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!
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.
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.
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.
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!
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
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
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 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.
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.
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.
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.
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.
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
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??
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.
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!
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
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 🙏
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?
@@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
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!
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)
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!!
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
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!
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.
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.
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.
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.
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.
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!
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. !!
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
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.
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.
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.
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.
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?
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.
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
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)
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!"
"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.
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
minored in mathematics in undergrad. went on to phd in mathematics at the university of houston. took modern algebra, functional analyiis, to[ology,...etc.
... 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
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..😃
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
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?
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 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.)
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.
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
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.
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?
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.
Great compilation. But you could've added "Linear Algebra Done Right" by Sheldon Axler. Very rigorous, emphasizes proof writing and solid interpretation as well.
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
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.
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.
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.
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.
Amazing video and work you have put into this I must say. I am in my 20s and love math although I am terrible at it. I want to learn Probability but I don't get the intuition behind the topics almost all the time. I am currently referring DeGroot's probability book and I struggle with coming up with my own solutions to the problems or even understand the examples they have mentioned. Do you mind giving me advice on how to get better at it?
I’ve been using DeGroot’s book, too, and I’m finding it overly complicated and vague. The only good thing I can say about it is it’s really making me put in the extra work and research to understand it 😅. I started a Probability & Statistics playlist of videos that have been helpful at explaining more simply, and some for entertainment/history to put the ideas in context. I’ve also been watching MIT OpenCourseWare’s Introduction to Probability here on TH-cam. And I just got Shaum’s Outline of Probability and Statistics 3/E Enhanced Ebook which seems to give a good amount of practice.
same here i like mathematics but I'm terrible at it but i see mathematics as a skill i started with calculus 1 and done some group theory and linear algebra but I'm not satisfied so I'm gonna go for different book but as time passes i can see that I'm getting better and better than before so if you have patience and consistency one day you'll learn anyway. My aim is to complete cal1 cal2 and mathematical analysis, whole abstract algebra and linear algebra on my own .it will take time but let's see what happens.
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!
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
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?
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.
I searched a lot about how to get started in mathematics for a beginner. And by chance this video came up to me.. very cool content.. thank you.. you really made my day
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.
Great video! I was wondering if you've got the Princeton Companion to Applied Mathematics, and if so, what you think about it? As I understand it, it's not a textbook, but a collections of articles introducing different areas of math, and then giving applications of it.
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!
There is one
@@MR-ww1zfyeah, where? Kahn academy?
There probably is an app that exist that does the idea you give. Probably something like Khan Academy but more specific
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.
It would be great if it tested you to unlock the next books based on the prerequisites for them.
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
This needs to be pinned
Thank you friend, you are a friend
Thank you so much for this breakdown ❤
Hey u skipped elementary statistics...
8:35 Smelling Books
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.
Go for it! Math rocks:)
The books are not so expensive, you don’t need too much money and you definitely don’t need a teacher!
Can Mathematical Modelling be done with a paper and pencil?
@@davidsoto4394 if you have great imagination(which can be trained) you can do it on your mind
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.
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.
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 brain died but I do math anyway
Please do videos on making mathamamatical modeling without a computer.
It's because he is a real "sorcerer"
Did you actually buy at least one book from the video?
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
Best of luck!
I graduated! I have a BS in mathematics.
congrats bro, wish me luck as well. I am dropping out of econ and going for applied math
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
Yeah i think so too.
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
no, gatekeeping is necessary
Just out of curiosity, why is it?@@robmartin5448
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.
U should read calculus made easy
@@user-og9nl5mt1b ty for suggestion 😀
That's amazing! Good luck! :D
Wow!! Awesome !!
@@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.
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.
Please go on ahead!
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.
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.
I’m turning 40 and your videos inspire me to learn maths and keep going even on days I don’t feel like it.
That's great!
@@TheMathSorcerer Sir, among the analysis books how highly do you rate the two volumes written by Terence Tao ? Are they beginner friendly ?
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.
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
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??
@@vectoralphaSeclibgen
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.
Same
TH-cam, places like math stack exchange and chat gpt can help you out a lot.
I can attest that it is really helpful. And trust me I am not brightest individual when it comes to maths 😅
@@lewessays 🙂
Learn proofs
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!
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
I love how you smell the textbooks. I do the same thing!
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 🙏
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?
@@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
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!
Hearing that you’re a physician, that’s wild that algebra must’ve been unnecessary for your career 😅
I wish my doctor would go back to school for a math degree. He’s so bad at statistics!
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)
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!!
Math is an art, a language. You're now reading its poetry.
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
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!
:)
Last year I made a wiseass comment, but this year I say this is an extra awesome video. Thank you for the guidance.
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.
These are the reasons why TH-cam is far better than any other social media.
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.
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.
I want to learn mathematics from absolute beginner to everything. Your videos always helped me for mathematics and physics stuffs
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.
Can't agree more!
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.
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!
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. !!
I'd be interested in a video on what books to work on to prepare for the math on the SAT.
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
I'll check it out!
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.
I also enjoyed Axler's style very much in his trigonometry and algebra books.
