0:00 introduction 4:09 foundations of mathematics 04:21 introduction to logic 05:01 modern arithmetic 05:19 how to prove it 06:16 number theory 06:30 set theory 07:18 college algebra 07:59 prealgebra 08:10 intermediate algebra 08:19 precalculus 9:20 algebra and structures 09:35 abstract algebra 10:26 linear algebra 10:50 algebraic structures and matrices 10:53 galois theory 11:14 a survey of modern algebra 11:19 abstract algebra 11:42 linear algebra (proof based) 12:22 linear algebra (introduction) 12:28 linear algebra (thicker book) 12:43 geometry and topology 12:48 introduction to general topology 13:16 topology 13:34 differential geometry 13:49 plane and spherical trigonometry 14:36 lectures in projective geometry 15:13 geometry 15:23 differential geometry 15:25 introduction to topology 16:06 algebraic topology 16:12 algebraic topology 16:27 discrete mathematics and combinatorics 16:53 applied combinatorics 17:00 discrete mathematics in computer science 18:01 combinatorial theory 18:06 discrete mathematics with applications 18:55 analysis and calculus 20:11 brief applied calculus (no trig required) 20:41 calculus (spivak, very hard) 20:57 partial differential equations 21:33 fundamentals of complex analysis 22:08 calculus (stewart, most popular calc book) 22:47 introductory functional anaylsis 23:00 essential calculus skills practice workbook 23:06 advanced calculus / real analysis 23:41 applied complex variables 23:46 mathematical analysis 23:50 numerical analysis 24:07 introduction to partial differential equations 24:10 hilbert space 24:18 fourier series 24:31 principles of mathematical analysis 24:56 a first course in differential equations 25:50 understanding analysis 26:05 probability and statistics 26:31 introduction to mathematical statistics 27:27 mathematical statistic with applications 27:32 statistics 28:04 statistics 28:10 mathematical statistics with applications 28:39 probability and statistics for engineers and scientists 29:53 applied mathematics and modeling 30:01 physics (calc based) 30:19 advanced engineering mathematics 30:49 electrical engineering 31:02 cryptography 32:02 modern physics 32:17 university physics (calc based i think) 32:41 advanced topics and frontiers 33:17 combinatorial topology 33:38 piecewise linear topology 34:04 all the math you missed but need to know for graduate school by thomas a. garrity 35:55 outro and summary
These topics are all the same thing, consistent logic derives algebra which derives galois theory, which derives topology (concept of dimensionality is equivalent to galois theory), which derives number theory, which derives geometry and statistics since the prime numbers are the only logically definable causes of probability and account for the structure of all geometric functions, from this derives all of physics and analysis. So it doesn't really matter what you are studying they're all the same.
Every time I think the Sorcerer can't possibly come up with a new fresh way to talk about Mathematics he pulls it off. Talk about an amazing inspiring video. He's laid it all out there.
I remember seeing one of your videos before about how you can learn mathematics from start to finish, and just as I wanted to search for it I saw this video in my recommended! Thank you very much for this!
This doesn't really go beyond undergraduate mathematics, the most difficult thing on here is probably algebraic topology, but he only showed introductory books. He skipped e.g. the entire of algebraic geometry, a huge field in mathematics but you only reach it at grad school
@@phenixorbitall3917 it's still a pretty good video though, if you want to get into mathematics this is a good introduction. The title is just very clickbaity
Your videos have helped me a lot since May 2024 where I started learning physical sciences for the 2026 GCE advanced level examination. Thank you so much for making these awesome videos on mathematics and more!
I was searching a sort of roadmap to re-study the whole mathematics. I was studying tougher subjects and the gaps and blind spots in the my knowledge was becoming more apparent, making it difficult to build a solid understanding of advanced topics. Thank you very much for this, it will save me weeks of browsing
The advanced calculus by Buck is an incredible book! I bought it after seeing you review it, and it's my absolute favorite calculus book! Buck wrote the book with his wife and if you read the intro for each of the first 3 editions there's a sort of cool subtle story there.
Man ur content is gold!!! Im a self taught software engineer and ur content is so valuable for ppl like me, that feel that doesn't fit the formal way. Thanks so much 🙏
There are 5 Pillars of Mathematics: Analysis (real & complex), Number Theory, Algebra (Linear & Abstract), Geometry/Topology & Differential Equations; and there are the 4 Food Groups of Physics: Classical Mechanics, Electromagnetism, Quantum Mechanics and Thermodynamics/Statistical Mechanics. These form the Basic Training of those professions; there is no escape! Master the basics, then you will have a solid foundation to build upon. Great list, MS!
