Learn Mathematics from START to FINISH (2nd Edition)

In this video I will show you how to learn mathematics from start to finish. I will give you three different ways to get started with mathematics. I hope this video helps someone.
Here are the books
Elementary Algebra amzn.to/3S7yG0Y
Pre-Algebra amzn.to/3TpW8HK
Discrete Mathematical Structures amzn.to/3eBYogb
Discrete Mathematics and its Applications amzn.to/3TvfThe
Discrete and Combinatorial Mathematics amzn.to/3CELUfO
How To Prove It amzn.to/3gcO4M8
Foundations of Higher Mathematics amzn.to/3CCQcV7
An Introduction To Abstract Mathematics amzn.to/3D4IzIg
How to Read and Do Proofs amzn.to/3VBWA7y
Plane Trigonometry amzn.to/3T9v9k5
Trigonometry(McMullen) amzn.to/3s85dZW
Pre-Calculus Mathematics(Shanks) amzn.to/3yNxWad
Precalculus (Stewart) amzn.to/3VBWLQg
Algebra and Trigonometry(Sullivan) amzn.to/3EN1Oay
Schaum's Trigonometry amzn.to/3TqjYTG
Algebra and Trigonometry(Cameron) amzn.to/3giyVZX
Algebra and Trigonometry(Stewart) amzn.to/3yMWzE7
A Graphical Approach To Algebra and Trigonometry amzn.to/3S7jalt
College Algebra amzn.to/3MGhBd6
Geometry amzn.to/3D4Jjgw
Thomas' Calculus amzn.to/3ML5HyY
Calculus(Larson) amzn.to/3CCQZW5
Calculus(Swokowski) amzn.to/3s55Kw2
Calculus(Stewart) amzn.to/3yNiIC8
Calculus(McMullen) amzn.to/3D7iDvW
Calculus with Multiple Variables(McMullen) amzn.to/3eBfRpg
Schaum's Probability and Statistics amzn.to/3eBfRpg
Elementary Statistics amzn.to/3rZFFym
Mathematical Statistics and Data Analysis amzn.to/3yLZWek
A First Course in Probability amzn.to/3CGjX7x
Differential Equations(Nagle, Saff, Snider) amzn.to/3S7AnLS
Differential Equations(Zill) amzn.to/3MF5lJV
Schaum's Differential Equations amzn.to/3D4dncc
Elementary Linear Algebra(Anton) amzn.to/3S9TdSn
Linear Algebra(Friedberg, Insel, Spence) amzn.to/3EOVgZh
Linear Algebra(Hoffman, Kunze) amzn.to/3MHs6xa
Schaum's Linear Algebra amzn.to/3D4L3q4
Schaum's Partial Differential Equations amzn.to/3S2X040
Introduction to Partial Differential Equations(Zachmanoglou, Thoe) amzn.to/3s3mV0M
Partial Differential Equations(Strauss) amzn.to/3ML7YKw
Partial Differential Equations(Miller) amzn.to/3TqCMSO
Schaum's Complex Variables amzn.to/3eKWTfE
Complex Variables(Brown, Churchill) amzn.to/3gd2dZJ
Fundamentals of Complex Analysis(Saff, Snider) amzn.to/3yRyBrh
Applied Complex Variables(Dettman) amzn.to/3EU3Tln
Complex Variables(Ablowitz, Fokas) amzn.to/3VLrP0e
Principles of Mathematical Analysis(Rudin) amzn.to/3SowgLD
Advanced Calculus(Fitzpatrick) amzn.to/3MHY5Nt
Understanding Analysis(Abbott) amzn.to/3MFzskD
Analysis(Lang) amzn.to/3yOmThc
Introduction to Real Analysis(Bartle, Sherbert) amzn.to/3s60yrH
Advanced Calculus(Buck) amzn.to/3g9kgQt
Abstract Algebra(Fraleigh) amzn.to/3S7lhFV
Contemporary Abstract Algebra(Gallian) amzn.to/3eDFQw9
Abstract Algebra(Dummit and Foote) amzn.to/3EMRwr2
Algebra(Artin) amzn.to/3EOUnQ9
Abstract Algebra(Saracino) amzn.to/3CAl9cq
Abstract Algebra(Beachy, Blair) amzn.to/3FcsTmr
Algebra(Lang) amzn.to/3s3v5GA
Topology(Mendelson) amzn.to/3SbpKaN
Schaum's Topology amzn.to/3T2dpXH
Topology(Gameline, Greene) amzn.to/3Sbpmcl
Topology(Munkres) amzn.to/3Ty9GkF
Number Theory(Long) amzn.to/3gjeKuw
Number Theory(Andrews) amzn.to/3g4l8ps
Number Theory(Dudley) amzn.to/3D567wH
Graph Theory amzn.to/3CIQEkr
Real and Complex Analysis amzn.to/3MHWO99
All The Math You Missed amzn.to/3s5ZMuN
Functional Analysis amzn.to/3rYNfcB
Concrete Mathematics amzn.to/3CHReiE
Advanced Engineering Mathematics amzn.to/3yIQetp
Cryptography amzn.to/3s4sts4
Basic Mathematics amzn.to/3MCj2tc
(these are my affiliate links)
If you enjoyed this video please consider liking, sharing, and subscribing.
Udemy Courses Via My Website: mathsorcerer.com
Free Homework Help : mathsorcererfo...
My FaceBook Page: / themathsorcerer
There are several ways that you can help support my channel:)
Consider becoming a member of the channel: / @themathsorcerer
My GoFundMe Page: www.gofundme.c...
My Patreon Page: / themathsorcerer
Donate via PayPal: paypal.com/don...

