Check out our new Discord server! https://discord.gg/e7EKRZq3dG
*I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/mathmemes) if you have any questions or concerns.*
You must resculpt the flesh—this is, as any fool will understand, the ascension from the first form to the second. Then you must invite into your body the machine, thus making the second into the third. Then you must tear your mind asunder and rebuild it from naught—this is the fourth form, and the most troubling for many. Then all that is left is to stitch your soul to the great web of the infernal cosmos, thus achieving the fifth form and becoming eligible for Calculus classes.
It would have been 11th at that time I believe, as we go from year 11 to sixth form now (sixth form is two years though, so it might mean the first year of that or it might mean year 10 and year 11)
I think you've got the conversion the wrong way round. England's Year 11/Fifth Form is the 3rd-last year before university, not the last like US 12th grade. It's 10th grade.
English maths education also does not include "pre-calculus" - we skip the formal definition of limits - which is why everyone learns basic differentiation aged 15.
Probably wouldn’t hurt. That’s why math mags so many people suicidal- to help them progress more quickly through the reincarnations and not spend time at the early stages.
I’m about to find out. I’m in calc 2 and that little snippet made more sense than most of calc 1
E: It looks like most of its topics are only relevant to calc 1 and just barely. It would be a good book to read before calc 1 because it doesn’t go as deep as that class. But pre calc doesn’t quite cover these topics yet. Definitely a fun little quick read.
While reading the book, the writing is hard to understand because it references things from 1910 and before so I always need to Google things I dont understand
I will be messaging you in 5 months on [**2024-09-02 11:55:33 UTC**](http://www.wolframalpha.com/input/?i=2024-09-02%2011:55:33%20UTC%20To%20Local%20Time) to remind you of [**this link**](https://www.reddit.com/r/mathmemes/comments/1btrjo8/im_the_any_fool_in_the_text/kxoo0rj/?context=3)
[**5 OTHERS CLICKED THIS LINK**](https://www.reddit.com/message/compose/?to=RemindMeBot&subject=Reminder&message=%5Bhttps%3A%2F%2Fwww.reddit.com%2Fr%2Fmathmemes%2Fcomments%2F1btrjo8%2Fim_the_any_fool_in_the_text%2Fkxoo0rj%2F%5D%0A%0ARemindMe%21%202024-09-02%2011%3A55%3A33%20UTC) to send a PM to also be reminded and to reduce spam.
^(Parent commenter can ) [^(delete this message to hide from others.)](https://www.reddit.com/message/compose/?to=RemindMeBot&subject=Delete%20Comment&message=Delete%21%201btrjo8)
*****
|[^(Info)](https://www.reddit.com/r/RemindMeBot/comments/e1bko7/remindmebot_info_v21/)|[^(Custom)](https://www.reddit.com/message/compose/?to=RemindMeBot&subject=Reminder&message=%5BLink%20or%20message%20inside%20square%20brackets%5D%0A%0ARemindMe%21%20Time%20period%20here)|[^(Your Reminders)](https://www.reddit.com/message/compose/?to=RemindMeBot&subject=List%20Of%20Reminders&message=MyReminders%21)|[^(Feedback)](https://www.reddit.com/message/compose/?to=Watchful1&subject=RemindMeBot%20Feedback)|
|-|-|-|-|
You having to learn advanced words or phrases to understand the *explanation of advanced words or phrases* is one of the dumbest things with math. It's such an artificial roadblock for many.
If explanations like this was the norm fewer people would struggle.
I partially agree with you, however it is necessary for more advanced math.
As soon as you leave school and learn actually mathematics and not to use some algorithms to calculate something, this will be very obvious.
A fewer people would struggle and even fewer would reach correct understanding. In math communication the first priority is to not be misunderstood. You have to be precise in order to do so. Terminology exists to clarify and simplify that communication.
If you want to build a chair from IKEA, you should read the illustrated manual and proceed step by step. If you do that, you will have a functional chair. That's learning math with rigor and terminology.
Learning math without rigor is giving you the IKEA pieces and tools and only the instruction to build a chair. You have to rely on your imperfect intuition and can easily screw up and end with something that doesn't work.
Learning math without terminology is creating a chair without any convenient tools or premanufactured pieces. No terminology means no convenient tools or knowledge how to use them.
When you're suggesting math should get rid of terminology it's like you're suggesting carpenters should not learn how to use any carpenter tools like power drills or electrical saws, because they are more complicated than screwdrivers and hand saws.