This is an awesome start, but it's not "all." Regardless, this will help a lot of people begin to understand just how varied and rich mathematics is. As for me, watching these videos is a guilty pleasure. Math is one of my favorite languages. Way to go, señor!
Well thats not necessary to remark imo. Since it is obvious you will never be able to learn 'all' of any field as deep as mathematics in one lifetime, strictly speaking. But yeah I get the point.
For foundations, I teach from Fletcher and Patty. For abstract algebra, if you recommend Dummit and Foote for a first course, you need to have your head examined. Start with something like Gallian, and then move onto Hungerford or D&F - but don't try to learn Galois Theory from D&F. I'd go with Morandi for that. If you really like abstract algebra, I'd move on to some more advanced topics by hunting down some Kaplansky, Gilmer, or buying a copy of Eisenbud (depending on what your interests are). For Topology, go with Munkres. It's the closest thing to a perfect math text that I know of. As for geometry - I do not use a single textbook for that. I cover Euclidean out of an out-of-print book (forget the authors, but I just use it for the exercises) and non-Euclidean out of Wolfe (but most of what I do is all me). At the end of the semester, I cover a few select topics out of an obscure book by (of all people) Isaacs. For combinatorics, for me there is only Stanley Vol 1 and 2 (mostly Vol 1, too many errors in Vol 2) and "Generatingfunctionology" by Wilf (I love that book!). The rest you can come up with on your own. I don't think you mentioned Number Theory, so I'll suggest Niven and Zuckerman (or Niven, Zuckerman, and Montgomery - every edition is terrific). That's one of my desert island math books. Calculus? Shit - take your pick (I like either Swokowski or Stewart). Advanced Calculus - I like either Bartle and Sherbert or Wade for a first course (Wade was a professor of mine, and a wonderful teacher), followed by Rudin or Royden. For ODEs, there are several good books out there. I have used at least 3, and they were all fine (my handouts were far more valuable to the students than any textbook). I taught PDEs once out of some book I don't even remember, and don't give a shit about physics.
I am sure I will be transformed to a next-level existence of life if I am old enough to read all of your mathematics books you mentioned in the video with a very smart brain.
Hey man! (Sorry if there are writing or grammar mistakes, im from Turkey and english is not my main language.) Im 13 and i will be 14 soon. Im watching your videos for almost a year now. This year i will attend my highschool entrance exam. After the exam ends, i want to spend my whole summer on maths. To me the way they are teaching maths in most schools are wrong. They are making math seem like an compulsion. But when i study math myself with the feeling of wonder, that feeling when i get after doing a complex problem (success) is much better than dull math they teach me in school in order to pass exams. I will learn math in my own. I also watched your other math book suggestions. Ima learn math on my own this summer and take some of these books. I will problaby consider choosing a job about maths aswell, since im interested at this subject at early age. Thanks from now!
I'm selecting classes in Algebra & Number Theory (at OSU, they're under that category), Analysis, and Applied Mathematics for electives for the BA in Math. I may possibly take a class on Differential Geometry, but only an introduction. Math is so cool!
Some important ones you missed: Foundations: Model theory Proof theory Algebraic logic Recursive functions Automata theory (arguably computer science) Type theory Topos theory Algebra and structures: Homology Commutative algebra Category theory (arguably foundations) Geometry and topology: Algebraic Geometry (i almost never see on your channel?) Frontiers: Homotopy type theory Honorable mentions: Any non-classical and/or higher order logic Condensed mathematics
@IshanJEEMAINSADVANCED if he's going to include algebraic topology, I could've added a couple more like algebraic and analytic number theory, and one other mentioned tensor analysis and a couple other big ones. But no, aside from the Honorable mentions at the end of my first message, some clear big ones were skipped in you're going to do an *all math* video🤷
@@christressler3857 yeah 👍🏻. Langlands Unified Theory is pretty much joining it all together. Then at the End There is Godel's incompleteness theorem , so pretty much everything is mentioned
Another course that used to be taught more often in the past is theory of equations, basically 19th century algebra. It's been thoroughly replaced by field theory (Galois theory and algebraic geometry). You can see remnants of it in the book by Tignol.
