The BIG Problem with Modern Calc Books
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- Опубликовано: 6 май 2023
- The big difference between old calc books and new calc books...
#Shorts #calculus
We compare Stewart's Calculus and George Thomas's calculus.
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![Sean Rii, Karyon, Sharzkii - Taungule [My Love] (Official Visualizer)](http://i.ytimg.com/vi/eJoMuypbSzQ/mqdefault.jpg)
I should clarify I like both of these books; all I'm doing in the video is pointing out the difference because I think it's amusing. I provide no commentary on it. The title of the video is a pun, nothing more.
EDIT: Reworded for less salt
Girl what's the pun 💀
@LadyEmaSkye "big" problem. there isn't really a problem with Stewart, the only downside of it being so thorough and containing so much content is that it is really big
You literally called it a “big problem” are you surprised people thought this???
@@WrathofMathalso thats super vague and unclear but I guess you are a mathematician not a writer
@@melody3741 thought what?
I have both books. I love them both. Even the 140+ pages it takes to arrive at the derivative in Stewart is full of a whole lot of nice little problems and explanations. I think Stewart’s treatment of the epsilon delta concept of the limit is clearer than Thomas. They’re both good.
Agreed! It's definitely funny how big some of these books have become, but they're good books. Some AP Calculus texts for example are half the size of a Larson Algebra 1, which amuses me, but it's not for no good reason.
Man doesn’t understand that there has become more understanding of a basic concept that allows for more complex manipulation techniques. Not only that learning the delta epsilon limit definition is vital for proofs. If you think math books are getting longer because they are putting more fluff that’s because less people are learning that fluff beforehand as people ignore the importance of a fundamental understanding of math
what a nerd
@@cyb3ristic bro are you rp'ing as a bully jock rn
Your comment has 666 likes!
The shrek makes it even better
Just got to the Shrek chapter with one of my students in an independent study, we're stoked!
omg I just looked this up. incredible
@@WrathofMath Nice pun lol
@@WrathofMath stoked… stoke’s theorem lol?
yeah guy
"Shrek is life , Shrek is love "
search for the video titled like this !
There's also the difference in inteded audience: Thomas is intended for well-qualified students taking the course in a small-ish class led by the professor where students can ask questions and have them be answered, Stewart is written for students who shouldn't have passed precalculus and are in a giant hall of 300 people where they can't even hear the professor and thus need to teach themselves.
Anyone who can learn from Thomas can also learn from Stewart, but not everyone who can learn from Stewart can learn from Thomas
I'd say mostly true, yeah. I live in Russia and the older the math book, the harder you know it's gonna be. Also, I have a few of my senior professor's modern textbooks and they are BRUTAL. I think, I formed a solid grasp of his Linear Algebra by the end of my second year, long after it was over. It really shows the difference in Soviet math. Or the brutality towards student, dunno.
I think it's best when you have both. I tended to learn with easier stuff because it allowed me to grasp the basics faster but going back to it, you really appreciate the creativity of proofs and insights that you would've never found on your own.
This discounts ADHD "can learn". Wading through pages of boring content can actually be a barrier to learning.
Conclusion unchanged; people are dumber than they used to be
Calm down. You’re not a genius
Looking down on anyone like that is so shitty dude.
Pictures, graphics, and specially exercises take a large amount of pages
Definitely, and Stewart excels in all those areas.
I know that you take no stand here, but as an amateur math teacher (ie, full time tutor), I greatly prefer the early modern approach. Give students the basic tools early and let them see the beautiful applications. They are easily motivated to fill in the details thereafter. Also, the lack of dumb infographics and five different kinds of nagging boxes, “DID YOU KNOW”s, cautions, etc is so refreshing in older texts. Give me clear, problem-oriented text and some beautiful, clean B&W pen drawings.
I agree with your sentiment, though I think Stewart is actually a good example of the figures and graphics being done well. The occasional historical note, as well as all the history present in select exercises, is quite tastefully done in my opinion.
Fun Fact: Stewart used his book profits to build a "Calculus Mansion". I'm not joking!
Learned about this from The Math Sorcerer, super cool!
Integral House, to be precise. It’s bacause he wanted it to have a lot of curves. There is a video on RUclips.
I looked it up... Stewart is literally bro from the math problems...
@@abc33155oh here we go... Another rabbit hole. 🐇
❤
about 20 years ago someone told me that math education changed in the late 50s to early 60s during the space race the study of physics became seen as very important and therefore general math education became geared towards calculus to the exclusion of other math topics. I used to have a math-for-non-math-people textbook from 1954 (unfortunately I leant it out and it was never returned) but it was interesting because it had a brief intro to calc, graph theory, abstract algebra, and a few other topics like that that most non-math majors would never see nowadays.
