Michael Spivak's Calculus Book

[@ryanrussell3241]

This book was the text used at my college for honors calculus students at my community college. That together with an excellent professor inspired me to be the unemployed mathematician I am today!

[@antikertech157]

There's many things you can do with mathematics....and monetize.

[@esra_erimez]

"the unemployed mathematician I am today" 🤣

[@taekwondotime]

Well said. The government (at the request of big tech companies like Google) is always pushing people to take more and more math, and to get into STEM fields. Meanwhile the world needs doctors, nurses, and skilled tradespeople.

[@taekwondotime]

@@antikertech157 If you can't build houses, do plumbing, install electrical wiring, do welding, or treat injured/sick people, then you have no skills worth anything.

[@antikertech157]

@@taekwondotime Jokes on you. I am also a salesman and copywriter, I use the knowledge of probability and statistics in my favour. Furthermore, I use my research skills to analyze the market for a good marketing strategy.

[@fernandomejias3854]

A classic of all times!! Unfortunally Professor Spivak passed away in 2020. "Calculus", as any other of Spivak's books is a real gem!

[@LucasDimoveo]

This book seems like a bridge to an intro Analysis course. I purchased it to start learning Analysis while keeping my computational Calc skills sharp

[@21ruevictorhugo]

I absolutely love this book. I learned math in a sort of backwards way, since I was a part time student and part time courses were very limited, but the math department decided I could just take whatever course I wanted as directed study - pick a book, no classes, no lectures, just read and come and ask questions. I started with abstract algebra and absolutely loved writing proofs. I then took a summer course in calculus - two weeks of all day classes. (That was my vacation from my job.🤣)Talk about cramming. I barely passed it. Then I did directed study with this book and loved it because abstract algebra and topology were all about writing proofs, so this book was exactly what I was used to.

[@dalitlegreenfuzzyman]

One of the best books ever written. No hyperbole. It’s truly a piece of art.

[@markcassidy2410]

I love this book. I used it to study/learn calculus on my own during one summer. The problems are hard. The text and approach are excellent. Really turned me onto math with its rigor.

[@scienceskills]

Ciao ! Spivak's Calculus is an amazing book. The depth with which he explains concepts is impressive. That's a real math textbook that mitigates the churn-and-chug approach of many students.

[@TheMathSorcerer]

Couldn't agree more!

[@akshaylenin7166]

In order to understand proofs and theoretical Mathematics, you need to have a large number of examples and do abundant computational style questions to understand the patterns

[@UnconventionalReasoning]

What concepts need to be explained in depth?

[@UnconventionalReasoning]

@@akshaylenin7166 Or the learner can read about the relationships and identify the patterns from that. Doing abundant computational style questions is extremely ineffective and inefficient.

[@akshaylenin7166]

@@UnconventionalReasoning both problems and practising Theorem proofs go hand in hand for better effectiveness

[@sergeydukman5832]

"That is crazy. Totally nuts" - exact thoughts of mine when I don't understand math

[@AnthonyLauder]

Spivak passed away in 2020, when he was 80 years old.

[@TheMathSorcerer]

wow

[@meteor8076]

yep, thats sad (

[@josepereira2759]

One great book from spivak is "calculus on manifolds". I ve used it on my "calculus 3" classes

[@jksmusicstudio1439]

I remember myself at first year of uni trying to understand the ε,δ definition of limits. I was stuck for about a month on the fifth chapter, reading again and again the explanations. I dont think that any other book would make it as clear as this one did. Definately one of the best introductory texts to advanced mathematics.

[@maximofeliz7324]

May this book be compared to this other vintage Book: calculus by Granville.?

[@sunglee3935]

Leithold calculus teaches epsilon delta really well.

[@adorp]

Haven't tried Spivak, but I found Thomas's limit chapter to be very good.