[@koyuki6113]

you know what would be cool, like a website where you could make an account and have like a skill tree which shows you the different books and the paths that are most recommended to take, just like this video but more interactive and visually pleasing. With sub sets of all the skills and topics that come in each subject, connected together like a cool spider web, that'd be awesome. But thank you for putting this out because this is already something really special!

[@MR-ww1zf]

There is one

[@thingthinkingthing5639]

@@MR-ww1zfyeah, where? Kahn academy?

[@jayoz7746]

There probably is an app that exist that does the idea you give. Probably something like Khan Academy but more specific

[@HaIsKuL]

The visuals are nice to have, but a checkpoint system would be great. After each concept, show an example, give exercise that repeats the example of the same complexity, then show them being solved, then increase complexity and give 3 exercises then provide solution. For every exercise not done correctly, it provides 3 more exercises of the same type and complexity. This is how quizzing should be done anyway, but it's not systematically improving someone's knowledge and skill, just showing who got it right the first time, which is not useful for the person that already got it for a slight ego boost and not useful for the person who didn't get it for demotivation.

[@a.s.vanhoose1545]

It would be great if it tested you to unlock the next books based on the prerequisites for them.

[@jonathanpopham5483]

Started this channel in my associates degree in computer science, struggling with calculus. Graduated with that degree now I'm getting my Math BS. Just finished Bridge to Abstract Mathematics and moving on to Analysis next semester. Thanks for the support

[@TheMathSorcerer]

Best of luck!

[@jonathanpopham5483]

I graduated! I have a BS in mathematics.

[@everline_builders]

I don't have the time or money to do a math degree but watching your channel has really inspired me to self study and getting a run down on what books to buy for my current math competency level is extremely helpful.

[@TheMathSorcerer]

Go for it! Math rocks:)

[@eklipsegirl]

The books are not so expensive, you don’t need too much money and you definitely don’t need a teacher!

[@davidsoto4394]

Can Mathematical Modelling be done with a paper and pencil?

[@rizzwan-42069]

@@davidsoto4394 if you have great imagination(which can be trained) you can do it on your mind

[@davidsoto4394]

If you did not already please do a video about Algarithyms but about math not the kind that they talk about when they are talking about computers.

[@beasthunt]

I had to do this at the age of 39-45. I started in community college and the first book was an addition sign.....lol. Fast forward 6+ years later and I'm 1 month away from graduating an electrical engineering program. God is good. For anyone that may read this in the future. Do not get excited thinking that DiffEQ is the last math class in engineering. Every class is a math class in an engineering program. Every last one. Minus the general education classes and some of them even have basic algebra.

[@yuto2497]

To be honest, I've binged watched the first start to finish video more than 5 times already lol. There is really something that makes me rewatch the same thing, even though it's just showcasing books lol. And now you made another one, and I can watch more, keep it up Prof!

[@TheMathSorcerer]

:)

[@masternobody1896]

​@@TheMathSorcerer brain died but I do math anyway

[@davidsoto4394]

Please do videos on making mathamamatical modeling without a computer.

[@emale03]

It's because he is a real "sorcerer"

[@eklipsegirl]

Did you actually buy at least one book from the video?

[@Galileo51Galilei]

There should be a video like that for every field of interest. Having someone familiar with his/her field and able to situate books to each other is really precious and necessary knowledge. Thank you sir

[@vectoralphaSec]

Yeah i think so too.

[@feather1229]

Yes but most youtubers simply pretend to be expert at felids in which they haven't even grasped it's basics. So it's rare to find actual experts

[@robmartin5448]

no, gatekeeping is necessary

[@GM-kf1oj]

Just out of curiosity, why is it?@@robmartin5448

[@gorsama-2190]

I recently dropped my video gamed addiction and picked up math instead and watched your first edition of “how to start math” video. I've started with discrete mathematic with application by Susanna Epp which you mentioned before, it's a little thicker than I thought (almost 900 pages) but I'm 200 through, and I've been having fun so far.

[@user-og9nl5mt1b]

U should read calculus made easy

[@gorsama-2190]

@@user-og9nl5mt1b ty for suggestion 😀

[@admiraloverdone]

That's amazing! Good luck! :D

[@TheMathSorcerer]

Wow!! Awesome !!

