Please Subscribe to the channel and share this video with as many people as you can to help grow faster! Tap into the list below to take notes about the desired source. In the video, I explain in detail which books to use for Theory, and which ones for practicing the acquired skills. HEALTH WARNING: I am not affiliated with amazon.com. All the recommendations I make in this video are based on my personal experience over the past years. Enjoy 😉 Salvo //-------------------------------------------------------------------------------- LIST OF BOOKS //-------------------------------------------------------------------------------- 0:22 - What kind of sources should I select? 0:39 - Set Theory ↪ How to Prove It A Structured Approach by Daniel J. Velleman 1:32 - Calculus ↪ Calculus by Michael Spivak (4th edition) ↪ Calculus. 11edition by Ron Larson 2:36 - Number Theory ↪ Elementary Number Theory, Seventh Edition by David M. Burton 3:15 - Real Analysis ↪ Analysis I, Third Edition by Terence Tao. ↪ Real Analysis (4th Edition) by Halsey Royden, Patrick Fitzpatrick ↪ Measure and Integral. An Introduction to Real Analysis by Richard L. Wheeden, Antoni Zygmund ↪ Principles of Mathematical Analysis, Third Edition by Walter Rudin 4:50 - Linear Algebra ↪ Introduction to Linear Algebra, Fifth Edition by Gilbert Strang 6:15 - Abstract Algebra ↪ Abstract Algebra. Theory and Applications by Thomas W. Judson ↪ Contemporary Abstract Algebra by Joseph A. Gallian ↪ Schaums outline of theory and problems of abstract algebra by Lloyd Jaisingh, Frank Ayres 6:51 - Topology ↪ Topology Through Inquiry by Michael Starbird, Francis Edward Su ↪ Schaum’s_Outline_of_General, by Seymour Lipschutz 7:23 - ODEs ↪ Elementary differential equations with boundary value problems by Charles Henry Edwards, David E. Penney ↪ Ordinary Differential Equations (Dover Books on Mathematics) by Morris Tenenbaum, Harry Pollard 8:16 - Complex Analysis ↪ Visual Complex Analysis, by Tristan Needham ↪ Complex Analysis, Fourth Edition by Serge Lang 9:19 - Differential Geometry ↪ A Comprehensive Introduction to Differential Geometry by Michael Spivak 10:18 - Statistics ↪ Statistics, Fourth Edition by David Freedman, Robert Pisani, Roger Purves 11:45 - Optimization ↪ Numerical Optimization, Second Edition by Jorge Nocedal, Stephen Wright 12:20 - Numerical Analysis ↪ Numerical Analysis by Richard L. Burden, J. Douglas Faires, Annette M. Burden
Critique for future videos to better satisfy and increase viewership ratings: Place bibliography within video description. Viewers are accustomed to locating said material in that location as indicated from comments below. This is the most logical place for this information. Cheers
@@musashi4856 Thank you, always welcome constructive criticism 😉✌🏻 I prefer to place the bibliography at the top of the comment section rather than right below the video. I use that section to describe the video's purpose and indicate some information that usually is skipped by most people who want to get to the point.
Thank you for the info, I had a rather strange journey in science, I went from being a nurse (BSN) at a hospital to being a bio systems engineer, it was inevitable no matter what I did I was always thinking of numbers, measurements and any other things that associates a value to an object like in chemistry. I couldn’t take it anymore and just went for it and did it, I did surprisingly well and it’s been a relief for me and well as my former co-workers who I no longer bore with chemical/pharmacological equations and algorithm efficiency outlines lol! I still love nursing (and will still do it on the side for proficiency sake), but I’ve always been the type not just to do but to want to understand why we do the things that we do and how to improve a process or replace it if needed. I really appreciate the info you provided, I honestly do best with those overly written frustrating type of books, especially the ones from the 50’s, because they force you to think and sometimes even guess if you need to, that’s the beauty of these books, there’s no scientist, mathematician or engineer that hasn’t been stumped or not failed in their pursuit of knowledge. Thank you again!
