1. Self study is fun and self guided 2. You're not being told what to do or evaluated for a grade 3. You remember things you read on your own time better, more personal 4. It sticks with you more 5. It makes you better at learning how to learn 6. It is rewarding and you can look back on your accomplishments

Discovering this channel is definitely one of the best things that happened to me this year. You are so passionate, keep it up!

I strongly believe that self study becomes invaluable when you realize that what you have been taught isn't enough.

Self-study is more fun. This morning I was doing a Fermi Problem in a physics textbook related to a pile of gold. I had to look into a calculus textbook to find the volume formula for a cone. I used it to solve the Fermi Problem and I got a close approximation to the actual answer. Self-study is like research without a deadline.

Totally agree! I failed Maths throughout Highschool, I hated it, I did not see any point in learning it - until I decided to study Engineering in University. Suddenly, I saw that soo many things could be done with simple maths! I still failed once or twice, but I least I did not feel repulsive by seeing numbers anymore hahaha

I just recently got back into college. Prior to that I spent a year teaching myself algebra. This semester is ending, and Im going to walk away with A's in two algebra courses I took simultaneously. I could not have managed that if I hadn't studied ahead of time. Im now using the same strategy to prepare for Trigonometry and Calculus. I am having more fun now than I have ever had in my life. 10/10 would recommend self-study.

I started self-learning topology a while ago, and boy!! What an amazing experience! I'm sure as hell I would'nt have enjoyed it as much if I was taking it in school. There's something about self-learning that makes it a unique and memorable experience; no exams, no pressure to finish this part or that, it's just you and the book in the entire universe!

My opinion : Self study increases our intelligence because we read , and reading makes us trying to understand and process the ideas . Moreover , while reading we try to understand from our own perspective which may be different from others , which is important because we can't understand everything the way others understand.

I self study not only for the sake of learning, also for enjoyment. Through self-studying, one learns self-reliance and learns to use own initiative.

I can't explain how much this video brings me joy. I pulled my struggling student from public school and began to homeschool her. Math was her nemesis, and just the *thought* of doing math was a painful experience for her. I found the perfect spiral math program for her and began to allow her to take control of her lessons, even grading her own material (with supervision). 2 years later as a 6th grader, she reads over her lessons, grades her own papers and redoes her own problems..and is excited to do so! Math has transformed from being something that dominates her to something that she takes ownership of. This confidence spilled over to asking daily to work on logic puzzles and reading classic books with vibrant language. Now she says she feels her brain feels like it's always hungry for more challenges. So, self study being the key to success in learning math?? 💯

Learning for the sake of learning is the perfect way to learn. When you finally solve the maths after 1 hr! Its undescribeable that kind of feelings you had. ❤

I am studying math with programming (algorithms) every exercise I work on it, I repeat it step by step with whiteboard or pen and paper example of writing an algorithm to calculate digital root after completely undErstanding the problem mathematically, imagine every math problem is converted to step by step algorithm and based on problem solving steps of an algorithm, your level will skyrocket. The most important is studying from beginner to complex level gradually and do not jump to the next level if you are not confident of your self. Studying math and algorithms together helps you to pay attention to details and this is the key to understand math.

I discovered self study very late but one thing that I immediately noticed is that you shouldn't read book on a pdf on a screen it will tire you eyes and brain I swear. The pleasure to have a book in your hands is something. And your eyes won't get tired as much as on a screen. I even bought books that I already had in pdf

I remember deciding to learn German about 11 years ago. I went to a Barnes and noble and picked up a random German course book and looking at the words completely intrigued and in the best way bewildered, thinking ‘one day I will understand this no problem’. It took a lot of work and investment, almost giving up 3 months in after studying for 3 hours a day and still being confused at a lot of things. I kept pushing regardless and I’m so happy I did. After that experience l know I can learn anything and now I’m teaching myself how to program and delving into math as well. Keep going and put in the work and it will pay off. The best part is it is it’s a gift you give to yourself.

I once read in a book.."Maths are the greatest collective intellectual endeavor/achivement of the human race". There's a feeling of satisfaction on solving math problems that no other intellectual activity can fill. There´s a feeling of wonderful joy on looking a notebook fill with numbers, graphs, ecuations and blots.