If someone isn't a math major they don't need to see it. When studying math did you see syntactic tree structures? We did in Linguistics. Did you read about Annales School of thought? We did in History. Math people are under this delusion that everyone must learn what they learn but the only reason they learn it is they actually need it.
@@BadgerOfTheSea Most people don't "need" to learn calculus either and will never see a derivative again outside of calc courses. The question was WHY calculus is taught so prevently over other areas of mathematics that are equally as useless.
@@BadgerOfTheSeanot only are you completely missing the guys point, but you’re just.. wrong? Math is like the foundation of ALL of industry. A lot of non math people need some kind of math.. only a fraction of them (pun intended) need calculus though.
@@BadgerOfTheSea Well, linguistics is the field people get into when they can't understand math
@@macicoinc9363 Did shitting on linguistics really make you feel better about yourself? Jeez.
Now I get why my parents always say to check the textbook, there’s was a lot more concise, mine takes some digging
I saw a jack-o'-lantern with a derivative carved on it. I asked the home owner about it and she said her daughter did it. I asked the daughter why she chose that and she said, "derivatives are scary."
Integrals are scary.
So what? You do calc one and in the first class you jump to page 144. We used this book when I was at the university in 2007 and it’s great.
and you paid for all 143 pages that you didnt use
Don't worry, the next edition will reorganize everything so you can't use the old one in class. One class I took, the professor had a 3rd edition, I had the 7th, and others had every edition in between. Nothing was arranged the same in any of those editions.
But like, you know page numbers isn’t a good measure of this, right?
Measure of what?
@@WrathofMath how long a textbook takes to reach a certain topic.
A much better measure would be the sections of the chapters
@@thecanmanificationThat's true, they're both important metrics. Either way, the Stewart book covers a lot of additional material before reaching derivatives that the Thomas book does not; whether counted by sections or pages.
One book assumes you have more knowledge about calculus than the other. It also has set assignments. Doesn’t mean it’s any worse at all.
My primary issue with the Stewart book is that my university was requiring the 8th edition for the new Calc 1 courses when I was a freshman, but everyone taking Calc 2 and above were using the 6th edition, and this was because the publishing company was pushing this. I got caught in the middle of it because I was accidentally scheduled to the calc 1 class at first (mixup by the registrar), and was later placed in calc 2 after I'd already purchased the book in the newer edition, while my classmates were using the older edition. Made for a frustrating class when I couldn't work with a classmate using their book for the homework problems that were different.
I find that many of my older math textbooks may be smaller but they're much more densely written and delve deeper into the subject matter. Although non-standard notation can be a bit hard to read at times 😂
yea and some of them use imperial units which is a massive pain
As someone who has used new and old books... You dont learn shit from the old ones. You NEED a teacher. With the new ones you could study it yourself.
you do if you’re not stupid
@@will-jh7yiok buddy
@@will-jh7yi nah, textbooks around the 90s and older are definitely made as a supplement to education. The difference between the styles of writing between an older textbook and a more modern textbook are stark
Completely opposite experience from yours. Older books are so much more dense with useful methods and theory in my experience.
@@RuthvenMurgatroyd I'd say both types have their own applications. Old style books are lacking in exercises and tend to skim through "trivial" points (which, in turn, is depending on what author of the book considers trivial), and new books have a lot of exercises (now, how different those exercises are, is up to discussion)
In Russian math books, usually, you have a theory book, which is vigorous (but sometimes it really is reliant on the author design) and, as separate books - work books with 1000+ exercises.
Why is it a problem? There could be multiple teaching styles.
If it spent that extra time explaining concepts that should have been covered in earlier classes rather than new material, I would argue that thats not good. If students need a refresher or need to have material explained again because they didn't absorb it in the prior classes, that's something that should have been handled in prior books not a calculus book.
I think is says more about how well prepared modern students are. Thomas is a significantly more mature book, but most students are under prepared. I found my thomas to be straightforward, but my math foundationa were drilled into me. Stewart is a probably a better general reference.
Thomas for engineering students
Stewart for the rest
You’ve got to explain limits before derivatives.
Agreed
I am so excited for class on Monday!
It's wild the number of courses for which i bought the whole textbook and used fewer than a quarter of the chapters.
Yeah it covers an immense amount of material!
