So you’re saying ∫ math d(society) = engineering? That doesn’t fit, there’s no society in the solution! The solution should be math * society + C, because math is a constant and society is the variable. EDIT: I forgot the integration constant, d'oh!
GRBTutorials Nice haha. Can’t that still work tho? Indefinite Integral of k dx is kx +c, so wouldn’t that still be math * society? (Ignoring the +C for now lol)
Not an outrageous comment at all. It really is all about the mindset with which you approach maths. If you think you’re bad at it, then you’ve put up a mental block. If you approach it as you would when solving a puzzle, you’ll see that it’s actually fun.
How to learn math and everything with ease. Seriously: How I learn math and everything else: I use what I call the “synthesis method”. When I’m studying math I don’t just read things and move on to the next things, I have the book and paper with me, and after everything I study, I have to synthesize what I just learned in my own words. After doing that, I use my own notes as reference for the material instead of the textbook I learned from. This method is slow in that i can only study about a dozen pages a day, but it has the following benefits: when I study something, I get FULL understanding, and I remember everything. And That’s what learning is: understanding + memorization.
Honestly, I do something very similar, especially with math and physics. I find though when I understand something I actually inherently remember because well... I understand it haha
I totally agree with this one. Reiterating or interpreting what you've just read with spoken words, most importantly, really helps drive that learning process. I say spoken words because it is a way for the thought to resonate in a space other than your head. I'm not really sure why this works for me. like Victor said this method is very slow. it is satisfying when you do figure something out using this method as it feels like a grind. however it is not very efficient for time-sensitive things like school or if you work too. But hey, it's the best i got for now lol.
I do the same things but to keep it succinct and time friendly I take notes on notecards and really try to parse the information into “concepts” and “skills” while leaving out the fluff. If I HAVE to know it it’s on the cards, any deeper understanding I usually trust will stay in my head
I find this method works better, I read through everything and put it in my own words while I read BUT I don't write it down. Then I come back a day or two later and do the problems. I work hard to recall the insights I made earlier. I always find once I recall something I remember it ten times better after that than just doing it thoroughly once.
From some simple deduction I’ve concluded you’re a multi-millionaire. You said you have four textbooks on quantum mechanics alone, no mere peasant can afford that many textbooks on one subject.
@@mikhailmikhailov8781 or buy a textbook from the 90s. Sure all the information may be wrong or outdated, but it only cost you $5 including shipping and handling!
Step 1: Identify your preferred pedagogical style (eg personally formality, precision) Step 2: Find nice theory books, read very carefully and fill in steps, make sure the book seems really difficult to you (Bourbaki) Step 3: Always do problems which are really really hard for you, get used to the frustration and the dopamine when you succeed (again Bourbaki) Step 4: Become obsessed with solving harder problems and learning more theory
This is inspiring. I am an aspiring Medical Physicist. I was originally a Philosophy major (I wanted to get my Ph.D. in Ethics) and I was always interested in Physics but I always doubted myself because I almost failed high school algebra more than 3 times. Just last week, however, I knew that my fate was to be a medical physicist and thus I switched my major to Physics and Biomedical Physics. I am currently in college algebra and taking several calculus courses scared me, but after watching this video, I feel motivated to continue this arduous path of becoming a physicist. THANK YOU!!!
OMG I’m the exact opposite. I’m really good at maths but I have a huge passion for philosophy and have done very poorly in my English exams so I decided to study theoretical ohysics.
I hated math back in elem and HS but I started to appreciate it when I took Philosophy as an undergrad... I hope I paid more attention back in the days
The secret in mastering math lies in patience. If you have a difficult math Problem to solve, try your best , even if it may take you hours, days or weeks. Solve it yourself. Math forces you to think for a long and exhausting time. I myself Need sometimes hours, days or even weeks till i manage to solve a math problem. And when you are really exhausted, tired and want to quit, there appears a stark of a brillant idea, the missing piece, which lets you See the beauty of math.
I love math. It frustrates the hell out of me sometimes but when I finally understand a concept that I've been struggling with, it gives me pure satisfaction.
What I think he meant to imply is that we luve in a society where math is important. Like really important because every thing we have is brought to you by math.
I’m currently self- teaching myself calc I, and doing great! If I could give one piece of advice to any individual who is struggling with math whether it be simple algebra or real analysis, practice. Do TONS of practice problems, and I mean tons. Whenever I’m stuck on a problem or topic I can’t wrap my head around, I try and approach the problem in a logical way and keep repeating problems for that particular topic. Eventually, I start to understand what I am doing wrong and use that knowledge to improve. I hope this has helped.
I am learning more about integration now and various physics concepts. Teaching myself too! I could have my face in a math or physics text/book all day everyday and never get tired of it. On my days off I'm researching from sun up to sun down. I love nothing more and there's so much to learn. I'm struck everyday by the beauty of math. I'm obsessed... and obsessive. :)
The Real Hal Jordan I know your pain I have ADD as well. I’m about to finish cal 4 and DE in a few weeks with an A in both. Just cause it’s hard doesn’t mean we can’t do it! Keep at it bud
The highest level of math I took in high school was algebra. I somehow placed into Calc 2. I am now teaching myself precalc and Calc 1 so I can keep up with my physics and astrophysics classes
I agree. I've been tutoring math at my school for the past few semesters, and it has made a world of difference on how I approach problems and new concepts. Tutoring other students helps keep me sharp, and prevents me from forgetting certain math skills that might not get used as often. Also, it gives me greater motivation to truly learn each concept in depth so that I can better explain it to students who may need help. Plus it's fun! Super helpful video, keep up the good work.
I got good at math because of my mom. She helped me solving problems when I was little and encouraged me. Solving problems gave me satisfaction so I liked it. Now I am on my own.
As an undergrad, you learn how to answer questions by solving *well-defined* problems. As a post-graduate, you learn how to ask *new* questions, formulate them into well-defined problems, and solve them independently. The former requires hard-work and intellectual horsepower while the latter requires hard-work, intellectual horsepower, AND creativity. With that being said, I think it is integral to take time from problem-solving and set it aside for play. After all, math is supposed to be fun!
For me the biggest thing was realizing that math is iterative! You NEED A to be able to do B, and you NEED B to be able to do C. This means you can't afford to skip steps. At all! This is literally the biggest mistake people make. Instead of solidifying themselves, they power through the next thing, and then they wonder why they struggle in Calculus 2, when they haven't fully mastered Calculus 1. And then they end up stressing out and ultimately hating math or physics. If you're struggling in an area, GO BACK! See the key skills required and ask yourself honestly if you have them. Go back to Elementary School algebra if you have to. There is absolutely no shame in that. Then SOLVE PROBLEMS. Repeatedly. How do you know you've mastered an area? Simple: if you can solve any given problem from this area confidently and comfortably given nothing but a pencil and an empty piece of paper. If you can't, you're not there yet.
@@gamerdio2503 Well, we could do an approximate: sin(0°) = 0 and sin(90°) = 1, we can approximate the values in between linearly, thus sin(x) ≈ x/90. So for sin(26.81) we roughly get sin(26.81) ≈ 26.81/90 = 30/90 = 1/3 ≈ 0.33 So we get the approximate sin(26.81) ≈ 0.33. But this is far away from computing the result analytically. You can do better approximates using 2nd or 3rd order Taylor approximations (which can be computed by hand), but this should work out quite well.
Quickly checked using a calculator: The true values lies around sin(26.81) ≈ 0.45, so an error of -0.12 might be okay given that I've approximated sin with a linear function 😅
If you do things wrong enough you actually learn a lot and going down different wrong paths to eventually find the right one I think is how you really start to get good at math. As you get further in math you really are looking for patterns, it is like playing a board game you have to learn the rules apply them in the correct manor but also you have to think in a creative way when you apply those rules so you can win at the game. It is not enough to know the rules but you have to know how to manipulate them
I was average at math until 4th grade and then I applied for a competitive math exam in 5th standard for which I studied from a different source and I suddenly started understanding it and math became fun. Now I'm pretty good at it and going to pursue an undergraduate degree in physics next year. P. S: I was first
I was average at math at up until year 7, then I started flying through math until year 10-11 where I was about average (in the top class of the school however). I then sat down for a whole month at the start of this year doing about 8-9+ hours of maths a day. ( I'd get up early and study ALL day, I don't get burnt out and I strive to understand rather than memorize so I don't forget as easily what I'm doing) I worked through Stewart's calculus chapters 1-11 (essentially calc 1 and 2) as well as the whole maths curriculum for year 11 and 12. I went from being average to top of the school. I'm in year 12 now, by the end I would have done Calc 3, ODE'S and linear algebra.