I would also recommend The Feynman Lectures on Physics for a science angle. Feynman's method of teaching derivitives is great!
Wow 2nd edition of an absolute classic
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.
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.
Thank you very much - from someone who had terrible mathematics education. It is very truly appreciated.
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.
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?
Excellent video, I just wanted to mention Salas and Hille's Calculus ... that's what I learned from and I love it !!!
This man is Gold!!
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.
The first start to finish video was great, this one was just as amazing. Thank you Math sorcerer for the wealth of knowledge.
You're very welcome!
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
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)
This video is just the dopamine hit I need to feel like I learned all of math without lifting a finger. Thanks!
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!"
I like how you put probability after calculus. The First Course in Probability has triple integral in it.
"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.
Oh my god!! Thank you for this. This video will be watched again and again
I lost it when you smelled the Pre-Calculus book 😂😂 Appreciate the video, thank you!
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
That's a good idea
minored in mathematics in undergrad. went on to phd in mathematics at the university of houston.
took modern algebra, functional analyiis, to[ology,...etc.
Gramercy! I wanna start to learn mathematics and your video is the most helpful on YT!
this is a good resource to self study
... 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
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..😃
Which of the two lists is the best? Do lists really cover all math from start to finish?
14 seconds in, I already love this man.
sir your videos are always very helpful for me
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!
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
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?
One of the best STEM channels on Utube....
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.)
Is that the one that has a Stanford MOOC?
@@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.)
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.
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
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.
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?
And now you made another one, and I can watch more, keep it up Prof!
Just what I was looking for
Thank you Math Sorcerer!
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.
"Knowing The Odds: An Introduction To Probability" by Walsh is a nice book for learning measure theoretic probability.
You have no idea how helpful you are.
Great compilation. But you could've added "Linear Algebra Done Right" by Sheldon Axler. Very rigorous, emphasizes proof writing and solid interpretation as well.
Another Great Review of Textbooks ... always a pleasure --- THANK YOU
Fantastic video, thanks. I love how you talk about the books as well!
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
Interessante!
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.. 👍
That's a great idea!
Does a simple webpage x with a flowchart y exist, such that y shows the math learning process from start to finish?
you can check out undergrad/grad curricula flow charts!
@@urieldaboamorte can you link them?
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.
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.
that's a GREAT book!!!!!
I really thank you for this video
Yes! Finally a second edition. I have been waiting for it for so long.
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.
This person is an incredible. Thank you for sharing these books. I wish I could have read these all books.
Another great vid as always
I used Swokowski (and still have it) in the early 80s in college. It had several supplementary work books to go with it.
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.
Thank you for spending your time making videos like this!
Amazing video and work you have put into this I must say. I am in my 20s and love math although I am terrible at it. I want to learn Probability but I don't get the intuition behind the topics almost all the time. I am currently referring DeGroot's probability book and I struggle with coming up with my own solutions to the problems or even understand the examples they have mentioned. Do you mind giving me advice on how to get better at it?
I’ve been using DeGroot’s book, too, and I’m finding it overly complicated and vague. The only good thing I can say about it is it’s really making me put in the extra work and research to understand it 😅. I started a Probability & Statistics playlist of videos that have been helpful at explaining more simply, and some for entertainment/history to put the ideas in context.
I’ve also been watching MIT OpenCourseWare’s Introduction to Probability here on TH-cam. And I just got Shaum’s Outline of Probability and Statistics 3/E Enhanced Ebook which seems to give a good amount of practice.
same here i like mathematics but I'm terrible at it but i see mathematics as a skill i started with calculus 1 and done some group theory and linear algebra but I'm not satisfied so I'm gonna go for different book but as time passes i can see that I'm getting better and better than before so if you have patience and consistency one day you'll learn anyway. My aim is to complete cal1 cal2 and mathematical analysis, whole abstract algebra and linear algebra on my own .it will take time but let's see what happens.
I needed this information. Thank you. I just wish you had shown at least some of the content list inside the books.
Great recommendations sir! 😄👍
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!
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
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?
I'm currently reading elementary algebra by Sullivan it is a spectacular book for amateurs like me.
Can you please describe me about that book,,, how it helped you because I also want to learn maths,
Always the same freshness and trust in human spark when proclaiming that maths are FOR EVERYONE ! The opposite of elitism ! ❤ Gracias, Brujo ! 😃
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.
Excellent comment, thank you so much!!
Also, Abbot’s Understanding Analysis is great! It’s where I started with self-study
I searched a lot about how to get started in mathematics for a beginner. And by chance this video came up to me.. very cool content.. thank you..
you really made my day
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.
Wow. Another one 😍. I was rewatching the first one.
Great video! I was wondering if you've got the Princeton Companion to Applied Mathematics, and if so, what you think about it? As I understand it, it's not a textbook, but a collections of articles introducing different areas of math, and then giving applications of it.
Oh that’s cool! No I don’t have that one yet thank you for suggesting it!
Oops, I just posted about that. It’s a really great survey book.
I just picked up a book per topic for a few of these
Thank you for sharing!