[@ai_serf]

When looking to get into analysis and develop a rigorous understanding of Calculus, I found 3 books always recommended: Spivak, Rudin and Apostol. I went with Apostol which I'm in love with; but if I had one extra life, I'd also like to spend the thousand or so hours I would take to go through every problem in Rudin and Spivak's Calculus books.

[@jesusandrade1378]

Spivak's Calculus Fourth edition differs from the third mainly in the inclusion of additional problems, as well as a complete update of the Suggested Reading, together with some changes of exposition, mainly in Chapters 5 and 20.

[@TheMathSorcerer]

Excellent thank you for this comment!!

[@Dhruba-t7n]

which one should i buy

[@fmeyer_]

Spivak and Apostol live rent free on the back of my mind.

[@johnnath4137]

Looking at your post brings to mind two interesting texts which I learned my analysis from in my youth. They were both originally published in German, and were later translated into English, which were the text I used. The author was the great German number theorist Edmund Landau (not the Russian Physicist L D Landau), who was originally a student’s of Frobenius (the mathematician who gave the first general proof of the Cayley-Hamilton theorem), with whom he did not get on, and later a student of Hilbert’s. Landau later went on to become one of the founding members of the Hebrew university, Jerusalem, and one of its leading lights. The two texts went by the titles Foundations of Analysis and Differential and Integral Calculus. The former gave a construction of the real number system from a simple postulate system for the natural numbers and naïve set theory and the second gave a rigorous development of the main theorems of the calculus. The text was severe in its approach to rigour - Landau boasted that you would find a single diagram in it. And the second theorem, after the definition of the derivative, was a proof of the existence of an everywhere-continuous-nowhere-differentiable function. I still have my copies of both texts, and I prize them. At high school I was introduced to rigorous calculus by a teacher’s lending me his copy of G H Hardy’s Pure Mathematics, at the time a seminal analysis text in English. At the time I had a lot of difficulty understanding irrational numbers - my problem was that they didn’t make any sense whatever. Hardy helped me resolve most of my difficulties. The two Landau texts removed them all. Alas! by that time I had already left high school..

[@akshaylenin7166]

Srinivasa Ramanujan Sir did his research under Prof G H Hardy

[@johnnath4137]

@@akshaylenin7166 Yes, but everybody knows that. What's your point?

[@akshaylenin7166]

@@johnnath4137 my point is that Srinivasa Ramanujan Sir had such superhuman intelligence to immediately grasp and drink those complicated Mathematical concepts without the help of a teacher which proves that a good guide book is equally powerful to understand complex concepts in simple way.Moreover, Srinivasa Ramanujan Sir is actually a higher dimensional being like Gauss, Euler,Cauchy, etc

[@akshaylenin7166]

Even to do research on composite numbers under Prof G H Hardy speaks volumes of Ramanujan Sir's brilliance and Calibre

[@arantheo8607]

A real gem! ( Essential Calculus with Applications, by Richard Silverman, great as well)

[@ap3montes739]

I tried reading it a while ago. Got to the exercises (those little proofs) in Chapter 1 and got completely stuck. I then decided to sharpen my skills, and began with the "A transition to advanced mathematics" book. I hope that my proof skills are enough by the time I finish it so I can comfortably read Spivak.

[@TheMathSorcerer]

Excellent!

[@thiagogalvao223]

Hey bro, can you give-me a feedback of your strategy? I mean, have you got the level for follow the book?

[@HJohannes93]

Great book! Combines conversational and motivating language with hardcore rigour (at least if it's for a first course in calculus). I only studied the first 12 chapters during one of my summer breaks of university, didn't manage to get farther than that... Maybe I'll pick it up again in the future :)

[@huiyinghong3073]

It still isnt at the Real Analysis level of rigour, more like a baby analysis book

[@HJohannes93]

@@huiyinghong3073 Of course, it’s still a calculus book but with emphasis on theory, not an analysis book 😊

[@huiyinghong3073]

@@HJohannes93 In my school at least, the distinction between calculus and analysis is never really so clear cut. They introduce a bit of analysis stuff in calculus courses to year 1 Math students before going full blown analysis in Year 2.

