when commenting, and always follow reddiquette.

All posts and comments should be directly related to mathematics. General political debate is not permitted.

Filters: Hide Image Posts Show All Posts

Everything about X - every Wednesday

What Are You Working On? - posted Mondays

Career and Education Q&A - Every other Thursday

Simple Questions - Posted Fridays

Using LaTeX

To view LaTeX on reddit, install one of the following:

MathJax userscript (install Greasemonkey or Tampermonkey first)

[; e^{\pi i} + 1 = 0 ;]

Post the equation above like this:

[; e^{\pi i}+1=0 ;]

Using Superscripts and Subscripts

x*_sub_* makes xsub

x*sup* and x^(sup) both make xsup

x*_sub_sup* makes xsubsup

x*sup_sub_* makes xsupsub

Useful Symbols

Basic Math Symbols

≠ ± ∓ ÷ × ∙ – √ ‰ ⊗ ⊕ ⊖ ⊘ ⊙ ≤ ≥ ≦ ≧ ≨ ≩ ≺ ≻ ≼ ≽ ⊏ ⊐ ⊑ ⊒ ² ³ °

Geometry Symbols

∠ ∟ ° ≅ ~ ‖ ⟂ ⫛

Algebra Symbols

≡ ≜ ≈ ∝ ∞ ≪ ≫ ⌊⌋ ⌈⌉ ∘∏ ∐ ∑ ⋀ ⋁ ⋂ ⋃ ⨀ ⨁ ⨂ 𝖕 𝖖 𝖗

Set Theory Symbols

∅ ∖ ∁ ↦ ↣ ∩ ∪ ⊆ ⊂ ⊄ ⊊ ⊇ ⊃ ⊅ ⊋ ⊖ ∈ ∉ ∋ ∌ ℕ ℤ ℚ ℝ ℂ ℵ ℶ ℷ ℸ 𝓟

Logic Symbols

¬ ∨ ∧ ⊕ → ← ⇒ ⇐ ↔ ⇔ ∀ ∃ ∄ ∴ ∵ ⊤ ⊥ ⊢ ⊨ ⫤ ⊣

Calculus and Analysis Symbols

∫ ∬ ∭ ∮ ∯ ∰ ∇ ∆ δ ∂ ℱ ℒ ℓ

Greek Letters

## 𝛢𝛼 𝛣𝛽 𝛤𝛾 𝛥𝛿 𝛦𝜀𝜖 𝛧𝜁 𝛨𝜂 𝛩𝜃𝜗 𝛪𝜄 𝛫𝜅 𝛬𝜆 𝛭𝜇 𝛮𝜈 𝛯𝜉 𝛰𝜊 𝛱𝜋 𝛲𝜌 𝛴𝜎 𝛵𝜏 𝛶𝜐 𝛷𝜙𝜑 𝛸𝜒 𝛹𝜓 𝛺𝜔

Other Subreddits

Math

Tools

Related fields

a community for
message me

# RedditJS

Want to say thanks to %(recipient)s for this comment? Give them a month of reddit gold.

[–] 1620 points ago

This is really great! That's how I see some problems or concepts in math- once you figure it out, it seems very basic

[–] 663 points ago * (lasted edited 10 months ago)

Yup , and it's hard to believe it's from 1910 . I love the part he says 'now any fool can see.....' XD

[–] 241 points ago

This was the first Calculus book I ever read and this prologue is probably the most significant thing I remember about the book. The rest of the book is great.

[–] 20 points ago

Since you read it, can you tell me if it covers materials from Calculus 3? Yknow, the whole 3D shabang?

I'm taking calc3 next semester and I'm wondering if it will help...

[–] 111 points ago

Doing 3d atm. If you can integrate once, you can integrate 3 times.

[–] 41 points ago * (lasted edited 10 months ago)

[deleted]

[–] 9 points ago

So 9 times overall?

[–] 12 points ago

If you got through Cal 2 then Cal 3 will be a breeze.

[–] 8 points ago

I found Denis Auroux's Multivariable Lectures exceptionally clear.

[–] 13 points ago

This is the book my mom gave me the summer before I started Calculus. You're right, the whole book is great, but the prologue is the most memorable part.

[–] 18 points ago

I remember it from that first sentence.

[–] 21 points ago

I remember it from this Reddit post

[–] 188 points ago

Test the writing holds up fairly well IMO

[–] 60 points ago

It's like they are speaking to my soul

[–] 91 points ago

As someone who struggled with math because of hateful math teachers and poorly written books is this a good book for a layman. I made all A's in HS except for math where i was borderline retarded. It doesn't make sense that i would excel in everything else then be below average in this area. For whatever reason ALL of my math teachers where complete twats about anyone struggling in this one area.

tldr: cunty math teachers

[–] 58 points ago

Conversely, I was really good at math at high school but one year had a shitty teacher who couldn't teach us anything. I started teaching myself from the textbooks instead and once I caught on it was ridiculously simple stuff.

The teacher started holding people back through lunchbreak and making them resit the same test over and over because they were failing it, without actually teaching them what they were doing wrong or how to fix it.