[@CK-iv1lq]

@@user-og9nl5mt1b Seconded, this is an excellent book. Only thing is the author teaches the subject using infinitesimals as the foundation, avoiding the concept of limits altogether (which is how calculus is usually introduced). This makes it a little atypical for a calculus book but it’s still a good one.

Get Started: 0:25 Pre-Algebra/Elementary Algebra 1:06 Discrete Mathematics 3:18 Proof Writing 5:23 Pre-Calculus/Trigonometry 9:46 Calculus 13:15 Differential Equations 14:40 Probability/Statistics 16:20 Geometry 16:40 Linear Algebra 18:40 Complex Variables 21:02 Partial Differential Equations 22:14 Abstract Algebra 25:39 Real Analysis 28:14 Number Theory 28:50 Graph Theory 29:20 Topology 31:25 Miscellaneous

[@niket527]

This needs to be pinned

[@yurisaraiva7980]

Thank you friend, you are a friend

[@lycorice2219]

Thank you so much for this breakdown ❤

[@parashantadna1624]

Hey u skipped elementary statistics...

[@bronsonschnitzel7493]

8:35 Smelling Books

[@lonnieporter8566]

I didn't pursue a math degree, but I have saved every textbook from every math class I have ever taken; from basic algebra to Calculus. I am retiring and will now have the time for the self-study I've been trying to do. I will most likely get some of the titles you recommend just to gain different perspectives on the topics.

[@zethcader6478]

There is something that keeps me coming back to the idea of learning mathematics, I dropped out of school at grade 6, I've learnt a teeny more maths since then and I love what I can do with it when I am able to apply it to the real world, I would love to bits to have more knowledge. I think I'm going to buy an algebra book and see where I go, really scared, but also excited.

[@thapsmohlala9699]

Please go on ahead!

[@icarussparks]

Failed college algebra and trigonometry multiple times but I desperately need to understand math to move forward with science classes. I'm here hoping to learn.

[@Guest44988]

I’m turning 40 and your videos inspire me to learn maths and keep going even on days I don’t feel like it.

[@TheMathSorcerer]

That's great!

[@aomoussynonymous8712]

@@TheMathSorcerer Sir, among the analysis books how highly do you rate the two volumes written by Terence Tao ? Are they beginner friendly ?

[@PunkerNinetySix]

The timing couldn't have been more perfect! I'm just about to begin my self study program. I had watched your "1st edition" video a few days ago and was planning to start by ordering a couple of those books this Wednesday. I'll have to see what's in the update first! Thanks for this. Looking forward to watching it this week.

[@alfonsodonotsi6691]

me too, I don't have time to go to university, but I want to study mathematics soo hard. but first I have to learn better English to understand the books

[@vectoralphaSec]

I dont have much money but i wanna start to buy some books too but don't know where? Do you recommend any websites or places where you buy math books for cheap/ low price??

[@DionysusWines]

​@@vectoralphaSeclibgen

[@lonelyrain583]

I wholeheartedly agree with what you said about topology. It's a very difficult subject and easy to lose your patience if you keep getting stuck. Awesome video, love seeing all your books!

[@ussdfiant]

I just finished Prealgebra and started algebra. I’ve got several algebra books, 3 geometry books and 2 calculus books already. Last night I asked my wife if it’s weird for a physician to be considering going back to school for a math degree. She was not amused!

[@Rudenbehr]

Hearing that you’re a physician, that’s wild that algebra must’ve been unnecessary for your career 😅

[@declanfarber]

I wish my doctor would go back to school for a math degree. He’s so bad at statistics!

[@eandoestyping39]

02:01 i heard somewhere that Ramanujan had incredible knowledge in certain areas and could solve super advanced problems but would be tasked with super super elementary problems he didn’t know and got them wrong it just proves that he skipped around learning the math he enjoyed and also proves that just because you don’t know a certain area in math doesn’t mean you won’t understand a more difficult area of math.

[@tejasvi18joshi]

Indian mathmatics was practical and easy. Modern mathematics is colonised. After crusade church got the hold over Arabic books which were translated from Indian books . then church started manipulation , planting fake non existent greek sources and fake greek mathematicians and also added Christianity myths and dogmas into mathematics which made this mathematics impractical, irrational and ambiguous. That's why decolonisation of mathematics is must.

[@peterslattery9581]

I am starting to fall in love with Pure Math Taking intro to abstract algebra this semester and today in class we showed how the set of complex numbers C is isomorphic to R[x]/(x^2+1) which Bassicly means the complex numbers are embedded in real polynomials we actually took a moment in class to just appreciate that fact I swear in that moment I was convinced math is a beautiful subject Can’t wait for more!!

[@argonwheatbelly637]

Math is an art, a language. You're now reading its poetry.

[@Kodlak15]

I got very interested in math after I finished college, and Ive been blown away by how many awesome resources (your channel included) there are out there for those of us who wish to continue learning outside of school. Ive bought a number of books that Ive come to love per your suggestions. Thank you 🙏

[@vectoralphaSec]

I dont have much money but i wanna buy some books too but don't know where? Do you recommend any websites or places where you buy math books for cheap/ low price?

