This book changed my life. The book reading and study transformed my further academic - and professional . development FOREVER. Twenty years after my university graduation I happened to become a peer of a full professor who graduated in Math at Duke and had been a student in Professor Spivak's class. Professor Spivak deserved a teaching Nobel Laureate, Unfortunately Teaching Excellence does occpy a mere ancillary position amongst academic competences.
I used this book in my honors calculus course, I recommend it to people who really want to be more familiar with calculus and who are building steps to approach real analysis.
With certain high profile books, like this one, it'd be great if you did a mini video series. Introduce the book then work selected problems in it and talk about why they're interesting. It'd be good content for sure.
Ten years into my prison sentence i found this book and it changed my life. Now I'm out on parole for good behaviour and looking forward to meeting the publisher to give my sincere thanks 🙏
Thank you for this video, it brought back great memories. We used this text with the great Professor Tom Storer in the Honors Calculus sequence at University of Michigan many years ago.
We used this textbook Fall 1971 for the new "honors calculus" course at UC Davis. I think Spivak gave a talk at UCD a few years later (which I missed), and so some my former classmembers got their books autographed.
That book is a masterpiece and should be read by anyone who loves mathematics. The explanation of the logarithmic and exponential function is the best among all math books.
This was our first 1st year text book at the University of Western Australia. All students wishing to major in Mathematics used this. I remember many a fond hour with this book back in the early 1980s. It's still on my bookshelf today!
!SUGGESTION!......When I was in school in the 70's, there was still a large Home Economic department. They didn't know calculus, but they could add, subtract, divide and do percentages in there heads at the speed of a calculator. They practiced that to the hilt, and the college guys couldn't begin to keep up. Maybe You would talk about that, and how we could learn the same thing. Thanks... Terry Drobeck.
This book has been a very important element of my formation as a mathematician, in fact, I regard It as Onésimo of the best and most beautiful books in the field (I am that Fernando Mejias who is mentionin the fourth edition’s preface). Read the text and work out as many of Its problems as you can, you will a lot of very deep mathematics!
Great vid! I learned Calculus in Hs, and later on in college as an undergrad where we used Howard Anthon's book (Calculus with Analytic Geometry). I still have that book.
Hi Math Sorcerer!I am a 16 year old high school student.I have learnt single-variable calculus on my own and planning to study real analysis in December and January and then study this book.I am grateful for your informative videos
This was the textbook that was used for my ‘Analysis I’ first-year undergraduate course at the University of Toronto many years ago; it is an amazing textbook!
I had just turned 17, and placed into Math 106, Honors Calculus, at Princeton, in 1977, where Prof. Dwork used this textbook. "The only math book with a plot."
Wow, i was just walking past a house in my neighborhood and someone had left this book and the solutions book (along with a few other books) out for “take/share” purposes (common in New York). I didn’t realize I had gotten the Calculus version of the Elements or the Philosophy version of the Critique of Pure Reason or the Programming version of the Structure and Interpretation of Computer Programs. Looking forward to digging in as an, at-best, good enough to get the degree requirement met math student.
Literally this was the best textbook I've ever read. What a fantastic book, and taught by a great professor at my university as well. I felt very privileged to have learned math in that course even if it was first year. Makes me curious what life would have been like if I continued, but I suspect it might have been slightly too difficult. Math degrees are not for the faint of heart
I really like the definition of trigonometric functions that appears in this book. The only book that gives a perfectly rigorous definition, yet related to our geometric intuition. I prefer that over using Taylor series or differential equations as a definition. You can define like that of course, but then problems like "can you square a circle" don't make much sense.
Spivak is great. I'm a fan of "Analysis on Manifolds" by James Munkres. The first half of the book covers calculus really well. It's like you get to learn about differential geometry as a bonus
This is basically advanced calculus or initial analysis. Good for epsilon-delta proofs. Rigorous. Very good for testing your concepts and developing greater insights. I'm working through this these days just to revise some old concepts and deepen my insights making me ready to study new techniques for differential equations and write some research papers.
