What is Mathematics?
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- Опубликовано: 10 сен 2024
- In this video I talk about an amazing book written by two legendary mathematicians. The book is called "What is Mathematics?" and it was written by Richard Courant and Herbert Robbins. I talk about various sections in this book and spend a lot of time talking about the Mathematical Analysis of Infinity. We discuss why there are just as many numbers in (0, 1) as there are real numbers. We also discuss why the rational numbers are countable and the real numbers are uncountable. I also go over the proof that (0,1) is uncountable(it's a beautiful proof by contradiction). Other topics explored in this video include continued fractions, deformations in topology, etc. This book covers A LOT of mathematics and I only briefly touch on some of the topics in this video.
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Thank you:)
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Just defended for my PhD in physics but I also love mathematics. Courant also wrote a mathematical physics book with David Hilbert if I’m not mistaken.
"Methods of Mathematical Physics" by Courant & Hilbert
@@douglasstrother6584 Yes! I remember it because my professor for Jackson EM mentioned it when we were studying how to determine Green’s functions. That was one of the most difficult courses I ever had.
@@physicshypernova2083 "Jackson": The Big Red Brick! (I still have my copy.)
Check out "Modern Electrodynamics" by Zangwill as well.
@@douglasstrother6584 I used the blue version of Jackson but I have seen the red brick before. I also have the book Zangwill and it’s easier to follow. Another book although old (1971) is “Introduction to the principles of electromagnetism” by Hauser. Based on the preface it was written to help prepare for Jackson.
Can you do physics books review ?
"Today some educational administrators are trying to demote mathematics from its traditional place." - From the Preface of this Book
This definitely stood the test of time. True today as well.
I started watching your channel in my community college precalculus class and now I've been accepted to study my BS in Mathematics at Indiana University this fall and I'm so excited. Math has been very helpful in my work as a software engineer and computer scientist. I will be reading this book! Thanks again, the math student community appreciates your support and benediction.
That's so awesome Jonathan! Keep it going
That is awesome! Go Hoosiers!
So you are a software engineer and a computer scientist without any math knowledge at all?
I'm working as a mathematics lecturer in India.. Sir.. You and Eddie woo are my inspiration❤️❤️
@Nova ❤️
You’re so right that this book is one to read throughout one’s life. My Dad literally has done that! He is 87 years old and got this book many decades ago, and he still dips into it to learn about maths.
It's so nice to see people being enthusiastic about math because all I hear from people my age and younger is that they hate math with a passion.
I'm 20, finishing the second year of computer engineering, and in the process of ditching my major for a degree in math instead. After 2 years of only caring about the calculus classes I finally realized what I truly want to learn, so I'm taking notes of all the books recommended in the comments to get me started. It's nice to feel like I'm on the right path for a change
so awesome! You sound a lot like me. Thanks for your comment!!
I have to admit that I was guilty of “hating math with a passion” as well because of the way the math courses I took were taught. The courses were just formulas and problems. It wasn’t the course’s fault but it was difficult for me to establish an interest in something that didn’t seem to have any meaning. That was until I watched some videos by Numberphile and sparked my interest in learning mathematics.
Maths is beautiful. People only hate it because they were overwhelmed with it early on.
@@saichandra5269 same thing
Sai Chandra,
I hated math for the same reason: just didn’t see how it meant anything. I finally picked up a book by Morris Kline: Mathematics for the Nonmathematician. It’s a cultural and historical overview of math written from a liberal arts perspective. I’m nowhere near finishing it, and it has already changed my life! Math is my new hobby!
In Physics grad school I had a course out of Courant & Hilbert. Courant was a student of Hilbert. My instructor was a student of Courant. Small World.
I bought the book! Printed in 1956 and never opened - a gem. Still haven't found the definitive meaning of Mathematics, but I'll be reading it all summer.
2 of my favorite books from my teenage years which inspired me to pursue mathematics and engineering:
(1) Number: The Language of Science, by Tobias Dantzig
(2) One Two Three Infinity, by George Gamow
Number the language of science is a great book. It gave answers to many of my questions.
Grabbed this book from my granddad's collection after he died and I'm so glad I did. Went on to get my math degree (as well as one in CS) and this book played a big role in my desire to get a math degree
Okay, but who is mathematics?
😂 good reference bruh
I love this book
1 year ago I was looking for good explanation for complex number , cause I nat getting that anywhere that I can understand , suddenly this book came my mind .