[@valentinov901]

@@vectoralphaSec you can find the math for dummies PDF books for 10-15 bucks the workbooks give a short explanation,a problem solving example and throw 10 to 20 exercises for you to resolve they cover pre-algebra,algebra,trigonometry,pre-calculus,calculus-1,linear algebra,calculus-2 so basically all maths up to 2do year of undergraduate college

[@elephantintheroom5678]

I hope that the books you have showcased truly show every step, stage and level of working out the maths as too many experts forget what it is like to be a beginner.

[@DLCS-2]

Same

[@jacksonh2083]

KZbin, places like math stack exchange and chat gpt can help you out a lot.

[@lewessays]

I can attest that it is really helpful. And trust me I am not brightest individual when it comes to maths 😅

[@elephantintheroom5678]

@@lewessays 🙂

[@JJSmalls]

Learn proofs

[@IssamHalabi]

Phenomenal video! I’ve been meaning to get back into Math. When I did my Bachelor’s in IT we did: Pre-Calc/Trig, Discrete, Finite, Introductory Physics, Stats I/II, Data Structures & Algorithms. The Comp Science majors followed Precalc/Trig with Calc I/II/III & Physics I/II

[@Belgarathe]

Just a bit of advice that I learned from my physics teacher Mrs Sprang. Always try to have two textbooks. All textbooks have their strength and weakness but more importantly some books speak more to you than others. So if you get stuck understanding a topic switch to other textbook and see if that helps. Just remember to ask why you are learning this stuff to keep the motivation up.

[@m0st4fabideer14]

Can't agree more!

[@thelastpersononearth9765]

These are the reasons why KZbin is far better than any other social media.

[@douglasstrother6584]

The Dettman text on Complex Analysis is great: the first half covers the mathematics of the complex plane and all that, and the second half covers applications (physics stuff) of complex analysis. This book coupled with the corresponding Schaum's Outline will help you skate on all of the Riemann Sheets like a pro!

[@TheMathSorcerer]

:)

[@aaronrocs]

I think it's cool how you collect math books. I always buy textbooks when I find 'em for super cheap at goodwill or garage sales, etc... I remember how much I paid for my school books, and so when I find them for cheap I get excited because there's soo much knowledge in there, it feels like the ultimate deal. I find it's pretty easy to find books for cheap as long as you aren't picky. Most formal classes require a specific book and the old editions aren't accepted, which makes them worthless to some people. They're big and bulky and people just want them gone (especially if they hated the class, lol)

[@tenminuteretreat807]

I love how you smell the textbooks. I do the same thing!

[@boudiarabeh4940]

I'm surprised you never mention the AOPS book series!!! it's one of the best math books IMO.. lots of gifted kids take it as their study guide. plus it has all kind of hard question that will make you a hard core problem solver... teaches you proofs and everything.. it's also used in math Olympiad camps. the Art of problem solving book series is the best IMO. it can be dry and hard to understand at first but its so worth it! highly recommend

[@TheMathSorcerer]

I'll check it out!

[@daniellindner826]

I‘ve watched the first edition multiple times already. So glad to see the second edition is out. You helped me so much. Thank you for so much for everything.

[@AnnLaustsen87]

I have a mechanical engineering degree, so I've been through a lot of math. If you can, try to get your hands on solutions manuals. Homework isn't weighted very heavily, and the manuals will come in handy when you're not able to get ahold of your prof during office hours. Also, I've done plumbing and HVAC design. We do very simple math. Like, I get excited when I get to take the cubed root of a number.

[@giannism3114]

your first video on this really helped me jump start my math journey. i am currently in high school and i wanted to be ahead so i don't fall behind when i don't fully understand everything

[@sumitvishwakarma1075]

I want to learn mathematics from absolute beginner to everything. Your videos always helped me for mathematics and physics stuffs

[@haripulakkat3490]

This is a nice list. Let me also add two exceptionally well-written books by George Simmons: Calculus with Analytic Geometry and Differential Equations. The first one is hard to get in print, but PDFs are easily available.

[@vectoralphaSec]

I dont have much money but i wanna start to buy some books too but don't know where? Do you recommend any websites or places where you buy math books for cheap/ low price?

