I learned entire calculus (years 1-3) myself as a high school student. Rn I'm in my junior year (3rd year) and you don't even know how great it is to have such a knowledge especially that I will go into astrophysics in college. I might skip 4-5 classes in college altogether. And I still have social life. It's not that learning is all I do. In age of information, so much is possible. You can do a lot to improve yourself on your own, and it's such a shame that not many people realize that

@Kennedy640

5 жыл бұрын

I did that too. I knew stuff in calculus before I even knew what precalculus was lol. And I had no idea about calc 3 or 2 until the end of my calc 1 class cuz i was a dumbass. I wanted to learn more cuz i had a book about theoretical physics htat i didn't understand (and probably still don't). Here's some advice (this is what i started doing recently): read a chapter a day from books about linear alg, diff eq, differential geometry, real/complex analysis, and so on. You have a lot of time which is great. Keep up the good work!

@droid264

5 жыл бұрын

Words of wisdom guys!!! Awesome

@chymoney1

5 жыл бұрын

Impressive what math you taking next? I took calc 3 as a senior in high school so I know how great of a feeling it is

@karolakkolo123

5 жыл бұрын

@@chymoney1 I'm thinking of linear algebra or differential equations. After I do those I plan on hopping hard into physics. Although, I'll probably need to know even more math for physics later on

@chymoney1

5 жыл бұрын

karolak kolo that’s exactly what I did :). After linear algebra and differential equations I took partial differential equations and complex analysis. I was unable to skip any physics courses so knowing more math than everyone made it way easier. From the all the math I’ve learned over the years it’s beautiful how it’s able to formulate such crazy physics( quantum and relativity). Right now what’s blowing my mind is how abstract mathematics like Lie algebra and group theory is able to predict the standard model of particles. These abstract maths are quite different than any of the maths I’ve taken

Another good idea is to read 3 books on the same subject. Sometimes an author may explains it better than another.

@xDomglmao

4 жыл бұрын

so much underrated. or tutorials. this is basically the reason I am doing much better in learning stuff

@loop5720

3 жыл бұрын

Holy crap yeah, this is such a great comment. I've read some books on the same matter, some are more detailed, some are more simplified but understandable

@sandraraynil

2 жыл бұрын

No one cared this? This is one of the best comment and this is what I do. Also, it helps to connect missing links

@njk2044

2 жыл бұрын

True !

@Mikebigmike94

2 жыл бұрын

I can second this. I tend to watch a good few lectures on the topic and then dive into the book and also do the problems. After watching so many videos of different people explaining the theory and solving problems the book becomes less daunting

_Highlights_ 0:35 Look ahead (get whole picture of what's to come) 2:42 Don't cram 4:00 Any progress is a good progress 4:40 Process over product From 'How to excel at math and science': 5:20 recall the material, don't want to reread it before you get it. 6:00 Beware of two modes of your mind: focused on task and diffused (distracted) and use their benefits. 7:01 Space repetitions 8:13 Interleaving 9:32 Enroll, please!

@mattezmatrick9429

5 жыл бұрын

Дмитрий Кондраев thanks :)

@stonedsloth6367

4 жыл бұрын

Well done

@srijansingh7190

4 жыл бұрын

Summary of *A Mind for Numbers* ;)

@JC-dq6us

4 жыл бұрын

Thank you.

@soumyajyotikundu7147

4 жыл бұрын

Thank you

my advice: don't memorize equations. in the real world, you'll have references. many of our professor stressed concepts over mechanics and I'm glad for that.

@isaacpreven3693

4 жыл бұрын

cedurick interesting. I heard John von Neumann memorized all the equations he ever saw and essentially had them in his memory. But he was John von Neumann.

@darthmath1071

4 жыл бұрын

@@isaacpreven3693 Never heard about this but he probably "memorized" them because he understood them, not by rote learning.

@chrisstubbs6391

3 жыл бұрын

@@isaacpreven3693 von Neumann was also a genius among geniuses when you look at everything he contributed to.

@loop5720

3 жыл бұрын

@@chrisstubbs6391 mhm, who is this man

@benhardsim8629

3 жыл бұрын

@@loop5720 he was the one who designed the basic architecture of computer we are using right now.