I was not quite familiar with this book but I just know that there is a book titled "what is mathematics" and it tries to explain many parts of mathematics.
That day I downloaded its pdf and started reading it . And I can , this book is on another level.
Thanks math sorcerer for reminding me of this book. I will pickup this book tonight
thanks for recommending this book sorcerer, when it comes to math you are my go to channel please never stop making such amazing videos
You've got a real treasure there for sure. Courant & his fellow peer, the great Hilbert, were both exceptional expositors of Mathematics. ANY written texts by them are literally CLASSICS!
Also noted the Book had a 'Strand' stamp, my fave 2nd hand Bookstore in NY...LOL
Ooooh so cool! I didn’t know they about the Strand stamp. Thank you !!
I stumbled upon this book in 10th grade by chance and ever since, going over and reading passages of this book and trying to get a deep understanding of math has kept my passion alive for the subject in spite of the relentless drills and monotonous questions bogging down by joy of the subject.
What is Mathematics? An example of a love/hate relationship ... Thanks for the very useful channel ... Cheers! Christopher
cheers:)
Professor, you said this book isn't philosophy, but in my point of view the explanation about Cantor's sets is quite philosophical!
❤️❤️
What a great surprise I had when I saw that in this video you presented the book that most inspired my taste for mathematics since my adolescence. The book was brought by a brother of mine who was doing a master's degree in engineering at SUNY University, I inherited it by chance and at that time this magnificent book inspired me with a great love for mathematics. I still have it and it is in Spanish version, 1964 edition. I keep it as a treasure!
I recently passed my Calculus 2 Exam, I have to say I feel deep respect and admiration for the people that try and make Mathematics easier to grasp and understand!
In the spirit of this topic, another excellent reference to survey is ... Numbers & Mathematics by Clayton W. Dodge -- long out of print, but copies still can be found via Amazon and other resellers.
I have the second edition of this book. It's a good starting point for someone to learn mathematics.
yes, but it requires a little bit of mathematical maturity
It's not a good choice to start with this book. It's great to read it after first course of university i think.
Your passion for mathematics is inspiring!!!
I'm going to start a masters course in math, i'm scared...
Oh that is soooooooooo exciting!!!! You are going to love it:) It's hard but it's also so fun:)
@@TheMathSorcerer Nice! Thanks
Today I read this book in the library of my university, but the one in the library was green. I'm studying an electromechanical engineering, but your videos inspire me to go further in math.
Wow!!! So cool to see these topics mentioned! I am finishing up a Discrete mathematics course and it’s so cool to finally recognize some of the concepts that you mention. I can’t wait to look back on some of your videos on abstract algebra/ real analysis in the next two years! Thank you for posting these videos and for being so enthusiastic, it really helps motivate the exploration of math!
How much time it take you to finish discret mathematics?
@@harshguler I took the course over the span of 6 weeks, but I feel like I don’t entirely understand how to prove every topic I’ve gone over. Now that the course is done though I plan to review in the next few weeks.
@@kethollingsworth3075 Ok
So accessible and inspiring. Don't stop til WE have enough ! ❤
I'm a new beginning to mathematics in this book will help me learn the basic skills of mathematics thank you so much keep the videos coming
I just bought the book primarily on the strength of your assessment that it is very well written and explains the math well. I think it was Richard Feynman who said that in order to understand how well you understand something, try explaining it to someone else. These people who muddle up their explanations make me wonder how well they understand it themselves.
I'd recommend the book "What is Mathematics, Really?", by Reuben Hersh. A deeo, extremely human approach, of the subject. Worthwhile!
That is one of the most amazing books I've read in my life. A beautiful and deep philosophy approach, that mainly deals with the subject how human (and not so exact or "godly") is Mathemathics.Excelent!!!
A necessary look. Good siggestion!
Reading Reuben Hersh blew my mind years ago. It should be studied by all students and ali people who is really intetested in Mathematics. There is no point in studying any subject if it is not seen by a humanistic point of view and understanding. What Science and technology have done to the world without it? We urgently need History and Philosophy in all fields of study !!!
Wow. I picked up that book up from my college library the other day just because the title appealed to me. My background is in History. But now I'm studying CS as a mature student and I've been struggling with Maths and Problem Solving. I started reading it again this morning. Coincidentally this video found me a few hours later whilst looking at something else. I have reading week atm. So I might as well get into that one and see where it takes me 🙂
I really enjoyed the book "What is Mathematics, Really?" by Reuben Hersch -- I read it at 19 years old when I had decided to major in math. In the foreword he presented it as a way of following up on "What is Mathematics", which I never went back and read. I'll have to order a copy tonight, since I'm on a heavy nonfiction streak right now.