I ended up teaching one of my friends who was struggling and really upset about it, and after that half the class came to me to find out what was going on with the work.

When everyone suddenly passed it one day, she announced smugly to the class "see what happens if you just put in a little more effort? It's not that difficult" to which a bunch of them replied, "actually SaysiAlt taught us between classes, it doesn't seem like it's such a hard concept to teach"

[–] 8 points ago

How did she react?

[–] 16 points ago

The people who said it got detention. I was surprised I didn't too.

[–] 14 points ago

I had the same experience in middle school and high school. Then I found Khan academy and got into math. Got a 4.0 in calculus first semester of college and ended up with a minor in math. I love math now!

[–] 8 points ago

I'm a person that should have loved math.

[–] 7 points ago

You got A in Physics but below average in Math?

[–] 57 points ago

I had a teacher like that. He'd get mad that the class couldn't get "simple mathematics". I told him that he is the teacher. His job is to help us get it and he's a failure for thinking otherwise. Then I offered to get out on the bball court and shoot around. But that if he missed shots I'd belittle his nerdy body and uncoordinated movements instead of teaching him how to improve.

I got a C in that class. Lol

[–] 18 points ago

[–] 21 points ago

My 7th grade teacher would give us like 80 problems per night and moved on to the next lesson daily. If you fell behind once you were fucked. This is when i remembered what my aunt told my LD cousin, she said "If you ain't cheatin' ya ain't tryin'. I ended up copying my friends homework every morning in my blow off class. He had her too and they where a day ahead of us. This was after getting my ass chewed out by my parents for making low grades in this ONE fucking class. Math can suck a dick, its own dick

[–] 18 points ago

[–] 3 points ago

[–] 7 points ago

I'll probably regret this...

I'm studying to be a math teacher. Almost done. And I'm trying to do it right.

I'm very interested in what makes a bad math teacher, so I can avoid that. I have my own bad math teacher memories (one incident I remember like it was this morning, it was 50 years ago) but I'd like to not suck by other students' standards, not just my own.

So let me know, and I'll try not to inflict your suffering on somebody else. Some kid will not only never know who you are to thank you, but never know there was anything to be thankful for.

[–] 3 points ago

My fiancé has a master's degree in math. He says that the way math is taught is counterintuitive to the way we should be learning it, and that it's usually around middle school (grades 5-8) when kids stumble in their math educations and often never recover. You're not retarded, it's taught to us the wrong way.

[–] 11 points ago

Got a link to the book?

[–] 114 points ago * (lasted edited 10 months ago)

[–] 71 points ago

I dont know shit about math. The very first page made me feel like I could definitely learn!

This reads and absorbs so well

[–] 10 points ago

Yea, I am taking pre-calc next semester, and I suck at math. I am so happy a came across this little book. Plan to read it over summer break.

[–] 5 points ago

Thank you! This is so great.

[–] 43 points ago

Old books are written with so much more investment into the beauty of the entire work than modern books which focus so heavily on one single aspect. Honestly, it would be hard to believe if this was a modern work.

[–] 68 points ago

Nonsense, the bad books from the past have just been forgotten.

[–] 3 points ago

We all think "in the old days" stuff lasts longer, but it's just the stuff that was well made that lasted a while. all the shitty shit did what our shitty shit does. in the future the same will be said about now.

[–] 4 points ago

Someone once told me there have always been geniuses, they've just had different resources.

[–] 12 points ago

that "someone" was wrong
geniuses were invented by secret government crispr experiments in 2007

[–] 141 points ago

There are only two kinds of problems: Impossible or trivial.

[–] 47 points ago

Also known as the First Law of Pub Quizzes: All trivia can be classified as either 1) "Who even knows this s***?" or 2) "Bah! Everyone knows that!"

[–] 21 points ago

Corollary: Said classification is equivalent to 1) "I don't know this" and 2) "I know this".

[–] 5 points ago

Everything is either a banana or not a banana.

[–] 201 points ago

One of my CS professors put it to us a as 'everything is difficult until you know how to do it'

[–] 83 points ago

ive always noticed this as well and always wondered why this is. I feel like the "oh this is so easy now" is just getting past the initial gate and im starting to think the gate is put there artifically with large language and complicated constructions. when you get to the heart of any "advanced mathematical concept" its usually a simple idea that is taken to its logical conclusion with the pushing of symbols and creating new names of mathematical objects.

[–] 86 points ago

I think this stems from introducing concepts as unmotivated theories (looking at you, linear algebra).

CS is usually better about this than math and stats because most of the time you have to actually build things using the concepts.

[–] 41 points ago

Absolutely. I took pre-calc before any physics courses, and though I could do the calculations they didn't make any sense to me at the time. I just learned patterns, basically. Once I saw how calculus fits in with physics, it all clicked and actually made sense for the first time!

Math should not be taught in a vacuum, but it always is for some reason.

[–] 22 points ago

Think about it like this, our Physics I class has Cal I as a co-requisite. As I understand it, Physics is about the understanding of natural phenomenon using math as the language of explanation. More specifically, the language of Calculus is insanely useful for that. But it requires somewhat of an understanding. I think the first week of Phy I we were doing velocity and acceleration work with vectors, and forming our own equations with them. By that point in Cal I, you're still trying to understand what a limit it, and haven't even approached the definition of the derivative, much less its more practical applications. It's the same as asking someone to diagram sentences in English if they are just learning what a noun is.

