You can fail as safely as you want when you self-study. And that won't stop your progress like it will when doing the failing within a class.

studying mathematics on your own is so much more fun.

You’ve inspired me so much through the last 2 years of my life. I self taught myself linear algebra and now I’m gonna study the Vector Calculus book you showed in your videos!!

Self Study math especially when your older, for me has been the very best way to go. You can set your on pace. And its terrific for the mind. It's like the old saying ' you'll lose it if you don't use it.'

You're the reason I considered writing a hard mathematics exam and oh boy am i grateful, i did not just pass the exam but got placed in the top 2 students, i really appreciate these videos

I realized that you need a structured and logical mind (but simple and flexible schedule as you mentioned), including a lot of patience and persistence. Also, you can feel bombarded with resources, but if you filter down to the greatest minds, it'll make your learning experience less complicated and more in-depth. For example, I didn't understand Calculus in high school. However, right after I bought "Calculus: An Intuitive and Physical Approach", by Morris Kline, and things just clicked. The same happened with understanding logic generally, where I was confused until I picked up "Introduction to Logic" by Patrick Suppes. Dover generally has a lot of great science and math resources. The best to you all!

I'm 65 years old and have just started to self study the Blitzer College Algebra text book based on your recommendation. I studied some math in college 45 years ago (1 year of Calculus and 1 yr statistics), but I am studying algebra again as one of my techniques to keep my brain's neuroplasticity as much as I can. I do about 45 mins of algebra every morning, and I have to say I'm actually enjoying it. I'm also studying German. So between the two I'm hoping to keep my brain as nimble as possible and stave off dementia for as long as I can.

I think we live in the best time ever to self-study a subject. The internet and KZfaq give us access to more resources than ever before. (Ofcourse, the caveats still apply.)

The new ChatGPT 4o Education GPTs are pretty good for an assistant/agent. Self-study is going to change across the board for education. However, nothing beats the human interaction between a good instructor and student. Just my opinion. Cheers brother!

Just want to say you inspired me so much to pursue graduate studies in mathematics. About a year ago I was occasionally commenting regarding my self study streak (Which concluded at over 320 consective days!) in preparation to hopefully transition from Engineering to Applied Mathematics. I'm happy to share that I will be beginning my PhD in the new year! Please do your best to keep inspiring, sorcerer.

the one thing i find intimidating about textbooks is the number of exercises. there is usually a lot. dozens of them, actually, per chapter. i wish they were separated into 'required' and 'okay to skip for now' or something.

Senior developer here. I always struggled with trying to "get it" in school. What I should have done was to timebox, learn the pattern and let it mature until I'd hopefully get the "Why". I could easily have been the poor Feynman interviewer in the "Why" interview. Now I want to relearn math, thank you for the inspiration!

Self-studying. I've taught myself math even without textbooks and just experimenting. The issue, is that sometimes you make critical and huge beginner's mistakes that can go not corrected for months of years. You can be really good, but have a huge misunderstanding about an issue. It's why accreditation exists and why degrees matter, especially in a lot of places where the safety of people is concerned, like engineering or equipments or any other applications of maths. Studying is still good, and perhaps if there were forums or message boards where people could ask questions, that can help. That's unfortunately not too popular nowadays. You can definitely teach yourself algebra, calculus. The other issue is that you might need multiple textbooks, because as you would well know, Sorcerer, all textbooks have different strengths and weaknesses. Also a lot of the upper level math textbooks tend to be concise and esoteric and almost written in a way that only the few people can understand, like they don't want certain knowledge to be accessible. Like Einstein said, if you jnderstand something, you should be able to explain it simply. Anyway, learning by textbooks is time-consuming, but a great way to learn any skill. The best part is that you can go at your own pace.

I can think of a number of reasons to learn math in college: 1) If doing it yourself, you don't know what is important and will be likely to gloss over things you don't understand. 2) If taking classes, you have someone to ask questions abut what you don't understand, either the teacher or other students. 3) If taking classes, you have someone to judge your solutions to problems and determine whether you did it right or wrong.