His "Introduction to Calculus and Analysis" is the best calculus book I've found anywhere.
😀
Thank you so much for posting this! Hope everything is going well!
Hello! Yes, GREAT!
One of my favorites and I thought most re-memberable - there are topics in it I remember but did realize were I read it!
This great book is now in paperback, 2nd edition.
I was able to find a second edition revised by Ian Stewart in 1996. It's still cool you have the original, @The Math Sorcerer.
I love older mathematics books. There's more clarity in them for some reason mixed with a bit of nostalgia. Your love of mathematics makes me want to pull out my copy of "Advanced Engineering Mathematics" by Kreyszig (not an old edition though unfortunately) that I picked up for a couple of bucks at Goodwill and start working through exercises.
This book, I completely agree with you, is so well written. It's one of the best I've ever read in terms of explanations of difficult concepts. The author did a great job, especially for the topics on topology, projective geometry and basic calc. Some of the exercises were doable, but often the way to solve them requires some original thinking! One of my all time favourites, for sure.
Omg I got confused by the cover until I remembered I already have that book in my math arsenal (with the new cover of course) :P
:)
I read some where that mathematics was derived from the Greek "mathesis" which means "purifying the soul" and largely relates the process and rituals relating to the mind. Most of the biblican and academic terminologies like theology, theory, thesis, mathesis and mathematics are interrelated.
Very sad this book is not available in a czech translation. This looks awesome. I guess i can try to broaden my English vocabulary but it'll be painful to get just through one page
I bough my copy in 1977 for about $10 (which was expensive at the time) and still pull it out to read occasionally. There was a biography of Courant at one time that's probably long out of print.
Cara, seus vídeos são sensacionais. Saudações do Brasil!
Ok, ok, FINE… I’ll get a copy. Haha. Seriously though, your enthusiasm is very motivating, and I’ve already bought a few of the books you suggested before.
Your videos are inspiring me to looking into a master in math. Thank you.
I keep saying to myself, no more books. But I think I will have to get this one
Love and humble respect from Bangladesh.
Definitely gonna pick up this book. Thanks!
You have a real love of books as well as mathematics.
Well this is one approach... It seems very non standard.
Mathematics education is not about understanding mathematics, it's about doing mathematics in the hopes that it leads to understanding mathematics. But even this isn't really expected. Perhaps there is this unstated belief by the community that doing the mathematics is more fundamental to the content of mathematics than its concepts; perhaps in the sense of believing that at some point words fail to explain what can only be demonstrated.
I tend to agree with the author that it's more a phenomenon of teachers letting the exercises do the job of explaining what they lack confidence in actually knowing. And it wouldn't surprise me that this would be a recurring/continual situation throughout education history.
Anyway, love the enthusiasm in the video, like the approach the author is taking.
Wow what a great comment, thank you 🙏
This is very interesting comment that reduces the pressure of trying to understand every little thing I encounter in Mathematics.
From India! I'm enjoying your videos although I'm a little weak in English but still I'm able to understand You ❤️
Awesome❤️
Does anyone know of any really good calculator apps an d calculator programs for computers?
Oh I read this book. I thought it was missing some details in a lot of the areas. They were good introductory material for say a high school student, before they have to tackle these in higher detail. The book develops good intuition.
Hey man, your vids are awesome and enjoyable. I can just relax and listen. This vid makes me want to buy a used hardcover, but it's hard to find--paperbacks are plentiful, so I'll probably just go for that. Although I think Springer sells it new for $107 or so--if I were wealthy, I'd get that version. But of course you've shown and explained stuff in the book so well, so I'm sure I'll forget all about the cover. Let me know if you ever want to sell your copy, which means I'll never buy it because you will never sell it! Wise😊🤣😊🤣😊
I love these math book discussion videos! please do more!
Will do!
This video actually made me laugh in excitement. I need a copy!! Preferably an old one like that, of course
Just got this book, it is so nice to re-explore complex analysis and other topics. Such a great read
Could you possibly do a vid on excellent workbooks that you are aware of?
Ooh yes great idea!