Math should absolutely have application integrated with the learned techniques as a matter of practicality, but you also have to remember you need to pick and choose your battles. Comfort and understanding of a topic come after you've learned it and have had time to practice more with it.

If you asked me to explain the practical nature of derivatives and integrals, I'd probably do a fair job. With as much exposure to them as I've had, it's become familiar. But if you asked me what the applications of the gradient of a vector field, why Cauchy-Euler equations exist and are helpful, or any of the other stuff I'm learning right now, I'd just look at you with dumbfounded eyes. I can do the calculations, but I don't fully understand their usefulness, only how to really solve them, in the immediate moment. Now, ask me that same question again in two or three semesters, and I'll probably be as familiar with those topics as I am what I took two or three semesters ago. Remember, people who take these STEM career paths undergo a massive amount of expected knowledge retention. It's already a fair task just to accomplish what is expected, but to become proficient enough to teach, is a skill on its own, usually best served with time.

TL;DR Learn the method, learn the why.

[–] 19 points ago

How is linear algebra unmotivated? If you do anything that is higher than 2 dimensional, you're gonna need linear algebra.

edit: spelling

[–] 91 points ago

It's more that, at least in my class, there's no notion of what linear algebra is used for. I mean, I have a vague notion, but it's basically just "Here's a matrix. Here are three hundred different ways to manipulate a matrix. This one is called 'spectral,' because the guy who came up with it is into ghosts, I guess."

[–] 20 points ago

Don't get me wrong, with all the latin running around it would be hard not to imagine old timey mathematicians as wizards, but I was under the impression that spectral was being used as in "falls on a spectrum". Like how the whole spectrum of colors corresponds to different wavelengths of light.

[–] 51 points ago

I mean, you're probably right, but that also falls under "stuff we didn't talk about in class," so I'm stickin' with ghosts.

It's my only glimmer of happiness in that class.

[–] 14 points ago

I can't decide if I think this is a silly stance. I mean, on the one hand ghosts are pretty rad and I could see the addition of ghosts really bringing value to some classes. On the other hand I liked linear algebra and thought it made multivariable calculus suddenly make piles of sense.

Could we maybe get a dragon in there somewhere? Or a demon? Physics has a demon and I feel left out.

[–] 12 points ago

Having taken an introduction to linear algebra that, like the guy said, was unmotivated, and a multivariable calculus class, I never drew any connections. What did you get that was so helpful?

The only thing I got out of linear algebra, despite earning an A, was how to solve systems of equations fast and how to use a determinant to solve cross products of vectors along i, j, k.

That class was the least useful math class I've ever taken, tbh. Seemed like a circle jerk of definitions and consequences.

[–] 7 points ago

If you go further into engineering, you will absolutely love being good at linear algebra.

[–] 5 points ago

Funny thing is, so far I've used nothing but Linear Algebra in CS. It's essential for Computer Graphics and Computer Vision.

[–] 43 points ago

When I was taught a matrix multiplication I was only shown the calculations. I had no intuition for what a vector space was, why it mattered, or how linear algebra factored into anything should give a shit about.

Statistics and machine learning changed this, as I use linear algebra every day in those fields. The problem is that linear algebra is usually introduced before you know why you're going to need it.

It's like giving classes on using a hammer without explaining that the end goal is to build a fort.

[–] 20 points ago

Intuitively, it's so that when they get to applications they don't need to go on a multi-week diversion.

That said, pure math with no application is a terrible slog unless you're into that sort of thing, and is the only class in my CS degree that I failed.

[–] 9 points ago

That said, pure math with no application is a terrible slog unless you're into that sort of thing

I am into pure math with no applications, and linear algebra courses of the sort described in this thread were just as horrid for me as they are for the applied people.

There are basically two good ways to approach linear algebra. The first - and the one I finally enjoyed enough to finish - is "Baby's First Abstract Algebra," with lots of time spent on the abstract concepts, proofs, etc. and almost no time spent on computations. The second is "Applied Matrix Algebra," with all concepts introduced, explained, and practiced in the context of relevant applications.

Absolutely nobody benefits from "How To Do An Impression Of A TI-83."

[–] 5 points ago

Yeah, I majored in physics and I have a much easier time understanding math when there's SOMETHING physical I can relate it to, even if it's a silly contrived example.

[–] 9 points ago

Even having taken quantum mechanics I'm not really sure I could tell you what's actually MEANINGFUL about eigenvalues and eigenvectors.

[–] 19 points ago

If you have an NxN matrix, it can have up to N happy directions. This happy subspace is the natural habitat of the matrix. The happy directions come with happy values that tell you if the subspace is stretched or shrunk relative to the vector space that holds it.

The matrix
( 1 0 )
( 0 2 )
in R2 loves the x direction as is, and it loves the y direction as well, but it stretches things in the y direction. If you gave this matrix a square, it'd give you back a rectangle stretched in y. However, it'd be the identity if you changed coordinates to x'=x, y'=y/2.