In my school they just made you memorise rules of differentiation by the start of 11th grade physics without any background whatsoever
oh same in india
The best way to teach if your goals are to erase critical thinking and ensure your students don’t actually understand any material conceptually
@@goofygoober7617 exactly
What's great is having such a variety of approaches to teaching things. A huge number of people explaining the same complex topics using different words.
Back in the day you got one text explantation of derivatives or integrals. Too many students needlessly confused for too long.
In the case of the short text book, some people love that. Right to the point. But some people need textbooks covering the same subject with a more conversational tone... With stories and more graphics.
For tech books the "dummies" books are a good example. Also the "big black book" line of tech books. So easy to follow.
It is not a “problem”. It is an improvement. You must understand limits before you can understand derivatives.
I don't agree it's a problem or improvement. Depends what you're looking for. I don't actually oppose their immensity and thoroughness though. I enjoy them!
It is a problem.
It doesn't take 140 pages to explain limits. Hell it doesn't take 4 pages to explain limits.
@@philipm3173yea I think Serge Lang’s explanation was a page, or hardly even that
@@thefranklin6463 You couldn't do it rigorously but for a low level introduction, you could say the following. A sequence can be thought of as a list of elements with a certain order. To introduce this in the context of real analysis, let's start by defining a sequence as a function of natural numbers (the domain being the set N) describing the positions of elements in the sequence. An arithmetic sequence is a type of sequence in which the difference between every consecutive term is the same, e.g. the natural numbers 1,2,3.... A subsequence partitions some elements while retaining the relative positions of the initial sequence. For instance, the even natural numbers have the sequence 2,4,6..., this is a subsequence of an. A sequence (an) is increasing if an ≤ an+1 for all n ∈ N and decreasing if an ≥ an+1 for all n ∈ N. A sequence is monotone if it is either increasing or decreasing. If a sequence converges, it gets arbitrarily closer to a particular value known as the limit. A sequence that does not converge is divergent (it blows up to infinity). It's a bit of a stretch to explain Cauchy convergence with any precision. The sequence (xn) of real numbers is called Cauchy, if for every positive real number ε, there is a positive integer N∈N
such that for all natural numbers m, n>N
∣xm−xn∣
I didn’t use the 2nd edition of Thomas, but it was an early edition before it became Thomas & Finney. My copy is signed by Professor Thomas. He was already an emeritus professor (at MIT) when I was an undergrad but he occasionally gave a guest lecture.
That is really cool! If you're ever looking to sell - consider me highly interested!
Why is it always written by James Stewart
In my calculus course the derivatives were only introduced after logic, limits, series, proofs, the analytical definition of sin, cos and e. The definition of e was used as an introduction to derivatives.
Sounds rigorous! I think logic is the most overlooked topic of mathematics.
I think that a set theory and introductory proofs class would be advantageous to calculus for most secondary students.
This is particularly true given that logic is crucial for computer programming. Considering edge cases is one of my favorite parts of mathematics and really forces you to slow down and thoroughly examine your logic.
Learning to think in terms of sets and logic for mathematics translates to better decision making in life for a person imo.
(Sorry for going on this long tangent in my reply 😬)
I remember in calculous 101 the professor was like "So we'll get to derivatives around the middle of the semester" and us the high-school-educated students were like "so what the h*l do we learn until then?!"
The Stewart is incredible. If you work every problem in that book you will reach a level of mastery that sticks with you for life
True
In my Calc 2 class I solved every single problem in the book related to Calc 2. When they handed me the test I was so unimpressed by it and finished it in a few minutes. That’s when I realized a single university course by itself isn’t difficult. What makes it difficult is juggling 5 of them at the same time plus a job and social life.
@@ipodtouch470 Wait! ... you had a social life?!
Thomas has a really good set of practice problems as well. I like that its old enough to find answer keys online without setting sail.
honestly a big part of this is that students aren't expected to actually read all 144 pages up to that point because they'll get taught in class and maybe assigned readings or problems from sections of the book. it's a great reference for anyone who wants depth but most students probably don't need to read all 144 pages
Certainly, it's very useful to have for students who need to review some of the basics necessary for calc
WHY IS THERE A SHREK PICTURE FOR VECTORS
If I remember correctly it talked about mapping and how it's used in computer graphics so they put Shrek as an example
Shrek was animated using some form of vector animation that was supposed to be horrible and hard to do, so there’s a story that dreamworld was working on another big movie and if someone messed up they got “Shrek’d” and got put to work on shrek which was supposed to flop
@@ow_lando whyd they continuemaking it if it was "supposed to flop"?