[@benhill3098]

Late comment here, but the 4th edition and the solutions guide arrived yesterday at my home (October 7 2022). Can't wait to use this as my supplement for calculus next year, along with the books by Stewart, Larson, Thomas, and a bunch of others I have 😄Thanks!

[@kray97]

First year in college for me. It is a great book, but some of the problems in there are pretty insane. It was also a my first course in proof based mathematics (not counting HS Geometry), and like you, I basically had zero proof writing skills. So this class was a chore and then some for me. Many of the kids in my class did have proof writing skills btw. You didn't learn any of this in AP Calculus.

[@user-qj3rv2mo1b]

I just got calculus by Spivak 3rd edition. The book looks great for someone willing to read cover to cover or use it as reference and not suitable for those who like to learn by grasping concepts delivered through solved examples. This is my first impression about the book.

[@maheshpadalingam3137]

I think I'm going to buy this after Thomas calculus. Oh, and can you do something like a self study asmr? I always to see more self study content, so that would be really cool to see.

[@TheMathSorcerer]

That's a great idea!

[@Singularitarian]

Great video! I’m such a fan of these book reviews / commentaries.

[@QuantumEntanglementForFun]

I learnt calculus from this book 40 years ago, probably from the first edition. Loved the book but my recollection was the book was much more theoretical with very few practice problems. I remember after taking the course that I could prove derivative/integrals existed but I couldn’t actually do them. I still have the book. I will have to compare this video to my book when I get a chance.

[@TheMathSorcerer]

Thanks for sharing!

[@UnconventionalReasoning]

There are only a dozen derivatives to "actually do".

[@QuantumEntanglementForFun]

@@UnconventionalReasoning I only count nine. Eight from the letters in “actually do”: d(“actually do”)/da = 2“ctually do”, d(“actually do”)/dc = “atually do”, d(“actually do”)/dt = “acually do”, etc. All others are zero: d(“actually do”)/db = 0, d(“actually do”)/de = 0, etc 😁

[@AlphaForgeMedia]

Hi sir I am from India, now I am in High school, in just 4 months i will join college for undergraduate course ,i love your videos ,thanks to spead this valuable knowledge.

[@AlphaForgeMedia]

Thanks for ❤️❤️

[@KMMOS1]

Note that between pages 619 and 662 in the fourth edition of Spivak's Calculus are answers to selected problems from the text.

[@FrancisCWolfe]

I felt the weak point of this book is the bit about integration by substitution, which didn't make sense to me to the same extent as the rest of the book. I was gratified to find an article by David Gale, "Teaching integration by substitution" which both reassured me that it doesn't sense as presented and explains it properly.

[@orestesdd]

This book by Mr. Spivak was used extensively in my first math semester ever at the university of Havana, and I consider it a math book GOAT!!! However, since I didn't fish my math studies in Cuba but in the US, I used it a lot here although it was never the main textbook at my college in California. 🤔

[@zgennaro]

You might consider George Simmons calc with analytic geometry 2nd edition. Non rigorous but makes everything “very difficult or impossible to doubt”. Has very good exercises that focus on understanding after the computational problems

[@TheMathSorcerer]

Thank you so much!!

[@joeaverage8329]

Very good author/mathematician indeed. Love his DE book.

[@azimuth4850]

Hey Math Sorcerer. Just wanted to tell you that my copy of Higher Algebra arrived today and it smells aaaaamazing! It smells like an old library. 😃😀🙃

[@TheMathSorcerer]

Oooh NICE!!!!!!!!!

[@azimuth4850]

@@TheMathSorcerer Yeah man!! lol 🤣 Keep it up, you are awesome!

[@ANTGPRO]

I like pretty much your books overview.

[@peterhi503]

Could you please do a video comparing Spivak and Apostol?