This video inspired me to do my Homework 👌

@Mezurashii5

5 жыл бұрын

That's a rare occurence

@bharatpenumutchu6487

4 жыл бұрын

Actually it should inspire you to understand your homework not just "do" it..

@yvngdoja

4 жыл бұрын

Inspired me to pick up my books

Any progress is good progress.... this struck a chord.

@carldrogo9492

4 жыл бұрын

Umbilical cord anybody...no?

@jullienbeaufond8333

4 жыл бұрын

Yes, that is a great message for self teaching. Just put yourself a goal and focus on really understanding because that will stick.

@iliveinsideyourhouse3943

4 жыл бұрын

I was trying to learned some quadratic function and then when I do it myself I messed up it very badly but I also learned quadratic formula along the way so it's still a good progress.

@SnoozeTheRecluse

4 жыл бұрын

Ah yes, a chord progression

@jl_woodworks

3 жыл бұрын

Abm7add9/G?

Summary: 1. Look ahead (get big picture of what's to come) * see where key words come again in future chapters * always skim through a section before going through it in order to see what the key material is 2. Don't cram, you won't retain the knowledge 3. With math, any progress is a good progress. Don't despair that you got a wrong answer to a math problem. Don't be overwhelmed by the size of the material. Instead focus on what you've learned from the problem or reading that you've just done. This understanding is the actual progress you're making and this is what you should focus on. 4. Practice recalling knowledge, for example reciting definitions and redoing problems that you've done before. Don't reread, recall from memory. Otherwise you will fool yourself into thinking that you remember this, while you don't. 5. Manage your focus mode and diffuse mode. For example, when you want to focus, remove any distractions and set a timer to make sure you are focusing for the desired amount of time, like 1 hour. After that, take an true brake. 6. Use spaced repetition. Repeat what you want to retain over a number of days and space this repetition out as the time goes. 7. Interleave, like mix up the problems you solve in order to learn how to identify various kinds of problems. This is good for exams where problems are mixed up like this. 8. When you get stuck, use the internet. 9. Check out a course on learning, like the one in the description.

@akimnerom8231

3 жыл бұрын

blessed

Thanks man! I'm in a similar boat to you- self-learning mathematics as an adult

“ Foreplay ”??😂😂😂

@douglasstrother6584

5 жыл бұрын

"Foreplay/Longtime" ~ Boston kzread.info/dash/bejne/iY1m0pOgg7LRY8Y.html

@sapientum8

5 жыл бұрын

That's how they rape you with hard science. I've been through that, the class was called "Complexity Theory". It was kind of a mathematics, but yet on a next level of abstraction. I was totally traumatized by the whole experience. Man, I should have suspected something just from reading its title before taking it. From then on, I vowed that I was not going to take any class without already knowing (mostly) the material that's supposed to be presented there.

@prince5922

5 жыл бұрын

@@sapientum8 I can so relate to that bro, but at least we learned a lesson lol

@abdallababikir4473

4 жыл бұрын

@@sapientum8 that way you'll never learn. Don't be afraid to explore and challenge yourself. I'd bet even the Complexity Theory course you took taught you something you'd much rather have.

@sapientum8

4 жыл бұрын

@@abdallababikir4473 indeed

I've been teaching myself advanced linear algebra...something I couldn't have done easily without the internet. Your videos as well as 3Blue's vids on matrices, higher dimensional spaces, etc have been crucial to my effort.

I regret not learning the content from school on my own with books. They basically taught us to memorize the quadratic formula, and don't ask why. I struggled so bad in Honors Algebra 2 and precalc because of that reason. I want to be a robotic engineer but that takes more than calculus 1. My plan is to take a gap year to learn more math on my own, then attend community college. I don't care about the piece of paper I get for graduation, I care about my own knowledge.

@yourdedcat-qr7ln

2 жыл бұрын

How you doing man

I’m so glad that I watched this video. You were so honest while explaining your reading and understanding pace. You keep it so real because professor expect us to learn a section or two per day, and youtubers are expect at promoting “learn this and that in a day” which is unreal. I thought I was dumb until I watched this video. LEARNING AT A UNIVERSITY LEVEL TAKES TIME AND EFFORT.