Rudin's "Principles of mathematical analysis" is an example 😆 Tough but it improves the ability to investigate and be better at dealing with frustrations. Science is clear on this point. Learning MUST come with frustration and failures if one wishes to improve. We actually know what we know because we have passed through a battery of tiny failures, but at times we fail to recognize that. Think of it for one moment. When you were learning the multiplication table at school...you were nothing more than a kid...did you learn to compute (as you do now) in 1 minute? Or did you pass through some initial setback? In math, we do welcome obstacles because that's the way that guarantees success in the future.
Complex Variables" by John W. Dettman is a great read: the first part covers the geometry/topology of the complex space from a Mathematician's perspective, and the second part covers application of complex analysis to differential equations and integral transformations, etc. from a Physicist's perspective.
Hey Bruce, 1) You can pause the video and take notes. 2) Please give a look at my comment in this section. There you find all the books you may need, enjoy ✌🏻
Keeping the images for such a long time would make uncomfortable those who want to watch the video without interruptions. It's important for you to focus on the content, not the images. Below the video, you find the list of the books.
Please also add both reading age, and prior maths experience needed. Why is no stats book included? I know it's boring and practical but it's fundamental and we need stats far more than we need differential geometry. Spoke too soon. You do include a stats book! I don't know why anyone - not studying for a (pure) maths degree - needs abstract algebra, topology, or differential geometry. This is all pure maths stuff.
1) I specify those are my favorite books 😊 2) The books i listed in the video are university books. You're not supposed to use them if you are 15 years old unless you're incredibly talented and you feel that, even though you're 14 years old, you can understand and study this level of math. 3) "not studying for a (pure) maths degree". That's simply wrong. At MIT they strongly recommend keeping the number of applied/pure math subjects balanced. That's what i also believe. Number theory is very important because it teaches how to prove and think through math difficulties. On top of that, there exists a large body of challenges and exercises that make this subject extremely challenging from a problem-solving standpoint. Topology is at the very foundation of the many branches of science and engineering. Knowing that gives a great advantage to those who need to understand how to apply math to practical issues. Math is beautiful, irrespective of whether it is pure or applied. 4) It's not true that i didn't include a statistics book. You gotta watch the videos entirely.
Isn't this a better study order? As one wants to study the more practical maths before the purer stuff? As I see it, these 7 subject areas are very practical, but the other 7 not so much. 1) Logic and Proofs tio 2) Set Theory 3) Calculus 12) Statistics 7) Linear Algebra 9) Ordinary Differential Equations (ODEs) 13) Optimization 6) Real Analysis 8) Complex Analysis 4) Number Theory 5) Abstract Algebra 10) Topology, 11) Differential Geometry 14) Numerical Analysis Please correct me if I'm wrong. What is a good book with takes lesser known maths (last 7 topics0, and shows the real-world applications? "real-world applications" = not string theory or any other branch of pseudo physics which may be real - but likely not in this universe.
1 & 2 is the foundation of all Mathematics, in particular 5,6,7,8,10,11, the pure. That in turn explains the remaining applications - using that word loosely - 3,4,9,12,13,14. From a logical point of view, but perhaps not a practical one, it makes the most sense to study the topics more or less in this order.
For optimization, do you recommend "mathematical optimization and economic theory" by intriligator? (For an econ student looking for mathematical rigor)
If you want math rigor, Fletcher's book is very very good. It's my favorite, but it requires math maturity. You risk to get overwhelmed by math if you do not know linear algebra, calculus, numerical analysis.....
Oh, just plow through thousands of books as recommended by folk on youtube, since there is no book lists and method that GUARANTEE at least a bachelor's level of competence.
You will find so many tech people trying to enter machine learning and data science but they don't know how to approach math. Please tell us how to learn that math without wasting time.
