Thank you all for expressing interest in my book! It has been a work in progress ever since I entered the masters program about 5 years ago. It is a long term goal, and I do not know when I will try to publish it. According to my ten goals, it should be published before 2030 but hopefully before then.
Since you are writing a Real Analysis textbook, here are some of the things I want to see in a new one, 1) All the proofs should be accompanied with extensive commentaries so the student can understand the whys and hows. 2) Most books give a lot of exercises at the end of the chapter but there is usually no solution or hint. I would like the book to include hints(The hints should be meaningful and clear) and there should be a seperate solution manual. 3) Texts like Bartle & Sherbert are excellent material but they aren't the most beginner friendly (Better than Rudin though). There is a book called "A Basic course in real analysis" by S Kumaresan and A Kumar. Which is one of the best Pedagogically but it has a lot of errata and it's hints are horrendous. I hope you will write a book with the pedagogy of "A basic course in Real Analysis", rigour of Rudin and as concise as Bartle Sherbert. I know these are big demands but If you can do it it will be a great book.
You are one of the few people I've met who switched from a non-math bachelor to a math bachelor. I also switched from Electronics Engineering in my bachelor's to a master's in math. Now that I am in my last semester, I recall how hard it was to study real analysis. I chose Baby Rudin before starting my master's program and it took around a year to go through the first 7 chapters and a lot of tears. There is definitely a big need for this kind of study guide. good luck :)
Hi, after three exhausting years I finally got my bachelor's degree in mathematics. I just wanted to say that your videos helped me a lot these last few weeks. They were extremely motivating and enligthening. Thank you.
Great job! Someone in the comments said to make it visual, that is the best way to learn analysis. Furthermore, have a section that explains how to prove things in Mathematics. Good luck!
I'm currently an applied science student but looking to take up paleontology as my actual degree, my library has some analysis books but they're all for those already with a lot of knowledge in analysis. Hopefully when your book finishes I'll be able to get it and could finally learn analysis.
I'm reading "How to think about real analysis" and "Book of proofs" as prep for self-studying real analysis. Also I'm watching Brightside of Math and some other channels. The actual textbooks are still a bit out of reach in terms of writing proof, but I'm starting to be able to read them. My current understanding is that its about axioms and definitions which you combine and play around with to find theorems. Then you play around with the proven theorems to find new theorems. It starts with axioms and definitions for the Real numbers and eventually builds up to calculus and beyond. In the end you will end up with the ability to fairly quickly see what possibilities you have to tackle calculus problems. Because you know exactly when and how calculus tricks work, like the chain rule or the power rule. Also at that point all the other higher mathematics open up to you since you're used to proof reading and writing and many concepts repeat across different contexts.
I have a year or two left for undergrad, so I really hope you get that survival guide published in that time frame! I will definitely read it and there's nothing wrong with going into grad school at least having an idea of what it will be like.
Every day, when I wake up, I often come across explanations in certain analysis textbooks that I find to be poorly articulated. And when I do manage to find a better explanation, I have the desire to compile my own analysis book with the best possible explanations. However, it's important to recognize that what works well for me might not necessarily work for the reader.
Great to know that you're not formally from a math background; i can relate to that, i too was a Physics student in my Bachelor's, had a rough transition to Mathematics especially since the University i got admitted to was a Pure Math Department essentially, none of the math i had cultivated previously was adequate to face the proof-based course and you correctly put it was more " philosophical" than science 😂😂😂 great memories
I hope your book emphasizes intuition more than anything. Like of course rigor is very important but just because a proof is short and elegant doesn't necessarily mean it's illuminating :) and of course I would hope your book also has some computational problems because math majors go too often without seeing the computational side
I think a more advanced version of Jay Cummings’ Real Analysis would be great. His books are the only math books I’ve ever thought were very well written.
Here in Germany, I'm currently in my 2nd semester of my Bachelor's degree. It's advised to take Analysis I - III in the first 3 semesters and these are extremely proof-heavy classes. There isn't anything like Calculus here. I think all of the German classes are more proof-based and personally I really like it that way. One of our instructors recently said "Here in Germany, we do Analysis, we're not in America where they do Calculus" and this has become somewhat of a joke among us students.
16:04 is very Pierre de Fermat-esque. Also, a French math guy. "I have a truly marvelous demonstration of this proposition that this margin is too narrow to contain." "It's there and I didn't have enough room." - Struggling Grad Student
I studied economics in undergrad and really want to study math. Did you make a video (or can you make a video) about that switch? How did you get admitted as a non-traditional student?