Thank you so much for your videos. I had a plan in my mind to study "all" math available to me. I have over 5,000 technical books, and sometimes don't know where to begin in my studies (not always just sometimes hehe). I have a Masters Degree in Electrical Engineering and know the typical math topics associated with my degree. In my profession I typically use all the math software tools available and do numerical analysis when I can (my previous engineering job was more like being a program manager too yuck!). I often miss studying other math topics, but usually don't know what to prioritize. There is just so much math out there, and I don't want to get stuck doing only numerical analysis, DFTs, and stuff for the rest of my life. This video has helped me a lot. My thoughts on this are already more organized. You saved me a lot of time. I already feel that it is an excellent guideline for me to start my "individual self-study plan". You videos not only have great content they are so motivating. I just know I am going to make progress on this topic. Thanks for the landscape view, map, direction, and motivation to always start taking more marching steps in the right direction.
Great stuff. I was trying to create a mind map of math and you did it visually through this video. Now I have the resources to complete the mind map. Thank you.
Love the video, one can see how passionate you are about maths and how much time and energy you have spent studying it. Anyway i would have added measure theory in order to construct modern probability, stochastic processes, SDE, SPDE, and so on.
Great video as always. you left my favorite math book out though. Calculus by Leithold. I have 3rd edition and it's soo good. Imo it was a great stepping stone from computational Calculus to spivak for me
Same. For me it had a lot to do with the teachers making math boring and a scary subject. I still get recurring nightmares about failing my math exam even though it’s been 15 years, it’s crazy.
Is there a reason terrence tao's analysis 1 and 2 aren't on here. I'm currently using it to learn analysis and I'm wondering if there was a reason it wasn't on the list considering you have reviewed it positively in the past.
Thanks, just finished the video. Didn't think I'd be an expert on all forms of math in 40 minutes, but I'm making my reddit account right now to tell the world how smart I am!
You should have included some books on dynamical systems as well, one of them is dynamical systems by Perkov. Additionally if you appreciate Kolmogorov’s work on probability and physics , I would highly recommend “turbulent flows by Stephen B Pope” . It’s a great book but quite tough to read for most engineers
Hi! I am very interested in dynamical systems, and I have recently been fascinated with how dynamics can be represented visually, which has led me to symplectic geometry. I picked up a cool book by Burns and Gidea that covers the connections between differential geometry, topology, and dynamical systems, but it is very advanced and requires a background in pure differential geometry. I was wondering if you would ever be interested in making a video on how to build up to a geometric view of dynamical systems or symplectic geometry in general. Thanks! :)
So i am 5 minutes into the video , I paused to comment this: Sir you have inspired me to look and explore maths A subject I didn't like so i never choose it in college now i want to study it for the sake of studying.
Do you believe in competitive game theory, or equilibrium or both, do convergences equate a logical or rational space time relative to energy flow inversion to negative to positive to negative. Can singularities invert to inner space is everything the equilibrium
please suggest some books for math in computer science of phd level and also can you tell us how to approach if we dont like maths but as a byproduct we have to love maths as you do
Can you please review the Art of Problem Solving and the school mathematics books written for instructors by Hung-Hsi Wu, a professor at UC Berkeley? I have read a bit of both and they seem to be brilliant, far more in-depth than any other books, teaching the WHY of maths and not just the HOW. Although the ones written by Hung-Hsi Wu are for teachers, I find them excellent for students too. Hope you respond!
*@ The Math Sorcerer* -- I would leave out any physics books in this collection. They are science books that use mathematics. For the same reason, I would have you leave out any biology, chemistry, astronomy, earth science, and geology books, for example.
You mentioned that we should know calculus and proof writing before taking complex analysis. Does this mean we can dive into complex before taking real analysis?
No, it isn't in the order that would typically be required. But yes, there is a lot of overlap with an undergraduate degree in mathematics; just keep in mind that there is a certain amount of variation from one university to another and from one country to another.