1) I have been preparing something for you guys for over the past three years that addresses this kind of needs. It is almost ready, i will make the announcement next fall, hopefully, if nothing unexpected comes about. 2) In general, what determines the degree to which a data scientist should approach math relates to the activities one is expected to carry out. Being a data scientist who is supposed to develop new algorithms and publish scientific papers involves a TOTALLY different math background and problem-solving skills than if s/he works as a "user" for a company. I do not believe in-depth understanding of K-Nearest Neighbors to be essential for the "user". I do not believe in-depth understanding of a function activation record in C++ to be essential for the "coder". But if you have to develop new methods, you cannot live without in-depth understanding. Or, at least, you can, but one would be doomed to failure.
@@scienceskills That's so great. I am so excited about the content you are preparing. Thank you so much for every minute you spent with us in this channel.
@@scienceskills I have been preparing something for you guys for over the past three years that addresses this kind of needs. Hi so what happened with this initiative? Did you give up on it?
@@encapsulatio Hi. Not at all. Last year, I published my online course, a top-notch approach to studying science. However, I unpublished it recently for further update. I would re-publish it in the future only if there's enough demand.
Please Subscribe to the channel and share this video with as many people as you can to help grow faster!
Tap into the list below to take notes about the desired source. In the video, I explain in detail which books to use for Theory, and which ones for practicing the acquired skills.
HEALTH WARNING:
I am not affiliated with amazon.com. All the recommendations I make in this video are based on my personal experience over the past years.
Enjoy 😉
Salvo
//--------------------------------------------------------------------------------
LIST OF BOOKS
//--------------------------------------------------------------------------------
0:22 - What kind of sources should I select?
0:39 - Set Theory
↪ How to Prove It A Structured Approach by Daniel J. Velleman
1:32 - Calculus
↪ Calculus by Michael Spivak (4th edition)
↪ Calculus. 11edition by Ron Larson
2:36 - Number Theory
↪ Elementary Number Theory, Seventh Edition by David M. Burton
3:15 - Real Analysis
↪ Analysis I, Third Edition by Terence Tao.
↪ Real Analysis (4th Edition) by Halsey Royden, Patrick Fitzpatrick
↪ Measure and Integral. An Introduction to Real Analysis by Richard L. Wheeden, Antoni Zygmund
↪ Principles of Mathematical Analysis, Third Edition by Walter Rudin
4:50 - Linear Algebra
↪ Introduction to Linear Algebra, Fifth Edition by Gilbert Strang
6:15 - Abstract Algebra
↪ Abstract Algebra. Theory and Applications by Thomas W. Judson
↪ Contemporary Abstract Algebra by Joseph A. Gallian
↪ Schaums outline of theory and problems of abstract algebra by Lloyd Jaisingh, Frank Ayres
6:51 - Topology
↪ Topology Through Inquiry by Michael Starbird, Francis Edward Su
↪ Schaum’s_Outline_of_General, by Seymour Lipschutz
7:23 - ODEs
↪ Elementary differential equations with boundary value problems by Charles Henry Edwards, David E. Penney
↪ Ordinary Differential Equations (Dover Books on Mathematics) by Morris Tenenbaum, Harry Pollard
8:16 - Complex Analysis
↪ Visual Complex Analysis, by Tristan Needham
↪ Complex Analysis, Fourth Edition by Serge Lang
9:19 - Differential Geometry
↪ A Comprehensive Introduction to Differential Geometry by Michael Spivak
10:18 - Statistics
↪ Statistics, Fourth Edition by David Freedman, Robert Pisani, Roger Purves
11:45 - Optimization
↪ Numerical Optimization, Second Edition by Jorge Nocedal, Stephen Wright
12:20 - Numerical Analysis
↪ Numerical Analysis by Richard L. Burden, J. Douglas Faires, Annette M. Burden
Critique for future videos to better satisfy and increase viewership ratings:
Place bibliography within video description. Viewers are accustomed to locating said material in that location as indicated from comments below.
This is the most logical place for this information.