I think what really makes self-study an op tool is: you're not supposed to do it the system is made around people that just stick to the minimum and pass classes barely, that's when someone who really do put the effort shines and make everything he/she wants just knowing the sacrifice, effort, consistency and discipline it requires it's really amazing and I love it

I don't know why, but you guys (mathematicians) from the US and Europe are so brilliant. You definitely know how to awake people's interest in math

My choice to sit and do maths, physics and chemistry was seriously worth it. And finding your channel motivated my math side of the brain, thanks!

one of the things i've learned while studying math is learning the rules instead of the methods to solving equations and then thinking about why the rules work makes math easier.

I set a number of pages to read everyday. It's my goal to read every page of a book. I write down the date on a notecard everyday I read. Limiting the pages I read keeps me from burning out and reading to much in a single day. It also helps me predict when I will finish books. When I get excited about math after reading for the day, I look for new books and applications. I have successfully completed over 50 books with my method. It took me years to be a successful self studier.

Yes its great to self study/self teach especially before you take a class. Learn the material before you take the class and you will do very well.

One of my New Year resolutions is to teach myself Math. When I was attending college you couldn't enjoy and appreciate the stuff you learned because you had to rush through all of the subject material. I always found math fascinating and looking forward to learn the subject at my own pace. Thank you so much for your educational and inspirational videos. Keep up the good work!!

Trust me, I have a silver at the Asian Pacific Math Olympiad and I did everything by myself. I am trying my best to make it to the indian team this year. I can confirm that self study is the best option atleast for math.

Self-study has formed the greater proportion of my math education. I was a poor math student in high school and college, and became interested in the years before I began graduate work in Slavic languages. I had to learn all the math I'd forgotten/never learned in order to be able to take classes at the university where I was working at the time, where nothing below calculus was offered. A book I read at the time, Ivan Niven's Numbers: Rational and Irrational (New Mathematical Library 1), showed me how to write proofs, which was like being introduced a whole new way of seeing the world. While in graduate school, I completed the equivalent of an undergraduate math minor, and continued to learn math intensely through self-study for several years after finishing the PhD. One thing I have found rewarding has been to keep all the work, proofs, thoughts in a series of solidly bound notebooks. This means that I have a chronological record of the work I have done, a kind of narrative of learning. I taught high school math for several years, and more than once had reason to go back into these records in order to enhance something we were doing in class. Those math notebooks are among my most precious possessions: they are like photo albums of my journey through math.

I can relate a lot. As a Chemistry student I used to know a lot of people who aced exams but couldn't do anything on their own inside a lab. While I was always getting around 6 out of 10, but I was the one teachers looked for when they needed a student to work on something. I barely know any chemistry at all, but I do know a lot more than the majority of students in my college that used to ace exams. It's hard to find some time to read the textbooks, you have a lot of classes, a lot of homework, all at the same time... But the teacher classes are usually their notes, the summary of a textbook, and their slides are the summary of the summary. When students think it's enough to just watch videos or attend classes, and to take notes of slides, they're summarizing the summary of the summary, that's why students often don't know anything at all, they're full of incomplete pieces of information, they don't really have any knowledge. The book is where the complete knowledge is to be found, all the other pieces are there for you to build the knowledge. If you want to be approved, you can attend classes, but if you want to learn you need to self study and read the textbook or a journal for new fields and recent discoveries. The problem is that you do need to be approved, and it's hard to balance attending classes and self studying time. Unfortunately education, at least in my country, are ignoring textbooks more and more, now even teachers don't have complete knowledge about the subjects anymore and actually they're already teaching things wrong in high school. It's a snowball effect in education, my country is already hopeless.

