This Will Immediately Make You Better at Math
HTML-код
- Опубликовано: 4 окт 2024
- In this video I talk about something you can do that will immediately make you better at math. I give some concrete examples and explain why this can help you tremendously. I used to not do this in the past but over the years I have started doing it much more often.
If you have any comments or questions please leave a comment in the comment section below.
If you enjoyed this video please consider liking, sharing, and subscribing.
You can also help support my channel by becoming a member
/ @themathsorcerer
Thank you:)
![Natanael Cano - Amor Eterno [Official Video]](http://i.ytimg.com/vi/EO4prCs6WpM/mqdefault.jpg)
I'm 23 y.o., having come from a bad high school we had almost zero math and zero physics (just random problems and equations), for a lot of years I disliked math, but given that I want to become a Game Developer I stumbled upon maths again, curious how I left programming for now and fell in love with math. Right now I'm preparing to go into public college to get a Bachelor in Mathematics, a small step but a step nonetheless. Since my high school was also a public school I have my doubts but I'm taking this opportunity even if it's standards are unstable. I'm halfway to finish the Precalculus course, with a book to go through it again, just to be ready for the admission test and avoid lagging behind too much.
Maths has been always a fascinating language, it amazes me, to see the equations and how they relate with the world in every single way. Right now, there is still a lot that I don't understand and it is like magic to see a calculus equation be solved in minutes but it excites me to think one day I might solve them too. 4 months ago I was oblivious of polar form or trigonometric functions, even word problems, now I understand them or at least I can work with them.
I know this comment is unrelated to the great advice that you are giving and I'm sure will make my journey more bearable, but is this channel among many others that are pushing me to the boundaries of my knowledge.
Thank you very much!
good post man and thank you!
Incredible! I have the same feelings...of love with maths, so deep that I have decided to resume, just like you. Thanks for the inspiring videos teacher! From Senegal.
It's actually an awesome BIG step, and anything about mathematics is related to everything about mathematics as far as I can tell!
Thank you. Restarting my math journey and its been tough.
You got this!
"Wisdom is the most important thing, so acquire wisdom, and with all that you acquire, acquire understanding." - Proverbs 4:7
Yes.
I find you have a very powerful voice to motivate people.
Thank you!!
I'm starting my own journey,my goal is to become an engineer. Your videos are really helpful,thank you!
Great to hear!
Your "good luck" feels like "May the force be with you"... You're a Jedi and I hope to be your padawan
👍💪❤️
Jesus man, more people should watch your videos. Just stumbled upon your content, and I gotta say, great advice!
thank you!
First,there's a hypothesis, and after that, there is an intuition, and then, there is rigorous proving.
I dont know if this is always true, but this is what I try, because I aspire to become a mathematician, and I try to do it like I'm inventing it, which gives me alot of joy!
Reflecting back on my work not only gives me many ideas , it also gives me a revision of what I did, and makes me thorough.
Well said sir, very true!
yes it definitely does these things yes!!! I really think it helps you remember things too, because it forces you to think harder about them.
I love your new icon!! Long Live the Rat Puppet!!!!!
@@TheMathSorcerer you are so kind sir!
My respect for you is immeasurable and you are my favourite person
Especially when studying dihedral groups
I don't usually comment, not that this was important remark, but with that said, I've watched 2 of your videos by now, the gift one and that one and I must say that I'm happy that I found your channel (by ad, so it works) and I just wish you good luck, definitely gonna dive into your stuff.
Wow, thank you!
@@TheMathSorcerer yeah, I found you because of an ad too. I couldn't be happier for it.
This is very true! Wow, I have been doing this ever since my math "journey" or "career". Whenever I read a proof or even learn something new, I always ask why and what it is t I am viewing? I think hard to find out what it really means even if I found the solution. Doing so, I realized that I am growing a sort of mathematical maturity. And, it develops an intuition and getting used to things.
definitely:)
At times I think I'm a math looser... You are restoring my confidence in me. By here we are compelled to give "the right answer". When I try ssomeone to think in their response I feel them think "Oh, he doesn't know *the answer* " But it's ok that because is that one who doesn't give credit on themselve.
I know, my English sucks but I think you got the idea.
I would like to thank Math Sorcerer for recommending a free book called The Book of Proof by Richard Hammack. I printed the whole book at home and made myself chapter books that I could individually study at Barnes&Noble. Absolutely brilliant book and very well written. Thank you.