I miss your youtube videos! glad to see you and thank you

I'll be turning 36 in a few months and I've always regretted my lack of math and, frankly, the lack of respect I paid to both the subject and my teachers in high school. I just didn't care for it at all. What little I did learn has long since atrophied to the point where even my arithmetic need to be properly re-learned. It's inexcusable. People have told me I'm wasting my time wanting to learn calculus etc. when I have no direct, practical need for it, but to someone who has never even grasped the basic concepts, it does seem like a kind of sorcery; magical incantations that allow you to model the world and express predictions. Time to crack open my dusty copy of Quick Arithmetic, I suppose...

Holy shit this sound quality is awesome

I love your math comedy videos. You have a natural talent and are very funny.😂

I am really loving this cosy background!

something that does help a ton with self-study is interacting with people who are passionate about the same thing. it inspires you and reignites the passion you feel towards the topic, and even if it felt dull before, it feels brand new when you just get out of your head and talk to people. hearing others talk about their love towards the topic cleanses you of any doubts you felt prior. sometimes you just need reassurance

Preach 🙌 setting up a system that’s easy to sustain has been necessary for me. It isn’t easy to self-study and work full-time, but habit makes it easier.

I love finding typos in problems. It keeps you on your toes, and it makes me remember the person who the book is human and makes careless mistakes like I do(but not as many)

I needed to hear this. Thank you 🙏

I just want to absorb your knowledge and experience without losing my hair, man. You are awesome.

thank you Dr.Jeff Bezos

This is an insane video. I've literally went through what you said just 2 months ago, and I've done heavy introspecting on it. Having a good reason is extremely important when planning to do anything for more than a month. If that reason/goal doesn't tingle your entire body when you think about it, you'll very likely not be able to overcome the burnout phase. I couldn't overcome it because my reason was shallow... Looking huge btw, keep the great content up 🤝 i love your maths videos but i dont comment on them, this one really hit me close to the feels

You really give me goosebumps! I have this problem right now, gonna keep grinding now. Thanks a lot! Btw, I've bought your Cal 2 on Udemy thank you.

This is absolutely correct. And for people who need college calculus for engineering, my advice is to self-study that book and solve every single problem before you ever set foot in the classroom. That is the way successful people do it. You simply cannot learn calculus at the pace they are going in a typical classroom. You MUST self study prior to taking the class. Just solve the problems as if they were crossword puzzles and you will absolutely ACE Calc I, II, III & IV.

I like the old math books for the reason that they tend to be quite rigorous in their approach to the various math topics and they don;t hold much, if anything back. Plus, the math itself is still 100% valid despite the age of the book. I have learned a lot of math via books ranging from books that are brand new recently published books to math books that were published well over 100 years old.

Nice camera quality! Love this look!

Take the classes if you can. If you meet the right teacher it makes so much of a difference. When you are done with good classes, continue on your own. People mostly just need some help to discover their own way to learn, the they can feed on curiosity and gain momentum on their own.

I feel so relieved when I watch your videos bc this how I do feel when I self-study maths esp graduate maths. The motivation really starts fading.

I wonder. Have you ever had a student who self-studied a course, and then after he or she attained a certain level of mastery, took a formal course in that very same subject? Why might one do such a thing? Because self-study is one thing, and self-testing is another kettle of fish entirely. One can study chess from a book, but until one sits down and plays an opponent, one cannot be sure how good (or bad) one really is.

Totally agree on creating a routine since we have a finite pool of willpower, and so with the routine, we don't have to use any willpower at all.💪

I love how you get goosebumps when you say something powerful yourself lol

I just started reading your book recommendation for beginner algebra. Your book lists are so helpful!

Thank you! I did engineering for a couple of years but felt voids in my fundamental understanding of math. I'm now reading a precalculus book, taking my time to grasp every concept and the reason behind everything. Really enjoing it. It's so different doing it to satisfy my own curiosity. My ultimate goal is to understand discrete diferential geometry for computational design and not feel I've hit a wall everytime an equation pops up when reading papers on the subject. Thanks for your advise!