Point is, I waaay surpassed people way more talented than me. Talent doesn't take you far, dedication and obsession can take you miles. I calculated that I can finish an entire physics degree worth of physics and math classes by the end of next year. Wish me luck, I hope you will one day stop letting yourself be spoonfed an education and push yourself beyond what is possible.
@@nathandaniel5451 Amazing! I myself found Stewart's book too "unmathy" after two or three chapters and went for Spivak instead, which has been the right decision in my own opinion, but for that same reason I still haven't gotten past the calc1 level(the book is an absolute monster in terms of difficulty for a self studying highschool student) and I am getting deeper and deeper into pure mathy stuff like topology, graph theory, abstract algebra, etc. Just started the first year of math undergrad two weeks ago. To solidify your point, it has taken me great deal of work and hitting the wall with my head for hours to get to the point where I can prove big theorems on my own before seeing the formal proofs, i.e. I try to be constantly ahead of the game and proving every major theorem myself, because I consider seeing it, before I struggle with it, a spoiler.
@@berserker8884 That's really cool, I considered Spivak. I try to figure things out before I get to them however in probably a less rigorous way. Ex. "Ooh next section is on surface area, let's try to derive it before I even see the actual formula, before I start the section". After I finish all the undergrad physics texts, I might get into real analysis and then some more pure mathy subjects before I start some higher level physics texts. The thing is, people vastly underestimate what people can accomplish, including themselves. For example, my goal seems far fetched for a lot of people but it's more than doable, even for someone like me who I think might actually have some sort of learning disability.
@@nathandaniel5451 awesome to hear such positivity! Today I had a rough depressing day with almost zero productivity, but your comment made me at least push myself a bit to work, so at least I did something today and you motivated me! Keep at it brother, may we all become masters of our crafts one day through hard work, determination, curiosity and a pinch of luck.
You hit the nail on the head. Teaching/explaining concepts to others is by far the best way to understand something. I didn't fully comprehend basic frikin limits until I helped someone study for a test years after hs. Then mind blow happened and started understanding all of it.
I just started watching a lot of math TH-cam content and found the things I was really interested in and used them as an entry point. I’m now almost done with a math minor
Don’t let that ever hold you back, even when you start studying things that seem impossibly hard. Those things will become easier in time. I knew I wanted to be a physics major and I left hs with not even a pre algebra understanding of math. I worked very hard and now I am a top student in my math and physics courses(: best of luck!
I tried speed the other day, and it just fucks my thinking. Makes me very enthusiastic and feeling so clear-headed and intelligent for a while until I notice that somehow my thinking is in fact severely impaired when trying to actually solve any problems. Maybe it does work for some people, like Erdős. Not sure about that. They might be deluded by this chemically-induced enthusiasm and just _feel_ more intelligent.
@@epajarjestys9981 Not sure what you're trying to say- I said it MIGHT be causative, and that it PROBABLY helped, are you trying to say that's a contradiction?
@@VinylUnboxings No, you said that it might NOT be causative, BUT it probably helped. Of course, neither of the two sentences _"It might be causative"_ or "It might *not* be causative" (which can be considered to be logically equivalent) stand in direct contradiction to the sentence _"it probably helped"._ However, the way you concatenated these last two sentences: _"... it might not be causative. But it probably helped",_ can give the impression that there is a possibility that it might not be causative, but yet at the same time still helped, which would be a contradiction. Not sure if you are a robot who does not understand how natural language works or just dishonest and pretending to be one. I believe it is the latter. In either case: Fuck you, you worthless piece of shit.
Consistent effort. Setting a goal. Not forcing myself (that has opposite reaction for me), more like dreaming and letting that dream inspire me. And mostly, because I enjoy it. Oh and holding myself accountable by doing statistics of learning - keeping track of hours and pages. I have this huge paper that has week, number of pages, topics ans number of done pages in textbooks. I track the hours in my planner. When I see I did above than average workload that week, it motivates me.
Thank you so much bro for the channel! I switched from a History major to Applied Physics last year, (don’t ask me why I initially chose History) and got a reality check when I discovered how much math is an integral part of high science. Your vids have inspired me though to continue working hard, currently in Calc 1 but excited to continue on to the end!
I failed alegbra TWICE when I began college, now I am in my final semester finishing a differential equations class. If you don't like the idea of never penetrating the alien symbols that math can seem to the uninitiated, then don't get discouraged no matter how "bad" at math you are. You probably will never feel that you are "good" at math because a) in college you realize how many people are smarter than you are b) the problems always get more difficult, BUT you will be much better than you were before and honestly it is worth it.
If I’m not interested in the subject well then I just have the mindset that I’m wasting my time (probably a huge flaw of mine), but if I’m interested in the subject you can bet I’m definitely going to give it my all in trying to grasp it. Math/physics is what interests me, so I get good at it because I want to get good at it. And then previously failing at understanding something that I want to understand is just another motivator to actually try and acquire that knowledge. Example, I was supposed to learn Riemann sums 5 years ago, but I just let them intimidate me back then and didn’t put in the work to learn them because I just didn’t care. But after going back last week and being like “Hey, I actually want to know how these things work” I put in the time and now I actually understand how they work.
I found it easiest to recognize patterns, with constant exposure. The thing I took from you after seeing your videos is that if your problem isn't working out then one of my initial assumptions is probably wrong. It is immensely helpful. You're awesome
It seemed like I was the only one who didn't have a difficult time in my math courses. I think I know why, but I'm just speculating. For one, I've self studied so much math and science that before I even take the course I've already learned around 50% of the information already. Secondly, I think a lot of students may be trying to memorize the material rather than actually understanding how it works. Memorization is short term. Learning is long term. Not to mention that learning is a hell of a lot easier than trying to memorize a bunch of information.
Haha I got good at Math by studying it for 3 years non-stop and taking extra courses. Honestly at the beginning, things such as Analysis 1 felt quite hard, but by just never stopping and always discussing the solutions with my friends I got better at it without even realising it. When I look back at the exercises I struggled with back in those days, I can't help but laugh at myself a little. Sometimes because your studies grow in difficulty as you grow and improve you fail to see the huge amount of improvement you've made.
When I realized that all theorems, derivations, and theories in any field of study be they political science, economics or physics, are found entirely from reasoning up from the definitions and axioms of a thing, my thinking became much more crisp and precise and that same week I was able to carry out proofs independent of guidance. I notice that EVERY interesting conclusion is just some implication of some set of axioms or definition. When facing a problem, ask yourself always, "what is a vector," "what is tangent?" "what is a force" or "what is angular momentum" hell even ask sometimes "what is height?" it's y = mx + b, so rewrite the thing in terms of x if necessary. But no matter what you do always go back to the definition of the thing and you cannot go wrong if the definition is understood.
For me as a highschool senior learning calc on my own , I found the best way I got better is by both practice and asking hard questions that relates to what's at hand. I found it takes me alot towards fundamentally understanding the theory and proofs behind what I'm working on which ultimately translates to the practice problems. Never be afraid to go off and explore a idea that just pops into your head while you just got done doing a proof , because ultimately that's where I found most of my learning was done , because you either end up reinforcing what you already know but in terms that you wrote down yourself which I found makes your understanding even greater , or end up with contradictions, potential mistakes, ect. Which only makes you ask more and more questions , thus making you learn more! Hope that helps!
watching lectures on youtube like prof. Leonard really helped tremendously just because he is a perfect example of a math prof that teaches you the fundamentals but not in a rushed manner and I really appreciated that because not a lot of prof in college like to take time, everything is rushed in class :/
"Its easier when you have to get better", thats so true, learned that with my accounting class. Started off with a 47 F, worked my butt off and finished the semester with a 93 A
This actually makes me feel extremely comfortable with my future academic goals. I'm a rising senior in highschool taking precalculus next year and to say the least math isn't my best subject.