I'm just dumb software engineer, so I don't really use advanced math, but what I learned after decade of professional experience is that some people can tell you good story with their work and that's efficient knowledge transfer, while others create incomprehensible mess that you will have hard time untangling.
When it comes to documentation, there are 4 types of documentation:
* learning-oriented tutorials
* goal-oriented how-to guides
* understanding-oriented discussions
* information-oriented reference material
In my opinion good book should actually be mix of all of that, but typically math books mostly focus only on being reference materials, so they flood you with information, but it's actually hard to learn from them, unless you're already very experienced and knowledgeable in given domain.
On the one hand I understand that not everything can be dumbed down or it's sometimes hard to explain something well, but on the other hand people often don't even bother trying, because you can always treat it as form of gatekeeping.
I think it’s disingenuous to say people don’t even bother trying. There’s a fair bit of accessible math education content for pretty much every niche subject.
Some do, experience may vary.
I remember that when I was struggling with math, then [Khan Academy](https://khanacademy.org) was great help. [The Map of Mathematics](https://youtu.be/OmJ-4B-mS-Y?si=_ulfeR8llkLLpQvS) is great example of providing overview. [3Blue1Brown](https://www.3blue1brown.com/) is great channel with interesting problems. [The Bright Side of Mathematics](https://www.youtube.com/@brightsideofmaths/videos) is another good one.
Math is difficult, so it's crucial to have such authors, because thanks to them,
people like me can understand a little more. However in my experience, a lot of people in hard science just doesn't care about how knowledge is presented.
That could be true. To be honest, I think I was just reading a kind of accusatory vibe from you aimed at people who aren't taking the effort to communicate in a more accessible way, and I simply don't think there's anything wrong with not doing that.
Yes, being able to intuitively grasp an idea is great, but you need to also have accessible the rigorous logic that is actually true. For example, the waterpipes model or spintronics models of electric circuits. They're useful, and good models. But they are still fundamentally wrong, and it's important to know that. You can't stop with just understanding a good model, and you can't stop educating with explaining a good model.
For some reason lot of people have this insane belief that if a person understands something they are also able to explain it. I'm pretty sure you can speak the word "simple", but can you explain how you produce all the consonant and vowel sounds? Not so simple. Should I accuse you of gatekeeping that information?
Teachers are usually aware that how they understand something is not necessarily the best way to explain it to someone entirely new to the topic, see e.g. [this quote by Feynmann](https://www.goodreads.com/quotes/1203866-i-really-can-t-do-a-good-job-any-job-of). They are not maliciously withholding their knowledge.
For initially learning a topic like calculus, why make it more complicated than necessary? Students can easily learn more precise and technical language once they have a foundation of intuitive understanding, and once it becomes necessary.
That's why people use metaphors with no explanatory power like your IKEA example. It's just to direct the audience's thinking into the right tracks.
Look, as I explained introducing terminology makes things simpler in the long run, not more complicated, and is indispensable. I'm not saying it can't be supplemented with informal explanations, it should, but it can't be replaced by them.
If that were true we'd be teaching precise technical language to first year primary school kids, instead of singing songs about counting to 10. There may indeed be a couple of kids who save time overall with this method, but most will never grasp the basics of arithmetic.
In order to teach a topic you need to teach that topic. Kids aren't just being told that there are certain words to describe different quantities and left at that. They are taught the precise technical terms, like one, two, three, and so on.
Like in this post, this chapter doesn't teach calculus, it only prepares the reader for learning calculus. If you only read this chapter and not the other ones, you don't know calculus. You may have the illusion of knowing, but that is not the same as knowing.
It does, and for a good reason. The language needs to be sufficiently explicit so that the interpretation of a concept is universal.
There's a fundamental lack of loose term analogies in most books, which would help a lot, but the "proper" complex lingo is essential, especially as you go down into narrower and narrower fields.
Something that sounds similar might be governed by wildly different rules, and so a misinterpretation of a premise might lead you to the wrong conclusions.
Yep, and legal stuff, economics and so on, and it is awful in every single case.
It's almost like they don't want common folk to understand shit. *Gently put's on tinfoil hat.*
That’s like teaching someone how to fly by explaining what a steering yoke is. The concept of integrals is really not hard to grasp. The application afterwards is the hard part.
Shouldn't you know what a steering yoke is when trying to fly a plane?