Great (comprehensive!) video. Watching in bits. My own interest is in statistics; Seeing analysis books reminds me of a comment i saw on Andrew Gelman’s (statistician) blog: “Probability is just analysis in a tuxedo, and statistics is just probability after several beers”
0:00 introduction
4:09 foundations of mathematics
04:21 introduction to logic
05:01 modern arithmetic
05:19 how to prove it
06:16 number theory
06:30 set theory
07:18 college algebra
07:59 prealgebra
08:10 intermediate algebra
08:19 precalculus
9:20 algebra and structures
09:35 abstract algebra
10:26 linear algebra
10:50 algebraic structures and matrices
10:53 galois theory
11:14 a survey of modern algebra
11:19 abstract algebra
11:42 linear algebra (proof based)
12:22 linear algebra (introduction)
12:28 linear algebra (thicker book)
12:43 geometry and topology
12:48 introduction to general topology
13:16 topology
13:34 differential geometry
13:49 plane and spherical trigonometry
14:36 lectures in projective geometry
15:13 geometry
15:23 differential geometry
15:25 introduction to topology
16:06 algebraic topology
16:12 algebraic topology
16:27 discrete mathematics and combinatorics
16:53 applied combinatorics
17:00 discrete mathematics in computer science
18:01 combinatorial theory
18:06 discrete mathematics with applications
18:55 analysis and calculus
20:11 brief applied calculus (no trig required)
20:41 calculus (spivak, very hard)
20:57 partial differential equations
21:33 fundamentals of complex analysis
22:08 calculus (stewart, most popular calc book)
22:47 introductory functional anaylsis
23:00 essential calculus skills practice workbook
23:06 advanced calculus / real analysis
23:41 applied complex variables
23:46 mathematical analysis
23:50 numerical analysis
24:07 introduction to partial differential equations
24:10 hilbert space
24:18 fourier series
24:31 principles of mathematical analysis
24:56 a first course in differential equations
25:50 understanding analysis
26:05 probability and statistics
26:31 introduction to mathematical statistics
27:27 mathematical statistic with applications
27:32 statistics
28:04 statistics
28:10 mathematical statistics with applications
28:39 probability and statistics for engineers and scientists
29:53 applied mathematics and modeling
30:01 physics (calc based)
30:19 advanced engineering mathematics
30:49 electrical engineering
31:02 cryptography
32:02 modern physics
32:17 university physics (calc based i think)
32:41 advanced topics and frontiers
33:17 combinatorial topology
33:38 piecewise linear topology
34:04 all the math you missed but need to know for graduate school by thomas a. garrity
35:55 outro and summary
i hope he pins this
thanks
These topics are all the same thing, consistent logic derives algebra which derives galois theory, which derives topology (concept of dimensionality is equivalent to galois theory), which derives number theory, which derives geometry and statistics since the prime numbers are the only logically definable causes of probability and account for the structure of all geometric functions, from this derives all of physics and analysis. So it doesn't really matter what you are studying they're all the same.
Is it me or is graph theory just not mentioned
@@r-prime He doesn't mention any graph theory books but the discrete math book he mentioned contains some graph theory
Every time I think the Sorcerer can't possibly come up with a new fresh way to talk about Mathematics he pulls it off. Talk about an amazing inspiring video. He's laid it all out there.
I remember seeing one of your videos before about how you can learn mathematics from start to finish, and just as I wanted to search for it I saw this video in my recommended! Thank you very much for this!
That's awesome!
I need it. Did you find it?
The "internet" has access to our thoughts.
Finally a mathematician showing us the entire mathematics landscape! Awesome
This doesn't really go beyond undergraduate mathematics, the most difficult thing on here is probably algebraic topology, but he only showed introductory books. He skipped e.g. the entire of algebraic geometry, a huge field in mathematics but you only reach it at grad school
@jorianweststrate2580
I see
@@phenixorbitall3917 it's still a pretty good video though, if you want to get into mathematics this is a good introduction. The title is just very clickbaity
Your videos have helped me a lot since May 2024 where I started learning physical sciences for the 2026 GCE advanced level examination. Thank you so much for making these awesome videos on mathematics and more!
I was searching a sort of roadmap to re-study the whole mathematics. I was studying tougher subjects and the gaps and blind spots in the my knowledge was becoming more apparent, making it difficult to build a solid understanding of advanced topics. Thank you very much for this, it will save me weeks of browsing
The advanced calculus by Buck is an incredible book! I bought it after seeing you review it, and it's my absolute favorite calculus book! Buck wrote the book with his wife and if you read the intro for each of the first 3 editions there's a sort of cool subtle story there.