[@yutubl]

I think everyone who interested in math also have math books with overlapping content. These are my math books: 1.) german translation of "Mathematics in the Making" from Lancelot Hogben, it presents the history of mathematics so good & interestingly that I later bought other popular pocket books (3., 4.). It was a gift from my boss after successfull education as a Radio- & TV Service technician. 2.) Gieck - Technical Formulary a pocket book and birthday gift from a friend. 3.) Foundations of Matrix calculus (Grundzüge der Matrizenrechnung Harri Deutsch) as a preparation for studying electrical engineering at Flensburg university. 4.) Bridges into Infinity - before I studied electrical engineering & computer engineering, 5.) Introduction into Higher Mathematics (Schaums outline) in german translation also as a preparation for electrical engineering. 6.) Foundation of Mathematics in historic development - without color pictures as 1.) but from egyptian until 20 century (proof theory). 7.) Mathematical foundations of electrical engineering (Mathematische Grundlagen der Elektrotechnik, Dirschmid, Vieweg) which covers Mathematics from real numbers Analysis to (complex) Function Theory. I bought it as a replacement of my 4 engineering math books (Harri Deutsch) which I sold to to younger students after I've been graduated Dipl. Ing. Technische Informatik in Flensburg. 8.) Curriculum Statistics (Weinheim: Physik Verlag) as a labority engineer. I also own engineer reference handbooks containing Mathematics as 1st chapter (like Gieck's Technical Formulary): 9.) Dubbel, 10.) Hütte - Ingenieurwissen.

[@hockeyKid7749]

Great introduction. For linear algebra, I would like to add one more book "Linear Algebra Done Right" by Sheldon Axler, it introduced me to a different way to understand linear algebra, very helpful.

[@psbjr]

I also enjoyed Axler's style very much in his trigonometry and algebra books.

[@blackcitadel37]

I decided i want to get a Electrical or Computer Engineering degree in the future but i want to prepare for the math classes beforehand through self-study. I just started studying the books you listed, starting with the Holt's Pre-Algebra beginner path.

[@Maths_for_WCS]

I am reading a "Comprehensive Course in Number Theory" [Cambridge University Press] from Alan Baker, Fields Medalist (1970) and FRS (Fellow of the Royal Society) & Fellow of Trinity College. Adams Prize (1972)

[@30803080308030803081]

You omitted the best differential equations textbook: Boyce and DiPrima. When I took differential equations, the assigned textbook was actually that Zill book that you have. However, I just did not like it. It didn't explain concepts clearly and omitted a great deal of important information and details. A math professor better than the one teaching my class recommended Boyce and DiPrima to me. It was the book he used in his course. I bought it and read nearly the whole thing. I used it throughout the course I was taking. Instead of reading chapters in Zill, I read the chapters on those topics in Boyce and DiPrima. And, I read several chapters of B&D on some really interesting topics not mentioned in Zill. All of the assignments and exams in the course were easy. Overall, B&D had extremely clear explanations of everything and really kept me mentally engaged in the subject. I don't know why you overlooked this book, but it is exactly the book that I would recommend to anyone learning differential equations for the first time.

[@TheMathSorcerer]

that's a GREAT book!!!!!

[@douglasstrother6584]

"Methods of Theoretical Physics, Parts 1 & 2" by Herman Morse, Philip M. Feshbach is *THE* heavy artillery of Applied Mathematics in the context of physical applications. It's old, out of print and expensive, but it is the best. One can find PDFs as well.

[@ryanchiang9587]

minored in mathematics in undergrad. went on to phd in mathematics at the university of houston. took modern algebra, functional analyiis, to[ology,...etc.

[@zachbangkok]

I still have the exact same copy of Swokowski Calculus from my early 1980’s college days in the U.S. Remember having done many of the exercises in the book. I enjoy this second edition review than the first. Thanks.

[@BennettAustin7]

I second learning cryptography. It’s probably the coolest applied math course. And actually I would say it’s still very much pure math as it’s basically algebraic number theory and geometry

[@SpocksCat]

I'd be interested in a video on what books to work on to prepare for the math on the SAT.

[@pizzaspy]

This video is just the dopamine hit I need to feel like I learned all of math without lifting a finger. Thanks!

[@sphires]

I would also recommend The Feynman Lectures on Physics for a science angle. Feynman's method of teaching derivitives is great!

[@pkyadav6230]

... i couldn't get great grip on mathematics neither my school or college faculties were...great enough to create intereste inside me...for mathematics.... but now i realise how beautiful thing mathematics is...now i m in my final years of my college...but i have great passion for mathematics... I don't know why this revolution is happening within me

[@florianbuerzle2703]

Awesome 2nd edition! 😀😀😀 Although my math library is far less comprehensive (my focus is more on physics books), I own quite a few books mentioned here. However, I have some additional suggestions not mentioned already, which I‘d like to share 😊 Perhaps, Math Sorcerer is going to buy some of them…? 😂 Alan Baker, A comprehensive Course in Number Theory (great, but probability not for beginners) Adams/Goldstein, Introduction to Number Theory Davenport, The Higher Arithmetic (imho great for beginners) Burn, A pathway into number theory (written in guided discovery style) Pommerheim et al, Number Theory (more breadth than depth, but truly a piece of art!) Bogart, Combinatorics through guided discovery Shahriari, An Invitation to Combinatorics Roe, Elementary Geometry Meyer, Geometry and its Applications Adams, The Tiling Book (he is the Knot Theory grandmaster, this one is his take on tilings - a beautiful book, the math combined with looots of very pretty pictures :)) Houston, Complex Analysis Butler, Lectures on Abstract Algebra Cummings, Proofs Cummings, Real Analysis Taboga, Lectures on Probability Theory and Mathematical Statisticas Riley/Hobson/Bence, Mathematical Methods for Physics and Engineering Krantz, Differential Equations. Theory, Technique and Practice

[@vectoralphaSec]

Wow thats a lot of books. I dont have much money but i wanna start to buy some books too but don't know where? Do you recommend any websites or places where you buy math books for cheap/ low price?