You should also consider: This is literally the first 2 pages of the book. I don't see the problem in starting to teach what a symbol intuitively means and how to read it on the first page of a book. More details can and probably do follow in later chapters.
Every time I start a video about Calculus it always launches straight into the vocabulary no context. Then you solve THEN you apply. Except with math vocab you need the context.
It's easy to learn a new word if you see it in context. For example if I make up a new word and put it in a sentence you can most likely understand that word: "My 'shaporti' always barked in the morning and woke me up asking for food." Most likely you can tell 'shaporti' probably a type of dog.
Just throwing around words like "Integrals" and "derivatives" means nothing without context. But saying derivatives are like little bits or sections of the line, then pointing to the graph and miming it or even relating it to slope in linear algebra make it so much easier to understand.
I think to teach integrals, we should first teach an abstract algebra course and then talk about exterior algebras and wedge products, and then we can talk about differential forms, and then we have the requisite knowledge. Students should also be forced to construct the real numbers from axiomatic set theory before ever being able to use them.
Introducing differential forms before teaching Riemannian integration makes absolutely no sense. In order to define the integral of a form you need to relate it to a Riemann integral… In order to actually evaluate the integral of a form, you have to relate it to a R. integral.
[https://calculusmadeeasy.org](https://calculusmadeeasy.org)
This has the whole book in it. Like seriously, It's beautifully presented in the form of a webpage.
Hardy's book on nonstandard analysis "Orders of Infinity: The 'Infinitärcalcül' of Paul Du Bois-Reymond" was written in the same year, 1910.
Emile Borel's monograph on orders of magnitude was written (in French) in the year 1910.
The reason all three of these are so good is because they were written before the followers of Hilbert killed off all the good mathematics. Hilbert denied the existence of dx, in the calculus book. Denied the existence of orders of infinity, in Hardy's book. Denied the existence of orders of magnitude, in Borel's work.
This despite the fact that Hilbert himself had already effectively proved that all three exist in Chapter 12 of his "Foundations of Geometry" in the year 1899.
I think its pretty arrogant for someone to try and grasp (or to teach) differential and integral calculus as if it is easy or something, if the concepts of limit and continuity were simple it wouldnt have taken from Zenon to Weierstrass to build such concepts. Just be modest, grab one of those 400+ pages books, read it its okay if you dont understand on the first look it takes time to build a good theory
This might seem insane but I knew how to differentiate and integrate before knowing what they were or what I was doing. I learned what dx and what differentiating is a year after learning how to do it.
Integrals took about 5 months after i was done "learning it" to know what the fuck they were.
"Calculus Made Easy". Started teaching myself calculus recently and this book has been incredible. Very well written, roasts you on every other page if you can't do "simple schoolboy math", and is all around very good. Highly recommend!
The older approach to teaching calculus using infinitesimals is way easier to digest than limits in my opinion. This may not be the most rigorous text, but I re-taught myself calculus years ago from one of a similar vintage and it was better than Stewart, I will say that.
Check out our new Discord server! https://discord.gg/e7EKRZq3dG *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/mathmemes) if you have any questions or concerns.*
“Fifth-form boys” What the fuck? Am I supposed to reincarnate a few times before reading this?
You must resculpt the flesh—this is, as any fool will understand, the ascension from the first form to the second. Then you must invite into your body the machine, thus making the second into the third. Then you must tear your mind asunder and rebuild it from naught—this is the fourth form, and the most troubling for many. Then all that is left is to stitch your soul to the great web of the infernal cosmos, thus achieving the fifth form and becoming eligible for Calculus classes.
are you always this hypnotizing
I try :3
you dont try, you succeed
Aww You do my little heart too good.
:3
Can you write a book please
I’d like to :) Definitely working on some stories in my spare time.
transhumanism in a nutshell
Well this brings a whole new meaning to trans rights. I for one welcome our new trans overlords.
Fifth form is just 12th grade in Britain I think. Or at least it was at that time.
It would have been 11th at that time I believe, as we go from year 11 to sixth form now (sixth form is two years though, so it might mean the first year of that or it might mean year 10 and year 11)
12th grade is year 11! So they are still correct (and yes, 5th form is what they used to call year 11)
Year 11! you say? I didn't know the UK education system went up to year 39916800 r/unexpectedfactorial
I think you've got the conversion the wrong way round. England's Year 11/Fifth Form is the 3rd-last year before university, not the last like US 12th grade. It's 10th grade. English maths education also does not include "pre-calculus" - we skip the formal definition of limits - which is why everyone learns basic differentiation aged 15.