This was my beginning honour calulus text at Berkeley. I later tutored a student with it who needed a credit at U of Toronto. I even tried to use it to teach a v-good high school course. It is excellent for the best students, and not very good for the lazy students.
I have this book, picked it up after having taken Calculus. I had got over 100% in all three calculus courses, yet I still was aware of my own lack of fundamental knowledge. Voicing my own inadequacies despite stellar grades often got me weird looks from other students. This book helps fill in the gaps you need to extend your Calculus into an adequate foundation for Complex Analysis.
I bought this book a couple of years ago on your recommendation, wow.. it's not pedestrian calculus. Most engineers get just enough calculus to be dangerous, then there are electrical engineers which get the full course. I should have picked up a math minor along with my EE degree(s), it was only three more classes. (I gave this advice to an engineer in college just the other day) I use it today as entertainment, just to go over the problems again and do the work keeps the mind working. I should purchase the answer book and do ALL the problems like I did in college, which makes you a better student IMO. Thanks for the recommendation, I have picked up a couple of the books off your channel (mostly on number theory). I look forward to more recommendations.
This was the textbook I used in Fall 1967 and Spring 1968 for Math 50 and 51 at University of Maryland. I had taken a Calculus/Analytic Geometry course in high school. First semester was a butt-kicking - got wasted on first hourly. Meanwhile all the engineering folks were using Calculus with Analytic Geometry by Edwin Purcell - I remember sitting in on their lectures and was so happy that I understood what was going on. Math gods smiled on me and 2nd semester was much better. Now to the changed lives portion: In 1975-76 I was in the MSIA (MS Industrial Administration) program at Purdue University where the challenge is to do 51 graduate hrs in 11 months. The legendary Prof Frank Bass taught the Econometric Course and the 4 hr midterm was 80% proofs. Spivak and the Math gods grinned!!
It indeed changed my life, it was my first year text at the University of Toronto and it quickly convinced me that there was no way mathematics as a career for me. I doubt I completed one exercise in it.
I always find it amusing when people who by nature are very accomplished in mathematics or who took the extra difficult versions of math courses, will talk about a book like this and say that it was great and others are not. I have taught Calculus for many years and have used the STEWART books for my students ( James Stewart was my professor and was an excellent and enthusiastic teacher ). Many of my students have gone on to great accomplishments in the field of mathematics and would eventually be well suited toward working with the Spivak book. But, many many more of my students have gone on to related fields where they needed calculus but did not need the difficult rigor of pure math. If I had used the Spivak book, most of my students would have struggled and may not have been able to go on.
chap 22 Uniform Convergence and Weierstrass Approximation - this is middle ground IMO for your spivak book avoidance. I neither like or dislike any of it. I am not a savage, after all.
also, delivering this kind of celebration of learning a topic that requires devotion to studying until you attain insights, while simultaneously blasting through some exercises in a speed and manner that's alienating to those not having acquired the know yet? ridiculous
...nice clean graphic design. Whoever designed this book, sure did a fine job of systematically aligning text and leaving empty space on the left for all the graphs that follow...:D
Hey Prof. I've been following your channel ever since I started studying Math at 26y/o, I would love to watch videos where you go through questions you find interesting like you did in the past.
Agreed. I never used or owned it but learned from Spivak's more advanced books, especially the classic "Calculus on Manifolds" which I really studied, and glanced at this when teaching, I always recommend the library copy to good students who want more rigor and precision and depth. It is really excellent. Spivak is a real mathematician, unlike some writers of texts, meaning although for whatever reason he himself didn't do a lot of research himself, he knows research-level high-level stuff especially and " and knows how to bring that perspective to Calc. Other GREAT undergrad texts are: Marsden 's Elementary Classical Analysis, Bartle's Measure and Integration, Lang's Complex Analysis, Knopp's infinite series (V I and II), Guillemin and Pollock's Differential Topology. Spivak also wrote a lot of AMS-tex and the famous book The Joy Of Tex. Spivak's multi-volume Differential Geometry texts I have only dived into parts of, but always excellent.