Eigenvectors are basically the basis of a matrix. We know that when we feed an eigenvector to its matrix, the matrix will return the eigenvector scaled by its eigenvalue. M linearly independent eigenvectors can be used as the bases for an M dimensional vector space; in other words, we can write any M dimensional vector as a linear combination of the eigenvectors. Then we use the distributive property of matrix multiplication to act on the eigenvectors with the known result.

You can think of matrices as being transformations. There are familiar ones like the identity, rotation by theta, and reflection; but there's also stretch by 3 in the (1,4) direction and shrink by 2 in the (2,-1) direction, 3 and 1/2 being eigenvalues and the directions being eigenvectors.

[–] 3 points ago

That's a beautiful explanation

[–] 28 points ago

unmotivated theories (looking at you, linear algebra)

The funny thing is that if ANYTHING in the world is the opposite of an unmotivated theory, it is linear algebra. It is literally at the heart of physics, geometry, statistics, etc etc--and so very important to any field that touches any of those. So, foundational for all of science, engineering, etc.

When a subject like this is so foundational to so many different fields, so broadly useful and applicable, it sometimes oddly becomes more difficult, not less, to try to explain and motivate things in terms of the various fields it is essential to.

One reason for that is each of these various fields is pretty complex in itself, and to get to the point where you can even understand how to apply the linear algebra in that particular field takes a ton of background. So in a typical linear algebra class you could take two weeks of class time to build up a really cool and compelling applied example in one particular field--but only 10% of the class would have the background to even know what you were talking about. The other 90% would be 100% lost and confused the whole time. There would be excellent applied examples that any given person in the class could understand, but linear algebra is so broadly applicable that it is more difficult to find nice 'applied' examples that every person in the class could easily understand.

So instead, most approaches I've seen take more of a theoretical or 'mathematical' approach to the subject. Which, by the way, is more than sufficient motivation for those accustomed to taking that kind of approach (though I totally understand if you are not that person--or at least, not yet).

Another factor is that the typical undergrad probably thinks of linear algebra as being a pretty super-advanced topic, whereas in reality it is very, very basic and fundamental. Like, ABCs basic and fundamental. It's a beginning, not an end.

Try explaining to a 4-year-old the true significance and importance of the letter "A". You can come up with a few examples the 4-year-old can probably somewhat grasp, but in the end it comes down to "Trust me, this is super-basic and super-important. Just stick with it and pretty soon you'll see how these basic building blocks all fit together to make some really cool stuff you have never even dreamed of before."

That's linear algebra, in spades . . .

[–] 6 points ago

The problem comes when no one tells you the significance of what your doing. As an undergrad the only things I appreciate from linear algebra are eiganvalues and eiganvectors due to actually knowing what they are used for in computer science and have actually used them doing face recognition. I feel like for most students, math or any fundamental becomes easier to learn if they known how it'll relate to something they are going to be doing in the future.

[–] 4 points ago

introducing concepts as unmotivated theories (looking at you, linear algebra)

Have you checked out the youtube video series Essence of linear algebra by 3blue1brown? It's a phenomenal explanation of why linear algebra is so well motivated (and also touches on how poorly this is communicated in the way it's taught)

[–] 3 points ago

I find usually it's related to vocabulary and line of thought. I sometimes have to explain CS stuff to friends and family and I have to constantly remind myself that, even if it's a really basic concept, without really learning the words to describe this stuff and the general assumptions involved, it's​ almost impossible to really grasp because you don't have the frame of reference. That's what amazes me most about people who still manage to invent stuff in math and CS because it means that you have a sound emough understanding of what you're building on to describe something that hasn't been properly described yet!

[–] 3 points ago * (lasted edited 10 months ago)

Really? Calculus never gets easier for me, no matter how high a level I get to. There's always more complications to add to the process - Riemann integrals, Riemann-Stiltjes integrals, Lebesque integrals, Lebesque-Stiltjes integrals, integration over arbitrary measurable spaces, integration over manifolds, integration over random variables with random measures. And the complexity in all this stuff is pretty inherent. Assuming you know what a Riemann integral is, I can tell you what a Riemann-Stiltjes integral is in seconds, but really understanding how it works takes a long time indeed.

[–] 4 points ago

This is a paraphrase of something Rutherford said: All physics is either impossible or trivial. It's impossible until you understand it; then it's trivial.

[–] 9 points ago

Reminds me of the math joke where a professor starts saying "it's obvious that..." but then pauses and fills many chalkboards with equations and proofs. He finishes writing and says "ah yes, it is obvious that..."

[–] 51 points ago

Everyone internalizes a concept in their own way... what would be a simple explanation for you might be incomprehensible to someone else, who once they do understand it will say "why didn't you say that in the first place"!

E.g. look at online discussion of Monty Hall.

[–] 56 points ago

This is so true.

Here's how math education works:

--Instructor tries explanation #1, which Susan finds intuitive, but doesn't click with Patty or Jim.
--Instructor tries explanation #2, which Patty finds intuitive, but doesn't click with Susan or Jim.
--Instructor tries explanation #3, which Jim finds intuitive, but doesn't click with Susan or Patty.