I never went to university (various reasons). I ended up getting into test prep (I test well). I then just started teaching myself material to help my students prepare for their masters programs. Initially it was the basics, like simple derivatives or introductory fluid dynamics. To do this though, I'd have to learn it myself. I'd always preface it by stating I've never studied this but this is my take on it. I've progressed up through hamiltonians, applied mathematics, statistical analysis, etc. My students include professors and doctoral students at Harvard, Berkeley, Carnegie Melon, etc. You don't need to learn something in a formal course structure; in fact, I'd say it's easier to learn on my own than in a course. However, you do need to have dedication to do it. Just keep working at it. Put in the hours. It's like going to the gym. It doesn't really matter how much natural talent you have, just keep going and you'll improve.

@usejasiri

4 жыл бұрын

So true. I think when one learns on his/her own, him/her can build intuition around the concepts

@theboombody

4 жыл бұрын

Man, I love learning on my own. I don't have to have a formal proof structure or work any problems. I feel like one of those guys who started painting in cubism in its early days when nobody else dared to paint anything less than realism. My math may not look as good as the formal stuff, but I'm having a good time slopping stuff up on the canvas anyway.

You just made me realize why I'm so good at learning and remembering. Im too lazy to take the book out and reread, so I force myself to remember. I'm not even doing it on purpose to learn the material better. I'm learning because I'm just too lazy to look the information up. Great to know.

@RobertFerro3

3 жыл бұрын

You would come in fourth place in the laziness olympics, that way you wouldn’t have to climb the winners podium

@loop5720

3 жыл бұрын

Oh man, this comment section is a gooood learning material

@KidAteMe1LetsBuildsAndMore

3 жыл бұрын

Fucking same. I feel like if I have to reread something, that'd be a waste of time so I make sure that I comprehend it so I never have to read again. It's peak laziness that turns me good at both remember things in the long-term, and forgetting things in the short-time

wow! you are just simply listing each and every thing I encounter during my self study....beautiful!

“Recalling material is more beneficial than rereading it” This is such a well-known truth, yet it’s always tempting to reference the text quickly and feel as if you truly know it just because it looks familiar. I lie to myself right after by thinking “yes, I remember this 🤓” but I didn’t recall it with raw memory. Reconstructing the material on your own is the goal and I have to remind myself this every time before I “fake remember” material while I’m studying. This is such a great video with helpful tips 👍

@DexterousKid1

4 жыл бұрын

Enroll in the course

We used equation tables actively in class. And after holidays were over, you forgot every little detail, so my new school doesn‘t allow these tables in exams, so i keep my hands off it, it really helps remembering everything. Most people underestimate active recall. They hear that i write everything down several times a week, and the typical response is of lazy nature really, and then you hear how they practiced 3-4 hours 1 day before an exam, instead of spreading it to 5 minutes active recall a day. Not only does active recall work, but you‘re also less stressed before an exam.

Perfect timing bro. I just downloaded 4 textbooks that almost have nothing to do with my major but I wanna learn for fun (overview of modern physics, intro to astrophysics, intro to pure mathematics, and Python for dummies). In the midst of the coronavirus, I think I have time for at least one book until the fall. This video will help a lot. Thank you

@kofirichter9753

4 жыл бұрын

Lool... enjoy quantum.

@aj4138

4 жыл бұрын

Can you tell me where you downloaded your books from? Any specific website for downloading math/science books??

@listentome5583

4 жыл бұрын

Kofi Richter I hope I do

@aj4138

4 жыл бұрын

@@listentome5583WOAH THANKS A MILLION DUDE! it's simply awesome I'm screaming rn!! You just made my (and my other nerd friends') lockdown days a LOT better!!! xx

@nahfid2003

4 жыл бұрын

@Mwaniki Mwaniki thanks a lot!

This video makes me so comfortable to start my self teaching journey. Thank you.

thank you for this video. I am currently teaching myself physics. I am using almost all of the studying techniques that you mentioned, and it helps a lot.