Also re self-study: that's mostly how I do it at present, and as an extra bonus I have a low-grade (so-called) job rounding up trolleys in a supermarket car park combined with some till work, and the former activity especially gives me time to think out mathematical problems and issues in depth. I think The Math Sorcerer's right - self-study is the ideal way to go off on profitable tangents. For instance working though Stephen Abbott's 'Understanding Analysis': one of the exercise questions sent me pursuing Dedekind cuts, and to understand that better, go on to least upper bounds, dense order, construction of real numbers... more reading around than necessary for answering that particular question but still very interesting! I read books, Wiki and other articles and watch videos. The ability to stop-and-start at the click of a mouse is magic - it transforms watching videos from passive gawping to very active. The minute I can't quite see how the presenter gets one of his results I pause the video, then either think it out or look up the topic on other online sources or a book, then start again once I'm happy I know what's going on. The best thing though about maths is being able to share it face-to-face, a bit difficult at present but not I hope for much longer with vaccines coming on stream. I went through the famous chessboard doubling-up problem with one of my store's cleaning staff who said she'd never seen or understood maths in that light before (comment on how it's taught I fear i.e. time pressure), and the volume of a barrel (the sort that looks like a wine keg whose sides curve outwards, not a straight-sided cylinder) with a recent maths 4-year course graduate. Explaining to someone else is one of the better ways of checking the soundness of your own thinking! Kevin Houston in How To Think Like A Mathematician strongly recommends it. The Math Sorcerer's video discussing the time it takes to learn mathematics properly is I think bang on target. Concepts like logarithms, 'e', the ubiquity of 'pi', the real nature of infinitesimals to name but a few take time to sink in properly, time unfortunately not made available on school and college courses. 'Sticking to you' - I still remember the penny dropping re the characteristic function of sets several years ago. For a long time I'd wondered why the cardinality of the powerset of X is 2^(cardinality of X). For instance the cardinality of the powerset of X={A, B, C} is 2^3 or 8. Then as I was pushing a row of trolleys past a pub (bar in the US) which shares our site the penny dropped. Either an element's in a set, or it isn't, i.e. a yes/no system. Bingo, binary like the OFF/ON elements in computer hardware, counting base 2, hence the link with 2 to the power something! And that insight's remained with me ever since. And yes, I also taught myself how to code - not 'C' however but Basic via a Sinclair Spectrum. I drew up a drawing package using vector graphics which also included a very basic modern-look font (caps only) and a FILL routine... all great fun! Also a primitive word-processor which did 'find and replace' - very useful for job applications: although I couldn't print to an acceptable standard, I could still do all the drafting on-screen, then copy by hand from the screen.

Maybe in grad school, one can get away with this, but I never had time to self-study or to let the information I was being forced to study marinate. Advanced math for me was just an extension of “plug-and-chug.” I’d learn whatever technique or memorize whatever proof I needed to pass and that was that - very little deep understanding. That’s one major complaint I have with the way mathematics is taught in the university setting.

I'm still somewhat young, but am hoping to go to waterloo for math. I found an old calculus book a few days ago (also has some linear algebra stuff in it) and have been going through a chapter a day. Taking 2 to 3 hours a day and just going through the stuff during winter break has just been cathartic. It's always a pleasure to learn (or relearn) a skill -- I felt euphoric after figuring how to integrate by parts this morning :)

I also taught myself to code before going to college! It was on a TI-55 programmable calculator (it was 1979). The small amount of memory meant that I had to "invent" indirect addressing and other techniques like that for myself. As a result of those few weeks of learning for fun, I was way ahead of my peers before I started college, and stayed ahead for the whole time.

When you're self studying you're both the teacher and the student. You have to he extra careful to get things right and this kind of engagement engraves the knowledge in your mind.

I have always preferred self studying than someone else teaching me. The whole concept of it makes me feel smarter. By the way, I bought your Udemy course and it's awesome!!!!!!!

Another good thing is you get to choose the instructor. In a university maybe you can choose from 2 lecturers. On the internet/library you can choose the highest rated, best seller, who explains things simply, and engages you.

I see self-study as learning and classes as accountability for that learning. Sure, classes provide you with a source of information, but we learn because we put in the effort to really understand a topic, not because someone makes you regurgitate a bunch of info. E.g., no one learns linear without taking time to build their own mental picture of a vector space and some transformations. I'd also note that if you're in a class and you leave each day understanding 100% of the material presented and you don't have to do any self-study, then you're probably in the wrong class.

One this is Amazing.... self studied material stays with you as it has a bonding with you... you taught yourself🥰

for me self study starts with reading books and asking my elder brother. this is 50 years ago :-) Today self study is internet and youtube. It is always good to have people to discuss with. Today I am study about finite loops (groups without ass-law) and second is 4D space. We can't understand 4D space, but we can thing about how it works. What is spoon, knife, fork, bowl, table, pipe, wheel, car in 4D. what is a painting in 4D what is a script look like?. I just start programing a game: moving yourself and playing with blocks in a 4D word.

I relate to a lot of what you said. I also remember bizarre things about the books I've read. Like when I was self-teaching differential Geometry and the author said "this formula looks complicated but to convince yourself that it isn't and how useful it is let's use it" to which I replied "sure" and then did it and it was very cool to me

Wow! You pretty much summed up my entire community college and University life at 2:58. I can't believe there are others like me, who would rather learn other things when they "have" to take a class.