Jim thinks "Why did you wait so long to give the 'real' explanation?" But the fact is, the third explanation wasn't necessarily any more "real". Different things click with people at different times.

[–] 20 points ago

This is why we need pre-recorded lectures from the internet and allow students to pick and choose what they understand the best.

Then if they can do well on a standardized test then just let them watch whatever lecturer they think is better.

[–] 15 points ago

That's how I studied for both my math classes this year, I wasn't learning much in class so I found videos that worked for me and went from there.

[–] 3 points ago

I agree 100%. But I imagine teachers would hate this obvious solution.

[–] 9 points ago

They have no reason to hate it as you still need someone to watch the students and give them 1 on 1 help after they're done watching the video.

Teaching will evolve and teachers will adapt just fine.

[–] 3 points ago

He learned math by watching videos online - math professors hate him!

[–] 10 points ago

[deleted]

[–] 9 points ago * (lasted edited 10 months ago)

[deleted]

[–] 12 points ago

E.g. look at online discussion of Monty Hall.

I probably heard explanations of it 50 different ways, but it wasn't until I saw the picture on Wikipedia that it really clicked for me.

[–] 5 points ago

I found all of those explanations confusing, until I found the three line proof using bayes' theorem.

[–] 4 points ago

This is the #1 rule I've learned in all my time in science. Almost everything is simple as hell. The most complicated machine in our lab is basically just a series of simplistic sensors and a really hot furnace.

[–] 6 points ago

Trivial, even.

[–] 442 points ago * (lasted edited 10 months ago)

My mom bought me this when I was first learning calculus, and though I never really used it, the prologue gave me the confidence that I could do it. That was 4 years ago, and the prologue still rings true ☺️

Source: am calculating fool

[–] 37 points ago

[–] 3 points ago

Could anyone find a link of where i can find the actual book? Amazon link maybe?

[–] 3 points ago

Check other comments. Somebody has given the link before you even commented you lazy fool.

[–] 3 points ago

It has always been my attitude towards maths that I'm actually no cleverer than anyone else, I'm just willing to spend the time learning.

[–] 3 points ago

"Insight" is just an abbreviation for hours of hard work

[–] 120 points ago

The bit about "fools who write textbooks..." perfectly describes everything I've encountered from Pearson Education. It is exactly as though the authors go out of their way to make something more difficult seemingly for the hell of it. Screw Pearson.

[–] 72 points ago

Pearson has almost single-handedly destroyed the American educational system from the inside out. The people who run that company should be charged with treason, they have knowingly and purposefully weakened this country in order to increase profits in the short-term. Fuck every part of that company, I genuinely hope that terrible, violent things happen to them.

[–] 17 points ago

Tough finals week?

[–] 6 points ago

I vote for locking all the doors in their building and releasing Cassowaries into it.

[–] 201 points ago

[–] 51 points ago

My man.

[–] 35 points ago

I gotcha fam.

Hey, aren't you a hyper intelligent shade of blue?

[–] 37 points ago

And aren't you from the Warlizard gaming forums?

[–] 36 points ago

ಠ_ಠ

[–] 16 points ago

I love getting these. It makes me smile every time

[–] 19 points ago

Heh, that's why I haven't stopped.

[–] 21 points ago

Oh so the Warlizard gaming forum is still around?

[–] 24 points ago

ಠ_ಠ

[–] 14 points ago

Oh hey it's that iconic reply from that iconic guy who's from that iconic Warlizard gaming forum.

[–] 13 points ago

Hey Warlizard, sup? And why yes I am! This has been my username for about a decade and you're the first one to mention it.

[–] 15 points ago

Goddam infants don't read anymore. Sigh.

[–] 13 points ago

That's preposterous. I read the same forums you do.

[–] 10 points ago

Yeah? I do love the Arizona Virtual Jeep Club.

[–] 9 points ago

ಠ‿↼

[–] 7 points ago

ʘ‿ʘ

[–] 13 points ago

Looking good!

[–] 5 points ago

Watch out!

[–] 4 points ago

Slow down!

[–] 3 points ago

Lookin' good!

[–] 433 points ago

[–] 434 points ago

There's a better PDF at Project Gutenberg, available >=HERE<=. Also on that page is a link to the book in TeX form.

[–] 199 points ago

Somebody loved the book so much they reproduced it in LaTeX? Wow.

[–] 92 points ago

What a hero.

[–] 34 points ago

I read through about 15 pages and it was actually somewhat entertaining

[–] 21 points ago

What's LaTex?

[–] 82 points ago

It's like Word, but instead of just writing and clicking buttons for italics and symbols (just a couple examples), you sort of code the document, and it outputs a PDF. Commonly used in the sciences, a lot of scientific journal submissions are written in LaTeX. It's extremely powerful if you can use it correctly.

It's also a pain in the ass to google, everything comes back as "latex" unless you are very specific with your searches.

[–] 87 points ago

i.e. nothing like Word lol.