For me it was just never stop doing math. It’s very easy to forget stuff so keep reviewing and keep exposing yourself to it. I’ve done lots of summer courses and now I have a very menacing transcript just because I never stopped. An object in motion should stay in motion.
Oh my god, you have no idea how badly I needed to hear your experience. I'm a first semester college student double majoring in physics and mathematics and I'm also starting from algebra II.
Walking through derivations of formulas and theorems line by line, while somewhat time-consuming (painful), really helps solidify my understanding of math concepts. I think I'm just inherently distrustful by nature, and want to understand HOW everything works before I start using it to solve problems.
How I got good at maths: I had an amazing teacher last year who would explain everything in detail and marked our books regularly and told us what to work on. He taught us things in so much details that we were sometimes doing A levels stuff (This is in England). He made us practice a lot of algebra which helped too
I completely agree with the necessity part. I took enriched physics in 9th grade which required us to know trigonometry. Had no idea what the hell Sin and Cos were until I took that class, and I was bit slow at first, but when it clicked in my head I was getting As on all the calculation problems. I considered physics to be the fun math class.
Chemistry student here. What u just said pretty much applies to every "pure" science, chemistry, math, physics. I just felt identified with what u said about learning something by teaching it.
This video is SO key, in particular the issue of deciding what problems to do. In some textbooks, there are SO MANY problems and while there is value in grinding out a ton for the sake of fluency, that should be what you do AFTER you've exposed yourself the the important types of problems in the chapter.
That is one characteristic to think about and admire in Americans. From high school algebra and prinstat to Quantum mechanics. Bravo sir! I was part of a 10h/week math, sciences and/or classical languages(ancient Latin and Greek) with an extracurricular economics option in high school. We went fairly deep in mathematics... Yet, No one dared touching Physics at university (in Belgium). As a matter of fact there is a huge shortage of physics masters (let alone PhD) in Belgium. Most who want to try physics go to what is called "theoretical engineering" school (largely for financial reasons).
Searching for multiple explanations is really good advice.. I tend to do this too, looking at the same problem from multiple angles until everything eventually starts to sing. Didn't Feynman say something of the following "Good physicists know at least a several different ways of describing the same phenomena... Each can have completely different philosophical implications, though..". Guess that is true for understanding things in general.. Abstracting away the underlying principles and being able to concretise into different "shapes". That's essentially what you need to do when you teach someone! You need to understand their way of thinking and find some of the things they already know, then find associations between the thing you're trying to teach and what they already understand. Great video! :)
Got good at math by necessity...HAD to know it for engineering. I was average at math in high school. Definitely the constant exposure and the need to know (and wanting to know) that helped the most.
How I got good at math: 1. I truly enjoy learning about it, so I study for understanding first and practice problems after. Some people dive on into problems without understanding the mechanics and reasoning behind every step. You just become a manipulater of numbers and operations, and that will only get you so far. Probably stops working at Calc 3. 2. I'm a math and physics tutor at my college, so everyday I'm faced to explain all types of math. Ranging from basic algebra all the way to differential equations. Hence, constant exposure along with necessity as Andrew stated.
Getting lots of different sources of information about the same subject is key I think. I have like 5 or 7 e&m books now that I can pull methods from and they all come together to fill in gaps in understanding. Also, looking at other people's solutions and examining their assumptions, their methods, filling in gaps where they made steps and performing mathematical cleanup duty really drives forward your exposure to the patterns that show up in problems.
I got better at math by finding little, interesting ideas and exploring them. I would often try to make an interactive graph on Desmos, which helped me get the idea solidly in my head.
I’m already pretty good at math and I agree with part of it. I think that looking at patterns in problems really helps. We are all good at identifying patterns. We have to make it logically make sense in our head. That’s why asking for different opinions or ways of explaining math helps.
The thing that hooked me in maths is that it builds upon itself,that very pleasure of using your previous learning in your current study and how these pattern recognition can be used for amazing stuffs in real life is what drives the curiosity and inspiration to keep learning and foremost PRACTISE,but it's not blind practice,after you solve a problem,try to see if there's any better and more efficient solution for it,it's fun(Atleast for me),and it u made any mistake try to think why u made that mistake and verify if u have any conceptual mistake and then rectify it.Advices from fellow grade 10 noob.
Something I find really useful is tutoring to younger people. I’m in college taking systems of differential equations and there’s no way I could tutor other people in my class because I’m still learning the content myself. However, I am a tutor for high school students because I’m familiar and comfortable with the topics they’re learning. Not only does this help them, it serves as a really nice refresher on the basics for me and has helped me become better at math. Even if you’re in high school, struggling with Algebra II or something, you may find that helping middle school students, for instance, may help you practice the basics and increase your confidence in your abilities. Just some food for thought.
I'm entering my third year of physics, and my advice for someone struggling with math is to spend a time to understand the theory behind a given math problem; If I'm struggling to solve a problem, I go back to the relevant section of the textbook and I just go over it until I understand what approach will work, sometimes you analyze a solution to a related or different problem and find inspiration for the problem you're working on. I also resonate with what Andrew says about picking problems to practice with, my first-year foundations of physics prof told me that it's better to pick a few hard problems and really understand them.
I agree with your view of what makes you "good at math". To me though, I've noticed that the most crucial part of maintaining a life-long interest in math is to develop a general view on math which motivates mathematical inquiry. During my years as student I've always had an aesthetic outlook on math. To me, the beauty and the variety of emotions evoked by problem-posing, conjecturing and proving has always been an essential part of my motivation of eventually "getting good". In summary, before one even tries to "get good" one should ask: "Why am I even doing this?" My answer will always be: "because the beauty of it."
At 3:30 where you talk about reading from different sources, in my experience, that is exactly what I found to be true! Year after year I would be stuck at the same point, I don't know how or why but I sat down and looked at the same thing from two different books and it "clicked", it was amazing! After that, I use that technique all the time!
I thought this video was going to be satirical, but I like the advice you give. I hope people who say they don't like math will have enough confidence to take the advice you give to heart and an open enough nind to follow it. Thank you for making this video, I think more people need to hear your message.
Self educating is the best way for me to learn math. I practice tons of problems with different situations every single day. This past few days, I was learning calculus integration. Maybe it's weird but whilst I'm solving math problems, I explain the process louder in short I am talking to myself like on how I can integrate or approach this kind of situation. Honestly, it's effective. Create system not goal. Now, I am going the beyond the depth understanding of calculus and physics.
The problem is, i'm afraid to try again and i'm afraid to practice. Once I understand how this method works I'm afraid to try it again on a different math problem because i fail or I forget how to do it then i lose motivation to continue learning math thinking "how I'm going to be good at this ? "
I got good at math by practicing it everyday, reaching out for help when i need it an taking advice from people who are just overall better at math than i am.
So, yeah, as you really well pointed out. Indeed, even if it doesn’t look like. The truth is, and you should get ready for this: that we, yes we do, live in a society.
I don't have anyone to explain it to, so i often just say everything that comes to mind aloud, and try anything that seems feasible. Ive found saying it aloud helps quite a bit.
I recommend being okay but convincing yourself and everyone around you that you're brilliant. It's not an ideal strategy, and in some contexts it can be fatal, but, and it's a big but, big butts are a sign of a smoker trying to quit.
3:09 "And your professor has the assumption that if you can solve the n = 2 case, you can solve the arbitrary n case" This hits so hard. A lot of your homework assignments for math classes will be like 3 problems and you'll get similar/harder problems on the test... life goes on.
I literally was bad at math till 2016. I had to learn math because of my passion for physics, so i got a private teacher for math and physics and he really helped me to vision math...literally, any mechanical procress i witnessed, i trued to use plane geometry and Newton's laws to explain it. I was almost too enthusiastic about doing math..keep in mind...as at the beginning of 2016, the most complicated math equation i knew was y =mx +b Behold, by 2017, i had been alsmost finished quadrics and Taylor expansion while i got onto uni by 2018 but i used my time doing advanced concepts like multivariable calculus and complex function qnd variables. Now im alsmost done and about to begin study Linear Algebra. In other words....personal study is the best.