The joy of self study is really great and awsome in any topic in particular in my case in math, the pleasure has no price and that give the strenght to continue to go deeper, but I see it like a tree, the main branches are given by an undergradute plan. (My particular case is undergraduate)... "The joy is in the detail". And as a cliche "The top of one mountain is the bottom of the next, so keep climbing".

I think you need a growth-mindset and wanting to learn for self-study to be “effective.” Otherwise, you may question why go through all the effort of doing so.

This is such a great channel ... this is totally the way it works ... and continues to work until you're 120 (if you're fortunate) ...

Happy New Year! Your channel is a breath of fresh air, *I* thought I was weird for liking to sit down in my free time and pick up a math textbook to work on. I relate to everything you said, and just to add a few things from experience: What I did by self-study the past few years wasn't necessarily studying something else. I'm in my last year of high school, but since two years ago I made a habit of going ahead of class with my own learning. I'm more of a "see it once and remember" kind of person, and my teacher likes to dive right into the hard stuff from the beginning. So it started as a necessity, but then I got back my passion for Mathematics when I taught myself the basics of a topic and let institutionalized learning take its course. I've always been this way to some extent, and always wanted to know what the next big thing we're learning about in Math will be, next year or so. That's how I understood the concepts of calculus (not able to solve the problems, but had the logic) before high school. Now, my next goal is taking up Linear Algebra and Advanced Calculus to make it easier in university. Wish u the best, sorry for the long comment lol Edit (I struggle with this too): if you're one of those people who can sit for hours on end and just do math, amazing. But remember to take short breaks every half-hour or so! Helps a lot

"Enjoy the formulas" reminds me of James Stewart calling calculus "intrinsically beautiful".

I really get motivated after watching your videos. I feel like one can achieve whatever they want. Especially through self-study one can learn everything.

It''s new year in a few hours! I'll start doing this a bit more :) Good luck everyone else on your goals! EDIT: Completely agree with the video. Tip for self studying: don't skip anything. I know it sometimes may be tempting. The feeling of "Oh just a bit more and I'll be learning partial derivatives!!" but try to enjoy the moment, not just the expectation. You can't know partial derivative without derivatives etc. So just hold tight and try your best!

Dude, there is more than math in your channel, it is pure educational!!! Math is so enjoyable, it is like poetry and nature. it is learning our own minds in a pure abstractional way and so efficiently being in Nature. Math is the essence of everything that is awesome!!!!

I am 71 years old. Some people do crossword puzzles for entertainment and that is fine, but I like studying math and working out math problems. So much more rewarding to me.

just so true. When reading books by myself, I go a little bit slower, but takes more time to think and understand deeper. And the class stuff seems simple as surface touch of the contents

My suggestion for anyone is just do it and you will really get addicted to the progress and knowladge you acquare through your own will, be it from online videos, books or both. It doesn't really matter!

Self study is the the best, I appreciate the advice on self study because some of the tips are actually how I study. Sometimes if you don't understand a certain material you need to have at least two or more materials on the particular topic because some materials are explained in a language that you can not understand. My advice is that when you read a math material you would not understand some of the terminologies in that material so you can read a topic and try to compare the the terminologies use in different books that way you would broaden the way you understand math.

Great. I believe that when we have a pure mentality of just learn, without streess and the obligation of a test, that makes us have pleasure in learning!!!

Probably what I will say next is already known to everyone, but if someone does not know, it follows. As a self-taught person, I learned that any exact science study, perhaps any discipline, should be done in a quiet place without distractions (there was already a video on the channel dealing with this subject). In addition, I always got better results when I took at least three readings from each chapter. First I try to have an overview and, therefore, I do not dwell on details or further reading. The second reading aims to understand how the sections of the chapter connected and solved the examples for me. In the third reading, already understanding the general purpose of the chapter and how things connect, I dive into the details and summarize what I studied. In that last reading, I solve ALL the problems. PS: All readings with pencil and paper.

I have the same strategy like you. Reading as much as i can and watching math videos from the math sorcerer and Dr. Peyam is way more beneficial than my university classes.

Self-study is also mission-critical for life after school. When you have a job, you will be faced with learning new skills (quickly!) as part of your job assignments.

Thank you 1. Self study is fun and self guided 2. You're not being told what to do or evaluated for a grade 3. You remember things you read on your own time better, more personal 4. It sticks with you more 5. It makes you better at learning how to learn 6. It is rewarding and you can look back on your accomplishments

Active mindset with assistance of a teacher makes a rockstar. You should not listen to what the teacher say, you should make him or her explain. That's the beauty of learning.