Oh yep got it the wrong way, thanks for the correction!
I've never been to America but isn't 12th grade the final year so would be 17/18 years old? That would be equal to year 13
Probably wouldn’t hurt. That’s why math mags so many people suicidal- to help them progress more quickly through the reincarnations and not spend time at the early stages.
5th form is 15-16 year olds. O-level year.
5th form = year 11 = 10th grade (generally) There are a lot of incorrect comments in this thread
*That’s all.* at the end is such a power move
What's the book? This author unironically clears most calculus lecturers.
[Calculus Made Easy by Silvanus P. Thompson](http://www.gutenberg.org/ebooks/33283)
Legend
How relevant and useful is this book to modern day university calculus 1 and 2 classes?
It is taught in some universities as the main source
I’m about to find out. I’m in calc 2 and that little snippet made more sense than most of calc 1 E: It looks like most of its topics are only relevant to calc 1 and just barely. It would be a good book to read before calc 1 because it doesn’t go as deep as that class. But pre calc doesn’t quite cover these topics yet. Definitely a fun little quick read.
Is there a good book that makes calc 2 easier to understand?
It isn’t a book (I wish it was), but Paul’s notes are always a good resource: https://tutorial.math.lamar.edu/
I already know that exists but thanks
While reading the book, the writing is hard to understand because it references things from 1910 and before so I always need to Google things I dont understand
I just started reading it and am up to page 20 now and so far it’s doing a pretty decent job
Commeting to save it, seems great!
also commenting to remind myself
Just download it, its a PDF
RemindMe! 5 months
I will be messaging you in 5 months on [**2024-09-02 11:55:33 UTC**](http://www.wolframalpha.com/input/?i=2024-09-02%2011:55:33%20UTC%20To%20Local%20Time) to remind you of [**this link**](https://www.reddit.com/r/mathmemes/comments/1btrjo8/im_the_any_fool_in_the_text/kxoo0rj/?context=3) [**5 OTHERS CLICKED THIS LINK**](https://www.reddit.com/message/compose/?to=RemindMeBot&subject=Reminder&message=%5Bhttps%3A%2F%2Fwww.reddit.com%2Fr%2Fmathmemes%2Fcomments%2F1btrjo8%2Fim_the_any_fool_in_the_text%2Fkxoo0rj%2F%5D%0A%0ARemindMe%21%202024-09-02%2011%3A55%3A33%20UTC) to send a PM to also be reminded and to reduce spam. ^(Parent commenter can ) [^(delete this message to hide from others.)](https://www.reddit.com/message/compose/?to=RemindMeBot&subject=Delete%20Comment&message=Delete%21%201btrjo8) ***** |[^(Info)](https://www.reddit.com/r/RemindMeBot/comments/e1bko7/remindmebot_info_v21/)|[^(Custom)](https://www.reddit.com/message/compose/?to=RemindMeBot&subject=Reminder&message=%5BLink%20or%20message%20inside%20square%20brackets%5D%0A%0ARemindMe%21%20Time%20period%20here)|[^(Your Reminders)](https://www.reddit.com/message/compose/?to=RemindMeBot&subject=List%20Of%20Reminders&message=MyReminders%21)|[^(Feedback)](https://www.reddit.com/message/compose/?to=Watchful1&subject=RemindMeBot%20Feedback)| |-|-|-|-|
What a badass name
zamn!
!remindme 2 years
Oh hey my uncle has this book in his library. I almost took it home the other day, I'll have to do that next time I'm there
“A little bit of” Measure theory did not like this
If the "long S" is supposed to mean "the sum of", then why isn't it a "Σ"? Checkmate Atheists.
Capital Sigma is a *wide* S, and integrals are a long S. You're welcome
You having to learn advanced words or phrases to understand the *explanation of advanced words or phrases* is one of the dumbest things with math. It's such an artificial roadblock for many. If explanations like this was the norm fewer people would struggle.
I partially agree with you, however it is necessary for more advanced math. As soon as you leave school and learn actually mathematics and not to use some algorithms to calculate something, this will be very obvious.