I really relate to this because it worked that way for me too. O igot in college in March and I couldn't even sum fractions, now I'm in my second semester and doing Calculus II and Physics I.
That last tip is gold. If you’re in highschool, see if you can help someone who is struggling with math homework by explaining it to them. You’ll never forget the concept after that.
Great advice. I have no fewer than 8 (yes 8) textbooks on Real Analysis. The various paths to correct proofs are the only way I was able to "get good at" (yeah right) proving the important topics. Thanks for the video & Cheers
thank you , i am in high school, and i always thought i was OK at math, but i could never excel, this has helped me to do just that . again... thank you.
Nice advice , I will add to what you said about solving problems , I usually do half of the first half of problems and two thirds of the second half ( usually where the "fun" ones are ) helps avoid repetition too much .
Not a physics major and I stopped taking Electrical Engineering at Tidewater Community College and your videos have been popping up over the passed year and I had no idea you are/were at ODU! Pretty neat stuff man and you have some great videos!
dude you basically just described me when describing yourself, highest I took was Pre-clac, couldn't do Calc till semester 3, still suck at math, and realizing that I need to practice....you're basically me from the future
"Read it from somewhere else" yes. Definitely helps, in my experience. Also exaplaining it to someone else. I always find where holes in my underatanding are if I start stumbling when trying to explain it to someone else.
My guy your videos are priceless for an engineering student like myself. I was wondering, could you do a video on deriving the formulas for circular motion (vector method)?
Friends: What do you wanna be for Halloween? Me: Integral of Sqrt(tanx) Even though I don't think I have to start from algebra in school, I still don't think I'm actually good enough at it when I see some calc 2 integration problems. Those really make me question myself, what I've really learnt, and whether I can EVER actually do one of these whack ass problems if I come across them randomly. P.S. Great video as always :] Really appreciate the videos ( both meme ones and the helpful ones ).
For me, the best way to git gud at math is to love the subject first. I'm quite good at math, but because I hate certain subjects (Matrices, vectors, probabilities, statistics, those are nightmares), I can't do well on them. And the teacher matters too. I don't know why but my first math teacher in high school has changed my mindset about math and makes me good at math. Maybe because how he teaches in slow pace makes me understand the concept a lot more better. Sometimes the students could be overwhelmed with a lot of math subjects thrown at them. They end up being bad at it just because they just can't understand the concepts as fast as the other students. I actually one of those students. Not in math though, but physics.
The funny and frustrating thing about math is how some people get it easy and others struggle for a long time. Solutions to a math problems seem obvious or self evident once you have confident grasp of the concepts. While tutoring I've always found that students have a eureka moment, and from then on those problems become part of their tool set. My method for getting to that has always been to try show how to do something in as many different ways as possible until one them sparks this moment.
Seeing your positivity talking about math really made me feel hopeful. I always tell myself I’m bad at math, so maybe I just need positive self encouragement. ☺️
5:23-5:24, "we live in a society" Immaculate, outstanding. Take this from someone who failed high school math courses, SAT failure, scraped into college, now lucky enough to be transferring to Harvard to study physics and math. I got "decent" at math by drilling problems from old various calculus and algebra books i got from my neighbor who passed (engineer, so a lot of good material collecting dust). I was put into physics 1 (algebra based) where the prof was my advisor, he loved teaching so much, on the side, we would work out the calculus behind the physics instead of algebra (so long as on exams i used algebra to solve them and not calc) I was in pre-calc at the time, took a test and got a shove into calc-2 and excelled, now in physics 2 online, labs suck but i use Griffiths like a bible. Ive almost done all the examples in Griffiths "intro to E&M". I have struggled a ton in the past, im illiterate, cant speak much or well, cant think quick, but now, i can do math problems like nothing for the most part of it. I also downloaded some physics textbooks online from free pdf sites and drilled those problems hardcore, but make sure you understand what is really going on. You can read pop-sci books and know everything ab black holes, or read a book on tensor calc, but drill the problems. (Especially schaums) deff spelled that wrong, the fuckin practice books Andrew talks ab yk the ones. But go at them, seek help all when you need, Chegg is also your friend, (fuck bartalby or yahoo answers), but In my case, for two years straight, during covid, online, with three lab sciences at once drill and drill, but understand what you are doing is more important.
In my experience, the only way to get good at math is to become as a visual person as possible. As you get more and more visual, when you go to bed, and you can just start seeing the problems in your head. This way helps me to understand math and physics. Especially when I’m studying relativity by myself.
For me the way I got much better at math was not just understanding the concept very well in one way, but understanding the concept really well in many different ways. For instance if you are solving a least-square problem, there are more than 6-7 ways to solve it- perhaps more. So I get really familiar with all the cases. If it's a more general concept, understand it's different proofs, the algebraic proof, a geometric one, and others.
Thank you for this video. I am currently taking AP Calc AB. Sometimes, I struggle a bit when the teacher dictates the number quickly, as english is not my first language. However, whenever I don’t understand a concept/problem, I search through a few sources (Khan Academy, textbooks, and TH-cam) :)
“What if we integrate math into a society?”
“You mean engineering?”
“Get out.”
There are no replies this day.....
as an engineering student I've literally spily my water
"Integrate" Hah I see what you did there
So you’re saying ∫ math d(society) = engineering? That doesn’t fit, there’s no society in the solution! The solution should be math * society + C, because math is a constant and society is the variable.
EDIT: I forgot the integration constant, d'oh!
GRBTutorials Nice haha. Can’t that still work tho? Indefinite Integral of k dx is kx +c, so wouldn’t that still be math * society? (Ignoring the +C for now lol)
One day I just decided that I'm good at math, and since then I've just been great at math. Simple really
Yeah thanks im a mathematician now
+God Guzzlord
Great, so tell me what a tensor is
Lol me too
it's all about mindset, really
Not an outrageous comment at all. It really is all about the mindset with which you approach maths. If you think you’re bad at it, then you’ve put up a mental block. If you approach it as you would when solving a puzzle, you’ll see that it’s actually fun.
When your homework is only three problems you know it’s bad
I think that depends on the level you're working at
every homework at MIT 😔
@@ashishkumarsharma1323 you studyin at MIT?
My homework is usually 7-9 questions, at PSU
@@Godakuri pathetic undergrad
Yep that's him
Physicist PewDiePie
*AndrewPie*
Btw that's actually helpful
Andrewπ
Why not approximate that to Andrew3?
@@dominicjohnmutholil but pi = e = 3 so we can also approximate as Andrew[lim(n->+oo)(1+1/n)^n]?
How to learn math and everything with ease. Seriously:
How I learn math and everything else: I use what I call the “synthesis method”. When I’m studying math I don’t just read things and move on to the next things, I have the book and paper with me, and after everything I study, I have to synthesize what I just learned in my own words.
After doing that, I use my own notes as reference for the material instead of the textbook I learned from.
This method is slow in that i can only study about a dozen pages a day, but it has the following benefits: when I study something, I get FULL understanding, and I remember everything. And That’s what learning is: understanding + memorization.
Honestly, I do something very similar, especially with math and physics. I find though when I understand something I actually inherently remember because well... I understand it haha
I totally agree with this one. Reiterating or interpreting what you've just read with spoken words, most importantly, really helps drive that learning process. I say spoken words because it is a way for the thought to resonate in a space other than your head. I'm not really sure why this works for me. like Victor said this method is very slow. it is satisfying when you do figure something out using this method as it feels like a grind. however it is not very efficient for time-sensitive things like school or if you work too. But hey, it's the best i got for now lol.