[@firebirdies]

I like how you put probability after calculus. The First Course in Probability has triple integral in it.

[@novembersuitealso1900]

i am so thankful for your channel, i dropped out sophmore year, but have always had a huge interest in math. it's been hard for me to find resources outside of school to learn, so this is a big big help! thank you so much!

[@williammcenaney1331]

I specialized in logic while earning my philosophy degree, so some mathematicians suprised me when I discovered that I knew more about logic than they did.

[@imagidan]

Wow 2nd edition of an absolute classic

[@sophie________]

pre algebra is an amazing way to get into math. even if you know basic math, you'll build your skills a lot when studying pre algebra

[@cohomological46]

Abstract Algebra: Vinberg "A Course in Algebra". Sadly Kostrikin's 3 volumes (I - introductory abstract algebra II - linear algebra III - much more detailed abstract algebra) of "Introduction to Algebra" were not translated well, otherwise I'd recommend them instead. Analysis: Zorich "Mathematical Analysis" volumes I and II Topology: Viro, Netsvetaev "Elementary Topology" - simply an incredible book. Lots of exercises with solutions.

[@photonpar]

This is the best video in the entire web about the essential math textbooks !! You told nothing but the truth sir and congratulations...its a really precious guide for all the math self learners on the planet...i have about the 2/3rds of the textbooks u suggest...however it would have been very very helpful if you posted which of them have a COMPLETE solutions manual nowadays(2022...) As you know its a matter of self esteem for a self learner(student or older) to have access to a solution of a mind breaking math problem ... he is supposed to have tried on his own of course before he uses the manual...not fool himself... CONGRATS AGAIN. !!

[@eflat6522]

Being a self-learner one of my favorite videos was your 1st edition of learn mathematics from start to finish. I have already bought some of the books recommended then. Thanks for the new version even though it will damage my wallet..😃

[@GaloSigma395]

Which of the two lists is the best? Do lists really cover all math from start to finish?

[@zerozephyr6264]

Thanks! I've basically been hiding from math my whole life. II took the ged, literally just guessed the math and somehow passed. Now I'm applying to college and they're making me do the same math i never did in middle and high school. So this is exactly what i needed, I'm glad the algorithm showed you to me. Wish me luck

[@sicko_the_ew]

For beginner logic, I'd recommend "Barwise and Etchemendy" (Language, Proof, and Logic). It comes with software and an account on their website that covers all the exercises (you do them on the computer). Instead of having solutions to the problems in the book, you try to solve the problem, then submit it to the website, and the website will tell you whether you got it or you need to try again. (So you're always aiming at 100%, so to speak.) (This info may be out of date. I used the book quite a long time ago, and it's possible that it never took off, and that the website is now down - although it looked like something that was self-contained, not requiring much in the way of maintenance, so maybe it's still going, even if the book died.)

[@paxdei1988]

Is that the one that has a Stanford MOOC?

[@sicko_the_ew]

@@paxdei1988 Sorry, I don't know what a MOOC is. I think Etchemendy was at one of the UC universities (Berkeley maybe), but can't be sure. (And I think Barwise is no longer with us, but also not sure.)

[@sicko_the_ew]

OK yes, it looks like it. (I asked Google about MOOCs and learnt something. Thanks.) John Etchemendy is one of the instructors on the MOOC, so it might be exactly the same.

[@njb1126]

I recently picked up pre-cal by Stewart, redlin, and Watson, schaums discreet math, explorations of elementary math by smith, and discreet math by levin among some others.

[@raponte303]

i would love to see a video like this but with physics/engineering topics, would be interesting to see textbooks leading up from basic mechanics and electromagnetism to whatever standard books in other fields

[@diomauia4295]

That's a good idea

[@guilherme992]

In my university in Brazil (Universidade Federal de Pelotas) we are actually learning discrete math before calculus in computer science degree, it's cool you talked about it

[@victornecromancer]

Interessante!

[@benhill3098]

Great 2nd edition guide for learning mathematics (and great 1st edition)! I like that more algebra books are covered in this edition, especially elementary algebra books like that from Sullivan. I can't wait to receive my copy of Lang's "Basic Mathematics" next week! Great job! Impressive selection of books! Thanks!"

[@AnonymousBosch3158]

You have no idea how helpful you are.

[@corbinwilson3781]

The first start to finish video was great, this one was just as amazing. Thank you Math sorcerer for the wealth of knowledge.

[@TheMathSorcerer]

You're very welcome!

[@pygmalionsrobot1896]

Excellent video, I just wanted to mention Salas and Hille's Calculus ... that's what I learned from and I love it !!!