This channel is literally the best channel for math. Advices, courses, damn this guy goes hard at math and I'm loving it. Thanks for the videos man, really appreciate it.

I was never the biggest class attender in my undergraduate. I went enough to know what was going on, but I did so much self study in my engineering undergrad it always put me to the top of the class on exam day. This is so spot on. Self study makes you construct knowledge for yourself.

I wish this channel (and KZfaq!) existed 20 years ago, when I was in high school and struggling with a lot of questions like these. Sighs.

Your comment about always wanting to study something besides what you are currently taking a class on really resonated with me. I thought that was just me, I’ve never heard anyone else verbalize that. Great video

Why I love the 'self study' concept: *True Mathematicians are curious by nature, hence we need to continuously expand our horizons *One could CHOOSE to specialize in a particular area / field OR *Explore unknown territories to broaden skill sets & take on challenges *Sometimes long after taking a particular course, one might find some new 'Gem' to renew interest & delve further into said discipline *& as an ardent admirer of 'The MS' background Library, I can personally advocate with 2 Math Degrees that...reading (Sci/Math) Textbooks is FUN, when the material is to your liking & choice!

Right now I am trying to better my mental math!! 57 and I do math for fun, love math. Some people do crossword books I do grade 2-5 math books right now. I Never use a calculator, love figuring it out! 😁😁😁

My tip - Try to write a guide explaining the topic as you study it. The forces you to explain all the thing happening in the topic and if you can't, you've found a gap and you can go and read up on it until you've learned how to explain it. It do this. Once it ended up as a published textbook.

1. Studying the definitions and theorems and working out example questions before looking at the solutions provided. This is more fun and can help a learner come up with different methods of solving the problems. This also helps the mind to be more creative and explorative, than merely going through the provided solutions. 2. Working Math problems back and forth. One of the greatest things I have learnt as I study on my own, is that studying problems back and forth helps to grasp the material better and easily apply it in answering assignment questions. It also helps to build my confidence. 3. My best pleasureable experiences have come not as a result of attending math classes, but as a result of reading and studying on my own. It has helped to have a deeper and clear understanding of topics that i barely knew. The moment I come accross text that explains things well, my heart lips for joy and I thank God for books. This experience cannot be compared to anything else.

I took an introduction to advanced mathematics course last summer and we ran through formal logic, truth tables, proof techniques, etc in 10 weeks. I was way too busy that summer and didn't get the chance to internalize the material like I wanted to. This summer, I don't have much going on so before I jump into self-studying analysis and abstract algebra I'm reviewing everything from last summer, and I'm glad I am! I'm finding it very enjoyable and it's extremely rewarding to fill gaps in my knowledge and build a strong foundation for my understanding in mathematics. Sometimes I'll get stuck on exercises or examples for a period of days, but even getting stuck is becoming quite enjoyable... I'm shifting to a state of mind where I am constantly digesting a problem even if I'm relaxing. I typically read and take notes until I find myself getting stuck, and then I recognize it's time to take a break. In a matter of hours I'll have my first idea for how to attack a problem, and it doesn't always work but I'll give it a quick try and step away for a while. So far, there's no problem I haven't been able to solve in my reading.

1-Fun. 2- More focused. 3-Time to read by yourself. 4-Everything stick with you. 5- Makes you better at what you're studying. 6- You can look back at what you've learned.

Hearing lecture from video and going to class tends to be passive learning (we're hearing somebody doin it but not us doin it), But it's different when were self study, our brain actively trying to connect things that we read. Doing problem is an active learning too, but self study reading laids the foundation for new materials. Active learning is more memorable for our brain, so it tends to stick in the memory longer.

As a math teacher, I recommend math learners to rewind, meditate and implement these 6 golden tips. If I may add, I would also insist on one important point while self studying in order to render it more attractive and efficient: 7. Challenge any established key theorems: interact or communicate to the book: e.g. why the pythagorean theorem works for right triangle on a 2-D plan, why not on a sphere for instance, etc. By doing so, you rootely understand the meaning of each necessary condition, and at the same time you expand your math knowledge. This 7th point enhences math learner's ability to spot quick countet-examples in mathematics to refute a conjecture, for instance. Don't forget, that proof by counter-example is very powerful in mathematics. THANK U FOR POSTING THESE 6 GOLDEN TIPS. And Happy New Year To All Math Lovers and Learners.