Man ur content is gold!!! Im a self taught software engineer and ur content is so valuable for ppl like me, that feel that doesn't fit the formal way. Thanks so much 🙏
There are 5 Pillars of Mathematics: Analysis (real & complex), Number Theory, Algebra (Linear & Abstract), Geometry/Topology & Differential Equations; and there are the 4 Food Groups of Physics: Classical Mechanics, Electromagnetism, Quantum Mechanics and Thermodynamics/Statistical Mechanics. These form the Basic Training of those professions; there is no escape! Master the basics, then you will have a solid foundation to build upon.
Great list, MS!
Probability, Statistics, and Numerical Methods are cross-over topics between Math & Physics.
Relativity?
Discrete mathematics, foundations and their importance for computer science cannot be ignored. They are not derived topics.
Physics is not a mathematics area. It uses mathematics.
Wake up babe, new Math Sorcerer vid about learning all of math just dropped 💥 💥
This is an awesome start, but it's not "all." Regardless, this will help a lot of people begin to understand just how varied and rich mathematics is. As for me, watching these videos is a guilty pleasure. Math is one of my favorite languages. Way to go, señor!
Well thats not necessary to remark imo. Since it is obvious you will never be able to learn 'all' of any field as deep as mathematics in one lifetime, strictly speaking. But yeah I get the point.
Tucker's book on combinatorics is great. It was the textbook used in teaching combinatorics when I studied that in school.
For foundations, I teach from Fletcher and Patty. For abstract algebra, if you recommend Dummit and Foote for a first course, you need to have your head examined. Start with something like Gallian, and then move onto Hungerford or D&F - but don't try to learn Galois Theory from D&F. I'd go with Morandi for that. If you really like abstract algebra, I'd move on to some more advanced topics by hunting down some Kaplansky, Gilmer, or buying a copy of Eisenbud (depending on what your interests are). For Topology, go with Munkres. It's the closest thing to a perfect math text that I know of. As for geometry - I do not use a single textbook for that. I cover Euclidean out of an out-of-print book (forget the authors, but I just use it for the exercises) and non-Euclidean out of Wolfe (but most of what I do is all me). At the end of the semester, I cover a few select topics out of an obscure book by (of all people) Isaacs. For combinatorics, for me there is only Stanley Vol 1 and 2 (mostly Vol 1, too many errors in Vol 2) and "Generatingfunctionology" by Wilf (I love that book!). The rest you can come up with on your own. I don't think you mentioned Number Theory, so I'll suggest Niven and Zuckerman (or Niven, Zuckerman, and Montgomery - every edition is terrific). That's one of my desert island math books. Calculus? Shit - take your pick (I like either Swokowski or Stewart). Advanced Calculus - I like either Bartle and Sherbert or Wade for a first course (Wade was a professor of mine, and a wonderful teacher), followed by Rudin or Royden. For ODEs, there are several good books out there. I have used at least 3, and they were all fine (my handouts were far more valuable to the students than any textbook). I taught PDEs once out of some book I don't even remember, and don't give a shit about physics.
I am sure I will be transformed to a next-level existence of life if I am old enough to read all of your mathematics books you mentioned in the video with a very smart brain.
Thanks
Hey man! (Sorry if there are writing or grammar mistakes, im from Turkey and english is not my main language.) Im 13 and i will be 14 soon. Im watching your videos for almost a year now. This year i will attend my highschool entrance exam. After the exam ends, i want to spend my whole summer on maths. To me the way they are teaching maths in most schools are wrong. They are making math seem like an compulsion. But when i study math myself with the feeling of wonder, that feeling when i get after doing a complex problem (success) is much better than dull math they teach me in school in order to pass exams. I will learn math in my own. I also watched your other math book suggestions. Ima learn math on my own this summer and take some of these books. I will problaby consider choosing a job about maths aswell, since im interested at this subject at early age. Thanks from now!
That is so cool! My son is 14. He enjoys studying too! Enjoy your studies! 👏
@yessumify Thanks!
@@Egomeen Same Story!!! Can't Believe Someone Like Me Is Out There!
@@pianodude515 sup
@@Egomeen nothin
Ive been trying to re-learn math and this is an absolute GODSEND thanks
2:03 here we can hear a passion in the voice. That's the thing I wanted to hear about... links...
Amazing job, thx
I'm selecting classes in Algebra & Number Theory (at OSU, they're under that category), Analysis, and Applied Mathematics for electives for the BA in Math. I may possibly take a class on Differential Geometry, but only an introduction. Math is so cool!