@@theodoremercutio1600 because it didn't flop
@@PrintScreen. They thought it would, though.
Understanding derivaitive sounds imposible without understanding limit first.
I mean, there's also a difference depending on rigor. You have have a hardcore analysis course that does formal limits, series, Banach spaces, and measure theory, before focussing on the Lebesgue derivative, keeping the standard derivative as an aside.
When I was in 4th grade my favorite book was my dad's old calculus textbook! I even told the whole class what my favorite book was when we were introducing ourselves, everyone gave me a dirty stare.
Where can I but the old one? But like not a revised version that become like the new one
When I first enrolled for Calculus I, I was very much decimated until i found "early transcendentals, Calculus, by Stewart"
The transformation that followed is unimaginable... The book is really very clear and concise!
The fact that I have yet to take a calculus class and basically wrote this equation while messing around in Desmos makes me so happy for some reason
I like the new one because it gives you a solid understanding before you reach the new topic like the derivative.
“I ain’t reading allat” 💀
But the old calc book doesnt have shrek in its table of contents now, does it
As a student, I HUGELY appreciate brevity in these older books.
mine starts derivation with the second volume, the first one covers general topology and continuity
That makes sense, the book I studied with sort of starts with an overview of maths in general. Like learning how to formulate profs, learning what a function is, etc.
What percentage is it of the books length?
I have not this books but I would also use this in future
I consider the
*Howard Anton*
calculus textbook, circa 1983 (just before the Graphing Calculators came along), to be the first important advance in the way that Calculus was explained to new students.
Dang, I just started learning about the derivative in class today (on page 123 of calculus: early transcendentales 4th ed.). I find it weird how it’s kinda just an easier version of the average rate of change functions. I wish we learned it sooner for tangent lines.
What is the best calculus math textbooks
For practical , problem solving thank you
Calculus concept 3 edition, Stewart
Calculus 3 or 5 edition , Stewart
Thomas calculus 12 edition
Calculus 9 edition, Larson
I used Stewart in college and I always wondered why there so many words and so many pages just to get a point across?
Isn’t deriving just the process of undoing any riving you’ve done?
That's right!
I have always had a hard time learning anything with modern textbooks. There's always a sense of "Information overflow" when I read them in depth but never actually get to understand the concept I'm working on. However this may be more a problem with every other subject than calc.
The thing is that in old times the people who really wanted to understand these things had their mind revolving around it all the time and hence they didn't need so much basics.
On the other hand, every student today in order to gain a long term goal ( a good college) has to study it even if its an area of no interest. Hence we need basics.
Shrek Calculus
Shrektor Calculus
As someone who learned from books in my own language, I noticed during college how US books tended to waste as much space as possible, as if the writers were paid by the page, not paid to cram as much knowledge into students minds as possible before they work in the real world . Now derivatives was a high school subject, so it was mixed into the same books as other high school math . Of cause I had more of it in math 101 in college, while doing linear algebra in another class that first semester . Use very little of it decades later .
Money the more pages yoy print the more money itll costh
Does the newer book require more pages to further explain each section?
My newest and thickest calculus book is Leithold The Calculus 7 (14 Chapters spanning 1600 pages), while my oldest and thinnest is Peterson Calculus and Analytic Geometry (24 Chapters spanning only 600 pages). Both books are great, I use TC7 as a foundations book since it has tons of examples and exercises and use CWAG as a reviewer since it took only 61 pages to see the definition of the derivative while TC7 took like 200+ pages before it got there. All in all this is actually a good strategy in learning Calculus imo, having a new and old book in your arsenal makes learning Calculus exciting (or however you put it, at least it is exciting for me lol) since there's two different ways in explaining the topics.
"Calculus" by Marsden & Weinstein (1980) Chapter 1 p.47. (A preceding Review Chapter covers Analytic Geometry.)
Newton never mentioned derivative.
How long did Newton take to get to mention fluxion.
Yea, I felt like calculus with the Stewart book for modern was a repeat of college algebra and trig for the first calculus. You learn the rules of derivatives and integration. But it took a long time to get there.
A difference that people might not agree with is that publishers want to turn a huge profit and they can’t do that with older books that might be in the public domain. So they make a revised version which pads out pages so there’s a sufficient difference with another textbook.
I totally agree.
I would argue that one is great at helping you understand the 'math' while the other is great at helping you understand the 'concept'
Page 144. But chapter 2.
So in essence. Pretty early too.
oh the new one is the book I study first year in college
Did the old book define the limit?