I love self-study because I can fill all of my gaps in knowledge. When you're taking a class, you can't do that, you can't go at a slow pace and identify/fill gaps in knowledge, because you're on a set timeline. With self-study, you can do those side-quests, and come back to the original topic you wanted to learn. It is incredibly wonderful, when you can gain an intuitive understanding, and self-study helps you achieve that.

I self study by working on homework problems suggested by the instructor. After 2 semesters I realized that going to lecture was mostly a waste of time ,and it exists to justify the professors salary. Professors who don't care and professors who want to inspire people try to do a good job, but it just never benefitted me intellectually. What really helped was using the theory myself and making it truely my own. I highly reccomend just studying off of instructors suggested or mandatory problems (these are the problems and concepts they expect you to know in and out in any shape or form), and if you have the luxary spend more time studying other problems you can solve using the same theory but with a different approach. Self study is very difficult and I found that utilizing office hours, online resources, your classmates, whatever it is will be necessary.

Self learning must be prioritized. School programs must guide students into self learning. Adults must make space in their life for self learning. This kind of videos do much as many people have no idea about self learning. Thank you.

I directly upgraded my work, hobbies, degree, and knowledge by tackling Kahn Academy at age twenty-five. I finished my bachelors in computer science, work as a contractor in multiple languages (I smiled when he mentioned teaching himself C), and I absolutely love math. It's unfortunate that more people don't take seriously the resources available to us. The quality of free content is absolutely mind-blowing.

I would even go one step further: If you can’t teach yourself math, you shouldn’t major in it, or dedicate your life to it. Mathematical self study is a lifelong process and a skillset that is integral to research. It is also an indispensable prerequisite for a mathematical career. Moreover, it demands almost heroic-levels of patience, dedication, self-confidence, enthusiasm, time management, and self-discipline.

I really love self studying and I had having classes. Of course, since I like studying I do well on my tests, I may not be the best student but I tend to remember for a longer preriod of time. Usually I tend to overthink problems and on exams we have a very retrictive amount of time, at lest in economics, and I really hate it. I do love studying math, and I've studied from Linear algebra (formal Linear algebra) to Fuctional Analisis or Topology and Abstract algebra all by my own, math is the only subject I've taken that can give a real feeling of satisfaction (coding also feels quite good). I have a racional love for economics and a passional love for math . (I love my boyfriend too, but that is another story)

Your love for mathematics is unreal bro...I am a 3 rd year engineering student and I do it only because I have it in my curriculum...I can't imagine living surrounded with it...hats of to you🔥

I just started distance learning at a staze owned distance university here in Germany. The combination of some homework and a lot of self study is really great.

I’m currently on my own self-study journey to study several subjects from psychology, creative writing, to maths (basics to higher level), history, biology courses and really whatever my heart desires! I do have a degree in education but I want to learn more and decided to self-study! I study by taking MOOC’s , reading and studying textbooks , loads of nonfiction books and free online lectures. I take notes, do practice tests and solve problems. All without the pressure of grades, just to learn abs challenge myself. I’m also logging my journey on my channel with study with me videos and I’m finding it so motivating to keep going every day!

I agree. I self studied abstract algebra last semester, and I'm doing topology this summer

Buying a big white board and doing math on that will make you better at math then doing it on a tablet or pen and paper , the more hand you use the better it sticks in the brain .

Self-study is absolutely the key to math and to learning every other subject, too. For example, in high school, I loved German, and I wanted to take a state-wide German test for non-native speakers. In addition to my normal German class, I set up an additional self-study program with extra German books and materials that I would study in preparation for the test. With all of the extra self-study, I ended up scoring in the top 10 out of 800 students both years I took the exam. My German teacher was super proud of me, and I was super proud of myself. Now, I’m much older and doing the same kind of self-study of mathematics and several other subjects. I was always so frustrated in my college math courses at the breakneck pace by which the instructors would blow through the material. I remember storming out of a College Algebra course once and dropping it because the instructor was covering an insane amount of chapters every week. It was like rushing through a fine meal, taking no time at all to savor and enjoy what was in front of us. I also never understood why math textbooks have to be written in such a dry, rigorous way. It would be better to explain each concept in depth at a dumbed-down conversational level and then followed up with a translation into more rigorous mathematical language. Students are not professional mathematicians, and they lose track of the story and big ideas because they are so busy learning tricks to manipulate problems, so they can pass a test. Finally, self-study is really the only way. You can move at the exact pace you need to, and you can do so for your own personal enjoyment. I encourage everyone to begin with self-study as young as possible. It will give you a great advantage in school and life. Good luck to everyone!