[@pandabearguy1]

"Knowing The Odds: An Introduction To Probability" by Walsh is a nice book for learning measure theoretic probability.

[@DD-cf2iv]

14 seconds in, I already love this man.

[@orlandochavez1697]

I lost it when you smelled the Pre-Calculus book 😂😂 Appreciate the video, thank you!

[@deanwhitlock3312]

I used Swokowski (and still have it) in the early 80s in college. It had several supplementary work books to go with it.

[@srivatsavakasibhatla823]

Great compilation. But you could've added "Linear Algebra Done Right" by Sheldon Axler. Very rigorous, emphasizes proof writing and solid interpretation as well.

[@shyamr-ind2can]

Oh my god!! Thank you for this. This video will be watched again and again

[@sanchayanghosh7434]

A really great book I want to recommend. Plane Trigonometry by SL Loney. At this point, it is super accessible, has a very comprehensive treatise on both rectlinear and angular coordinate systems, and is frankly a beautiful stepping stone towards vector algebra

[@Carlos-qz7ul]

Always the same freshness and trust in human spark when proclaiming that maths are FOR EVERYONE ! The opposite of elitism ! ❤ Gracias, Brujo ! 😃

[@DavidCosta85]

this is a good resource to self study

[@tyal-q9x]

This man is a man among men. "Do not feed any man; teach him to fish instead." You are a special kind of Guru. Thank you.

[@EdwinDalorzo]

This video is incredibly useful. Thanks a lot for sharing this extraordinary list of books. I started to study math a year ago and I've buying books myself as I go, but I'm seldom sure of what is the best book for every particular topic or area of math that I need to learn. I will be using your list of books from now on. I'm also a collector of books, so hopefully, one day, I will have a nice collection like yours.

[@vectoralphaSec]

I dont have much money but i wanna start to buy some books too but don't know where? Do you recommend any websites or places where you buy math books for cheap/ low price?

[@lock0nstratos416]

I graduated as a mechanical engineer 4 years ago. I loved math and have been trying to go back into it and transition into data science or machine learning. What's a good starting point for someone who has done probably the first half of these books and wants to go deeper? Should I start from elementary algebra to review?

[@PatrickBateman969]

This man is Gold!!

[@AndreTJones]

I was failing Calculus 1. I recently dropped as of this writing. I am eager to buy and study these books. Hopefully this will give me a leg up on Calculus when I return to it next semester.

[@carlos9000]

I'm currently reading elementary algebra by Sullivan it is a spectacular book for amateurs like me.

[@DD_Bhagyesh]

Can you please describe me about that book,,, how it helped you because I also want to learn maths,

[@ripperduck]

One of the best STEM channels on Utube....

[@Joe-pz2fs]

Just what I was looking for

[@Joe-pz2fs]

Thank you Math Sorcerer!

[@mincedmeatchops3208]

Here I come with some rambling nonsense. Discourse always appreciated. If I were to start all over again, I would definitely start with Discrete Math and a little bit of proofwriting! The early introduction to sets and logic is really important imo, and proofs diverge (no pun intended) from the standard “mechanical” problem solving that mathphobes bemoan; the creative side of math is sorely underrepresented in early math education. The basics of sets and propositional logic could be explained to a child, and they will be a great boon in nearly all the math you will study and in the real world. Multiplication principle and subtraction/addition are both very easy to understand, and they lead naturally into combinatorial proofs which can be delightful (cf Proofs That Really Count). Counting also leads naturally into probability, which answers the “I’ll never use this!” crowd. Bijection proofs introduce functions in a much more intuitive way, imo, than the graphic approach used in high schools, and are much more interesting than the dry linear functions they start you with in precalc. After that, I would start on elementary number theory for proofs and algebra. I would then take a historical approach to number systems, algebra, and analysis. They are so much easier to motivate in context, and it shows students how math is really done. Call me crazy, but I would also approach category theory from a very very very elementary perspective, again motivated by history. Then perhaps geometry, from Euclid forwards. Students aren’t interested in a topic when you just throw equations and theorems at them, and then send them right away to problems. They should understand how the mathematics arose and why. Most importantly, I think they should be exposed to the beauty of math as an art Calculus is interesting and very useful, but the only reason it’s so emphasized (hot take incoming) is the engineering/finance assembly line. I would argue we are doing students a great disservice by shoehorning them into this path.

[@TheMathSorcerer]

Excellent comment, thank you so much!!

[@mincedmeatchops3208]

Also, Abbot’s Understanding Analysis is great! It’s where I started with self-study

[@Curtessiupostol]

at what point I could study numerical analysis, differential topology,differential geometry?

[@pepperpeterpiperpickled9805]

Can you direct me to people who can provide similar roadmaps for chemistry, engineering, computer science, biology and physics?

[@markharder3676]

There is a Dover version of the Bert Mendelson topology book.

[@robinsnotes]

I would love to study from these books but these books are expensive, would love to get cheaper options. I did try finding cheaper options but i don't know if they will have it all.