Measure theory is so abstract; if your book gives concrete examples as to why we need the theory in relation to Lebesgue and Riemann integrals --that would be wonderful, I guess, in my opinion.
can you record a video on your process of typing, like the process of transferring your notes to the type version, and also on latex, like what application you use for typing latex, or graphings and details.
if you're doing a study guide for introductory real analysis you have to provide some text explanation and graphically show why these proofs are true with actual integers and spaces. Otherwise it's just what you would get from a $200 text book.
Good work Mate. I am also in first year of PhD. That is lot of Analysis. It would be helpful if you can share what is your typical day looks like when you are taking classes. Like do you go over your notes after every classes days or you study a month before exam? It would be interesting to know. Thank you!!
I will give hints: (2) Apply Cauchy Schwarz inequality to f-1. (6) consider the difference of the two sums and look at the difference of terms. How do they simplify and behave as n tends toward infinity?
Wow environmental science. That's a very broad subject, what's your specialisation (like, it's a rather new course and different countries focus on different broadness)
Hey 👋, Please can I contact you if there's any way to do this. Can you tell me some standard books for the following topics :- 1. Linear Algebra 2. Differential Calculus 3. Group Theory 4. Real Analysis 5. Integral Calculus 6. Multivariable Calculus 7. Differential Calculus
1. Linear Algebra done right by Axler 2. Calculus by Edwards Hostetler and Larson 3. Algebra by Isaacs 4. Real Analysis by Royden and Fitzpatrick 5-7 Bartle and Sherbert
@@PhDVlog777 Okay interesting. I study in Austria and we covered everything up to the Lebesgue measure in the first semester in Analysis and some things (but more) in Functional Analysis in the fourth semester. The Lebesgue measure we covered in third semester.
Your notes are neat and the proofs are elegantly written. Great work! Have you also encountered Riesz-Markov theorem? If so, can you suggest a good reference for that with proof?
Thank you, I found a proof that is a little lengthy from Rutgers University but it seems pretty straight forward. See what you think: sites.math.rutgers.edu/~carlen/502S17/hahnsaks.pdf
Frankly, you learn to write on the computer, and the second one hides the chapters and topics, only the public learns from the points where the end of the transaction is not researched.
I see you working very hard to understand your classes, but you have to think about money in the future. You know, the clock's ticking, and all you've done is math, there's more to life than that. I do hope all of this pays off (with both monetary and satisfactory gain) in the end.
Wow, switching from an environmental science bachelors to a math master degree is impressive!
I had started as a math major and made it through calculus 3. After that, we started proof based math which is when I switched to EES.
Now I have to make a list too what i want to achieve in 10 years.
Same xD
Thank you all for expressing interest in my book! It has been a work in progress ever since I entered the masters program about 5 years ago. It is a long term goal, and I do not know when I will try to publish it. According to my ten goals, it should be published before 2030 but hopefully before then.
I have a PhD in electrical and computer engineering and not an expert in pure mathematics, however I would buy your book to support your work!
Since you are writing a Real Analysis textbook, here are some of the things I want to see in a new one,
1) All the proofs should be accompanied with extensive commentaries so the student can understand the whys and hows.
2) Most books give a lot of exercises at the end of the chapter but there is usually no solution or hint.
I would like the book to include hints(The hints should be meaningful and clear) and there should be a seperate solution manual.
3) Texts like Bartle & Sherbert are excellent material but they aren't the most beginner friendly (Better than Rudin though).
There is a book called "A Basic course in real analysis" by S Kumaresan and A Kumar. Which is one of the best Pedagogically but it has a lot of errata and it's hints are horrendous.
I hope you will write a book with the pedagogy of "A basic course in Real Analysis", rigour of Rudin and as concise as Bartle Sherbert. I know these are big demands but If you can do it it will be a great book.
(1) and (2) is already covered by Real Analysis by Jay cummings.Great book with explanations and ideas/intuition behind every proof
ok....sure....💩💩💩
You won’t get the pedagogy if you want it to have the rigor of Rudin
You are one of the few people I've met who switched from a non-math bachelor to a math bachelor. I also switched from Electronics Engineering in my bachelor's to a master's in math. Now that I am in my last semester, I recall how hard it was to study real analysis. I chose Baby Rudin before starting my master's program and it took around a year to go through the first 7 chapters and a lot of tears. There is definitely a big need for this kind of study guide. good luck :)
Hi, after three exhausting years I finally got my bachelor's degree in mathematics.