Most of my self study of mathematics has been in the context of physics; for example, as a young student studying hybrid atomic orbitals, I encountered group theory, and so found myself delving into group theory. It's quite a common pastime for physicists, who tend to raid mathematics for tools. (Of course Galois theory is elegant enough to be enjoyed on its own merits, mathematician-style.) I remember Edward Witten, at Princeton's Institute for Advanced Study, being seen with a copy of Alain Connes' "Noncommutative Geometry" - a case of self-study, surely - and suddenly string theorists were all looking into the subject. Power of FOMO! I can think of so many examples of physics-initiated self study of mathematics: an interest in "magic numbers" in nuclear stability theory leads to a study of Ramsey Theory (which came about after a discussion with a mathematician friend), wanting to explore non-Gaussian scalable processes leads to study of Mandelbrot's statistics, etc. Certain pastimes lead naturally into self-study of math, I think: woodworking, origami, gaming, investing, and so on.

"You do not rise to the level of your goals. You fall to the level of your systems" - James Clear (Atomic Habits) We all share the goal to learn math and as you mentioned some "make it" and some don't. What differentiates these people are the small actions they take everyday to simply get better at math. Much like the example you gave of conquering the day by getting your math study out of the way every morning. In other words, as Brian Tracy would say, eating that frog. Another great video and always love these more discussion type videos.

In my school days, when I used to solve mathematics ' questions and see their answers in the answers, which are given at the end of the text book, I become very happy, when the answers were correct, and become very sad, when the answers were wrong. Like my comment who all have experienced like this in their school days.

I've been learning Korean for about 14 years. Everything he says is true. Motivation is really hard after the beginning phase. You have to have some routine, when it's all just mud in your mind. What does everybody seek: some skill for not much effort: business, money, languages but it just doesn't happen like that.

You're helping me a lot

Thanks Math Sorcerer for recommending How to Prove it by Daniel Velleman... I'm self-studying math proofs, logic, and set theory using this book.... Doing it daily for an hour or two. Currently on chapter 4 on Relations. I carry that book with me everywhere, with a notebook for exercises. It's so much fun.

Self studying olympiad mathematics has been such an endeavour from me, but yet I'm still motivated by your videos to keep gping, thank you!

My biggest piece of advice is learning to understand concepts and ideas before learning the process and application. Don't start with short readings and problems - that's a pit fall a lot of people fall into. Don't be afraid to start with the very basics, and don't be afraid to question. While mathematics is a very technical field, with a lot of rules and techniques, the core fundamentals stay the same throughout. Question why it is we do things the way that we do, question the stories of the early mathematicians and their ilk, and then apply it in what you already know before starting the newer work. It's boring, but I guarantee it'll help a lot. Many people can do maths, few people understand it, and even fewer know the reason why we do specific things the way that we do. Understanding maths like a language is far more important, I've come to learn, than completing something quickly

I started out in college as a physics major, and I tried to do a math major when that failed, which only lasted another semester before I switched to Political Science. Being in college as a teenager just wasn't the time for me to excel in math. Maybe it had to do with effort and organization, but I think the pressure was sort of an insurmountable factor at the time. I'm not self-studying math at the moment, more so reading books on logic and philosophy of mind, but the idea of self-studying math at some point is really appealing. While I've found a field and a career path that I enjoy outside of math, the initial appeal that math had - the search for truth - is coming back to me, and it feels like I'm reconnecting with myself in a way by becoming interested in math again. Doing so without feeling like my whole future depends on it just seems much more reasonable.

Mr. Sorcerer, you are goated.

This thing touch me directly, I am a self-tough in a few topics, mostly mathematics, I did not go to college and my father is retired from collage-teaching nowadays… and even him in some point agreed with my decision. The fact is in my opinion that in middle of XX century in a little village of a developed country you could not self study a good level, much worst in a country without mathematics tradition. Now, with internet and the right indications from outside and inside academy you can be equal or superior formed like in universities from any part of the world. In my opinion, with free KZfaq content, a few good books (choosing it wisely) and internet free applications (calculators/tests) to exercise, consulting encyclopedias to ensure you do not reinvent the well and most important enough time to really focus in study... you will be fine, more than fine. Good luck everyone.

Watching your videos motivates me so much! Thank you!