[@mohamedmounir6770]

I think this is the calculus book 📖 for the simple meaningful words and the way you get the information either you're a math major student or simple person who get interested in calculus.

[@granteckhardt4878]

8:22 made me chuckle. I said wow twice just as you did haha!

[@Apuryo]

Is there a multivariable calculus book with the same approach like this book? I have been doing Spivak for a while and want to have some practice with 3d+. Do you think Buck's advanced calculus or Loomis calculus would be good?

[@jotteria79]

on page 247, exercise 12-8 ("...lacking a car, bicycle, or trusting friend...") was just needlessly cruel lol

[@jadeharley413]

BRO I WAS JUST READING THAT EXERCISE LMAO

[@maccleary9576]

Looks cool, I'm not fully at that level yet, I have only just started doing calculus. I'm taking the Neil DeGrasse Tyson approach of letting the cloud and fog clear as time goes on, ie. just sticking at it. The good thing about math is that it is precept upon precept.

[@hatemalkd1633]

I hope in some day see your book And guess it will be brilliant book I don't know but I guess it will be about calculus because I saw you interested so much at calculus Good luck for you

[@billmorrigan386]

Yeah, this is a superb very advanced book on the single variable calculus. Inclusion of the proof for the irrationality of pi is really commendable as are numerous challenging problems with asterisks. In comparison with standard books, the challenge problems in this books are way harder. What's more, most people might find standard Spivak's problems (with no asterisks) already very challenging.

[@luigiguilli9346]

My undergrad school used this also for their honors calc sequence at University of Rochester.

[@TheMathSorcerer]

Oh wow that's pretty cool.

[@BBVictini1]

Ayy fellow UR student!

[@slowjazz5932]

I asked you about this book a few videos ago. I like to think that I caused you to talk about it again lol. I encountered this book from going to a certain liberal art college in Florida, they used this book for a class call "Calculus with theory", it's more like baby analysis for freshmen.

[@TheMathSorcerer]

Oh wow that's cool that they used it there.

[@thecodingcanuck]

I absolutely love this book!

[@JR-uc3nk]

The fourth edition exists - I have it, definately excellent!

[@satyavivekanandbattula1091]

Thank you Sir. Useful video.

[@dwdei8815]

Funny that you chance upon the Cauchy-Schwarz inequality on p 276 - because Spivak first demands you present a proof of it in ChPater One (Basic Properties of Numbers)! I'm slogging through it untutored, self-learning, and my goodness it's hard going! Some of the formulas like the product and sum ones I treat like mechanisms, each element in them a cog, and I have to write narrative of how they work before I can fully encompass them.

[@jostpuur]

It is extremely common that teaching materials on calculus omit the proofs of the most difficult theorems, and give heuristic justifications only. Does Spivak do the same, or does this book contain serious proofs of the difficult theorems too?

[@JohnVKaravitis]

I had this in high school back in 1980-1981.

[@TheMathSorcerer]

oh wow that's awesome

[@daxramdac7194]

Those insanely difficult derivatives actually look fairly easy bro, I remember taking calc 1 and, compared with integrals in calc 2 where you had to think and be a little creative, with calc 1 once you found the ultimate pattern of derivatives, it made doing 99% of derivative problems a matter of pattern recognition and careful rule application. The difference between easier and harder derivatives being a test of your patience and attention span.

[@tobeornottobehaidar4493]

Please make a video about Thomas calculus book twelfth edition....Thank you for your best efforts,I dare to say this channel is the best.

[@jesusandrade1378]

I think that the 9th Revised edition of 1996 is the best Thomas' Calculus edition, and it was the last edition he himself wrote before passing away. The newer editions were written and adapted by different authors.

[@licorice4956]

Maybe you could do a video on the famous calculus books(Spivak, Apostol and Courant) and your thoughts on them and their differences. I think you would need to look around for the solutions manual for Courant by Blank on the internet archive, though.