The thing about this book is that it blurs the line between calculations and proofs. Calculations are proofs and proofs are calculations. Mathematics is mathematics. This book is a masterpiece of mathematics.
I cursed this book when studying Mathematics in the early 1980s ... then learned to appreciate it fully as a reference throughout my working life. It's still on my bookshelf. Thanks for the memories.
This textbook was used in my Calculus course in 1970. I have a first edition of the textbook. I should get a more recent edition. Spivak shares a characteristic among the great mathematicians who made mathematics more teachable and accessible to more people The current notation we use for the calculus is due to Leonard Euler, of Euler's Constant fame, who founded entire branches of mathematics, in particular graph theory which is the foundation of topology . Spivak is a working topologist. Euler was a genuinely kind and pleasant person, a characteristic that Spivak shares. I have this on good authority as my college roommate took a summer math course from Spivak. Also, my college roommate told me that Spivak drove a VW beetle and adored Bach and jokes about Yellow Pig, who is the Y. P. referred to in the dedication to this book.
It is the best book on calculus I know. It helped me a lot during my studies (end 70ies beginning 80ies). Before this book I understood almost nothing about calculus. After working through the book I understood (almost) everything. And: It was fun to read. Also for me this is the truth: It changed my life for the better. A didactical masterpiece.
perfect example of what a good writer can do with a subject. the only way anything would remain unexplained would be due to the infinite ramifications of the subject. I wish I had more time to read it, but the small part of what I read at the beginning was pure beauty and art.
I did my undergrad at Waterloo, i dont remember what the required book was but i remember getting this later in my undergrad from a profs recommendation
Hi 👋 I watched a few other book recommendations on your channels bit this math's book stands out for me since I'm a first year moving to second year in software engineering diploma so. I'll go through the book within a month or so and we'll try some of the hard questions 😂 and I'll look for some more math books. My thinking is if I find really hard questions the easier ones will just be faster to solve and get the tests done quickly.😅
Do you think this book and Abbott are good to prepare for my first class in real analysis next semester? I already know how to prove things since i took a rigorous linear algebra class (with Axlers book) and I am kind of familiar already with epsilon delta.
Have you never heard the old adage “Publish or Perish” before? It was meant to reflect the fact that those living in the world had to publish or never get tenure and stuff like that.
Interesting. I have a English version of this book (just one volume), and also a Spanish version (two volumes). I think it has to do with the fact that it is a more verbose language. Anyway, one of the 2 books I use frequently. The other is James Stewart's Early Trancedentals.
How about James Stewart's best-selling series of calculus textbooks: Calculus, Calculus: Early Transcendentals, and Calculus: Concepts and Contexts, which are used by 70% of students in North America?
i am just going to finish calc 1. if you know algebra trig and geometry well its super easy. i am sure you are ready. dont be afraid. (i wouldnt recommend starting out with this book though)
This is similar to my Calculus book during my engineering days 23 years ago. Wonder if you have a good differential equation book with similar lot of examples and problems to solve. Thanks in advanceُ
never got past algebra 2 and i got a masters degree in cyber security. wanted to learn more math growing up but didnt.....tried trig, failed, tried stats twice, failed, tried proofs...never learned geo so failed that but worked very hard for that D-.
I've been using this book for Calculus 1. It is a good book but it was not my favorite as it lacked some content that i was looking for I really like Calculus with analytic geometry by Earl W. Swokowski And the Thomas Calculus new edition The best
Have you ever heard of any cases in learning where someone has trouble understanding basic calculus, but has an easier time learning things like partial differential equations and certain aspects of mathematical physics (like differential geometry)? Sometimes it's easier for me to grasp complex subjects in mathematics than it is to get easy subjects and I have to learn from the top down. This means I have no structure in learning and I'm scattered. Hopefully you can give me your thoughts on this
I am keen on history. I noticed that Apostol gives a history context in his explanations. What do you think about Apostol, mostly in comparison to Spivak, professor? Thanks and greetings from Brazil!
in 1964? they introduced"new math " halfway threw my 4th grade class..I was lost and done with math for the rest of my life I shut up and became the quiet guy in the back of the classroom no one cared and the teachers ignored me.