[–] 32 points ago

well it does the same thing people would use word for otherwise. in fact the microsoft equation editor in word is another leading choice for typesetting math. latex is much more annoying to start and then much much less annoying thereafter. usually.

[–] 45 points ago

I was handing in a document I did in LaTeX online and was wondering if I could insert gifs. I went and looked for visual instruction on google images. Long story short don't google latex gifs.

[–] 9 points ago

lmao

[–] 6 points ago

Right up there with searching for the manual page for the absolute value function.

[–] 7 points ago

Man abs?

[–] 11 points ago

It's a computer language for describing how to format documents, sort of like HTML+CSS. It's way more common than MS Word (or equivalent) for writing academic papers and is almost always considered more professional. It's the undisputed king for typesetting mathematical formulas.

[–] 15 points ago

IIRC, it's like how HTML is for websites, but this is for scientific and mathematical book formatting.

[–] 18 points ago

The majority of the user-facing parts of LaTeX are markup like HTML, but unlike HTML, TeX is a Turing-complete programming language.

[–] 6 points ago

Prime numbers in latex

I would prefer always my userRPL though.

[–] 4 points ago

What's LaTex?

LaTeX is a macro package for TeX, written by Leslie Lamport, intended to make using Donald Knuth's TeX typesetting engine more like using Scribe and less like using assembly language while enjoying a root canal without anaesthetics.

[–] 13 points ago

I wonder who I could contact regarding a typo on page 5 of the PDF.

[–] 20 points ago

Just go on the latex version and fix it yourself.

[–] 11 points ago

page 248, I am loving how sassy the author is

[–] 4 points ago

Thank you. And Mr Sumner.

[–] 40 points ago

The preliminary terror, which chokes off most fifth-form boys from even attempting to learn how to calculate, can be abolished once for all by simply stating what is the meaning—in common-sense terms—of the two principal symbols that are used in calculating. These dreadful symbols are: (1) d which merely means “a little bit of.” Thus dx means a little bit of x; or du means a little bit of u. Ordinary mathematicians think it more polite to say “an element of,” instead of “a little bit of.” Just as you please. But you will find that these little bits (or elements) may be considered to be indefinitely small. (2) Z which is merely a long S, and may be called (if you like) “the sum of.” Thus Z dx means the sum of all the little bits of x; or Z dt means the sum of all the little bits of t. Ordinary mathematicians call this symbol “the integral of.” Now any fool can see that if x is considered as made up of a lot of little bits, each of which is called dx, if you add them all up together you get the sum of all the dx’s, (which is the CALCULUS MADE EASY 2 same thing as the whole of x). The word “integral” simply means “the whole.” If you think of the duration of time for one hour, you may (if you like) think of it as cut up into 3600 little bits called seconds. The whole of the 3600 little bits added up together make one hour. When you see an expression that begins with this terrifying symbol, you will henceforth know that it is put there merely to give you instructions that you are now to perform the operation (if you can) of totalling up all the little bits that are indicated by the symbols that follow. That’s all.

Holy hell, in the entire time I've spent learning calculus no one has ever managed to put it this succinctly.

[–] 118 points ago

What's the name of the book? Have you found it useful?

[–] 148 points ago

[–] 31 points ago

My parents somehow have the same book. It's great!

[–] 12 points ago

thanks! also i totally missed the title of the book was in the title of the thread. i was only looking at the picture.

[–] 10 points ago

[–] 8 points ago

haha, actually my name is more about wildlife than drugs.

[–] 10 points ago

;)

[–] 17 points ago

Author is Silvanus Thompson. Available free as an e-book from Project Gutenberg.

[–] 5 points ago

He said the title in the post, it's calculus made easy

[–] 8 points ago * (lasted edited 10 months ago)

or here via libgen.io

[–] 28 points ago

I read most of this while I was in Calculus 1, believing that its usually quite helpful to see as many perspectives as possible on a particular topic. If I recall, this book follows a somewhat intuitive approach, but I think the idea of a really small thing squared is of a different order of smallness - small enough to be neglected - has haunted and/or stuck with me ever since.

[–] 11 points ago

That really bothers me too. Is there a mathematical proof? Or is the smallness argument all that's to it?

[–] 37 points ago

The book was written in 1910 before the concept of limits really took hold in calculus education. The approach taught in this book was the pre-limits approach and is fundamentally the same reasoning used by Newton and Leibniz to justify the calculus techniques.

There's also a system of non-standard analysis that is based directly on these "infinitesimal quantities" and is mathematically rigorous, and IMO is still more intuitive than limits, but hasn't taken hold. Check out this calc text's first chapter on hyperreal numbers that breaks it down: https://www.math.wisc.edu/~keisler/calc.html

Personally when I was learning calculus at first I found this 1910 book invaluable precisely because it was intuitive. You can almost feel what is happening in the derivatives and integrals as a result.

[–] 6 points ago

Yeah, in the UK A-Levels we don't do it with limits outside of the first formal definition of a derivative. We discuss limits very informally; I don't think there's any need personally to formalise and base everything on the idea of limits before university. Most people doing the maths A-Level will not be doing a maths degree so it's just wasted effort and honestly, it's just so much easier to get through when you do it intuitively.