[@imdarealani]

I've considered trying to read this book. I'm still not sure whether I should go for it. Thanks for making a video on it.

[@mdmojibar5326]

I like the early trencedentals by james steward

[@UnconventionalReasoning]

For the derivatives shown in chapter 1: "The Chain Rule: One Rule to Rule the Rules".

[@FullmetalPain]

Have you ever read "Measure and Integration Theory" by Heinz Bauer? It's a classic here in Germany and I wonder what you might think of it. Especially compared to something like Donald L. Cohns book.

[@TheMathSorcerer]

I have not, thank you for the suggestion!!

[@aigeanthokchom3797]

REQUEST FOR MATH BOOK REVIEW: Author Name: Mark Dugopolski, Book: Elementary and Intermediate Algebra, College algebra. Hey math sorcerer, I have been trying to find good books on basic math. Many people suggest me to watch khan academy but I think watching videos is not enough. I watched many of your book reviews and after doing a little research myself, I found these books by Mark Dugopolski. I want to know what you think of them. Thanks.

[@Chris_Bonner]

I just watched your other video on this same book from a few years aho

[@Chris_Bonner]

Years ago*

[@Feynman-fj2gr]

I read it when I 14 was one of my dream solve the problem with two stars

[@evaisthisiaeclaire6365]

Could anyone explain why that question 40 is considered hard? Isn't it easily provable using L'Hospital's Rule?

[@vegenzohrabian5340]

it is "such a cool book"... great collector item in any lilbrary

[@rk99688]

You know what is sad that they expect you to learn this stuff with no prior proof experience from high school. Uwaterloo loves to make things harder on purpose.

[@lucasbomfim00]

It's like when the first thing they talk about programming is recursive functions. Seems like gatekeeping.

[@catafest]

It seems like a very good book, can it be converted into an open-source format like epub? Copyright? There should be no impediments with a scanner, a text converter, and Latex formulas.

[@fernandocupil.6463]

Estoy apunto de hecharme los dos paquetitos jeje. El libro de Cálculo de Spivak y su solucionario, ya casi junto el dinero :) pero no he encontrado ningún review en KZbin hasta ahora que muestre el solucionario. Espero poder verlo en KZbin antes de poder comprarlos. Saludos :)

[@TheMathSorcerer]

Voy a tratar de hacer un vídeo en el Libro de soluciones. Yo lo tengo aquí. Gracias y saludos!

[@jesusandrade1378]

Hay un Manual de Soluciones que combina las dos ediciones, Tercera y Cuarta.

[@fernandocupil.6463]

@@TheMathSorcerer Kheeeeee????? Ya tienes el solucionario???!!!! ME dices que vas a hacer un review!!! Bro vas a ser el primero que emocióoooonnnnn😭😭😍🤩😱😱

[@TheMathSorcerer]

Lo voy hacer ahora mismo

[@ADDISONxz]

I go to the University of Waterloo and unfortunately they no longer use this text (at least in my honours math classes).

[@TheMathSorcerer]

Oh I see, interesting.

[@ADDISONxz]

@@TheMathSorcerer We actually have a lot of textbooks made by professors at UW now. I could send you the electronic copies if you're interested.

[@huiyinghong3073]

What about Multivariable calculus? Does this book include that as well?

[@MarcusAsaro]

My recollection is it does not.

[@aayushvinay1492]

I've read this, it's really good 👍

[@DropTehBazz]

Contemplating whether to buy the Apostol Calc. books or this one. How do they compare? (The more thorough the book is the better as far as I'm concerned)

[@marcelsmolik9469]

Hi great video as always. Do you have some probability/statistics books?

[@user-qj3rv2mo1b]

How about teach calculus by Spivak on KZbin by solving selected problems. Thanks

[@SwaIok]

Sensei your book collection is like a zen garden, peacefully quite and equal parts awesome! Namaste.🥷🥷.

[@alvinah830]

I love mathmatics but i do not have more book I hope i have this book

[@excuilax1325]

I really like this book, i've been using it as a supplement for my calculus course.