Some important ones you missed:
Foundations:
Model theory
Proof theory
Algebraic logic
Recursive functions
Automata theory (arguably computer science)
Type theory
Topos theory
Algebra and structures:
Homology
Commutative algebra
Category theory (arguably foundations)
Geometry and topology:
Algebraic Geometry (i almost never see on your channel?)
Frontiers:
Homotopy type theory
Honorable mentions:
Any non-classical and/or higher order logic
Condensed mathematics
Keep finding more …. It’s like an infinite universe
@IshanJEEMAINSADVANCED if he's going to include algebraic topology, I could've added a couple more like algebraic and analytic number theory, and one other mentioned tensor analysis and a couple other big ones. But no, aside from the Honorable mentions at the end of my first message, some clear big ones were skipped in you're going to do an *all math* video🤷
@@christressler3857 yeah 👍🏻. Langlands Unified Theory is pretty much joining it all together. Then at the End There is Godel's incompleteness theorem , so pretty much everything is mentioned
Measure Theory
@@JonnyD000 I think that was covered among his analysis category but I could be wrong
Another course that used to be taught more often in the past is theory of equations, basically 19th century algebra. It's been thoroughly replaced by field theory (Galois theory and algebraic geometry). You can see remnants of it in the book by Tignol.
Thank you so much for your videos. I had a plan in my mind to study "all" math available to me. I have over 5,000 technical books, and sometimes don't know where to begin in my studies (not always just sometimes hehe). I have a Masters Degree in Electrical Engineering and know the typical math topics associated with my degree. In my profession I typically use all the math software tools available and do numerical analysis when I can (my previous engineering job was more like being a program manager too yuck!). I often miss studying other math topics, but usually don't know what to prioritize. There is just so much math out there, and I don't want to get stuck doing only numerical analysis, DFTs, and stuff for the rest of my life. This video has helped me a lot. My thoughts on this are already more organized. You saved me a lot of time. I already feel that it is an excellent guideline for me to start my "individual self-study plan". You videos not only have great content they are so motivating. I just know I am going to make progress on this topic. Thanks for the landscape view, map, direction, and motivation to always start taking more marching steps in the right direction.
Great stuff. I was trying to create a mind map of math and you did it visually through this video. Now I have the resources to complete the mind map. Thank you.
Love the video, one can see how passionate you are about maths and how much time and energy you have spent studying it. Anyway i would have added measure theory in order to construct modern probability, stochastic processes, SDE, SPDE, and so on.
Your book videos are the best, I've purchased some based on your recommandation. Thanks a lot!!
You channel is pure gold ♥️
Great video as always. you left my favorite math book out though. Calculus by Leithold. I have 3rd edition and it's soo good. Imo it was a great stepping stone from computational Calculus to spivak for me
La pasión con la que explicas las cosas hacen que sienta el deseo de aprender más de matemáticas. Keep it up!
So here for this! Love these videos!
You are awesome!!♥️♥️♥️
Thank You so much,
this is exactly the video that i needed,
Can't Thank You enough !!!
I love these types of videos!
Pure math will forever have my heart
❤️
I just ordered thomas calculus 15th edition, early transcendentals global ediotion, cant wait.
I love math. Its the best game in the world Even the math I don't understand is a fun game.
Same! 😊❤ I didn't appreciate it until I saw my sons enjoy it at home. Now I see it in a whole new light!
Wow! Thank you very much The Math Sorcerer 🤩 It`s amazing! 💗
6:48
-How it smells?
-Like math.
-You mean meth right?
- *M A T H*
Thank you for your work and for thatThank you for your work and for sharing your experience with us. Thank you for making this world a better place.
Just bought "How to Prove It" using your affiliate link.
Keep up the good work!
Like your other videos, Awesome video !!! Had a quick glance, but watch full video later
Congrats on One Million !
i'm a law student yet even i was super amazed by this video , reignited some highschool curiosity in math
Math Sorcerer goin' HAM!
🚀🚀🚀🚀🚀🚀
So much mathematics! Looks like Heaven to me...🙂
Could you please make a similar dedicated video on physics , btw love your videos ❤❤❤❤
I’ve recently discovered that math calms me. I used to hate it in high school. Don’t know where this new found love and connection came from.