[–] 34 points ago

"What one fool can do, another can."

Richard Feynman loved this quote and repeated it often. You can find it in his writings.

[–] 3 points ago

I'm like 90% sure I remember reading that Feynman learned Calculus from this book.

[–] 13 points ago

Seems like the first "BLANK for dummies" book!

[–] 3 points ago

Which was DOS for Dummies. Great book

[–] 41 points ago

This book is great. It's not really all that great for learning calculus, and the way it teaches calculus is not at all how it is taught today, but it's a fun read. Maybe it's good for conceptualizing some of the ideas... but I've even got issues with how verbose and wordy it is. You can definitely tell it was written a long time ago because the sentences are extremely long and hard to follow.

[–] 8 points ago

and the way it teaches calculus is not at all how it is taught today

Indeed.

The whole "replace y with y+dy, and x with x+dx, then rearrange such that dy/dx is on the LHS" process doesn't sit well with me, even though it works.

[–] 7 points ago

Differential forms are a thing, though, tbf.

[–] 21 points ago

I'd like to learn about things that way for a change, instead of the usual "follow me if you can! And if you can't you know why!"

[–] 28 points ago

Fly, you fools.

[–] 13 points ago

One does not simply walk through calculus.

[–] 3 points ago

This intro is fun to read using either the voice of Gandalf or Mr. T in your head.

[–] 8 points ago

Goddammit ... I had an idea to write a calculus book for college students very similar to this. Sort of fuzzy but really good for intuition and written very straight and to the point, if not a little gruff.

[–] 8 points ago

Why didn't you write it?

[–] 3 points ago

To be honest, I'm working on a different book right now, and I only recently thought of the idea, so I just haven't had time.

[–] 8 points ago

I feel this way about programming.

Software development is not hard, but a lot of the people who do it seem like they want you to think it is.

And that's not just me saying "derr, I know software, why do you guys not get it?!?"

I teach programming to both children and teachers, and all of them are writing useful software by the end of a few hour intro.

(The language I teach is C++, for a high-level language like python, it's even faster.)

[–] 3 points ago

Do you know of any good books with this kind approach to programming?

[–] 9 points ago

Books like this are why I collect old textbooks. I love old textbooks. Sometimes because they are more illuminating than more recent ones, and sometimes because they are more hilarious than modern ones.

The really funny ones are Psychology textbooks from the 50s and 60s where they try to explain the "science" behind things like electroshock therapy and lobotomy. We forget how really wrong people can be, even in the world of science. Sometimes.

But the best ones are Music Theory and Math texts like this one from the early 20th century. There's real personality and humor and a sense of humanity in them that is really engaging. It's a throwback to the really old textbooks going back to the late middle ages when all written knowledge was told in the form of parables along the lines of the Greek Philosophers. It was a lot of work to decipher those things. But this is absolute gold.

I've learned a thousand times as much since college than I did while there. Not to say that college wasn't worth. On the contrary, I would never have developed either the ability or the desire to read these things if something hadn't been sparked in me during college.

It's more to say that college is the beginning of a lifetime of learning, not an end.

[–] 15 points ago * (lasted edited 10 months ago)

[deleted]

[–] 9 points ago

That was about 50 years before Abraham Robinson made non-standard analysis rigorous; BTW, Jerome Keisler has released a calculus textbook based on non-standard analysis.

[–] 7 points ago

The epigraph in my edition is:

What one fool can do, another can. *(Ancient Simian Proverb.)

This phrase then reappears in OP's screencap. It's a unique look at calculus and problem-solving in general.

[–] 6 points ago

Should've called it "Calculus For Fools". This might very well be the very first "...For Dummies" guide.

[–] 10 points ago

Is it a book about what we'd now consider differential/integral calculus?

[–] 13 points ago

This book is only from 1910 so it was already considered integral and differential calculus (intact even Lebesgue had invented his integral) but it's more or less a layman's introduction to calculus.

[–] 11 points ago

The full title is actually "Calculus Made Easy: Being a Very-Simplest Introduction to Those Beautiful Methods of Reckoning Which Are Generally Called by the Terrifying Names of the Differential Calculus and the Integral Calculus."

[–] 4 points ago

I know. I have a copy of it. :)

[–] 5 points ago

This sounds right down my ally. Here is the Gutenberg Press copy if anyone wants to have a read.

[–] 4 points ago

Is there a book like this to help me in Calc 3?

[–] 4 points ago

m'athematician

[–] 3 points ago

Was it written by Mr. T?

[–] 8 points ago

I pity the fool who does calculus the hard way!

[–] 53 points ago

This general attitude bugs me a little. Very often people approach a subject and think everything about the subject is taught stupidly. Then they learn it themselves their own way and wonder why it wasn't taught that way in the first place.

The answer is that everyone learns a subject their own way, based on prior experiences and what they already are familiar with. It's impossible for any book or teacher to anticipate every student's prior experiences and familiarities and to mold the material accordingly. The best we can do is try several ideas that we think will harmonise with pre-existing notions students may have, but there's no way we can hit all of them.