Never thought I'd see Shrek in a Calc book
How to buy those books
Ohhhhh…. The BIG problem. That is pretty good
this guy gets it!
Wonder how much of the page difference is from explaining limits and how much is from having less text and more images on each page. Obviously the older textbooks could never have flashy images and had to rely a lot on text. If the Stewart book was formatted like the Thomas book I wonder how many pages it would take to get to derivatives. Probably a lot more than four but quite a bit less than 144.
I am looking at that Stewart book on my shelf. Well...not that exact book, but a copy.
What about spivak?
Percentage wise what is it? I assume the Stewart book has more (maybe even considerably more) pages. It definitely has more images.
I’d even be interested in percentage based on word count! But that might be a bit difficult to get.
My professors writes their own books. Seeing the old one they are quite similar. Ive dealt with the long winded books before and just end up not reading them. I’m so happy we don’t have that in math.
Thats hilarious😂
Hours of entertainment before you even think about taking a derivative! 😂
@@WrathofMath They should put that on the back of a calc textbook
As someone in Calculus with Analytic Geometry online right now I have no lectures my teacher just threw the openstax book at us and we’re all not doing well. What is the Stewart book and would that help? Title and edition please
And it's getting further back also. I have the 4th edition of Stewart Published 1999. And for me it's on page 129.
We now have 3 data points. Any one up to do some analysis on this?
That Calculus book by James Stewart has caused me so much pain
Isn’t the beginning of the Stewart book a review of pre calculus?
My school used thomas, and I still keep it around for reference.
It's a great book!
What is that in terms of % of the book though? The second one looks longer overall.
Old authors were legends. This is why I don't throw away old class notes.
I’m pretty sure we’re taught Calculus in the reverse order of how it was discovered so either way isn’t too crazy. I think area under a curve was discussed well before the idea of what a limit even was.
This is mostly because Newton and other mathematicias of the time were almost primarily physicists. The need for mathematical rigour arose much later in 1800s, primarily with Cauchy. It was built up even more until most settled on the foundation set (no pun intended) by Zermelo and Fraenkel
What is that Delta symbol in the old book (I think it's delta. The triangle)
Bro why was shrek in there 💀
Won't somebody think of all the trees that die for modern Calculus books?
not a chance
At least the page number is perfect square .
I don’t know how much thruth it’s in it, but I think this is an issue with american text books in general, as the writer often gets paid per page instead of per book. At least that was what I was told when I went to uni here in Sweden.
I'm not sure; I know a fair amount of how publishing deals work in the fiction business but for textbooks I am not sure. I highly doubt it is paid by the page, as the textbook manufacturers want to be able to produce the books as cheaply as they can. This often impacts formatting, and is also part of why a complete set of answers is never provided - it would simply take too much space. But as Stewart's Calculus, and similarly designed books, can be used for three college math courses - a moderately high price is fair. And when you think of it that way, it makes it all the more understandable that they'd include a fairly thorough chunk of review at the start of the book - for many students this book will be a constant companion for some time.
I was reading a book for calculus and up to the 30th page I was like why is this so easy? It all seems familiar. I noticed the table of contents say it was like a recap on Algebra and other stuff. The derivative was on page 70 I think.
They are both however included in chapter 2
This doesn't mean anything without context, I am not saying you are wrong just you were not persuasive and I don't think it's possible you could have been in a short.
Agreed. I am just pointing out the difference because I think it is amusing especially to an audience that probably grew up on Stewart. I'll take a more in depth look at these books in another video when I have the time.
@WrathofMath as long as you know lol. I understand the need to be engaging without nessisarly persuasive sometimes.
Who noticed that 23rd page is after page 24... 🤔
Saxon?
Please make a video about lost mathematical inventions in the field of Differential and integral calculus after once that Rules ,Formulas,and Equations are invented then The evidence of that Calculus inventions Vanished From the earth by any Fire burned on the Mentioned pappers or put the valuable papper to garbage or waste with out knowing the Value or thruth of invention of equation or formula etc......
What do you think about calculus: a rigorous first course by Daniel velleman? Thinking about studying it after i master precalc. Ive also been studying his "how to prove it" book.
Thomas is the gold standard
Now try Cours d'Analyse by Cauchy.
In my opinion, neglecting the infinitesimal definition of a derivative is the main issue with calculus textbooks. I know that Mathematicians don't like it, but Physicists use infinitesimals all the time, and knowing about them really help to lead into both derivative rules and differentials.
This is study books in general. Filled with fluff and case examples which change annually to sell new editions
I have the 15th edition of the new book and nothing has changed
When people back in the day say education was harder