I do the same things but to keep it succinct and time friendly I take notes on notecards and really try to parse the information into “concepts” and “skills” while leaving out the fluff. If I HAVE to know it it’s on the cards, any deeper understanding I usually trust will stay in my head
I find this method works better, I read through everything and put it in my own words while I read BUT I don't write it down. Then I come back a day or two later and do the problems. I work hard to recall the insights I made earlier. I always find once I recall something I remember it ten times better after that than just doing it thoroughly once.
i prefer osmosis by keeping the textbook next to my belly under my shirt
From some simple deduction I’ve concluded you’re a multi-millionaire. You said you have four textbooks on quantum mechanics alone, no mere peasant can afford that many textbooks on one subject.
*Khmm khmm* Search for some pdf's on the internet *khmm khmm*
Or just sell drugs to afford the physics books.
@@mikhailmikhailov8781 or buy a textbook from the 90s. Sure all the information may be wrong or outdated, but it only cost you $5 including shipping and handling!
wat, prev editions, ebay ebooks, and used textbooks can be found for prices surely agreeable with the common man
Work a hard job, live with family, pinch pennies, spend surplus on books rather than other things.
Step 1: Identify your preferred pedagogical style (eg personally formality, precision)
Step 2: Find nice theory books, read very carefully and fill in steps, make sure the book seems really difficult to you (Bourbaki)
Step 3: Always do problems which are really really hard for you, get used to the frustration and the dopamine when you succeed (again Bourbaki)
Step 4: Become obsessed with solving harder problems and learning more theory
Dopamine releases when you anticipate a reward, not when you actually obtain it.
I'll try it
@Tracchofyre I think that you are completely right sorry
Lova aaa I didn’t know the Bourbaki books had exercises in them.
Only step 4 that dose the trick
How to “git gud” at math
I'm sorry I donut undiestand ur engrish
plese spel rite bro ur weerd
You need practice and patience...and Black Knight pen.
Man of culture I see
Praise the math .
You want to be a better person ?
Be more person
Uh
Genius
you want to be a better person?
do more people
getting constant exposure to better people actually wouldn't be a bad idea
"Read more"
This is inspiring. I am an aspiring Medical Physicist. I was originally a Philosophy major (I wanted to get my Ph.D. in Ethics) and I was always interested in Physics but I always doubted myself because I almost failed high school algebra more than 3 times. Just last week, however, I knew that my fate was to be a medical physicist and thus I switched my major to Physics and Biomedical Physics. I am currently in college algebra and taking several calculus courses scared me, but after watching this video, I feel motivated to continue this arduous path of becoming a physicist. THANK YOU!!!
you've got this, my friend! How's it going?
OMG I’m the exact opposite. I’m really good at maths but I have a huge passion for philosophy and have done very poorly in my English exams so I decided to study theoretical ohysics.
I hated math back in elem and HS but I started to appreciate it when I took Philosophy as an undergrad... I hope I paid more attention back in the days
It’s been a year. How are you know?
@@willb295 He most likely gave up. People who share their plans on social media/youtube never follow through.
The secret in mastering math lies in patience. If you have a difficult math Problem to solve, try your best , even if it may take you hours, days or weeks. Solve it yourself.
Math forces you to think for a long and exhausting time. I myself Need sometimes hours, days or even weeks till i manage to solve a math problem. And when you are really exhausted, tired and want to quit, there appears a stark of a brillant idea, the missing piece, which lets you See the beauty of math.
That's good advice
exactly, that's the beauty of mathematics
I love math. It frustrates the hell out of me sometimes but when I finally understand a concept that I've been struggling with, it gives me pure satisfaction.
@@josh1234567892 don't give up man!!! That's the spirit!!!
If it's taking you weeks to solve one math problem...I think it's time to move on..
We do live in a society. Jesus...
BOTTOM TEXT
What I think he meant to imply is that we luve in a society where math is important. Like really important because every thing we have is brought to you by math.
I’m currently self- teaching myself calc I, and doing great! If I could give one piece of advice to any individual who is struggling with math whether it be simple algebra or real analysis, practice. Do TONS of practice problems, and I mean tons. Whenever I’m stuck on a problem or topic I can’t wrap my head around, I try and approach the problem in a logical way and keep repeating problems for that particular topic. Eventually, I start to understand what I am doing wrong and use that knowledge to improve. I hope this has helped.
Proving every theorem. I like that idea. Did it work for every concept in algebra, trigonometry and caluclus?
Doing tons of problem need tons of time!!Remember you are not just studying one subject.
my ADD is really fighting me when I do math for a long time, but I will prevail
I am learning more about integration now and various physics concepts.
Teaching myself too!
I could have my face in a math or physics text/book all day everyday and never get tired of it.
On my days off I'm researching from sun up to sun down. I love nothing more and there's so much to learn. I'm struck everyday by the beauty of math.
I'm obsessed... and obsessive. :)
The Real Hal Jordan I know your pain I have ADD as well. I’m about to finish cal 4 and DE in a few weeks with an A in both. Just cause it’s hard doesn’t mean we can’t do it! Keep at it bud
The highest level of math I took in high school was algebra. I somehow placed into Calc 2. I am now teaching myself precalc and Calc 1 so I can keep up with my physics and astrophysics classes
aldo martin why tf would u think it’s a good idea to skip calc 1?
“What do you do?”
*Kevin Malone voice* “I do the numbers.”
never forget Ryan started the fire rip cheesy pita
RIP Sour Lemon Milk
I agree. I've been tutoring math at my school for the past few semesters, and it has made a world of difference on how I approach problems and new concepts. Tutoring other students helps keep me sharp, and prevents me from forgetting certain math skills that might not get used as often. Also, it gives me greater motivation to truly learn each concept in depth so that I can better explain it to students who may need help. Plus it's fun! Super helpful video, keep up the good work.
Learning not to be afraid of equations. Play with them, plug in numbers, see what happens. Really help me.
I got good at math because of my mom. She helped me solving problems when I was little and encouraged me. Solving problems gave me satisfaction so I liked it. Now I am on my own.
As an undergrad, you learn how to answer questions by solving *well-defined* problems. As a post-graduate, you learn how to ask *new* questions, formulate them into well-defined problems, and solve them independently. The former requires hard-work and intellectual horsepower while the latter requires hard-work, intellectual horsepower, AND creativity. With that being said, I think it is integral to take time from problem-solving and set it aside for play. After all, math is supposed to be fun!
Beautifully put
For me the biggest thing was realizing that math is iterative! You NEED A to be able to do B, and you NEED B to be able to do C. This means you can't afford to skip steps. At all!
This is literally the biggest mistake people make. Instead of solidifying themselves, they power through the next thing, and then they wonder why they struggle in Calculus 2, when they haven't fully mastered Calculus 1. And then they end up stressing out and ultimately hating math or physics.
If you're struggling in an area, GO BACK! See the key skills required and ask yourself honestly if you have them. Go back to Elementary School algebra if you have to. There is absolutely no shame in that.
Then SOLVE PROBLEMS. Repeatedly.
How do you know you've mastered an area?
Simple: if you can solve any given problem from this area confidently and comfortably given nothing but a pencil and an empty piece of paper. If you can't, you're not there yet.
Well, there are problems that can't be solved analytically :D
sin(26.810 degrees). Can't do it with only paper and pencil? Sorry, go back to trig class
@@gamerdio2503
Well, we could do an approximate:
sin(0°) = 0 and sin(90°) = 1, we can approximate the values in between linearly, thus sin(x) ≈ x/90.
So for sin(26.81) we roughly get
sin(26.81) ≈ 26.81/90 = 30/90 = 1/3 ≈ 0.33
So we get the approximate sin(26.81) ≈ 0.33.
But this is far away from computing the result analytically. You can do better approximates using 2nd or 3rd order Taylor approximations (which can be computed by hand), but this should work out quite well.
Quickly checked using a calculator: The true values lies around sin(26.81) ≈ 0.45, so an error of -0.12 might be okay given that I've approximated sin with a linear function 😅
@@BlockOfRed Sorry, but that's only an approximate answer. Its not the true answer. You haven't learned trig /s
If you do things wrong enough you actually learn a lot and going down different wrong paths to eventually find the right one I think is how you really start to get good at math. As you get further in math you really are looking for patterns, it is like playing a board game you have to learn the rules apply them in the correct manor but also you have to think in a creative way when you apply those rules so you can win at the game. It is not enough to know the rules but you have to know how to manipulate them
I was average at math until 4th grade and then I applied for a competitive math exam in 5th standard for which I studied from a different source and I suddenly started understanding it and math became fun. Now I'm pretty good at it and going to pursue an undergraduate degree in physics next year.