Cheers
@@musashi4856 Thank you, always welcome constructive criticism 😉✌🏻
I prefer to place the bibliography at the top of the comment section rather than right below the video. I use that section to describe the video's purpose and indicate some information that usually is skipped by most people who want to get to the point.
Thank you for the info, I had a rather strange journey in science, I went from being a nurse (BSN) at a hospital to being a bio systems engineer, it was inevitable no matter what I did I was always thinking of numbers, measurements and any other things that associates a value to an object like in chemistry. I couldn’t take it anymore and just went for it and did it, I did surprisingly well and it’s been a relief for me and well as my former co-workers who I no longer bore with chemical/pharmacological equations and algorithm efficiency outlines lol! I still love nursing (and will still do it on the side for proficiency sake), but I’ve always been the type not just to do but to want to understand why we do the things that we do and how to improve a process or replace it if needed. I really appreciate the info you provided, I honestly do best with those overly written frustrating type of books, especially the ones from the 50’s, because they force you to think and sometimes even guess if you need to, that’s the beauty of these books, there’s no scientist, mathematician or engineer that hasn’t been stumped or not failed in their pursuit of knowledge. Thank you again!
Rudin's "Principles of mathematical analysis" is an example 😆 Tough but it improves the ability to investigate and be better at dealing with frustrations.
Science is clear on this point. Learning MUST come with frustration and failures if one wishes to improve. We actually know what we know because we have passed through a battery of tiny failures, but at times we fail to recognize that.
Think of it for one moment. When you were learning the multiplication table at school...you were nothing more than a kid...did you learn to compute (as you do now) in 1 minute? Or did you pass through some initial setback?
In math, we do welcome obstacles because that's the way that guarantees success in the future.
Thank you SO much for this video, greetings from Costa Rica.
Hola amigo, estoy feliz que tu gusto el video!
Hasta luego ✌🏻
I agree that elementary number theory book is the best to start learning number theory
I like your studio. It is simple and beautiful!
The first book I see, Proofs and Fundaments, changed my life.
I think your video is very well done and, to me, most valuable! Thank you!
I always enjoy your reviews ... thank you (again)!
Complex Variables" by John W. Dettman is a great read: the first part covers the geometry/topology of the complex space from a Mathematician's perspective, and the second part covers application of complex analysis to differential equations and integral transformations, etc. from a Physicist's perspective.
Ciao Douglas, thanks for your contribution!
Hi I am a recent graduate Engineer and this has given me some clarity on what I should pursue in maths for my engineering career.
What engineering's branch?
Mechanical Engineering
Would you please mentioned the book link on your description?
Read my comment on the top...
Loved your video, thanks a lot, I was wondering if you can suggest me books to probability and partial differential equations, regards!
You didn’t leave the pictures of the books up long enough to write them down.
Hey Bruce,
1) You can pause the video and take notes.
2) Please give a look at my comment in this section. There you find all the books you may need, enjoy ✌🏻
Would have been good if you'd shown the books on screen for more than 3 seconds.
Keeping the images for such a long time would make uncomfortable those who want to watch the video without interruptions. It's important for you to focus on the content, not the images. Below the video, you find the list of the books.
Please show cover of the books on full screen.
thank you :)
Please also add both reading age, and prior maths experience needed.
Why is no stats book included? I know it's boring and practical but it's fundamental and we need stats far more than we need differential geometry.
Spoke too soon. You do include a stats book!
I don't know why anyone - not studying for a (pure) maths degree - needs abstract algebra, topology, or differential geometry. This is all pure maths stuff.
1) I specify those are my favorite books 😊
2) The books i listed in the video are university books. You're not supposed to use them if you are 15 years old unless you're incredibly talented and you feel that, even though you're 14 years old, you can understand and study this level of math.
3) "not studying for a (pure) maths degree". That's simply wrong. At MIT they strongly recommend keeping the number of applied/pure math subjects balanced. That's what i also believe.