Definitely changed my life for sure. Took MATA37 at UofT Scarborough with Prof. John Friedlander. The course was tough for sure. But I definitely gained an appreciation for mathematical proof that I had never experienced before. Became a physicist instead of a mathematician, but I always appreciated what I learned in math from my univeristy undergrad days.
using this book right now in first year analysis at uoft and i’m getting absolutely destroyed by it haha, it’s definitely not an easy jump considering how easy high school math was
I really have no clue about any of this, but I am interested in how this stuff is used in the real world . Is it ACTUALLY useful,or just enjoyable for mathematics buffs? I ‘M asking this seriously , not sarcastically.
It was my 1st year calculus book in 1980 and it did change my life. High school math was just an exercise in being taught an algorithm and then repeating it over and over again. This book exposed me to Mathematics. It was a religious experience. To this day I can rime of the epsilon-delta proof. I have often said that if my house was burning down, I would grab this book first. If civilization collapsed and I could ensure one thing would make it to future humans, it would be this book.
I bought this as a first time calculus learner on my own and it was just increasing my neurons at each problem
lmao best comment
same
Too bad it couldn't fix your English.
E.g., ‘neuronal perspicacity, elasticity, efficatiosity, etc…’ 😎🌵
heyy lol
This book changed my life. The book reading and study transformed my further academic - and professional . development FOREVER. Twenty years after my university graduation I happened to become a peer of a full professor who graduated in Math at Duke and had been a student in Professor Spivak's class. Professor Spivak deserved a teaching Nobel Laureate, Unfortunately Teaching Excellence does occpy a mere ancillary position amongst academic competences.
I used this book in my honors calculus course, I recommend it to people who really want to be more familiar with calculus and who are building steps to approach real analysis.
This book did get me to change majors an o into a field where I didn’t need much advanced math.
With certain high profile books, like this one, it'd be great if you did a mini video series. Introduce the book then work selected problems in it and talk about why they're interesting. It'd be good content for sure.
I have the Fourth edition and the Combined Answer book. Great book. Pretty sure this is one of the first books I bought on your recommendation.
Awesome!!
Ten years into my prison sentence i found this book and it changed my life. Now I'm out on parole for good behaviour and looking forward to meeting the publisher to give my sincere thanks 🙏
wow !!
lol
Weirdest internet comment of the decade.
@imacmill You haven't been around long, have you ...
Good luck!
My math prof for analysis, Ed Perkins at UBC, in the 1980s told me this was his favourite calculus book. I've always wanted to check it out.
That's awesome. You should definitely check it out.
And now, a thousand years on, your still talking about it lol. Do it already 😤
Velleman has his own Calculus book and it’s really, really cool! It’s subtitled: “A Rigorous First Course”.
Thank you for this video, it brought back great memories. We used this text with the great Professor Tom Storer in the Honors Calculus sequence at University of Michigan many years ago.
We used this textbook Fall 1971 for the new "honors calculus" course at UC Davis. I think Spivak gave a talk at UCD a few years later (which I missed), and so some my former classmembers got their books autographed.
That book is a masterpiece and should be read by anyone who loves mathematics. The explanation of the logarithmic and exponential function is the best among all math books.
chap 22 Uniform Convergence and Weierstrass Approximation - I have strong thoughts on it.
This was our first 1st year text book at the University of Western Australia. All students wishing to major in Mathematics used this. I remember many a fond hour with this book back in the early 1980s. It's still on my bookshelf today!
!SUGGESTION!......When I was in school in the 70's, there was still a large Home Economic department. They didn't know calculus, but they could add, subtract, divide and do percentages in there heads at the speed of a calculator. They practiced that to the hilt, and the college guys couldn't begin to keep up. Maybe You would talk about that, and how we could learn the same thing. Thanks... Terry Drobeck.