Very nice video on Courant and Robbins book. There are many stories around this book (including an attempt of plagiarism) but l am not into that because Courant was a very controversial mathematician. However, there is something about Courant books, they are too 'wordy' so sometimes they require a lot of effort from the reader. Courant belonged to a group of mathematician that were against the Bourbaki style that took over the mathematics in 50 and 60 of the xx century, and still remains in some branches of mathematics (for example algebra). Somehow the book 'what is mathematics?' is an attempt to present mathematics as a language that develops from intuitive ideas and not as a formal theory developed from a set of axiom.
Just purchase this book ! AMAZING
awesome!
Thank you. I like mathematics but I also have hated the philosophical aspects of it. Especially when they say about it being "perfect" when in real life scenario I can't ever see anything that relates to the perfection. I just like the different ideas that come up and explore the pattern and it's just like a candy world where different flavoured candies come up each time. When they put all the philosophy though, especially that of strictly sticking to deductive proof and having the perfection it really gets on my nerves. I know I screwed my academics trying to understand that "perfection" but it never worked out. Now I don't bother about it anymore. I just like to see and explore and enjoy the new ideas that can come up all the time.
A must-read!
for any mathenthusiast
Just ordered the book
How do you compare this book with Garrity's "All the Mathematics that you have missed"? Because that is also a proof based book, in which I got thanks to your advice. I haven't read it yet, because I am still recapping my college mathematics from scratch and want to approach it when ready. I also wonder how do you compare this one to Spivak's? because his is also about analysis.
What is Mathematics in one sentence?
It's a gradual cognitive discipline requiring the ability to explore patterns seeing from different perspectives, and to represent them using math symbols.
How can one make mention of "math" symbols before defining Mathematics(i.e., answering the question, "what is Mathematics?")?
@@AajanmaHindu I guess just using "symbols" instead of "math symbols," since I dont think there is a way to say whether a symbol is mathematical or not. Making this little change circumvents the necessity of defining "math symbols"
It really did help. Thanks for the great content
Favorite Math book by far
That continued fraction bit was awesome
Have you ever heard about «Fundamental Principles of Mathematics» by Bento de Jesus Caraça?...
Amazing astounding super!
Wow this book is very clear and concise, I love it!❤
Nicely done bro
My high school Calculus teacher used to say "the Calculus." Eleanor Brevard -- one of the greats.
I should check this out thank you!!!!
@@TheMathSorcerer Perhaps I was misunderstood. That's the name of my high school Calculus teacher.
I would like to own this book just to practice writing Fortran Programs.
What I think would fascinate me about this book - is support for my belief that one understands the definitions of mathematics concepts and language improves the capability of problem-solving; other than by example, after example.
What contribution did Robbins make to the 2nd edition?
This book is good, thank you for give the information
How can I get this version of the book. I'm obsessed and I can't find it anywhere
👍Not sure if you've had time to review another General book, Fundamentals and Foundations by Eaves
Absolutely brilliant book
I have My own Copy of this Masterpiece thanks foto share
Must take a look to see if it's available in the UK.
can you help all my use of logarithmic scaler have atrophied or forgotten?
I did a search. You can get a copy for under $10.
very nice!!
I think you might get a kick out of Category Theory ✨
Conceptual Mathematics: An Introduction to Categories
helpful video
Great Video! Love it!
Thanks for the recommendation!
Very useful to me Thanks.
I'm looking for good calculator programs and apps for math principles and applications
Everyone asks "what is mathematics?"
Nobody asks "how is mathematics?"
I love old hard cover math books - they have a certain aesthetic quality..
The old head line cook I worked with from the Bronx completely disagrees.
You will do this video in your Spanish channel?? / Harás este video en tu canal en espáñpñ¡
Ay si que buena idea, muchas gracias!!!
what is the precalculus book that you recommend ?
Hey sir, I 've recently discovered a book by the name of higher algebra written by Barnard and Child. I decided to download it and read some portions of it. I'm no mathematician but the notations it uses are really weird. Also the way of writing is extremely tough. If somebody here is familiar with this book, can you please tell me if this is a good book to use today and if its content is that of an algebra book and not a number theory book. Thanks in advance
Hey sir, can I read calculus made easy and directly go to baby rudin or analysis by tao? Thanks in advance
{ n, m | n = unique phrase, m = unique correct phrase(s) } Mathematics is m.
And this is an amazing book:
Mathematics and the Search for Knowledge
Book by Morris Kline
Have you ever reviewed the four-volume set "The World of Mathematics" by James R. Newman? I think it's pretty cool. This was a must-have for a math lover when I was a bit younger.
Good day struggling to grasp linear algebra ,any advice on how to tackle it ,i am using axler linear done right
Thanks a lot!