Thank you, you have encouraged me to keep learning and self teach with the mentioned suggestions .

You're an inspiration Zack, thank you for this videos

I took both of the courses you show in this video and they are really great. Thanks for your recommendations. Great video :)

Brilliant channel. Love it so much 😀

THis is truly gold... Thanks @MajorPrep

I admire your work. Congrats!

Yes thank u!! Exactly what I needed rn. I'm gonna start as soon as my textbook is delivered. Need to prep so badly for uni

> Knows Zach as an entertainer. > Finds out he's a genius. > Have an existential crisis.

@douglasstrother6584

2 жыл бұрын

> Knows Zach as a genius. > Finds out he's an entertainer. > I laugh a lot!

That was unexpectedly a good video. Thank you.

Did you read my mind? I need this so much. Thanks

This is a nice concept of learning man, love it

Awesome channel, fast, informative!

This video is a gem. I had been thinking on the same lines for a long time to know Math by myself with real world applications which unfortunately is never taught in schools.

Cheers Zach - thanks for that.

Thanks brother ❤️ I really need this

I agree with you. I think the best way to archive ''diffuse mode'' is to do some sport like for training in the gym or just go outside to take a walk.

I love this!

Ive hit the bell after a long time. Ready good content keep it up 👍👍👍

Today I finished with all my finals, and want to learn calc 2 during the summer better after taking it this semester this video is definitely going to help

very good advices ! thx. I like the "don't cram"

Thanks for this great video.

I rewatch your video over and over

Hey, that's what I'm doing right now. I'm not allowed to do any math-related courses at my university because of prereqs, so I'm just doing it myself. Nice to see someone made a video on them doing this, as it's my first time doing this, having some tips and tricks is pretty helpful.

This video can be made into a course. Well done !

a very honest video with hidden gems. T.u.

First video of yours I’ve watched. I enjoyed it and found it useful. Liked and subscribed.

Good video, I am self studying math right now and needed this advice. BTW..I like the way you slide-in that Coursera ad lol

I really like your channel bro It's so inspiring 😊

diffuse focus is definitely the best advice. It always helps if you just briefly see something, but not get into too much detail at the time. Think to yourself "I'm not doing this now" and let everything work its way to your mind. Eventually, when you do come back, all the pieces will fit in nicely.

thank you . this video was so helpful. i used same method like u did. From now on i ll use it more. 🙏😌😌

Some useful tips, thanks. I don't go to college or sixth form and I actually failed math in high school. I have bad anxiety which stops me from going to college but I really want to re-teach myself maths. I dont believe a sheet of old paper saying that I failed is going to stop me and if somehow it does, I'll find a way around it. I recently re-learned the bodmas method, how to convert and reverse fractions and what the difference sequence of numbers are. My memory isnt good and I'm taking it pretty slow but although these steps are small, they're significant to me.

Cool stuff bro!!!

I'm retaking my math class because I didnt understand it despite me "technically" passing it, and taking my time on my refrigeration course until I know it well. Might take me time to finish but I WILL know my stuff.

Good video, greetings from Argentina 🇦🇷

Thank you ☺️ I can relate with this video

Diffuse mode: waking up and having the solution of a problem

This is sooo helpful

I am trying to learn an entire college book of organic chemistry

@tc3800

4 жыл бұрын

How is it going ?

@listentome5583

4 жыл бұрын

Should I do this too? I’m still in gen chem 1

@levibeam100

4 жыл бұрын

Taeef Jihaan There’s never a bad time to get an advantage in something like that. If you have time to do it, do it.

@still_have_chaos

4 жыл бұрын

Same, for a college engineering entrance exam...except that the course I want has absolutely nothing to do with any kind of chemistry..XD

@nahfid2003

4 жыл бұрын

Same solomons and fryhles. But i have read some general chem. On the 3rd ch rn. Nice recap. Kinda skeptical about 4-5 chapter onwards. New stuff

Good advice for life after school, too.

As you did this would you do video on the books you went through in college that helped you ?. Really nice video

Lack of interleaving made me almost fail my differential equations class. Will literally never be able to make that mistake again. Such important advice!