Same. For me it had a lot to do with the teachers making math boring and a scary subject. I still get recurring nightmares about failing my math exam even though it’s been 15 years, it’s crazy.
Is there a reason terrence tao's analysis 1 and 2 aren't on here. I'm currently using it to learn analysis and I'm wondering if there was a reason it wasn't on the list considering you have reviewed it positively in the past.
Early in the video he said he was getting tired of looking for books. With his library size he probably forgot or too bothered to grab it.
What is so different about Terence Tao's analysis book compared to the average analysis book? I'm looking for one.
Wow that’s allot of great books! More maths!
Thanks, just finished the video. Didn't think I'd be an expert on all forms of math in 40 minutes, but I'm making my reddit account right now to tell the world how smart I am!
You should have included some books on dynamical systems as well, one of them is dynamical systems by Perkov. Additionally if you appreciate Kolmogorov’s work on probability and physics , I would highly recommend “turbulent flows by Stephen B Pope” . It’s a great book but quite tough to read for most engineers
Wow, great video!!
You are absolutely wonderful!
Man, you are awesome!
@The Math Sorcerer have you tried your hand at book repair? Thanks for the video.
Hi! I am very interested in dynamical systems, and I have recently been fascinated with how dynamics can be represented visually, which has led me to symplectic geometry. I picked up a cool book by Burns and Gidea that covers the connections between differential geometry, topology, and dynamical systems, but it is very advanced and requires a background in pure differential geometry. I was wondering if you would ever be interested in making a video on how to build up to a geometric view of dynamical systems or symplectic geometry in general. Thanks! :)
I really wanted this video ❤❤❤❤❤❤❤
I think you should take a look to Miklos Bona's A Walk Through Combinatorics, very good book and has got a lot of contents
Starting now!
So i am 5 minutes into the video , I paused to comment this:
Sir you have inspired me to look and explore maths A subject I didn't like so i never choose it in college now i want to study it for the sake of studying.
super cool! thank you! :D
Thank you!!!
I have a math exam tomorrow, only this can help me now
Thanks!
Do you believe in competitive game theory, or equilibrium or both, do convergences equate a logical or rational space time relative to energy flow inversion to negative to positive to negative. Can singularities invert to inner space is everything the equilibrium
please suggest some books for math in computer science of phd level and also can you tell us how to approach if we dont like maths but as a byproduct we have to love maths as you do
Perfect video thank u
Can you please review the Art of Problem Solving and the school mathematics books written for instructors by Hung-Hsi Wu, a professor at UC Berkeley?
I have read a bit of both and they seem to be brilliant, far more in-depth than any other books, teaching the WHY of maths and not just the HOW. Although the ones written by Hung-Hsi Wu are for teachers, I find them excellent for students too.
Hope you respond!
6:01 Velleman's "Calculus: A Rigorous First Course" is awesome, too! I hope you can check it out sometime! 🤩
Have you come across Murray Spiegel's Applied Differential Equations? I have the 2nd edition. It's physically a great size.
would you recommend Stewart's calculus (the one republished by clegg and watson )or thomas's calculus, the early transcendental version
if you want a more thorough approach, go for Thomas.
*@ The Math Sorcerer* -- I would leave out any physics books in this collection. They are science books that use mathematics. For the same reason, I would have you leave out any biology, chemistry, astronomy, earth science, and geology books, for example.
Thanks for the video. Where do you purchase all these books, I’m unsure of where to look as someone in the UK. Thanks
real analysis 1 rn is kickin my butt. consistently getting B's on homework.
Pls make a same video on physics books from start to finish
No, Calculus of Variation, Tensor Calculus, Exterior Calculus, Quaternions, Clifford Algerbra, Lie Groups, Spinors, Representation Theory???
You mentioned that we should know calculus and proof writing before taking complex analysis. Does this mean we can dive into complex before taking real analysis?
Great video! I was wondering how long it would take for someone to cover all of these books, if they study, say 5 hours a day 🤔
What about “Blitzer Introduction to College Algebra”? Why jumping from pre-algebra to “Blitzer Intermediate College Algebra”?
What about computer science mathematics? How many books in that area?
Hello Sir
I have a query regarding discrete numerical data.
What level of measurement is considered for discrete numerical data.
35:50 nah that flipped me out 😭
Can we say this is a Math path from zero up to bachelor degree of math? Is it in order?