I just wanted to say that your videos helped me a lot these last few weeks. They were extremely motivating and enligthening.
Thank you.
Great job! Someone in the comments said to make it visual, that is the best way to learn analysis. Furthermore, have a section that explains how to prove things in Mathematics. Good luck!
👏 bravo! I had a friend who would write course materials in LaTeX as she followed the class (and they where very well explained as well)
I would love to see these resources soon! As a Math PhD. student, this would be really helpful for me!
I'lll be starting my pure math degree over the summer, and your videos have been very inspiring and educational! Keep it up man :)
I'm currently an applied science student but looking to take up paleontology as my actual degree, my library has some analysis books but they're all for those already with a lot of knowledge in analysis. Hopefully when your book finishes I'll be able to get it and could finally learn analysis.
I'm reading "How to think about real analysis" and "Book of proofs" as prep for self-studying real analysis. Also I'm watching Brightside of Math and some other channels.
The actual textbooks are still a bit out of reach in terms of writing proof, but I'm starting to be able to read them. My current understanding is that its about axioms and definitions which you combine and play around with to find theorems. Then you play around with the proven theorems to find new theorems. It starts with axioms and definitions for the Real numbers and eventually builds up to calculus and beyond.
In the end you will end up with the ability to fairly quickly see what possibilities you have to tackle calculus problems. Because you know exactly when and how calculus tricks work, like the chain rule or the power rule. Also at that point all the other higher mathematics open up to you since you're used to proof reading and writing and many concepts repeat across different contexts.
I have a year or two left for undergrad, so I really hope you get that survival guide published in that time frame! I will definitely read it and there's nothing wrong with going into grad school at least having an idea of what it will be like.
love seeing your vids in my sub box theyre always like Putting Myself In Another Special Pain Cube That Causes Me Extreme Pain For Another Semester
Every day, when I wake up, I often come across explanations in certain analysis textbooks that I find to be poorly articulated. And when I do manage to find a better explanation, I have the desire to compile my own analysis book with the best possible explanations. However, it's important to recognize that what works well for me might not necessarily work for the reader.
Great to know that you're not formally from a math background; i can relate to that, i too was a Physics student in my Bachelor's, had a rough transition to Mathematics especially since the University i got admitted to was a Pure Math Department essentially, none of the math i had cultivated previously was adequate to face the proof-based course and you correctly put it was more " philosophical" than science 😂😂😂 great memories
I hope your book emphasizes intuition more than anything. Like of course rigor is very important but just because a proof is short and elegant doesn't necessarily mean it's illuminating :) and of course I would hope your book also has some computational problems because math majors go too often without seeing the computational side
Wow, it would be interesting to read this book in its entirety. Good job!
I think you should type it straight away. Because you can read it wherever you want and correct the typos easily.
Please make a day in the life video
I love this
I think a more advanced version of Jay Cummings’ Real Analysis would be great. His books are the only math books I’ve ever thought were very well written.
yo can we get a sample of these books like a pdf version?
Good luck!
Jay cummings book is that book which I wanted as an undergrad
Here in Germany, I'm currently in my 2nd semester of my Bachelor's degree. It's advised to take Analysis I - III in the first 3 semesters and these are extremely proof-heavy classes. There isn't anything like Calculus here. I think all of the German classes are more proof-based and personally I really like it that way. One of our instructors recently said "Here in Germany, we do Analysis, we're not in America where they do Calculus" and this has become somewhat of a joke among us students.
Don’t know why they always put down others. Easy to talk trash about them in return. Doesn’t do good for anyone.
16:04 is very Pierre de Fermat-esque. Also, a French math guy. "I have a truly marvelous demonstration of this proposition that this margin is too narrow to contain." "It's there and I didn't have enough room." - Struggling Grad Student
Real analysis
Complex analysis
Your book: unreal analysis
I'm fresh out of highschool and I'd buy your book tbh
I studied economics in undergrad and really want to study math. Did you make a video (or can you make a video) about that switch? How did you get admitted as a non-traditional student?
He did talk about it in this video! th-cam.com/video/90twUkUiri8/w-d-xo.html
where can I get a print fof this ? hehehe AMAZING WORK THO!!
If you publish them one day, plz tell me, I would buy a copy.