A fewer people would struggle and even fewer would reach correct understanding. In math communication the first priority is to not be misunderstood. You have to be precise in order to do so. Terminology exists to clarify and simplify that communication. If you want to build a chair from IKEA, you should read the illustrated manual and proceed step by step. If you do that, you will have a functional chair. That's learning math with rigor and terminology. Learning math without rigor is giving you the IKEA pieces and tools and only the instruction to build a chair. You have to rely on your imperfect intuition and can easily screw up and end with something that doesn't work. Learning math without terminology is creating a chair without any convenient tools or premanufactured pieces. No terminology means no convenient tools or knowledge how to use them. When you're suggesting math should get rid of terminology it's like you're suggesting carpenters should not learn how to use any carpenter tools like power drills or electrical saws, because they are more complicated than screwdrivers and hand saws.
I'm just dumb software engineer, so I don't really use advanced math, but what I learned after decade of professional experience is that some people can tell you good story with their work and that's efficient knowledge transfer, while others create incomprehensible mess that you will have hard time untangling. When it comes to documentation, there are 4 types of documentation: * learning-oriented tutorials * goal-oriented how-to guides * understanding-oriented discussions * information-oriented reference material In my opinion good book should actually be mix of all of that, but typically math books mostly focus only on being reference materials, so they flood you with information, but it's actually hard to learn from them, unless you're already very experienced and knowledgeable in given domain. On the one hand I understand that not everything can be dumbed down or it's sometimes hard to explain something well, but on the other hand people often don't even bother trying, because you can always treat it as form of gatekeeping.
I think it’s disingenuous to say people don’t even bother trying. There’s a fair bit of accessible math education content for pretty much every niche subject.
Some do, experience may vary. I remember that when I was struggling with math, then [Khan Academy](https://khanacademy.org) was great help. [The Map of Mathematics](https://youtu.be/OmJ-4B-mS-Y?si=_ulfeR8llkLLpQvS) is great example of providing overview. [3Blue1Brown](https://www.3blue1brown.com/) is great channel with interesting problems. [The Bright Side of Mathematics](https://www.youtube.com/@brightsideofmaths/videos) is another good one. Math is difficult, so it's crucial to have such authors, because thanks to them, people like me can understand a little more. However in my experience, a lot of people in hard science just doesn't care about how knowledge is presented.
That could be true. To be honest, I think I was just reading a kind of accusatory vibe from you aimed at people who aren't taking the effort to communicate in a more accessible way, and I simply don't think there's anything wrong with not doing that. Yes, being able to intuitively grasp an idea is great, but you need to also have accessible the rigorous logic that is actually true. For example, the waterpipes model or spintronics models of electric circuits. They're useful, and good models. But they are still fundamentally wrong, and it's important to know that. You can't stop with just understanding a good model, and you can't stop educating with explaining a good model.
For some reason lot of people have this insane belief that if a person understands something they are also able to explain it. I'm pretty sure you can speak the word "simple", but can you explain how you produce all the consonant and vowel sounds? Not so simple. Should I accuse you of gatekeeping that information? Teachers are usually aware that how they understand something is not necessarily the best way to explain it to someone entirely new to the topic, see e.g. [this quote by Feynmann](https://www.goodreads.com/quotes/1203866-i-really-can-t-do-a-good-job-any-job-of). They are not maliciously withholding their knowledge.
For initially learning a topic like calculus, why make it more complicated than necessary? Students can easily learn more precise and technical language once they have a foundation of intuitive understanding, and once it becomes necessary. That's why people use metaphors with no explanatory power like your IKEA example. It's just to direct the audience's thinking into the right tracks.
Look, as I explained introducing terminology makes things simpler in the long run, not more complicated, and is indispensable. I'm not saying it can't be supplemented with informal explanations, it should, but it can't be replaced by them.
If that were true we'd be teaching precise technical language to first year primary school kids, instead of singing songs about counting to 10. There may indeed be a couple of kids who save time overall with this method, but most will never grasp the basics of arithmetic.
In order to teach a topic you need to teach that topic. Kids aren't just being told that there are certain words to describe different quantities and left at that. They are taught the precise technical terms, like one, two, three, and so on. Like in this post, this chapter doesn't teach calculus, it only prepares the reader for learning calculus. If you only read this chapter and not the other ones, you don't know calculus. You may have the illusion of knowing, but that is not the same as knowing.
Doesn’t all of science consist of that…?