A professional math class taker...you remind me so much of my friend Ryan. Dentist by trade that has three PhD's in math based subjects. Our first conversation occured in 1999 about Strum-Liouville equation.

Your videos are the best videos about math, actually. I study math because I have a hunger for it. And the morning is the best time of the day to do it that’s true

I took some classes and started collecting the workbooks you suggested along with some Shaum’s books. It is so fun rn being on summer break to know enough to sift through them. To start on chapter one and proceed to the next chapters when I get bored of the previous bc I actually have no stress and only time rn to grasp it and work on a manageable amount of problems. I hated school last semester but taking a break and being able to breathe into the math books I choose is so much better. I like math more than piano rn. That is the opposite of last semester 😂❤ PS. I love when you smell the math books, I am not alone on this! Are there more like us?? Hehe PPS. Thank you for speaking about burn out. It hit me so hard last semester to the point where I had to find resources. Things got ugly 🤦🏼‍♀️ so no. Not that random. Pretty relevant❤

The beautiful advice in the video transcends beyond studying maths, perhaps applicable in all the aspects of learning and life. I am a medical student and maths comes much less often less than any other field but I always adored the mathematics in me and you have helped me to keep that interest alive. So thank you for your advices, they do mean a lot to people like me. Keep going, keep growing. Best wishes!

I'm lost, thank you for making this video. Your efforts are appreciated.

I majored in math in college and enjoyed the experience, but self-study is the way to go in my opinion. The only book we completed cover-to-cover (and it was over 1000 pages) was the calculus sequence, but that was over 3 semesters. No other math course I took did we come even close to completing the whole text; hard to do anyway in a one quarter or one semester time frame. With self-study you can take things slower and cover everything in the text, if you're interested and motivated enough. I've done that.

you have more passion and will - making studying and comprehending faster/// college is more formal, that's why college is garbage (if you have relations or are rich, you can pass any college 'paying the right people'), if you're a normal person like all of us, then taking correctly college exams is a challenge (not in math, but in all the fields!). Conclusion, self-study - your pacing + self-will (not imposed for passing an exam or getting a specific grade), diminishing anxiety and concentrating more (you learn more about yourself) ... I think the future of education should be 'DIY' than 'official institution that make idiots with diplomas - see the new generations'... Conclusion 2 - combine videos, books, notes etc. the more senses you use, the faster you will learn... cheers.

You are such a constant source of inspiration. Thanks for what you do.

I've just finished giving some exams so to go to a university (its a thing we have here in Greece idk if its the same somewhere else). I was waking up in the mornings and within half hour I had grabbed my book and I was reading theory/solving exercises for 4~6 hours. That were happening for 9 months straight (exept 3~4 days). Now that I have finished I almost feel weird for not studying (like I felt at the begging having to wake up and study). My advice is just not think about it a lot when you wake up. You 'll end up procrastinating. Make a study plan. Write down your goals and the time you are willing to allocate to complete them. PS. Math Sorcerer I can say that you were the person that motivated me somewhere in the middle of the year to wake up and grab the book to study. I really appreciate that. You are making really good videos and really motivational some times.

On time! Thank you❤

my biggest enemy in learning anything is impatience. i tend not to do enough exercises for what i am learning and keep trying to move forward. i found that school classes, more precisely online classes (have not taken an in person college math class), made this problem worse for me. you have to keep up a certain pace and the way the assignments/exams are set up i detested strongly. i would agree that self study can be better for you if you possess a strong self-discipline and know a little bit about learning as well.

That's the funny part. Conventional school does not work in my favor because of the way I learn. If a professor tries to vocally explain something to me, I process around 20 to 30% of the information I'm being told. Whereas if I actually sit down and read and re-read and then look up explanations and videos, I process 100% of the info. Students are a burden to me because I tend to work solo. I dont use the other resources the school provides and I would find it too much of a hassle to get a tutor. So more often than not it was just me and a book. And I got real good grades.

So helpful, it's just good to be reminded of these things once in a while. Thank you ❤

as a person who is trying to self study... a lot of math recently, it's kinda goddamn hard. resources are hard to find for free or even cheap, i don't know who to ask for help unless someone on youtube has done it, and the motivation itself is hard to get. But, it's been somewhat fun, trying to understand things completely. I think it's gonna be fun and worth it, which is why im doing it. haven't watched the full video yet, this is just my initial 2 cents.