This book has been a very important element of my formation as a mathematician, in fact, I regard It as Onésimo of the best and most beautiful books in the field (I am that Fernando Mejias who is mentionin the fourth edition’s preface). Read the text and work out as many of Its problems as you can, you will a lot of very deep mathematics!
Great vid! I learned Calculus in Hs, and later on in college as an undergrad where we used Howard Anthon's book (Calculus with Analytic Geometry). I still have that book.
Hi Math Sorcerer!I am a 16 year old high school student.I have learnt single-variable calculus on my own and planning to study real analysis in December and January and then study this book.I am grateful for your informative videos
You are insane dude😭
I aspire to be someone like you🙏
@keanusamuel4392 Thnx buddy
If you use Rudin's real analysis in December, then you don't need this book.
@@kleinbogen Rudin's book is too rigorous for a beginner,I plan to start real analysis with Bartle and Sherbart's book
Keep crushing, then come join us build the Golden age. We need more great minds that have grit and determination,
I'm a maths grad and I'm enjoying working though this book. Glad to hear that you also think some exercises are really hard!
This was the textbook that was used for my ‘Analysis I’ first-year undergraduate course at the University of Toronto many years ago; it is an amazing textbook!
I had just turned 17, and placed into Math 106, Honors Calculus, at Princeton, in 1977, where Prof. Dwork used this textbook. "The only math book with a plot."
His Comprehensive Introduction to Differential Geometry is beautiful! I also have his new classical mechanics book which is pretty amazing!
Wow, i was just walking past a house in my neighborhood and someone had left this book and the solutions book (along with a few other books) out for “take/share” purposes (common in New York). I didn’t realize I had gotten the Calculus version of the Elements or the Philosophy version of the Critique of Pure Reason or the Programming version of the Structure and Interpretation of Computer Programs.
Looking forward to digging in as an, at-best, good enough to get the degree requirement met math student.
Literally this was the best textbook I've ever read. What a fantastic book, and taught by a great professor at my university as well. I felt very privileged to have learned math in that course even if it was first year. Makes me curious what life would have been like if I continued, but I suspect it might have been slightly too difficult. Math degrees are not for the faint of heart
I really like the definition of trigonometric functions that appears in this book. The only book that gives a perfectly rigorous definition, yet related to our geometric intuition. I prefer that over using Taylor series or differential equations as a definition. You can define like that of course, but then problems like "can you square a circle" don't make much sense.
Spivak is great. I'm a fan of "Analysis on Manifolds" by James Munkres. The first half of the book covers calculus really well. It's like you get to learn about differential geometry as a bonus
This is basically advanced calculus or initial analysis. Good for epsilon-delta proofs. Rigorous. Very good for testing your concepts and developing greater insights. I'm working through this these days just to revise some old concepts and deepen my insights making me ready to study new techniques for differential equations and write some research papers.
This was my beginning honour calulus text at Berkeley. I later tutored a student with it who needed a credit at U of Toronto. I even tried to use it to teach a v-good high school course.
It is excellent for the best students, and not very good for the lazy students.
Wow those worked solutions are a gem ! Self-study is possible.
I have this book, picked it up after having taken Calculus. I had got over 100% in all three calculus courses, yet I still was aware of my own lack of fundamental knowledge. Voicing my own inadequacies despite stellar grades often got me weird looks from other students. This book helps fill in the gaps you need to extend your Calculus into an adequate foundation for Complex Analysis.
I bought this book a couple of years ago on your recommendation, wow.. it's not pedestrian calculus. Most engineers get just enough calculus to be dangerous, then there are electrical engineers which get the full course. I should have picked up a math minor along with my EE degree(s), it was only three more classes. (I gave this advice to an engineer in college just the other day)
I use it today as entertainment, just to go over the problems again and do the work keeps the mind working. I should purchase the answer book and do ALL the problems like I did in college, which makes you a better student IMO.
Thanks for the recommendation, I have picked up a couple of the books off your channel (mostly on number theory).