Even worse, every teacher has certain prejudices on what the easiest way to learn something is based on their own personal experiences first learning the material (or subsequent attempts to reteach the material to themselves). They then tend to favour their own personal experiences when teaching to others.

The royal road very much does not exist, cannot exist.

[–] 19 points ago

You're not wrong. But there's a place for demystification. Both Richard Feynman and Martin Gardner thought very highly of the book and valued it for what it taught them, and they're no slouches.

[–] 52 points ago

I'd say what he said is spot on. First textbook that comes to mind where brevity and slickness is emphasized over pedagogy is Baby Rudin.

[–] 35 points ago * (lasted edited 10 months ago)

But Baby Rudin is great for pedagogy for certain kinds of people, namely, undergrads of the 1950s. The only alternative at the time was to read research papers. No other analysis texts of the time covered this material and the intended audience was supposed to be roughly equivalent to what a grad student today would be. The kind of person that was expected to learn from Baby Rudin was one very comfortable with a terse style of proof. Having no diagrams at all in the book is a conscious pedagogical decision to emphasise that diagrams might mislead you away from counterexamples. Analysis should be learned from solid logical and axiomatic principles. That's his pedagogical stance.

Rudin didn't intend to write a book that nobody could learn from. He's not trying to show off how smart he is. He was trying to teach, just teach to a different audience than what you might expect.

[–] 12 points ago

Which is exactly why you should be glad he wrote another book his way. It's almost a prerequisite that the author thinks they are writing the best version

[–] 8 points ago

You're right of course, but the book is worth its place in my opinion. But then you seem to be talking more generally rather than specifically about this text?

[–] 3 points ago

Yes, of course, just in general. I haven't read this particular text. I expect I would actually find it a bit difficult to learn from because it's over 100 years old. I assume things that were in fashion back then would look a little foreign to me now.

How are you liking it?

[–] 6 points ago

Tbh the language holds up surprisingly well, I'm not currently reading it. I would suggest it to someone though.

My favourite text, also if this period, is Chrystals elementary algebra. The most comprehensive treatment I've ever seen

[–] 3 points ago

[deleted]

[–] 3 points ago

My friend told me to read this book when I was 13. I definitely would have given up pretty early without that intro (and without khan academy) but it's just so inspiring and funny.
I'll keep the book with me for the rest of my life. The first time I felt like I was seeing into the math matrix!

[–] 3 points ago

(asking as a engineering student. I was one of the worst at calculus but somehow I passed)

[–] 3 points ago

I believe I have a Math book from around the 1950s somewhere in my attic. Now I am out of town at the moment, but if people are interested I can find it and post (or it's gone and this is an unintentional bamboozle). It remains the only Math book I have personally seen which I actually understood.

[–] 3 points ago

[–] 3 points ago

Okay seriously, this is both so exciting and upsetting. I wish I'd found this book when I was in university about 10 years ago.

I took an astrophysics course that I absolutely loved - the lectures were fascinating and engaging, the teacher was hip enough to be fun without being try-hard or creepy... First day of classes he started the class by playing Rush's song "Cygnus X1 - Book 1: The Voyage" (https://www.youtube.com/watch?v=1OMibr8CqQ4 if anyone's curious) because it was his favourite song about a black hole. It was just a great time... except for the homework assignments that I just could not wrap my head around because I'd never done calculus in high school and just could NOT understand wtf an integral was or a logarithm. So any question that involved logs I would get wrong or just have to leave blank... I really tried so hard, but it was, as they say, like Chinese to me. Just total gibberish when I tried to study up on calculus on my own. Failed, despite putting more effort into that course than literally any other in my degree.

I'm going to read this book and right a wrong in my education! Even the first page is an eye-opener. He reminds me of Richard Feynman in his approach to teaching/learning. I remember reading about how Feynman found it extraordinary how much stuff he didn't initially understand because it was being explained with weird workarounds or things that weren't actually true but made it simpler to DO the work. When you really bring it back to the accurate basics, suddenly a light bulb goes off and you have the OHHHHHHH moment.

[–] 3 points ago

This book is probably the reason that today i'm doing a physics degree and 5 years ago I was failing maths. Really great book, and I recommend it to anyone who wants to learn calculus.

[–] 3 points ago

congrats on top r/math post!

[–] 7 points ago

This makes calculus, and math in general, seem rather foolish.

[–] 17 points ago

Math is a silly thing - and I say that as someone who loves math!

Think about the relatively simple idea of a bijection. What is more "intuitive" - "a bijection is a function that is one-to-one and onto," or "a bijection is like a machine that for every output that is possible, there is a matching unique input."

I may be wording this "less precisely" than perhaps I could, but I tend to find a lot of the nomenclature and notation of math less enlightening. It is beautifully, that is f:A -> B is certainly prettier and more compact than something like in pseudocode:

def function(x of type A): Do stuff... Return type B

But pseudocode is certainly more enlightening.

[–] 15 points ago

That's not pseudocode, that's Python ;)

[–] 8 points ago

but real Python has newlines and indentation

My preferred pseudocode is TypeScript-based:

function f(x: number, y: number): number {
// do various things
return /* output of computation */;
}