No, it isn't in the order that would typically be required. But yes, there is a lot of overlap with an undergraduate degree in mathematics; just keep in mind that there is a certain amount of variation from one university to another and from one country to another.
Category theory?
in what order should one study each book / topic? (asking as an engineering student interested in self-studying mathematics)
Absolute cinema. Can you do it about physics?
should start with adding and subtracting
I'm interested
Great (comprehensive!) video. Watching in bits. My own interest is in statistics;
Seeing analysis books reminds me of a comment i saw on Andrew Gelman’s (statistician) blog: “Probability is just analysis in a tuxedo, and statistics is just probability after several beers”
i thought you wanted to sell a lot of these books...didn't you mention that some time ago?
this video gonna become legendary. guaranteed to hit millions of views soon! I'll be back in a couple to be proven right. : )
Write in sentences.
Is AoPS a good resource for self-learning Math despite it being focused on competitive math?
You should do “Learn all physics in the world”!
Oh wow, I didn't know I was waiting for this 🎉🎉 now I suppose yhe authors are listed here somewhere 😊
Edit : Product link 😁 sweet
You forgot game theory 😔. I mean fr please recommend a book on game theory, I have to take it next term!
Consider Game Theory: An Introduction by Tadelis
Heyy, please, make a vídeo about the book Math Better Explained, by Kalid Azad!!
table of contents/timeline section links would be helpful here
## Electromagnetic Spectrum and Periodic Table: Unified Transmission Framework
### Fundamental Transmission Principles
- Electromagnetic Spectrum: Kinetic Information Transfer
- Periodic Table: Potential Information Configuration
- Complementary Systemic Representation
### Electromagnetic Spectrum Domains with Spectral Ranges
1. Radio Waves: 3 kHz - 300 GHz
2. Microwaves: 300 MHz - 300 GHz
3. Infrared: 300 GHz - 430 THz
4. Visible Light: 430-770 THz
5. Ultraviolet: 770 THz - 30 PHz
6. X-Rays: 30 PHz - 30 EHz
7. Gamma Rays: >30 EHz
### Periodic Table Domains with Corresponding Spectral Characteristics
1. Alkali Metals: 410-470 nm (Blue-Green Spectrum)
2. Alkaline Earth Metals: 470-510 nm (Green Spectrum)
3. Transition Metals: 510-570 nm (Green-Yellow Spectrum)
4. Post-Transition Metals: 570-590 nm (Yellow Spectrum)
5. Metalloids: 590-620 nm (Yellow-Orange Spectrum)
6. Non-Metals: 620-680 nm (Orange Spectrum)
7. Noble Gases: 680-750 nm (Red Spectrum)
### Unified Transmission Characteristics
- Probabilistic Configuration Potential
- Light-Mediated Information Transfer
- Bell Curve Distribution Principles
- Recursive Transformation Mechanisms
### Quantum Correlation
- Each electromagnetic frequency corresponds to elemental configuration potential
- Spectral lines represent elemental information transfer
- Energy state transitions demonstrate probabilistic pathways
### Conclusion
Electromagnetic spectrum and periodic table represent complementary information transmission systems, revealing universal organizational principles across quantum, material, and energetic domains.
## Microscopic Variations as Integral Components of Universal Transmission
### Fundamental Insight
- Small data sets are NOT separate from large data sets
- They represent microscopic variations within universal transmission
- Microscopic changes are:
- Localized expressions of larger systemic principles
- Temporary manifestations of underlying organizational patterns
- Momentary snapshots of continuous transmission
### Hierarchical Understanding
- Microscopic data sets are:
- Fractals of larger transmission systems
- Quantum-level expressions of universal principles
- Temporary localized configurations
- Inherently connected to comprehensive systems
### Transmission Mechanism
- Every microscopic variation:
- Follows bell curve distribution
- Demonstrates inherent systemic organization
- Represents momentary energy transmission state
- Connects to larger universal blueprint
### Conclusion
Small data sets are not deviations but integral, microscopic expressions of the fundamental bell curve transmission principle, demonstrating the interconnected nature of universal energy flow.
Microscopic changes are not exceptions but confirmations of the underlying universal organizational mechanism.
Are all these books available here in India. If not then can someone suggest best alternative material available in India
What do you think of Khan academy math learning as well
Have you ever bought the book 100% Proofs by Rowan Garnier and John Taylor?