I look forward to more recommendations.
i bought this and studied it a lot before starting college. he sent me the solutions manual as well
This was the textbook I used in Fall 1967 and Spring 1968 for Math 50 and 51 at University of Maryland. I had taken a Calculus/Analytic Geometry course in high school. First semester was a butt-kicking - got wasted on first hourly. Meanwhile all the engineering folks were using Calculus with Analytic Geometry by Edwin Purcell - I remember sitting in on their lectures and was so happy that I understood what was going on. Math gods smiled on me and 2nd semester was much better.
Now to the changed lives portion: In 1975-76 I was in the MSIA (MS Industrial Administration) program at Purdue University where the challenge is to do 51 graduate hrs in 11 months. The legendary Prof Frank Bass taught the Econometric Course and the 4 hr midterm was 80% proofs. Spivak and the Math gods grinned!!
This is awesome thx for sharing !!
Spivak Calculus absolutely changed my life! We used it at UGA for honors calculus.
It indeed changed my life, it was my first year text at the University of Toronto and it quickly convinced me that there was no way mathematics as a career for me. I doubt I completed one exercise in it.
I always find it amusing when people who by nature are very accomplished in mathematics or who took the extra difficult versions of math courses, will talk about a book like this and say that it was great and others are not. I have taught Calculus for many years and have used the STEWART books for my students ( James Stewart was my professor and was an excellent and enthusiastic teacher ). Many of my students have gone on to great accomplishments in the field of mathematics and would eventually be well suited toward working with the Spivak book. But, many many more of my students have gone on to related fields where they needed calculus but did not need the difficult rigor of pure math. If I had used the Spivak book, most of my students would have struggled and may not have been able to go on.
chap 22 Uniform Convergence and Weierstrass Approximation - this is middle ground IMO for your spivak book avoidance. I neither like or dislike any of it. I am not a savage, after all.
also, delivering this kind of celebration of learning a topic that requires devotion to studying until you attain insights, while simultaneously blasting through some exercises in a speed and manner that's alienating to those not having acquired the know yet? ridiculous
...nice clean graphic design. Whoever designed this book, sure did a fine job of systematically aligning text and leaving empty space on the left for all the graphs that follow...:D
Hey Prof. I've been following your channel ever since I started studying Math at 26y/o, I would love to watch videos where you go through questions you find interesting like you did in the past.
the book which has made people switch careers🥶🥶🥶
Yes lol
how ? explain?
@@arifaahmed5454the book introduces serious real beautiful mathematical thinking. Many people can’t handle it
Also Rudin
😂😂
Agreed. I never used or owned it but learned from Spivak's more advanced books, especially the classic "Calculus on Manifolds" which I really studied,
and glanced at this when teaching, I always recommend the library copy to good students who want more rigor and precision and depth.
It is really excellent. Spivak is a real mathematician, unlike some writers of texts, meaning although for whatever reason he himself didn't do a lot of research himself, he knows research-level high-level stuff especially and "
and knows how to bring that perspective to Calc. Other GREAT undergrad texts are: Marsden 's Elementary Classical Analysis,
Bartle's Measure and Integration, Lang's Complex Analysis, Knopp's infinite series (V I and II), Guillemin and Pollock's Differential Topology.
Spivak also wrote a lot of AMS-tex and the famous book The Joy Of Tex. Spivak's multi-volume Differential Geometry texts I have only dived into parts of, but always excellent.
For me, the best calculus book for introducing Calculus. Also a very good book is Mathematical Analysis, by Apostol.
The thing about this book is that it blurs the line between calculations and proofs. Calculations are proofs and proofs are calculations. Mathematics is mathematics. This book is a masterpiece of mathematics.
I cursed this book when studying Mathematics in the early 1980s ... then learned to appreciate it fully as a reference throughout my working life. It's still on my bookshelf. Thanks for the memories.
what has been your profession?