P. S: I was first
I was average at math at up until year 7, then I started flying through math until year 10-11 where I was about average (in the top class of the school however). I then sat down for a whole month at the start of this year doing about 8-9+ hours of maths a day. ( I'd get up early and study ALL day, I don't get burnt out and I strive to understand rather than memorize so I don't forget as easily what I'm doing) I worked through Stewart's calculus chapters 1-11 (essentially calc 1 and 2) as well as the whole maths curriculum for year 11 and 12. I went from being average to top of the school. I'm in year 12 now, by the end I would have done Calc 3, ODE'S and linear algebra.
Point is, I waaay surpassed people way more talented than me. Talent doesn't take you far, dedication and obsession can take you miles. I calculated that I can finish an entire physics degree worth of physics and math classes by the end of next year. Wish me luck, I hope you will one day stop letting yourself be spoonfed an education and push yourself beyond what is possible.
@@nathandaniel5451 Amazing! I myself found Stewart's book too "unmathy" after two or three chapters and went for Spivak instead, which has been the right decision in my own opinion, but for that same reason I still haven't gotten past the calc1 level(the book is an absolute monster in terms of difficulty for a self studying highschool student) and I am getting deeper and deeper into pure mathy stuff like topology, graph theory, abstract algebra, etc. Just started the first year of math undergrad two weeks ago. To solidify your point, it has taken me great deal of work and hitting the wall with my head for hours to get to the point where I can prove big theorems on my own before seeing the formal proofs, i.e. I try to be constantly ahead of the game and proving every major theorem myself, because I consider seeing it, before I struggle with it, a spoiler.
@@berserker8884
That's really cool, I considered Spivak. I try to figure things out before I get to them however in probably a less rigorous way. Ex. "Ooh next section is on surface area, let's try to derive it before I even see the actual formula, before I start the section". After I finish all the undergrad physics texts, I might get into real analysis and then some more pure mathy subjects before I start some higher level physics texts.
The thing is, people vastly underestimate what people can accomplish, including themselves. For example, my goal seems far fetched for a lot of people but it's more than doable, even for someone like me who I think might actually have some sort of learning disability.
@@nathandaniel5451 awesome to hear such positivity! Today I had a rough depressing day with almost zero productivity, but your comment made me at least push myself a bit to work, so at least I did something today and you motivated me! Keep at it brother, may we all become masters of our crafts one day through hard work, determination, curiosity and a pinch of luck.
You hit the nail on the head. Teaching/explaining concepts to others is by far the best way to understand something. I didn't fully comprehend basic frikin limits until I helped someone study for a test years after hs. Then mind blow happened and started understanding all of it.
I just started watching a lot of math TH-cam content and found the things I was really interested in and used them as an entry point. I’m now almost done with a math minor
This video is a confidence booster. I'm in algebra and I'm a first year physics major. Oof.
bro I almost failed geometry , but I placed into calc for my first. Don't every doubt yourself. But good luck for calc 3 lol
Don’t let that ever hold you back, even when you start studying things that seem impossibly hard. Those things will become easier in time. I knew I wanted to be a physics major and I left hs with not even a pre algebra understanding of math. I worked very hard and now I am a top student in my math and physics courses(: best of luck!
I started out in algebra and now I’m finishing up multivariable calc! We can dooo itttt
Abstract algebra?
me too ahaha, God is good though- we can do it!!
Actually I started getting better at math when I started using amphetamines. But I don't think there is a correlation between the two events.
Well it sounds like there is a correlation, but it might not be causative. But it probably helped.
I tried speed the other day, and it just fucks my thinking. Makes me very enthusiastic and feeling so clear-headed and intelligent for a while until I notice that somehow my thinking is in fact severely impaired when trying to actually solve any problems.
Maybe it does work for some people, like Erdős. Not sure about that. They might be deluded by this chemically-induced enthusiasm and just _feel_ more intelligent.
@VinylUnboxings If it helped then that's causative. Duh!
@@epajarjestys9981 Not sure what you're trying to say- I said it MIGHT be causative, and that it PROBABLY helped, are you trying to say that's a contradiction?
@@VinylUnboxings No, you said that it might NOT be causative, BUT it probably helped.
Of course, neither of the two sentences _"It might be causative"_ or "It might *not* be causative" (which can be considered to be logically equivalent) stand in direct contradiction to the sentence _"it probably helped"._
However, the way you concatenated these last two sentences: _"... it might not be causative. But it probably helped",_ can give the impression that there is a possibility that it might not be causative, but yet at the same time still helped, which would be a contradiction.
Not sure if you are a robot who does not understand how natural language works or just dishonest and pretending to be one.
I believe it is the latter. In either case: Fuck you, you worthless piece of shit.
As a high school student, I found this video highly informative. Thank you!
Consistent effort. Setting a goal. Not forcing myself (that has opposite reaction for me), more like dreaming and letting that dream inspire me. And mostly, because I enjoy it. Oh and holding myself accountable by doing statistics of learning - keeping track of hours and pages. I have this huge paper that has week, number of pages, topics ans number of done pages in textbooks. I track the hours in my planner. When I see I did above than average workload that week, it motivates me.
Thank you so much bro for the channel! I switched from a History major to Applied Physics last year, (don’t ask me why I initially chose History) and got a reality check when I discovered how much math is an integral part of high science. Your vids have inspired me though to continue working hard, currently in Calc 1 but excited to continue on to the end!
This gave me so much confidence... I scored in algebra too now I know I can get to calculus just like you thank you
I failed alegbra TWICE when I began college, now I am in my final semester finishing a differential equations class. If you don't like the idea of never penetrating the alien symbols that math can seem to the uninitiated, then don't get discouraged no matter how "bad" at math you are. You probably will never feel that you are "good" at math because a) in college you realize how many people are smarter than you are b) the problems always get more difficult, BUT you will be much better than you were before and honestly it is worth it.
The last one, about explaining math to somebody, there’s a problem - nobody would listen to me. Nobody in my class is as much into math as I am.
Relate
My constant exposure is watching every Flammable Maths video and doing thr questions with him.
I recently taught myself calculus and now physics at age 35.
Congrats !!!
how
niceee!
If I’m not interested in the subject well then I just have the mindset that I’m wasting my time (probably a huge flaw of mine), but if I’m interested in the subject you can bet I’m definitely going to give it my all in trying to grasp it. Math/physics is what interests me, so I get good at it because I want to get good at it. And then previously failing at understanding something that I want to understand is just another motivator to actually try and acquire that knowledge.
Example, I was supposed to learn Riemann sums 5 years ago, but I just let them intimidate me back then and didn’t put in the work to learn them because I just didn’t care. But after going back last week and being like “Hey, I actually want to know how these things work” I put in the time and now I actually understand how they work.
A method which really helped me to understand new topics, is to see and intuit how it is connected to something I already understand.
As a high school student, I’m glad that you finally made a video I can understand :)
I found it easiest to recognize patterns, with constant exposure. The thing I took from you after seeing your videos is that if your problem isn't working out then one of my initial assumptions is probably wrong. It is immensely helpful. You're awesome
It seemed like I was the only one who didn't have a difficult time in my math courses. I think I know why, but I'm just speculating. For one, I've self studied so much math and science that before I even take the course I've already learned around 50% of the information already. Secondly, I think a lot of students may be trying to memorize the material rather than actually understanding how it works. Memorization is short term. Learning is long term. Not to mention that learning is a hell of a lot easier than trying to memorize a bunch of information.
Haha I got good at Math by studying it for 3 years non-stop and taking extra courses. Honestly at the beginning, things such as Analysis 1 felt quite hard, but by just never stopping and always discussing the solutions with my friends I got better at it without even realising it. When I look back at the exercises I struggled with back in those days, I can't help but laugh at myself a little. Sometimes because your studies grow in difficulty as you grow and improve you fail to see the huge amount of improvement you've made.