This page is amazing just amazing!!!! I was reading measure theory today and was so confused and lost my motivation. This is just coincidence but this video was helpful! And one more thing, Im not math student but self studying math and the motivation is at some points learn geometric analysis and become expert in PDE. I think math is the language of nature and learning one page of it helps you to talk with nature. So so so much thanks for your videos!

Thanks for that advice! It’s difficult to impose discipline, but a regular schedule is obviously very important. Perhaps most important. Thanks again.

Thank you so much for your video, ive been struggling with self-studying but i do definitely think i need to be patient with myself

im not currently taking any maths classes in university right now, maybe its a bit of maths here and there , but this video and others are transferrable to other studies. i think this is one of the channels relating to education , studying and maths that i will always come back to . and this is coming from someone who hated highschool maths and never thought about looking at them in university lol

Love these types of videos

Talking about easy math books-for me, some Calculus are surprisingly easier than others. I don't like saying any math is easy. But I think Calculus books without trigonometry are easier for me. I mean, Calculus by Marvin Bittinger is easier for me than Calculus by James Stewart. I have the 1 semester 8 chapter version of the Bittinger book. I try to keep a routine too. I do dance workouts and lots of walking as part of my routine and exercise. I did about 15 math problems today. Working through the most simple math right now: adding, subtracting and multiplying polynomials. Its so simple to do. .For a challenge, I do some calculus later tonight

The school environment is great for some subjects, but I think that's more due to the structure. I utterly failed at mathematics during my time in school, and developed all types of math anxiety over that. It wasn't until I decided to give self-study a try that I even began to believe I had some hope. It must be taken into account that the ways of teaching math ( and a lot of other subjects ) is probably much different in the 2000s than they were back in the 1970s.

I am math teacher and I am learning CS. I watch for motivation. Thanks! Hello from Togo.

Actual class time is beneficial for the tacit knowledge you get from a real teacher -- not just the material, but what is important, and why.

I have low tolerance for frustration at this moment and on my past, and I really struggled with going on without motivation, my brain always tells me to leave it and give up, it's hard work, but I'm working on it and learning to shut down that part of my brain that keeps seducing me to distract or to succumb to vices, fuck that great video really resonated with me

Regarding topology, I've just bought a book from Hilton and Wilie on algebraic topology from the sixties that assumes absolutely no previous knowledge and I will use it to teach myself the basics of topology needed to understand another book on rational homotopy that I bought on a whim before.

if you just follow the motivation, sooner or later it will disappear, and you will give up. I think creating a routine and sometimes doing things just for the pleasure of learning new stuff is essential. subscribed:)

I hope you get a million

As a physicist, when looking to learn QFT and high energy physics I found myself shat in the face with high level differential geometry, group theory, analysis, and some algebraic topology. Its taken nearly a year but through self study I’ve been able to just grasp the key things. Diffeo isomorphism still tricks me though

Thanks for the video. I needed it right in time.

I feel like university study gives me direction, but admittedly you do need to learn it yourself. It's sort of the same with CS. Near impossible to learn without direction, but to get the most out of it, you need to put in the effort yourself.

Your absolutely right but books can help for things you didn't see yet but absolutely you yourself will learn more doing it yourself and you'll always need something to compare it to and for me it is always the question😊

new camera? loving the new look!

I spent a full night on night shift at work, when I was working on the autonomous drill ( I could stufy and work) I had no one to talk with and no internet service and could not for the life of me figure out how to expand brackets. This was my first course for math at entry to uni so I had forgotten so much from school and that night fucked me so much and the answer was so simple. I then figured out that I cannot just study without help or a good guide to show me what to do with examples of a good explanation.

I have to self study maths for my work. I find that being able to explore while under some pressure from work keeps me moving forward.

First thing in the morning to study math. This is very important. I lived an accidental experiment taking a math course that I can not even remember at this moment. If I attended the night class VS studying first thing in the morning before work the difference in my performance was shocking to me. By the end of the semester I figured that fifteen minutes studying in your underwear before starting the day was worth more than the three hour session at night school, a lot more.