I'm a math major drop out due to collage and I am so glad I found this channel. I haven't to a point where I am consistent with my self study. Though you and your words give me inspiration!

I don't know how many people knew this but mix up problems from different topics, it might feel difficult at first but you remember these more than when you just slog through a whole chapter.

This is so true!! Nothing sucks out the joy of learning like school. As soon as the pressure is gone the knowledge seems to flow in.

I'm very into self study. It's loads of fun and I have a rigor that I never had at uni. Take your time and focus on learning the material deeply. Don't be in a rush to get to the next thing. Study the derivation, take notes, definitely do the problem sets. If applicable, learn to program the topics you're learning. I really enjoy numerical methods and differential equations so I look for opportunities to employ these techniques. For example, coding a simple n-body system in Python is a great way to use these skills. Write your own integrators using Simpsons rule or runge-kutta. Whatever it is that interests you, pursue it with excellence, then take the time to reflect now and again and enjoy how far you've come. Oh, and go easy on yourself. Nearly everything worth pursuing is hard and there will be times when you're frustrated. Make persistence your super power and you'll push through the times when you're struggling with a concept or subject. Finally, try to find a few different perspectives on a topic. Sometimes one author presents the info in a way that just clicks with you.

Talking of books, I highly recommend 'How To Think Like A Mathematician' by Kevin Houston. Well written with quite a dose of humour, and the best end-of-chapter and in-text exercises I've ever seen.

True, I wish more books were designed for self study. Not having solutions to "keep students from cheating" is silly.

It's so true. I remember being 14 (I'm 15 now 😂) and looking at integrals for the very first time, thinking "I want to do this too" and after learning about it I wanted more and more maths, that's crazy

I love the passion you have when you talk about how self-study is great.

I am constantly on the move so it's difficult to keep books I want to read, always with me. And seeing people say and write about how it's actually not too great to only read ebooks, I think someone might end up leaving the habit to read ebooks altogether and so, I just want you to know. It's alright no matter what form your book takes, to read. You are not sacrificing the beauty of reading by preferring pdfs over paperbacks

Knowledge builds upon itself; self study will eventually make you better at your mandatory studies too. When you acquaint yourself with a variety of disciplines within a field, they each give bits and pieces that can be applied elsewhere. This is why I'm always digging around, filling in the bigger picture, finding how everything relates to everything else. Math used to be purgatory for me in high school, I'm retaking it independently now and can't understand why it was so painful back then. If you have low self-confidence in an area of study, you'll approach it differently than if you believe you'll understand it. I check myself by thinking back to stuff I was good at and remembering how I went after those things, and applying the same courage to learning maths. Self-study is the well of happiness, it recharges you and keeps you fresh. I've done self-study since junior high, teaching myself a bit of Latin, a bit of Irish, Middle English, medieval literature, archeology, just stuff that caught my fancy at the time. Helped me think independently and was useful even at university. Love tumbling down a rabbit hole like that. Thanks for a great channel!

My God, it makes me so happy to hear someone else say this. School is immensely hard (Not the subject itself) and sets me back when it comes to learning. I learn on my own and I am already deeply interested in the subjects to begin with. I don't need assignments and group work to be involved. I did Pre-calculus last semester and I swear I remember nothing because I was having a mental breakdown trying to do all the homework and pass the tests. Yet, from self study I did last year and from 5 years ago, I remember the exact word for word definition of Algebra, decimals, ratios, abscissa and ordinate and a ton more, not because of rote memorization but because these definitions blew my mind and made me so much better at math. I'll never forget how insightful it was to really understand what Descartes did when he created the cartesian coordinate system and how revolutionary it was but understanding what the abscissa and ordinate really is just blew my mind. It seems simple and trivial but to me it isn't. These three facts of what Descartes did, what the abscissa and ordinate is has guided me through every graph and function I have ever drawn. Those few definitions I mentioned above played a major role in me getting an A in that class. In truth, those 4 months were wasted. I could have learned and retained far more. But of course we can't always get the best.

I'm taking an online math class that is entirely self-paced. Is that self-study? Probably not, but it does allow me to take the time to understand why things are happening. When the lecturer makes an assertion, I can pause it and start working through the problem. When I start it up again, I haven't missed anything! (Which was a big problem for me all through school--when I'm on the cusp of understanding something, I want to work it out right then; otherwise, I'll lose that brief magic, and it will be very hard to get back there.) I love it.

