Learn ALL THE MATH IN THE WORLD from START to FINISH

[@sophieeee_____a]

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

[@Limeglow.]

i hope he pins this

[@blackpawa]

thanks

[@jamesedward9306]

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.

[@UrosFred]

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!

[@TheMathSorcerer]

That's awesome!

[@i_youtube_]

I need it. Did you find it?

[@Egomeen]

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!

[@yessumify]

That is so cool! My son is 14. He enjoys studying too! Enjoy your studies! 👏

[@Egomeen]

@yessumify Thanks!

[@douglasstrother6584]

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!

[@douglasstrother6584]

Probability, Statistics, and Numerical Methods are cross-over topics between Math & Physics.

[@FR4NKTUB3]

Relativity?

[@Snap_Crackle_Pop_Grock]

Wake up babe, new Math Sorcerer vid about learning all of math just dropped 💥 💥

[@ReadrOFilz]

Tucker's book on combinatorics is great. It was the textbook used in teaching combinatorics when I studied that in school.

[@eccentricorgan]

Math Sorcerer goin' HAM!

[@TheMathSorcerer]

🚀🚀🚀🚀🚀🚀

[@jayy_04411]

Pure math will forever have my heart

[@TheMathSorcerer]

❤️

[@soyoltoi]

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.

[@FR4NKTUB3]

You channel is pure gold ♥️

[@shivanijugran485]

You are awesome!!♥️♥️♥️

[@aleterra]

I just ordered thomas calculus 15th edition, early transcendentals global ediotion, cant wait.

[@jonathannoeverdin-gonzalez5364]

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!

[@314calls]

I love these types of videos!

[@christressler3857]

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]

Keep finding more …. It’s like an infinite universe

[@SamSepiol-n6y]

Your book videos are the best, I've purchased some based on your recommandation. Thanks a lot!!

[@mutabazimichaeljean]

i'm a law student yet even i was super amazed by this video , reignited some highschool curiosity in math

[@lamewatcher1]

this video gonna become legendary. guaranteed to hit millions of views soon! I'll be back in a couple to be proven right. : )

[@barrilha]

So here for this! Love these videos!

[@argonwheatbelly637]

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!

[@anniesizemore3344]

I love math. Its the best game in the world Even the math I don't understand is a fun game.

[@yessumify]

Same! 😊❤ I didn't appreciate it until I saw my sons enjoy it at home. Now I see it in a whole new light!

[@Ammaaad-k7x]

Thank You so much, this is exactly the video that i needed, Can't Thank You enough !!!

[@David-pq6wt]

Great video 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

[@sirtytade7613]

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.

[@chickenstrangler3826]

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.

[@Geoffsmeg]

Wow that’s allot of great books! More maths!

[@swenic]

Congrats on One Million !

[@godkeshavyt7229]

I really wanted this video ❤❤❤❤❤❤❤

[@JLKeener77]

So much mathematics! Looks like Heaven to me...🙂

[@anshshinde5623]

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

[@simongail8428]

Starting now!

[@JutBolo]

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.

[@brownjenkin8422]

"Augustus Prince" is a fantastic name.

[@moularaoul643]

Thanks!

[@dimitrijestankovic6199]

As an mechanical engineer numerical analysis is my number one.

[@Zantorc]

Category theory?

[@PabloGarcia-hv8gp]

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

[@kevinsellers7566]

No, Calculus of Variation, Tensor Calculus, Exterior Calculus, Quaternions, Clifford Algerbra, Lie Groups, Spinors, Representation Theory???

[@renniczc]

Perfect video thank u

[@surrealistidealist]

6:01 Velleman's "Calculus: A Rigorous First Course" is awesome, too! I hope you can check it out sometime! 🤩

[@devondevon4366]

One will never 'learn all the math the world '

[@TheMathSorcerer]

❤️

[@allthesepollitos8891]

Then don’t do it negative Nancy

[@razuahmed1977]

I am working on a project. which may cover all math of the world.

[@Katie-k4m]

Definitely not with dyscalculia

[@Zephyrr25]

Not with that attitude

[@jaopao73]

Absolute cinema. Can you do it about physics?

[@ishanpurkait9124]

would you recommend Stewart's calculus (the one republished by clegg and watson )or thomas's calculus, the early transcendental version

[@chancebowman9464]

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! :)

[@secret4ever2]

Dear Sorcerer do you think 1 month is enough to cover algebra 1 and 2?

[@TheMathSorcerer]

Anything is possible! It depends how much the person studying knows 😃

[@douglasstrother6584]

24*30 =720 hours. It all depends on how much sleep you need!