When I realized that all theorems, derivations, and theories in any field of study be they political science, economics or physics, are found entirely from reasoning up from the definitions and axioms of a thing, my thinking became much more crisp and precise and that same week I was able to carry out proofs independent of guidance.
I notice that EVERY interesting conclusion is just some implication of some set of axioms or definition. When facing a problem, ask yourself always, "what is a vector," "what is tangent?" "what is a force" or "what is angular momentum" hell even ask sometimes "what is height?" it's y = mx + b, so rewrite the thing in terms of x if necessary.
But no matter what you do always go back to the definition of the thing and you cannot go wrong if the definition is understood.
The first principles
The most important factor for me was finding a passion for the subject!
For me as a highschool senior learning calc on my own , I found the best way I got better is by both practice and asking hard questions that relates to what's at hand. I found it takes me alot towards fundamentally understanding the theory and proofs behind what I'm working on which ultimately translates to the practice problems. Never be afraid to go off and explore a idea that just pops into your head while you just got done doing a proof , because ultimately that's where I found most of my learning was done , because you either end up reinforcing what you already know but in terms that you wrote down yourself which I found makes your understanding even greater , or end up with contradictions, potential mistakes, ect. Which only makes you ask more and more questions , thus making you learn more! Hope that helps!
watching lectures on youtube like prof. Leonard really helped tremendously just because he is a perfect example of a math prof that teaches you the fundamentals but not in a rushed manner and I really appreciated that because not a lot of prof in college like to take time, everything is rushed in class :/
"Its easier when you have to get better", thats so true, learned that with my accounting class. Started off with a 47 F, worked my butt off and finished the semester with a 93 A
This actually makes me feel extremely comfortable with my future academic goals. I'm a rising senior in highschool taking precalculus next year and to say the least math isn't my best subject.
For me it was just never stop doing math. It’s very easy to forget stuff so keep reviewing and keep exposing yourself to it. I’ve done lots of summer courses and now I have a very menacing transcript just because I never stopped. An object in motion should stay in motion.
Oh my god, you have no idea how badly I needed to hear your experience. I'm a first semester college student double majoring in physics and mathematics and I'm also starting from algebra II.
Walking through derivations of formulas and theorems line by line, while somewhat time-consuming (painful), really helps solidify my understanding of math concepts. I think I'm just inherently distrustful by nature, and want to understand HOW everything works before I start using it to solve problems.
How I got good at maths: I had an amazing teacher last year who would explain everything in detail and marked our books regularly and told us what to work on. He taught us things in so much details that we were sometimes doing A levels stuff (This is in England). He made us practice a lot of algebra which helped too
I completely agree with the necessity part. I took enriched physics in 9th grade which required us to know trigonometry. Had no idea what the hell Sin and Cos were until I took that class, and I was bit slow at first, but when it clicked in my head I was getting As on all the calculation problems. I considered physics to be the fun math class.
Chemistry student here. What u just said pretty much applies to every "pure" science, chemistry, math, physics.
I just felt identified with what u said about learning something by teaching it.
This video is SO key, in particular the issue of deciding what problems to do. In some textbooks, there are SO MANY problems and while there is value in grinding out a ton for the sake of fluency, that should be what you do AFTER you've exposed yourself the the important types of problems in the chapter.
That is one characteristic to think about and admire in Americans. From high school algebra and prinstat to Quantum mechanics. Bravo sir! I was part of a 10h/week math, sciences and/or classical languages(ancient Latin and Greek) with an extracurricular economics option in high school. We went fairly deep in mathematics... Yet,
No one dared touching Physics at university (in Belgium). As a matter of fact there is a huge shortage of physics masters (let alone PhD) in Belgium. Most who want to try physics go to what is called "theoretical engineering" school (largely for financial reasons).
Searching for multiple explanations is really good advice.. I tend to do this too, looking at the same problem from multiple angles until everything eventually starts to sing. Didn't Feynman say something of the following "Good physicists know at least a several different ways of describing the same phenomena... Each can have completely different philosophical implications, though..". Guess that is true for understanding things in general.. Abstracting away the underlying principles and being able to concretise into different "shapes". That's essentially what you need to do when you teach someone! You need to understand their way of thinking and find some of the things they already know, then find associations between the thing you're trying to teach and what they already understand. Great video! :)
Got good at math by necessity...HAD to know it for engineering. I was average at math in high school. Definitely the constant exposure and the need to know (and wanting to know) that helped the most.
Excuse me, what is math?
*meth
Hahah just thought about the song Excuse me by Nothing but thieves.
Insert that falsetto after your question.
nice question, mr Newton)
THE FUTURE IS NOW OLD MAN
Says someone who invented calculus😂😂😂
How I got good at math:
1. I truly enjoy learning about it, so I study for understanding first and practice problems after. Some people dive on into problems without understanding the mechanics and reasoning behind every step. You just become a manipulater of numbers and operations, and that will only get you so far. Probably stops working at Calc 3.
2. I'm a math and physics tutor at my college, so everyday I'm faced to explain all types of math. Ranging from basic algebra all the way to differential equations. Hence, constant exposure along with necessity as Andrew stated.
Getting lots of different sources of information about the same subject is key I think. I have like 5 or 7 e&m books now that I can pull methods from and they all come together to fill in gaps in understanding. Also, looking at other people's solutions and examining their assumptions, their methods, filling in gaps where they made steps and performing mathematical cleanup duty really drives forward your exposure to the patterns that show up in problems.
I'm watching videos on how to get good at math rather than practicing
I got better at math by finding little, interesting ideas and exploring them. I would often try to make an interactive graph on Desmos, which helped me get the idea solidly in my head.
I’m already pretty good at math and I agree with part of it. I think that looking at patterns in problems really helps. We are all good at identifying patterns. We have to make it logically make sense in our head. That’s why asking for different opinions or ways of explaining math helps.
The thing that hooked me in maths is that it builds upon itself,that very pleasure of using your previous learning in your current study and how these pattern recognition can be used for amazing stuffs in real life is what drives the curiosity and inspiration to keep learning and foremost PRACTISE,but it's not blind practice,after you solve a problem,try to see if there's any better and more efficient solution for it,it's fun(Atleast for me),and it u made any mistake try to think why u made that mistake and verify if u have any conceptual mistake and then rectify it.Advices from fellow grade 10 noob.
Something I find really useful is tutoring to younger people. I’m in college taking systems of differential equations and there’s no way I could tutor other people in my class because I’m still learning the content myself. However, I am a tutor for high school students because I’m familiar and comfortable with the topics they’re learning. Not only does this help them, it serves as a really nice refresher on the basics for me and has helped me become better at math. Even if you’re in high school, struggling with Algebra II or something, you may find that helping middle school students, for instance, may help you practice the basics and increase your confidence in your abilities. Just some food for thought.
I'm entering my third year of physics, and my advice for someone struggling with math is to spend a time to understand the theory behind a given math problem; If I'm struggling to solve a problem, I go back to the relevant section of the textbook and I just go over it until I understand what approach will work, sometimes you analyze a solution to a related or different problem and find inspiration for the problem you're working on. I also resonate with what Andrew says about picking problems to practice with, my first-year foundations of physics prof told me that it's better to pick a few hard problems and really understand them.
I agree with your view of what makes you "good at math". To me though, I've noticed that the most crucial part of maintaining a life-long interest in math is to develop a general view on math which motivates mathematical inquiry. During my years as student I've always had an aesthetic outlook on math. To me, the beauty and the variety of emotions evoked by problem-posing, conjecturing and proving has always been an essential part of my motivation of eventually "getting good".
In summary, before one even tries to "get good" one should ask: "Why am I even doing this?" My answer will always be: "because the beauty of it."
At 3:30 where you talk about reading from different sources, in my experience, that is exactly what I found to be true! Year after year I would be stuck at the same point, I don't know how or why but I sat down and looked at the same thing from two different books and it "clicked", it was amazing! After that, I use that technique all the time!