I'm self-studying and redoing my math education through the Brilliant app. I'm really enjoying it right now 🙂 Of course I'm going to supplement with books soon, because you need to do that. I enjoy self-study. I don't always like being told what to do. I learn quickly and I ace tests, but the pressure is there, and it doesn't stick as much. I'm like you. I can be defiant. 🙂

I am self-studying Algebra and later Trig, preparing myself for calc. For algebra I am using two books right now (Algebra 2 by Holt & Algebra II by McDougal). I will read the chapter/section in one, answer ALL the exercise questions, then do it again in the second textbook. It is tremendously rewarding reading them and truly understanding the concepts and not thinking "ok what will I need for the quiz". Some topics are taught better in one book than the other, so they give me a view from two different perspectives of a topic. It is even more rewarding when I check my answers to the exercises and see that I got >95% of them correct based on my own studying and understanding. It is addictive realizing that I, and anyone else, can learn math and you dont have to have the "math gene". Just TIME and PRACTICE. Admittedly, I have two graduate degrees in the sciences (Bio and Statistics) but without them I would never have been able to realize that if I want to learn something I CAN! AND SO CAN YOU! Thank you Math Sorcerer for your vids. I have been watching many of them. They are instructional and motivational. Keep it up and be safe my friend.

Say I want to self learn some Discrete Mathematics... I am right now... I try and find a full course video, and I binge watch them all. I don't worry about understanding everything I just want to orient myself in the unknown landscape I'm in. Full course videos often have a textbook that I can find online. I just don't start a topic unless I have the materials I need. Then I read the book in the same way that I watched the video. This time through, I understand where I am much better, and I have some advanced concepts to help guide me through the reading. I inevitably pick up any number of mind blowing things I missed watching the video. Then I start at the beginning and do problems, a few of each kind. Mostly I do problems that interest me based on my earlier surveys. The book generally has good advice on how the problem sets are organized, and I try not to get bogged down on any one problem or type of problem. But if I really can't let something go, I tend to watch a lot of different videos specifically focused on helping me understand. Sooner or later a rock shakes itself loose and I figure out how to proceed. Trying to do it all on a schedule would be horrifically stressful. {checks his watch and screams} "UNDERSTAND IT NOW!" Taught myself Algebra, Trig, and a first course in Calculus like this. Scattered exposure to a bunch of other topics, just to get a sense of what some particular kind of math is about. Your videos are very helpful. It's kind of weird, I don't have any college degree. I don't really enjoy all the stress associated with classes, but learning math/whatever is an itch that I can't stop scratching even though I don't use it for much except fun and as kind of an personalized trivia service for my family's use. Some of it I just forget because I'm not so interested in that particular topic. But lots of times it works out that I find a use and then just need to review. I ramble...

I love self studying. I think it has to do with curiosity. I learn what I want to learn, not what someone else told me. Something that helps me alot is video lectures of someone just talking passionately about whatever I am learning. I feel like when I have that, when I hear someone talk passionately about the topic I am learning, it's very easy to stay motivated. I am trying to get out of this habit tho cause for alot of stuff I want to learn, I can't find any video lectures on the internet.

I couldn't agree more. I was shocked at how much quantum mechanics I forgot after finishing my physics degree. I've spent the last year self studying the material again, and I cannot tell you how many subtle connections I failed to see during my undergraduate studies that I've somehow picked up on now. Not only is self studying more fun and enjoyable, but it is not hurried either. Spending a couple extra days or weeks on a difficult concept is a luxury that's hard to come by with a full course load of classes.

this is so accurate, i self studied in science, biology is really not my type though. i always think of physics because it's so good, i practiced it for months, i failed alot of times doing my science homeworks because i don't follow the formats and steps, and in our 3rd quarter exam, my teacher gaved us a powerpoint presentation reviewer about how to calculate speed and velocity, none of my classmates liked it but i'm glad i did learn it in advance, and turns out i got good grades !

I haven't self-studied much, but the few times that I did, it was amazing. I actually remembered the content in the long term and somehow enjoyed it much more than learning things in school or university. I hope to continue to self-study after I graduate.

Exactly man! I've thought the same thing ... there's no way I could ever have learned what I've taught myself from anybody else.

One thing came to mind. Self study usually implies that you are interested. And well, it's all you need to learn something. Interest