[@farhanniazi94]

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”

[@user-fy9lv9qs7v]

should start with adding and subtracting

[@edal7066]

i thought you wanted to sell a lot of these books...didn't you mention that some time ago?

[@nasrullahturke4480]

Hello Sir I have a query regarding discrete numerical data. What level of measurement is considered for discrete numerical data.

[@AnonymousBosch3158]

This is our late christmas present!

[@hannibalfreeman5713]

Math Sorcerer got that work to feed the math streets lol…💯💯💯

[@nejckarehafner5490]

Heyy, please, make a vídeo about the book Math Better Explained, by Kalid Azad!!

[@pyotryigitaydogan4846]

my heart skipped a beat at the end when he smell that book and it sounded like a paper tearing

[@jhg12989]

table of contents/timeline section links would be helpful here

[@AmmarAbbas-o9s]

Are all these books available here in India. If not then can someone suggest best alternative material available in India

[@i_youtube_]

Can we say this is a Math path from zero up to bachelor degree of math? Is it in order?

[@mishapurser4439]

It does bother me that statistics is so unpopular when it's so useful. I think everyone should at least try to learn some statistics as it (along with other topics) will help you to be more able to navigate other subjects, including politics and economics, much better.

[@TracyR4]

Have you ever bought the book 100% Proofs by Rowan Garnier and John Taylor?

[@WitchLuw]

What do you think of Khan academy math learning as well

[@qazizayad]

You forgot game theory 😔. I mean fr please recommend a book on game theory, I have to take it next term!

[@julianwilson9919]

Consider Game Theory: An Introduction by Tadelis

[@anik3t]

dangerous video for those who never learned mathematics (not schooling part) and watching first time a math video on youtube

[@Helmutandmoshe]

Not all the math in the world. No person has that capacity, not even the great mathematicians.

[@kirbyurner]

Then there’s math-lit like Flatland, Gödel Escher Bach, and philo-math like Synergetics (Fuller’s, mostly prose and pictures, not Haken’s which is more conventional Springer-Verlag). It’s a matter of partially overlapping vocabs aka namespaces.

[@shivanijugran485]

❤❤❤❤

[@phosphor3617]

cool

[@chrisgrad9004]

Dear Sorcerer do you think I can become decently good at math even though I can’t go back to college ? I kinda of regret my previous degree.

[@TheMathSorcerer]

Absolutely !!

[@naveenr5946]

Me too I'm the same as you

[@myrtlealley]

Future tiger mom here *adds to playlist*

[@ethangleason1760]

do you think someone could teach themselves purely from books and strong curiosity?

[@sophieeee_____a]

I taught myself arithmetic, algebra 1 and 2, trigonometry, calculus 1, and a good chunk of calculus 2. it can be really hard sometimes but with modern recourses you could learn literally anything you want with enough patience and will power. theres ways to get free books online or you can find them for dirt cheap at used book stores / online stores

[@Ash__7]

based book sniffer

[@WeirdPixel]

Are these books suitable for people who have autism or adhd? Cause we’re slowww

[@lamewatcher1]

I only watch videos but dont learn any math.

[@pauldavies7746]

Make a New Year resolution to learn maths.

[@Egomeen]

@@lamewatcher1 Watching videos are not enough if you want to truly learn math. You gotta take action yourself.

[@MrMegatherium]

My problem is I tend to like what I'm bad at, and waste my time.

[@aleterra]

I don't believe that, with the right approach and support everyone can learn math. Hard work and dedication can trump talent.

[@MrMegatherium]

@@aleterra Have you even been to University? You don't seem to know how it works.

[@aleterra]

@@MrMegatherium I have 2 master degrees in engineering in two different countries.

[@MrMegatherium]

@@aleterra Ok Man, I am just saying Mathematics is a talent-based subject. Don't agree? No problem.

[@AliResool-k8z]

Where is game theory?

[@TheIllerX]

Good luck learning all known math if you got a couple of millenia to spare.

[@benzemamumba]

Engineers are not considered math people! 😭

[@EIswazi]

This is an exceedingly far reaching claim for a title of a video that doesn’t really show any math concepts even past undergraduate. Even concepts that are elementary in graduate mathematics aren’t shown, like representation theory, category theory, and (most egregiously in my opinion) measure theory. Not to even mention topics like k-theory or universal algebra that fall unbelievably far outside of the scope of these books. Also at the end, combinatorial topology is just an antiquated name for what we now call algebraic topology.

[@odopaisen2998]

Hi Sorcerer: Math is a despriptive language -- pls thry to adress why to speak any of the sections you created