I love your videos nice teacher!

When we lose motivation we listen to the Math Sorcerer! ❤

I feel like this applies to self-studying things in general, not just mathematics.

You look like a rock star from the 80's !

You have to study "on your own" anyways because only you can process the information and translate that in your system. Might as well learn it this way. Sure sometimes it can be cool and enlightening to talk to a peer in the field but most of it is within reach if you have good resources.

The reason I tend to finish my hobby software projects is the goal in my mind that makes me never quit despite heavy burnout. Those goals are sensible and I'm able to think about them. This is not the case for learning math at least for me personally.

I think i failed 090 or 099 college algebra 6-8 times before I gave up. And this is not an over-estimate. It wasn't a result of it being too hard, it was a result of me going to class a couple times, procrastinating on the work, getting behind and eventually crushed by the work needed to catch up and dropping the class. Over and over and over again I did this.

I have a textbook about astrodynamics and space systems engineering. It has lots of math in it. When I was younger I struggled with math, but my interest in the subject matter has given me lots of confidence in understanding math.

I think that it's true, to learn anything well you need some kind of external resources eventually, but there are some hidden benefits to self-studying as well. Primarily, I don't think I could ever be successful in mathematics if I were to go to school for it, particularly because when you go to school to learn a subject, you are not just having to learn the subject, you are having to learn the subject on a time limit and are somewhat trapped learning specific things. Self study is great because it allows a person like me to take as long as I feel I need to understand and enjoy what I'm learning without any pressure, and at any point I have the option to go off on a tangent to look harder at the things I am interested in because there is absolutely nothing to lose in doing so. Furthermore, many professors seem to have no issue if you as an outsider ask to sit in on their lectures. I mean, you aren't paying so you're not going to get a degree or anything, but if you just sit in the back to listen in, I don't think most people have a problem with that (also considering that if you have questions, you might want to hold onto them to research yourself or ask when everyone else is gone so as to not take any time away from the paying students). But it is very interesting what resources actually exist for self-study when you really consider what you could try. I also wanted to say thank you, and that I enjoy your videos a great deal. I have started on one of your recommended books (discrete mathematics with applications by Susanna Epp) and as someone who previously disliked math, I am enjoying working through it quite a lot.

Looks like it's a new camera congrats ! Excellent video btw

its cheaper than college you can hire ur own personalised tutor to get personalised help , there is no deadline so you can learn at ur page rather than cope learning or rote learning .You also choose to just learn what u are interested and you dont have to delve into modules you arent interested in .

My self study "routine" is to write x units of 30 minute math study blocks onto my daily "to do" list. Then I set my timer for 30 minutes and work until the bell. Then cancel that from my "to do" list. If I do more than I planned, I add those as I do them and strike them off. I try to do two every day. Using a timer helps me a lot to complete if I'm bored or to stop before I burn out. I'm usually not bored by it though. Anything counts for "self study" - working through problems, reading in a book, watching videos... .

I remember that we had to offer math courses in the engineering department as the students would come back with too many D grades from calculus and linear algebra courses from the math departments

My goal for self study is to become a n amateur number theorist. I am currently almost finished Blitzer’s Algebra for College students.

Thanks for this video. I think a very big problem with self studying math is lack of universal and standardized certification. Let's say I want to move a little ahead of my math in college and study intro. to topology, and I crammed for 6 months, finished the book, all the exercises and everything. I have nothing to show for it to the outside world, because as far as I know there's no universally accepted certificate that says this person has completed this portion of math within the generally accepted hierarchy of math that I can put on my CV. So outside of the high tuition high cost world of academic degrees, there's very little to prove that a person has self-learned that specific subject at this time. Don't get me wrong, I love math even though it has tortured me a lot sometimes, I would study it even in prison (hypothetically), but there must be some record of achievement beyond the pleasure and at the moment I don't think there is.

I needed a break for a while from math. It mystifies me what I remember and what takes a long time to learn. I backtrack and try to find a point to restart from. My intention, as a senior, is to get to a point where I could do, what you call, college level math.