Number theory is very important because it teaches how to prove and think through math difficulties. On top of that, there exists a large body of challenges and exercises that make this subject extremely challenging from a problem-solving standpoint.
Topology is at the very foundation of the many branches of science and engineering. Knowing that gives a great advantage to those who need to understand how to apply math to practical issues.
Math is beautiful, irrespective of whether it is pure or applied.
4) It's not true that i didn't include a statistics book. You gotta watch the videos entirely.
Isn't this a better study order? As one wants to study the more practical maths before the purer stuff?
As I see it, these 7 subject areas are very practical, but the other 7 not so much.
1) Logic and Proofs tio
2) Set Theory
3) Calculus
12) Statistics
7) Linear Algebra
9) Ordinary Differential Equations (ODEs)
13) Optimization
6) Real Analysis
8) Complex Analysis
4) Number Theory
5) Abstract Algebra
10) Topology,
11) Differential Geometry
14) Numerical Analysis
Please correct me if I'm wrong.
What is a good book with takes lesser known maths (last 7 topics0, and shows the real-world applications? "real-world applications" = not string theory or any other branch of pseudo physics which may be real - but likely not in this universe.
What's your personal mission?
1 & 2 is the foundation of all Mathematics, in particular 5,6,7,8,10,11, the pure. That in turn explains the remaining applications - using that word loosely - 3,4,9,12,13,14. From a logical point of view, but perhaps not a practical one, it makes the most sense to study the topics more or less in this order.
204
For optimization, do you recommend "mathematical optimization and economic theory" by intriligator? (For an econ student looking for mathematical rigor)
I don't know this book 🤷🏻♂
If you want math rigor, Fletcher's book is very very good. It's my favorite, but it requires math maturity. You risk to get overwhelmed by math if you do not know linear algebra, calculus, numerical analysis.....
@@scienceskills thanks for the response!
Would be nice to provide access to a bibliography. Otherwise nice video.
Ciao David!
Do you suggest that I should provide below the video the entire bibliography I have described in it?
Yes, they are flashed on the screen rather quickly. Having a list to accompany the video affords one an ability to take notes.
@@davidallhusen I agree, it's an intelligent idea. I will try to provide the list by the end of tomorrow ✌🏻
Oh, just plow through thousands of books as recommended by folk on youtube, since there is no book lists and method that GUARANTEE at least a bachelor's level of competence.
You will find so many tech people trying to enter machine learning and data science but they don't know how to approach math. Please tell us how to learn that math without wasting time.
1) I have been preparing something for you guys for over the past three years that addresses this kind of needs.
It is almost ready, i will make the announcement next fall, hopefully, if nothing unexpected comes about.
2) In general, what determines the degree to which a data scientist should approach math relates to the activities one is expected to carry out.
Being a data scientist who is supposed to develop new algorithms and publish scientific papers involves a TOTALLY different math background and problem-solving skills than if s/he works as a "user" for a company.
I do not believe in-depth understanding of K-Nearest Neighbors to be essential for the "user".
I do not believe in-depth understanding of a function activation record in C++ to be essential for the "coder".
But if you have to develop new methods, you cannot live without in-depth understanding. Or, at least, you can, but one would be doomed to failure.
@@scienceskills That's so great. I am so excited about the content you are preparing. Thank you so much for every minute you spent with us in this channel.
@@scienceskills I have been preparing something for you guys for over the past three years that addresses this kind of needs.
Hi so what happened with this initiative? Did you give up on it?
@@encapsulatio
Hi. Not at all.
Last year, I published my online course, a top-notch approach to studying science.
However, I unpublished it recently for further update.
I would re-publish it in the future only if there's enough demand.
@@scienceskills How do you expect enough demand since you do not have any links to the course?
where is differential equation
Read my comment below. I talk about ODEs at the minute, 7:23
Are you a engineer?
Any great book for function and mapping.
You should be more precise because there exist many areas of math dealing with functions and mapping. 😊
you are using macbook - you are not supposed to know whatever, my friend
list of books please