This textbook was used in my Calculus course in 1970. I have a first edition of the textbook. I should get a more recent edition. Spivak shares a characteristic among the great mathematicians who made mathematics more teachable and accessible to more people The current notation we use for the calculus is due to Leonard Euler, of Euler's Constant fame, who founded entire branches of mathematics, in particular graph theory which is the foundation of topology . Spivak is a working topologist. Euler was a genuinely kind and pleasant person, a characteristic that Spivak shares. I have this on good authority as my college roommate took a summer math course from Spivak. Also, my college roommate told me that Spivak drove a VW beetle and adored Bach and jokes about Yellow Pig, who is the Y. P. referred to in the dedication to this book.
Who or what was the Yellow Pig that Spivak referred to?
@@jonroberts6131 i am naively thinking it was a pig painted yellow that was the mascot of a university :P
It is the best book on calculus I know. It helped me a lot during my studies (end 70ies beginning 80ies). Before this book I understood almost nothing about calculus. After working through the book I understood (almost) everything. And: It was fun to read. Also for me this is the truth: It changed my life for the better. A didactical masterpiece.
This book was used in an honors Calculus class in UC Berkerley 30 + years ago when I was a student there.
perfect example of what a good writer can do with a subject. the only way anything would remain unexplained would be due to the infinite ramifications of the subject. I wish I had more time to read it, but the small part of what I read at the beginning was pure beauty and art.
Don't know anything that was said, but did realize I need to stop drinking.
And smoking crack
Drinking and smoking 📈🥉
Calculus of Manifolds is his (Mr.Spivak's) other book. Nice one. This one is also good one. 👌🤘👍. Thanks bro. 🤝🙏
Bro really had to whip out the scratch paper in the middle of the review. Sold
Read this and worked through some of the problems a while ago. I'm back to it now to attempt to complete all of the problems!
I did my undergrad at Waterloo, i dont remember what the required book was but i remember getting this later in my undergrad from a profs recommendation
Was it for the advanced sections (147/148/247)? I did the regular stream so I have PMATH 333 coming up, hopefully Spivak will help. 🤞🤞
@ansonpang8468 nope 130s series. I only got interested in maths, academics aside, after I started my master's (not in maths, but related)
I'm pretty sure I used the first edition of this textbook in Freshman Calculus in 1979, but watching this makes me wonder if I even took Calculus.
“This.. is.. Spivak”, King Leonidas
Hi 👋
I watched a few other book recommendations on your channels bit this math's book stands out for me since I'm a first year moving to second year in software engineering diploma so. I'll go through the book within a month or so and we'll try some of the hard questions 😂 and I'll look for some more math books. My thinking is if I find really hard questions the easier ones will just be faster to solve and get the tests done quickly.😅
Maybe this book is a different type of hard than what you need.
one of the best math books i have read
A book which is something between "Calculus" and "Real Analysis". A great book, and the problems were amazing!
Yeah those problems are pretty awesome.
I found his book "Calculus on Manifolds" to be perhaps the most clear, wonderfully concise advanced math text I have ever read.
I dont know about Calculus but it is worth looking into books writen by Belarusian professor Boris Demidovich
Legendary math book! His writing style is so lucid
Spivaaaaaaak!*
*Like Sheldon screams Wheeaaaton!
We used this in first year calculus/analysis at UofT. It really pushes your math intuition and has really hard exercises😂
That book is clear and concise. Physics for Mathematicians is also a great book, which is by Spivak as well.
Do you think this book and Abbott are good to prepare for my first class in real analysis next semester? I already know how to prove things since i took a rigorous linear algebra class (with Axlers book) and I am kind of familiar already with epsilon delta.
Definitely !!
There is book by how to think about analysis by lara alcocok. check that
Have you never heard the old adage “Publish or Perish” before? It was meant to reflect the fact that those living in the world had to publish or never get tenure and stuff like that.
Interesting. I have a English version of this book (just one volume), and also a Spanish version (two volumes).
I think it has to do with the fact that it is a more verbose language.
Anyway, one of the 2 books I use frequently. The other is James Stewart's Early Trancedentals.
How about James Stewart's best-selling series of calculus textbooks: Calculus, Calculus: Early Transcendentals, and Calculus: Concepts and Contexts, which are used by 70% of students in North America?