I'm a tutor and Math is something I tutor a lot. For Geometry proofs I notice students want to jump in immediately and start writing. I always say : stop and think. What are you trying to prove? State it in your own words. Do you believe the statement you're trying to prove? Why? Can you explain in a non formal way why a kid should believe the statement?
Students can get pretty good at processing these questions fast. It makes the formal proof so much easier. You said it, MS: reflection is everything!
Love videos like these. Im in my first proofs class right now, taking advanced calc next semester, you’re videos make a lot of sense to me
awesome!
@@TheMathSorcerer take a look at India jee
Finding this channnel must be the best thing i found on internet. Greetings from lima Perú
THANK YOU AGAIN .. . I am not an engineer, and I did study Algebra and Calculus 1 back in college.
I want to learn optimization and statistical process control. So, I began to study mathematics some time ago in my free time.
I am currently learning derivatives and related rates of change.
One thing I have learned is that there is a very thin line when studying mathematics. One runs the risk of just using formulas as cooking recipes.
Hence, I began to study the formula itself - what it means, how it came into existence, ie., the derivation of the formula.
It has taken me 3 weeks to understand the limit definition applied to differentiation - the feeling is one of security.
One has to take the time to reflect on the subject matter.
I have been watching your videos, they are AWESOME - EXCELLENT advice.
Thank you, very much appreciated.
GOD bless you and yours always.
By the way, I am glad to know that math books have to read slowly. It was obvious to me but I thought it was because I am not a mathematician.
Carlos from Monterrey, NL, Mexico.
OK, you have me convinced.
Definitely agree with this
Well said. Applies to much more than math too. What is humorous is to reflect on one's own work from decades past ... whether math or whatever ... and say, "Wow! I must have been clever at some point, because I have no idea what I did" (a good reason to comment source code with derivations). Sure - it's partly because of not being in the focused moment of the old work ... but I have noticed the loss seems to correlate to when I just pushed something through, versus when I reflected more at the time of completing the work. Reflecting better permanently ingrained the concepts (and even the given problem) into the mind. Great channel ... mathematicians are people too ... hehehe
Going back to do mechanical engineering thank you
👍
The induction example was spot on :D
❤️
An excellent suggestion! I hardly reflected on my work before because I thought I had too many other problems/proofs to work on. Basically it was TIME; this is always a constraint - can never have enough of it.
Absolute truth. One thing I learned in engineering is that it is infinitely more beneficial to derive where simple equations come from. The TdS relations in Thero, for example, describe so much of the natural world and come directly from Newton's pivotal 2nd law; they're worth deriving by hand and reflecting on in my opinion, mainly because of the sheer volume of times I've been able to abuse them to approximate specific boundary conditions and ball-park what my answers should be.
I am afraid sometimes to reflect as I feel like I am wasting too much time and should be getting more problems done. Quality or quantity ? that is the question
Agreed as critical. I'm far from a perfectionist, but it OFTEN happens that we may feel compelled to go one of two ways :
rush through, get the answer, get the work done, prep for the tests/exams ...
OR
study, find some statement or text and then fan that spark.
For instance, back in grade school (pre college) when they said exponents are subtracted when dividing, try to focus on the ramifications of that -- feel free to dwell in it. Notice that it shows why a number over itself is one, and it shows how negative exponents work.
It's a throw-away topic, and you could just take-away 'ok, it's division, just subtract' but by doing so, you do yourself a profound (long term) disservice.
And remember, most of the time, the teachers would LOVE to help you dive more deeply into these finer points (maybe not during the class lecture itself tho).
27 yo, finishing my industrial engineering degree and preparing for pursuing a second one in math or stats on 2022 or 2023.. you've been provinding great advice.
Something Maryam Mirzakhani did while she was studying math as a high schooler was to find 4 different ways to solve a single problem. Each time you do that you are exponentially building up your problem solving vocabulary and it's fun! I highly recommend it
I just try to find another teaching book for a certain course, which isn't mentioned in the course (sometimes for obvious reasons, like finding the secret exercise source for the assignments or even for the exam) but should become my favorite book. I got three quite unknown books about abstract algebra, which were more helpful than the official books used in the course (Serge Langs Algebra book was also mentioned lol). On top of that, I try to search for books in another language (english in general, french for algebraic number theory). The topics are the same, but they're structured in different ways among the selected book, helping me to understand a topic from different perspectives.