I thought this video was going to be satirical, but I like the advice you give. I hope people who say they don't like math will have enough confidence to take the advice you give to heart and an open enough nind to follow it. Thank you for making this video, I think more people need to hear your message.
Self educating is the best way for me to learn math. I practice tons of problems with different situations every single day. This past few days, I was learning calculus integration. Maybe it's weird but whilst I'm solving math problems, I explain the process louder in short I am talking to myself like on how I can integrate or approach this kind of situation. Honestly, it's effective. Create system not goal. Now, I am going the beyond the depth understanding of calculus and physics.
The problem is, i'm afraid to try again and i'm afraid to practice. Once I understand how this method works I'm afraid to try it again on a different math problem because i fail or I forget how to do it then i lose motivation to continue learning math thinking "how I'm going to be good at this ? "
I got good at math by practicing it everyday, reaching out for help when i need it an taking advice from people who are just overall better at math than i am.
So, yeah, as you really well pointed out. Indeed, even if it doesn’t look like. The truth is, and you should get ready for this: that we, yes we do, live in a society.
we need book review video
I don't have anyone to explain it to, so i often just say everything that comes to mind aloud, and try anything that seems feasible. Ive found saying it aloud helps quite a bit.
I'm almost done with my math PhD and I'm still not good at math...
@teawsome 123 that you probably infinitely suck at math
I recommend being okay but convincing yourself and everyone around you that you're brilliant. It's not an ideal strategy, and in some contexts it can be fatal, but, and it's a big but, big butts are a sign of a smoker trying to quit.
what's your research?
@@ethan_martin yeah ask him ?
Your probably just at such a high level that you are more aware of your mathematical shortcomings than most people.
3:09 "And your professor has the assumption that if you can solve the n = 2 case, you can solve the arbitrary n case"
This hits so hard. A lot of your homework assignments for math classes will be like 3 problems and you'll get similar/harder problems on the test... life goes on.
I literally was bad at math till 2016.
I had to learn math because of my passion for physics, so i got a private teacher for math and physics and he really helped me to vision math...literally, any mechanical procress i witnessed, i trued to use plane geometry and Newton's laws to explain it.
I was almost too enthusiastic about doing math..keep in mind...as at the beginning of 2016, the most complicated math equation i knew was y =mx +b
Behold, by 2017, i had been alsmost finished quadrics and Taylor expansion while i got onto uni by 2018 but i used my time doing advanced concepts like multivariable calculus and complex function qnd variables. Now im alsmost done and about to begin study Linear Algebra.
In other words....personal study is the best.
I really relate to this because it worked that way for me too. O igot in college in March and I couldn't even sum fractions, now I'm in my second semester and doing Calculus II and Physics I.
That last tip is gold.
If you’re in highschool, see if you can help someone who is struggling with math homework by explaining it to them. You’ll never forget the concept after that.
Great advice. I have no fewer than 8 (yes 8) textbooks on Real Analysis. The various paths to correct proofs are the only way I was able to "get good at" (yeah right) proving the important topics. Thanks for the video & Cheers
thank you , i am in high school, and i always thought i was OK at math, but i could never excel, this has helped me to do just that . again... thank you.
You have to love it. You have to find the challenges inspiring, and you have to want to learn more.
Beginning: Hey what's going on SMART people
Me: I'm just gonna head back to doing my dumb stuff
Nice advice , I will add to what you said about solving problems , I usually do half of the first half of problems and two thirds of the second half ( usually where the "fun" ones are ) helps avoid repetition too much .
Yes the high school students needed this. Thank's.
Tysm for making this. It's amazing how far you've come from testing into algebra and I'm worrying about taking calculus before I graduate highschool.
This really helped me remove my nostril hair more effectively. Thank you.
Not a physics major and I stopped taking Electrical Engineering at Tidewater Community College and your videos have been popping up over the passed year and I had no idea you are/were at ODU! Pretty neat stuff man and you have some great videos!
dude you basically just described me when describing yourself, highest I took was Pre-clac, couldn't do Calc till semester 3, still suck at math, and realizing that I need to practice....you're basically me from the future
"Read it from somewhere else" yes. Definitely helps, in my experience. Also exaplaining it to someone else. I always find where holes in my underatanding are if I start stumbling when trying to explain it to someone else.
You just perfectly weave helpful advice and meme shit posting together, don't you? That super saiyan 3 line really hit me good😂
My guy your videos are priceless for an engineering student like myself. I was wondering, could you do a video on deriving the formulas for circular motion (vector method)?
Friends: What do you wanna be for Halloween?
Me: Integral of Sqrt(tanx)
Even though I don't think I have to start from algebra in school, I still don't think I'm actually good enough at it when I see some calc 2 integration problems. Those really make me question myself, what I've really learnt, and whether I can EVER actually do one of these whack ass problems if I come across them randomly.
P.S. Great video as always :] Really appreciate the videos ( both meme ones and the helpful ones ).
that integral is 3spooky5me
420spooky69me
Just put the integral into wolfram alpha
For me, the best way to git gud at math is to love the subject first. I'm quite good at math, but because I hate certain subjects (Matrices, vectors, probabilities, statistics, those are nightmares), I can't do well on them. And the teacher matters too. I don't know why but my first math teacher in high school has changed my mindset about math and makes me good at math. Maybe because how he teaches in slow pace makes me understand the concept a lot more better. Sometimes the students could be overwhelmed with a lot of math subjects thrown at them. They end up being bad at it just because they just can't understand the concepts as fast as the other students. I actually one of those students. Not in math though, but physics.
The funny and frustrating thing about math is how some people get it easy and others struggle for a long time. Solutions to a math problems seem obvious or self evident once you have confident grasp of the concepts. While tutoring I've always found that students have a eureka moment, and from then on those problems become part of their tool set. My method for getting to that has always been to try show how to do something in as many different ways as possible until one them sparks this moment.
Seeing your positivity talking about math really made me feel hopeful. I always tell myself I’m bad at math, so maybe I just need positive self encouragement. ☺️
5:23-5:24, "we live in a society"
Immaculate, outstanding.
Take this from someone who failed high school math courses, SAT failure, scraped into college, now lucky enough to be transferring to Harvard to study physics and math. I got "decent" at math by drilling problems from old various calculus and algebra books i got from my neighbor who passed (engineer, so a lot of good material collecting dust). I was put into physics 1 (algebra based) where the prof was my advisor, he loved teaching so much, on the side, we would work out the calculus behind the physics instead of algebra (so long as on exams i used algebra to solve them and not calc) I was in pre-calc at the time, took a test and got a shove into calc-2 and excelled, now in physics 2 online, labs suck but i use Griffiths like a bible. Ive almost done all the examples in Griffiths "intro to E&M". I have struggled a ton in the past, im illiterate, cant speak much or well, cant think quick, but now, i can do math problems like nothing for the most part of it. I also downloaded some physics textbooks online from free pdf sites and drilled those problems hardcore, but make sure you understand what is really going on. You can read pop-sci books and know everything ab black holes, or read a book on tensor calc, but drill the problems. (Especially schaums) deff spelled that wrong, the fuckin practice books Andrew talks ab yk the ones. But go at them, seek help all when you need, Chegg is also your friend, (fuck bartalby or yahoo answers), but In my case, for two years straight, during covid, online, with three lab sciences at once drill and drill, but understand what you are doing is more important.
In my experience, the only way to get good at math is to become as a visual person as possible. As you get more and more visual, when you go to bed, and you can just start seeing the problems in your head. This way helps me to understand math and physics. Especially when I’m studying relativity by myself.
For me the way I got much better at math was not just understanding the concept very well in one way, but understanding the concept really well in many different ways. For instance if you are solving a least-square problem, there are more than 6-7 ways to solve it- perhaps more. So I get really familiar with all the cases. If it's a more general concept, understand it's different proofs, the algebraic proof, a geometric one, and others.
Thank you for this video. I am currently taking AP Calc AB. Sometimes, I struggle a bit when the teacher dictates the number quickly, as english is not my first language. However, whenever I don’t understand a concept/problem, I search through a few sources (Khan Academy, textbooks, and TH-cam) :)