[@florianzellmer8735]

Dear Math Sorcerer and community! I am taking an introductory course in numerical mathematics right now, but unfortunately we did not get book recommendations. Can someone help me out finding a good one? Thanks a lot in advance!

[@meteor8076]

What kind of chat room are you talking about ? is it still active ?

[@varungk3388]

Please review Richard Courant's Calculus and Mathematical Physics books.

[@Jonathan-wo6kf]

Have you ever heard of the Tau manifesto? It's a pretty compelling argument that tau should replace pi that is fairly convincing. The idea comes from a guy named Michael Hartl if you want to check it out.

[@henriquenascimento5451]

Do you know a good book about multivariable calculus with the same style as this one?

[@sophiahitch726]

I need master sorcerer's guidance to help me in my math battles

[@Diaming787]

How does it compare to Abbot "Understanding Analysis"?

[@michaelsommers2356]

Is the yellow pig still in the index?

[@kevincline9155]

She was fathered by Mike Spivak in a bar across the street With a beauty in her bosom but only sixteen feet Because she was consistent, she could hardly be complete Her proofs go marching on.

[@sundaymanali5854]

should i read this if i alrdy took calculus?

[@dacioferreira7127]

Are this book or Apostol's book better?

[@user-yp6ze3dh5j]

The way I learn English ☺

[@TheMathSorcerer]

Oh that's awesome!

[@WaelAjam]

Please math sorcerer what are the standard textbooks for the undergraduate math majors in the US?

[@TheMathSorcerer]

For Calculus something like the book by Stewart or the one by Larson is very standard.

[@canusakommando9692]

Waterloo is an excellent school.

[@sloppycee]

This is not a book to _learn_ calculus, it's to **derive** calculus with proofs.

[@TheCrusaderRabbits]

Waterloo is a good school.

[@giovannifontanetto9604]

The questions are written like a math professor is coming out of the book and joking in your face

[@meteor8076]

guys, look at the image on the Spivak's wikipedia page, he is trying to sniff his own socks :D :D

[@jesusandrade1378]

That image is from 1974. And Spivak was showing his flexibility by touching the tip of his foot (tennis shoe) with his nose.

[@mhas9110]

A calculus course - which solves all the problems in the book... 😁

[@vinayabhat6006]

But is it good for Like the first intro to calc...

[@coleyoutubechannel]

I'd go with Stewart Calculus for a nice intro to calculus. This might be better suited for someone who has taken a proof writing course

[@khawar0o7]

This book is not for beginners. Read Stewart's Calculus and do practically every problem from RD Sharma. Also take a look at Amit Agarwal's Play with Graphs.

[@lacku2677]

God no lmao

[@meteor8076]

@@coleyoutubechannel yes, this book is named "calculus", but actually it is real analysis

[@vinayabhat6006]

@@khawar0o7 Ok thankyou

[@mikeshivak]

Neat name

[@SL-lu1wv]

👍🏻

[@josephpuentes4160]

Hi Professor, Could you apply some aspects of decision theory to the Nord Stream destruction? That is, could one mathematically determine by inference who did it to a certain degree? (Parameters could include: value of gain/loss, timeliness, location to neighboring countries, etc.) (Not a math major, but rather a student of philosophy)

[@dylanparker130]

I wonder what you had to do / say to get kicked out of a Math chat-room! Perhaps talk trash about Euler or Gauss? 😅

[@TheMathSorcerer]

hahahaha those chat rooms can be fairly brutal:)

Leithold, THE bible

[@710Chri]

What the fuck

[@ldslmikm9393]

What is ur book colection worth?🧩

[@antoniomantovani3147]

Baby Rudin its the way to read and prof...maybe not so pratical as spivak

[@evaisthisiaeclaire6365]

Could anyone explain why that question 40 is considered hard? Isn't it easily provable using L'Hospital's Rule?