When I was in college, in the weeks before some classes began, I would read through a book on the subject to get an overview. I would read the relevant parts of text book the day before the class so that I would already have some idea of what the instructor was going to say, so that I would have questions, if needed, at the ready. With the instructor reinforcing and clarifying what I already learned.

Just have fun learning to make your self comfortable with learning. I completed while igcse computer science syllabus in a day.

Just turn on hacking music

@DrProfessor143

4 жыл бұрын

Yeah this is big brain tumor

@DrProfessor143

4 жыл бұрын

*time

@DrProfessor143

4 жыл бұрын

Sorry my phone erected

@DrProfessor143

4 жыл бұрын

*autocorrected

@blakemusonda5896

4 жыл бұрын

@@DrProfessor143 lol

You're so inspirational. I learning advanced calculus (Culc 3) and linear algebra II on my own. I wanna study mathematics and physics.

I couldn't agree more that the "why" is such an important factor when learning. All of the material we see developed over time and for a reason. Learning the motivation and time evolution puts one into the right perspective for learning. I also find it useful to copy the block scheduling we go through in school for self study. There's a website called worksheetworks.com that has printable customizable planners. I usually print out a months worth and make a lesson plan.

I did very well i math class and I did all of this basically. It works great!

I hope you make more videos about Chemical Engineering!

1. Process over product 2. Practice I always keep that two in mind whenever I wanted to learn something

my understanding of electronics started when I was 6 yo. I would build fantasy sculptures on wooden boards with nails and wire. I knew nothing but I had invented breadboarding and network analysis. Intuitively that is. Loveing your subject is necessary for mastery. I subsequently looked at any and all textbooks on electronics for circuit beauty and still did not know any math. Later in college I completely aced the subject and the formal analysis and creative solution finding were all intuitive. To this day I can visualise entire circuits in my head including mathematical analysis and build a circuit without documentation. I debug with my lab tools oscilloscope etc.. My instruments.

Thank you!

Nice video !! :)

If something I've learned from school is learning on my own time. I did better not from what my teacher taught, I literally in my senior year decided to take the textbook and test my theory. I learned the major components while following my teachers lesson but learning ahead on my own time. I did better bc I did it my way. Everyone has a different way of learning. And I honestly thought I was dumb bc I couldn't follow along with the lessons as well as my classmates. I learned schools taught their own course of learning but it doesn't always help you and your mind of thinking.

I did this with discrete mathematics. I really liked it.

I am 58, and reviewing pre- calculus in order to learn calculus.My goal is to be able to solve problems of Statics. I am using the pre-calculus of Stewart.Thanks for the advice and the resources I will apply them, maybe I might become an engineer.LOL

A good proofs book for self study is Hammack’s “Book of Proof”. It’s available for free as a pdf on the net.

I tried to review the all the Differential & Integral Calculus from Stewart's 8th Edition. Within a span of 45 days (including days where I didn't do any math), it turned out that reviewing a huge chunk of stuff you learned in your previous year in the summer wasn't so bad after all and once I get out of school, I can't wait to do something like that again. Unfortunately I was only able to almost finish 2 out of the 7-8 chapters. What are your thoughts on the Feynman Technique? I've seen several videos thrown around about it and would like to see your take on it.

I realised I'm already doing these things without knowong it. Like for example learning by understanding things in science is wayyyy more efficient than just learning without understanding in a long term perspective

Right now I’m study for the FE exam. I’m reading whole textbooks to do this. This will be the first time I am able to study at my own pace. Currently I’m on book 2.

As a middle schooler who does this in advanced math and physics textbooks I REALLY appreciate this video ! Thanks Zach !

@marilynm4354

3 жыл бұрын

as a five year old who does this in college level organic chemistry and mechanical engineering textbooks, I really appreciated it too (sarcastically), all jokes but that's awesome ur in middle school and wanting to learn more about all sorts of stuff!

Spaced repetition is probably the hardest for me. I just can't figure out a pattern to effectively space time to re-learn concepts and things. I've used Anki in the past (for like 2 months), but it's more hassle than good (not blaming Anki, maybe my way of learning is different?). What's working for me was going back to the material I learn today, a long months later. Like, 2 or 3 months, and somehow everything clicked after that lol. I do it with books too. I read maybe one book this month, and 3 month later I reread it again. And somehow I got different insight and new knowledge I didn't see before.