Measure theory is so abstract; if your book gives concrete examples as to why we need the theory in relation to Lebesgue and Riemann integrals --that would be wonderful, I guess, in my opinion.
can you record a video on your process of typing, like the process of transferring your notes to the type version, and also on latex, like what application you use for typing latex, or graphings and details.
Is pdf available?
Please send 😊
Make it extremely visual. I love love love pughs book because of this.
Making your own book 😱, that's some gangsta shit bro. I can't even solve books 😱
What is “solving a book”?
if you need any illustrations I recently learned manim so I can make them
if you're doing a study guide for introductory real analysis you have to provide some text explanation and graphically show why these proofs are true
with actual integers and spaces. Otherwise it's just what you would get from a $200 text book.
There's a big room for a book like that but it's not an easy thing to do
i would love to buy your book :)
Are there any videos on TH-cam that you know of where mathematicians sit down and collaborate with each other? I'd like to see what that looks like.
Good work Mate. I am also in first year of PhD. That is lot of Analysis. It would be helpful if you can share what is your typical day looks like when you are taking classes. Like do you go over your notes after every classes days or you study a month before exam? It would be interesting to know. Thank you!!
Hello can you do a video on how to start with math? It would be so helpful THANKS.
Hi, what probability and statistics books would you recommend? My level is a big higher than beginner
Do you have any fellow Math graduate students from a CS background?
I want it someday
Kinda of a weird question but what pens do you use ?
I like the G2 pilot pens the most, they are expensive 💸
How do you prove exercises 2 and 6 from that last Page? I feel like I've done 2 before but forgot how it goes. No idea about 6 though.
I will give hints:
(2) Apply Cauchy Schwarz inequality to f-1.
(6) consider the difference of the two sums and look at the difference of terms. How do they simplify and behave as n tends toward infinity?
@@PhDVlog777 That's my goat. Thank you ❤️
Wow environmental science.
That's a very broad subject, what's your specialisation (like, it's a rather new course and different countries focus on different broadness)
My courses focused on waste management, air quality, and epidemiology. So more so public health and less Earth sciences.
Hey 👋,
Please can I contact you if there's any way to do this.
Can you tell me some standard books for the following topics :-
1. Linear Algebra
2. Differential Calculus
3. Group Theory
4. Real Analysis
5. Integral Calculus
6. Multivariable Calculus
7. Differential Calculus
1. Linear Algebra done right by Axler
2. Calculus by Edwards Hostetler and Larson
3. Algebra by Isaacs
4. Real Analysis by Royden and Fitzpatrick
5-7 Bartle and Sherbert
@@PhDVlog777 Oh okay, Thank you so much
Just send me the pre-order link
Would the content of you book be covered in an undergraduate math course in the US?
It depends on the school, but for me, this book would be more of a transition book between undergrad and grad school.
@@PhDVlog777 Okay interesting. I study in Austria and we covered everything up to the Lebesgue measure in the first semester in Analysis and some things (but more) in Functional Analysis in the fourth semester. The Lebesgue measure we covered in third semester.
14:15 What theorem does "BTC" stand for?
Bounded convergence theorem
@@PhDVlog777 Thanks.
15:39 you little fermat
Your notes are neat and the proofs are elegantly written. Great work! Have you also encountered Riesz-Markov theorem? If so, can you suggest a good reference for that with proof?
Thank you, I found a proof that is a little lengthy from Rutgers University but it seems pretty straight forward. See what you think: sites.math.rutgers.edu/~carlen/502S17/hahnsaks.pdf
@@PhDVlog777 Thanks for this. I'll read it.
6:37 who's a good boy
Lmao
Do you have a patreon?
this channel rules
Wow, impressive stuff! I am making a video series on Complex Analysis if you would like to collaborate?
👍
Frankly, you learn to write on the computer, and the second one hides the chapters and topics, only the public learns from the points where the end of the transaction is not researched.
Are you gonna sign your book as struggling grad ... That would be utterly funny at least make it part of the dedication 😂
is it just me but is all you do just memorise proofs?
Sometimes I memorize problems and find new exercises on the internet.
I came too soon :)
Can be a silly question but why don't you use an ipad or a tablet for taking notes that may be easy to manage?
I don’t have a good answer. I just like pen and paper, it’s what I’ve always used to practice math.
"promo sm"
I see you working very hard to understand your classes, but you have to think about money in the future. You know, the clock's ticking, and all you've done is math, there's more to life than that. I do hope all of this pays off (with both monetary and satisfactory gain) in the end.
Shut. Up. Take. Money.