[@laughingvampire7555]

for Discrete Mathematics in my school we had "Discrete and Combinatorial Mathematics: an applied introduction" by Ralph P Grimaldi.

[@Hmongboi228]

Is it possible to make a simple webpage (link included) with a flow chart of the math learning process from start to finish? 🤔🤨🤝 Great content.. 👍

[@TheMathSorcerer]

That's a great idea!

[@varunramakrishnan7676]

Does a simple webpage x with a flowchart y exist, such that y shows the math learning process from start to finish?

[@urieldaboamorte]

you can check out undergrad/grad curricula flow charts!

[@abuhammer7450]

@@urieldaboamorte can you link them?

[@declanfarber]

It depends on where you want to _go_. The Princeton Companion to Mathematics (and the associated Applied Mathematics book) are a really nice survey of the field. I would mischievously suggest that you leaf through them every night before you go to bed, and get to know the prerequisites to the prerequisites to the prerequisites. There are so many destinations.

[@argonwheatbelly637]

I still have my B&S Real Analysis book from when I was an undergrad back in the mid 80s. 😊

[@11111653]

thanks I'm Oppenheimer now

[@AmitKumar-os8xq]

😂

[@abhinavs4326]

Actually professor I have a suggestio. If anyone wants to learn actual math and improve on problem solving - Indian Books are quite decent . the advantage being most are in basic english. If someone is strong at really basic algebra - they can start with RD Sharma's 10th grade/ 11th grade book or even the NCERT Mathematics (tho this is not recommended as they are just way too vanilla style ones). after that you can jump to harder ones like Cengage's JEE series - the one written by G Tewani. However these books are only good for high level multi concept problem solving rather than indepth into one topic . Proof writing books are very rare in Indian scenario coz most exams here are about solving . As a engineering student tho - I prefer books like jreyszig erwin or for discrete math I go with kolman busby ross. I find foreign authors book strong in theory but the exercises are easy. The Cengage still has some reallly kicker questions that even some BSc math/ phy or some BTech Electronics grads find hard. I am from a tier 2 engineering college and suprisingly the calculus in engineering had much easier problems than the questions I solved for my high school terminal exams/ board / diploma exam. In 12th grade we focused a lot more on calculus tho - especially inegrals , differential equations and applications of the same (area under curve , applications of derivatives )

[@kaustubh3334]

sir your videos are always very helpful for me

[@joncyprus1304]

Aw man. I just bought all the books from the first video. Time to watch and pick up some more!

[@iamaperson5695]

Hi Math Sorcerer, I noticed Solid Mensuration Book is not discussed. Geometry books nowadays do not discuss this but very useful for applied mathematics and engineering alike.

[@smokeythebear1633]

Thank you very much - from someone who had terrible mathematics education. It is very truly appreciated.

[@grussell76]

I think your videos are great, and I like your choice of topics. I am a retired actuary and have taught part-time at a local community college and have found that to be enjoyable. I've worked through several math texts on my own to get back in "math shape" and that's been fun, too. For this particular video, a question came to mind. Do you have a recommendation for a numerical analysis text? I have one by Burden and Faires from my actuarial exam days, but I think there might be something better out there. Any suggestions would be greatly appreciated.

[@selimfazliu577]

Great!!! I have bought some books u have recommended so far but had no idea how to start it. This video is exactly what I need!

[@cranictoon5958]

I really thank you for this video

[@NFM1337]

Thanks! I started out doing physics and then ended up in biology and I sorta know all the math I need for my research, but I just miss math a bit. I've been looking for a way to just have some fun with it and I think All the Math You Missed might fit the bill. So I'll check it out. Thanks!

[@karar5387]

I have question please: what about advanced topics in mathematics such as; Differential geometry or algebraic geometry or algebraic topology...ect. i heard that you must study differential geometry before topology... what do say?

[@bm-br3go]

Normally one studies differential geometry after a basic course in point-set and algebraic topology. Michael Spivak has a classic book on the subject if you're interested. Algebraic topology requires point-set topology. Hatcher's book is light-years ahead of every other book on the topic, and most experts will tell you the same. Although it is jam-packed with a lot of information. Algebraic geometry is a whole other beast in itself. If you have a good grasp on basic algebra (through Galois theory) then Fulton's "Algebraic Curves" is the best go-to book in my opinion. There's also the more advanced book "Algebraic Geometry - A first course" by Joe Harris, or "Complex Projective Varieties" by Mumford. All of these require a great deal of comfortablilty with polynomial rings and field theory.

[@sebastianarteaga8401]

i recommend W.W. Sawyer Mathematicians Delight. a must read for any beginner. some other good books are Paul Lockhart, Measurement and David Acheson, The wonder book of geometry. (Leonhar euler elements of algebra, Henro poincare and David hilbert famous Quotes.) Is by logic that we prove, but by intuition that we discover. -Henri poincaré.

[@jessstuart7495]

You can only asymptotically approach the "math finish line".