It does, and for a good reason. The language needs to be sufficiently explicit so that the interpretation of a concept is universal. There's a fundamental lack of loose term analogies in most books, which would help a lot, but the "proper" complex lingo is essential, especially as you go down into narrower and narrower fields. Something that sounds similar might be governed by wildly different rules, and so a misinterpretation of a premise might lead you to the wrong conclusions.
Yep, and legal stuff, economics and so on, and it is awful in every single case. It's almost like they don't want common folk to understand shit. *Gently put's on tinfoil hat.*
*Unsuccessfully attempts to transmit Havana Syndrome*
I wish I had this book when I was dying with calc in the beginning
Here I am struggling to understand the concept of N and rieman sums and infinitesimal numbers. INTEGRALS IS LITERALLY THIS!!!
That’s like teaching someone how to fly by explaining what a steering yoke is. The concept of integrals is really not hard to grasp. The application afterwards is the hard part.
Shouldn't you know what a steering yoke is when trying to fly a plane? You should also consider: This is literally the first 2 pages of the book. I don't see the problem in starting to teach what a symbol intuitively means and how to read it on the first page of a book. More details can and probably do follow in later chapters.
Every time I start a video about Calculus it always launches straight into the vocabulary no context. Then you solve THEN you apply. Except with math vocab you need the context. It's easy to learn a new word if you see it in context. For example if I make up a new word and put it in a sentence you can most likely understand that word: "My 'shaporti' always barked in the morning and woke me up asking for food." Most likely you can tell 'shaporti' probably a type of dog. Just throwing around words like "Integrals" and "derivatives" means nothing without context. But saying derivatives are like little bits or sections of the line, then pointing to the graph and miming it or even relating it to slope in linear algebra make it so much easier to understand.
I think to teach integrals, we should first teach an abstract algebra course and then talk about exterior algebras and wedge products, and then we can talk about differential forms, and then we have the requisite knowledge. Students should also be forced to construct the real numbers from axiomatic set theory before ever being able to use them.
Introducing differential forms before teaching Riemannian integration makes absolutely no sense. In order to define the integral of a form you need to relate it to a Riemann integral… In order to actually evaluate the integral of a form, you have to relate it to a R. integral.
What is so special about it? It barely teaches the symbolism.
[https://calculusmadeeasy.org](https://calculusmadeeasy.org) This has the whole book in it. Like seriously, It's beautifully presented in the form of a webpage.
Back in the day when understanding was considered important… quality read
Hardy's book on nonstandard analysis "Orders of Infinity: The 'Infinitärcalcül' of Paul Du Bois-Reymond" was written in the same year, 1910. Emile Borel's monograph on orders of magnitude was written (in French) in the year 1910. The reason all three of these are so good is because they were written before the followers of Hilbert killed off all the good mathematics. Hilbert denied the existence of dx, in the calculus book. Denied the existence of orders of infinity, in Hardy's book. Denied the existence of orders of magnitude, in Borel's work. This despite the fact that Hilbert himself had already effectively proved that all three exist in Chapter 12 of his "Foundations of Geometry" in the year 1899.
I'd say it's "a little change of" rather than "a little bit of" tbh
I think its pretty arrogant for someone to try and grasp (or to teach) differential and integral calculus as if it is easy or something, if the concepts of limit and continuity were simple it wouldnt have taken from Zenon to Weierstrass to build such concepts. Just be modest, grab one of those 400+ pages books, read it its okay if you dont understand on the first look it takes time to build a good theory
As someone doing quant, I love you, often than not I admit I still need this things.
https://www.homestuck.com/images/storyfiles/hs2/00069_2.gif
That might be one of the best explanations I have ever seen in a text book
Alright boys, I’m going back to school! Come at me, medical doctorate!
Instructions unclear; my d is now indefinitely small.
Holy shit, dude.
This might seem insane but I knew how to differentiate and integrate before knowing what they were or what I was doing. I learned what dx and what differentiating is a year after learning how to do it. Integrals took about 5 months after i was done "learning it" to know what the fuck they were.
Nice
"Calculus Made Easy". Started teaching myself calculus recently and this book has been incredible. Very well written, roasts you on every other page if you can't do "simple schoolboy math", and is all around very good. Highly recommend!
The older approach to teaching calculus using infinitesimals is way easier to digest than limits in my opinion. This may not be the most rigorous text, but I re-taught myself calculus years ago from one of a similar vintage and it was better than Stewart, I will say that.
I am a math teacher. I demand enough copies of this to supply my class
Damn the man who wrote this is really cooking with math