I've been stuck at precalculus for the past three years 😅... But hopefully soon..
i am just going to finish calc 1. if you know algebra trig and geometry well its super easy. i am sure you are ready. dont be afraid. (i wouldnt recommend starting out with this book though)
learn your derivatives and some integrals then start over one more time!
This is similar to my Calculus book during my engineering days 23 years ago. Wonder if you have a good differential equation book with similar lot of examples and problems to solve. Thanks in advanceُ
Really good book. I learned from iit rigorous Analysis. Only thing i do not like is the way it introduses and presents Taylor Series .
It changed my life.
never got past algebra 2 and i got a masters degree in cyber security. wanted to learn more math growing up but didnt.....tried trig, failed, tried stats twice, failed, tried proofs...never learned geo so failed that but worked very hard for that D-.
I've been using this book for Calculus 1.
It is a good book but it was not my favorite as it lacked some content that i was looking for
I really like
Calculus with analytic geometry
by Earl W. Swokowski
And the Thomas Calculus new edition
The best
I am taking calc 1. next year. Would you recommend this to someone as supplementary material who is new to calculus?
And I have it baby!
Have you ever heard of any cases in learning where someone has trouble understanding basic calculus, but has an easier time learning things like partial differential equations and certain aspects of mathematical physics (like differential geometry)? Sometimes it's easier for me to grasp complex subjects in mathematics than it is to get easy subjects and I have to learn from the top down. This means I have no structure in learning and I'm scattered. Hopefully you can give me your thoughts on this
11:28 I thought it was my stomach that was growling 😆
Read "Real Analysis" and "Proofs" by Jay Cummings instead. Prof. Cummings is the GOAT
Been on the list for a while
this guy is literally a wizard
I'm a programmer and I feel like I want to buy it.
Have you ever encountered “Introduction to Calculus and Analysis” by Courant and John?
Courant and John is the best for calculus
I found this video very _handy_ .
Is this book also for a person like me that I have been away from maths for many years but would like to exercise my brain?
I am keen on history. I noticed that Apostol gives a history context in his explanations. What do you think about Apostol, mostly in comparison to Spivak, professor? Thanks and greetings from Brazil!
Best Calculus book ever!
in 1964? they introduced"new math " halfway threw my 4th grade class..I was lost and done with math for the rest of my life I shut up and became the quiet guy in the back of the classroom no one cared and the teachers ignored me.
Definitely changed my life for sure. Took MATA37 at UofT Scarborough with Prof. John Friedlander. The course was tough for sure. But I definitely gained an appreciation for mathematical proof that I had never experienced before. Became a physicist instead of a mathematician, but I always appreciated what I learned in math from my univeristy undergrad days.
Whats a good book to learn real analysis or complex analysis for self learner?
why will this book change my life? are you familiar with my life? I take everything literally.
The fact that 98% of the math books used in grade school and college aren't licensed under Creative Commons is a travesty.
using this book right now in first year analysis at uoft and i’m getting absolutely destroyed by it haha, it’s definitely not an easy jump considering how easy high school math was
My analysis 1 book as a physics student. it is quite nice
I really have no clue about any of this, but I am interested in how this stuff is used in the real world . Is it ACTUALLY useful,or just enjoyable for mathematics buffs? I ‘M asking this seriously , not sarcastically.
Courant and John or Stewart are better for real world calculus.
I wonder if you could recommend a great book on Abstract Algebra
I think something - something must be zero unless you are dealing with negative numbers.
Please try out Keshabchandra Nag's (KC Nag for short) Mathematics book for class 9 and 10 (2 separate books).
Is this a good book for first timer?
It was my 1st year calculus book in 1980 and it did change my life. High school math was just an exercise in being taught an algorithm and then repeating it over and over again. This book exposed me to Mathematics. It was a religious experience. To this day I can rime of the epsilon-delta proof. I have often said that if my house was burning down, I would grab this book first. If civilization collapsed and I could ensure one thing would make it to future humans, it would be this book.
dealing with Latex is a lot of work
I believe that the University of Toronto still bases analysis 1 off of this