Damn free neurology lesson

Best channel

Hello MajorPrep, can you please make a video on Actuarial Science? It's a pretty new thing in my country, and i'd like to learn more about it in more detail, thanks!

DUDE!! His logo is the cinquefoil knot!

Good ideas. They are similar to what I've followed since I left high school. A few comments: 1. Need to be careful about *which* book you choose to work through. A few books are very good, most are not. It's good to compare multiple books or courses, before you commit yourself. 2. It's important as you go along, to consult alternative sources of info. You mention that you relied on KZread for explanations. Excellent! Often another book or video will just click with you,. Or they will give you an different viewpoint, so you become well-rounded and don't just parrot what one author says. 3. You're studying with the TV on! Aagh! That would drive me crazy. 4. If you feel enthusiasm or excitement, that's a sign that you're on the right track. You're studying what you want to be studying, and you're making progress. If you're bored or frustrated, it may be time to try a different approach.

So last month I had this really really important exam. It's the exam all 8 th graders will have to pass. So this exam basically determines what highschool and what "division" (like the university ones) you are going to join. There are 2 big divisions: one division teaches kids subjects like math, informatics, phisics, chemistry and other subjects, but less, and the other one teaches kids subjects like grammar, literature, foreign language, history, filosophy, and of course some other subjects but less than these. I wanted to join the math division but my parents didn't allow me. So I joined the other one and now I won't study math and I am really sad as I liked math. Hope this is going to help me.

I'm a self thought chemistry student but i do the same with everything else and im also doing maths, so yay

I spent a few months trying to learn analysis and calculus in 10th grade . I was definitely out of my depth, but it gave me the background to skip a few classes later on

I immediately recognized that table of contents from vellemans “how to prove it”

The main thing I've learned studying math is that sometimes people just don't explain things properly. In fact, often no explanation is given at all! You just need to look somewhere else (other textbook, KZread, etc.) to find it. Also, if multiple textbooks are available (and they usually are), it's worth finding one you actually like, since you're going to be spending a lot of time with it.

Thank you wish had new this earlier

"Just think about when you leave an exam and figure out the solution to that one problem within a minute of walking out the door" Just define my entire college career in one sentence, why don't you? Jeez....

man you're a role model and i love the modesty !!! btw what was the book about ?

@zachstar

5 жыл бұрын

Thanks! And It was an introduction to proofs book (logic, sets, proof techniques, etc).

@TheTariqibnziyad

5 жыл бұрын

MajorPrep great !!!

The biggest problem I have is applying math. I can do most math by following steps from books, but as soon as it comes to a real problem where you need to use different elements of what you've learned... I might as well be doing Mandarin.

@Linux333

4 жыл бұрын

JSkillz try to dissect key words from the problem - those details are what you put together to form the big picture.

@mellima4226

3 жыл бұрын

@@Linux333 Thank you Samir.

That plane joke made me laugh so hard for a minute

8:41 Gilbert Strang! I'd recognize that formatting anywhere (because I'm using that exact book)

For spaced repetition use ANKI

I might have done better in math when I was a kid had I thought of it this way. I always was terrible at math and I'm still incredibly slow or just having to triple read things and then I still don't get a light bulb. When I went through Calc 1 (had to take it twice) I didn't even get the light bulb to even flicker until I made it to Calc 2 and then for some reason I just completely understood some of it. Tried to go back and see what I remember and it's definitely a big fat "nothing". I can't even remember how to do derivatives. To be fair to this, my first Calc teacher was actually throwing us concepts the same way you described. I had taken Pre-calc in highschool and NONE of that came up until Calc 2. No idea why the classes didn't mesh together either. Lots of bippity boppity boo = x-shazam. Recently I've been wanting to re-learn some of the advanced maths that I studied 10 years ago. I think I'm going to have to start at Algebra 2 or so. Trig was super easy for me for some reason.

This happened to me when self studying for ap physics C E/M. I subconsciously applied these techniques and got an easy 5