Lecture notes from another professors (from another universities) also helped me. This is one of many reasons, why I love this channel.
Thanks to professor for advices
You're most welcome!
Whenever I get stuck on a math problem, for too long I start crying. My basics aren't clear. I'm in 10th grade. Please help!! 🥺
Great video, man. I always complain that differential equations professors have at my school focus solely on teaching the algebra of solving equations but don't ever look at the meaning behind the equations.
It’s frankly disgusting, I guess it’s for the engineers, whose whole major is more or less plug and chug
Thank you!
Just my opinion - I think you inspire a lot of people by sharing your own personal struggles.
For example, when you said it takes years! It is a life long journey.
I can definitely relate to that! Some Calculus material has taken me many years.
It really is a life long journey!
Couldn't agree more. I think it's one of the fundemental skills to build understanding. Probably one of the reasons I loved linear algebra so much was you could look at something a billion ways and still find something new about it that just blows your mind.
I'll also share my thoughts on this since I think it's a really under appreciated approach.
Aside from the review aspect I find a lot of these things are also applicable for while you're learning something. Say for example in class during a lecture, sure you can understand the simple messages and copy down the process your professor does but there is so much more you could be doing. Like thinking of the applications and motivations for doing what's being taught at that moment, or the why you do certain steps in a proof. Obiously you have much more time to explore ideas after the fact when you reflect on your notes but you can have the same active thinking mentality throughout. If you spend more time thinking about it over trying to memorize it you'll both remember and understand the subject better.
Very Inspirational ! Reflection is certainly one of the best way to develop mathematical maturity. However, from personal experience, as an undergrad, I never had the time to contemplate or reflect on all the math that I was learning (being an engineering undergrad, the work load was very high).
The power of reflection and contemplation on mathematical concepts only came to me when I was studying in graduate school. Yes, during grad school you have more time to reflect on what you study. In graduate school mathematical concepts are harder, but in return, you have less workload which means more time for reflection. Personally for me, I tend to reflect on math concepts right before bedtime at night. Lying down on bed before I snooze off. Its weird, but on many occasions the "ah-haaa" moments just comes.
Thank you for the advice and stay safe :)
missed this video, really insightful thanks
Thank you again, never seen things like you explained. It's really impressive how simple advices could help a lot. I'm gonna try implement this in my math.
Thank you for this! This was really helpful.
You are welcome!
I appreciate your wisdom and videos
❤️
I apreciate a lot your videos and the subjects you talk about. Thanks
👍
@@TheMathSorcerer take a look at jee exam indai
Absolutely true!
I would bet money that the theorem that you are talking about in the video is the sylow 1 where you prove by induction on the order of G, and yes that’s after group actions. 😉 keep up with the good work.
Thx 👍
Great Advice! I also learnt from the book 'make it stick' to randomly go over different questions from different units sporadically, because i found when i work through a unit like a story i intuitively know from the last question where this is going which makes it too easy. I also learnt that the harder you can make your learning the deeper it sits on the neural track you have created in the brain.
Great advice, the key is reflection. Theres not many books on how to start a formal reflective practice, those that are are for nurses as they use reflection alot.
Oh wow yes I totally agree with your strategy about going over different units. It also makes it more fun.
Interesting about the books on reflection, I never even considered that. Nurses? Wow very interesting stuff!!!!
Again starting my math study after 10 years.
I really like your shirt (your videos are great, too!).
Thank you!
I usually understand the broad ideas of a concept yet when it comes to math problems, I don't fully understand it until I do a real-world word problem involving a concept. I don't know if that I'm more of an applied mathematical minded person if that is the case. Sometimes I don't know why I do certain things in solving a problem, sometimes I go by the book and if that doesn't help I go online to find an idea. Understanding is something I question and worry about every time I do math
that's really good that you are that way!!! better to question it and reflect on it:)
Absolutely agree with this. Even up until very recently (this past fall), I wasn't very good with reflecting upon my work. I'm not sure how, but the habit gradually infected me and now I try to justify to myself every step I take, even if it's basic arithmetic. Heh, 's also good to consider alternative methods. I love ur vids btw
What a good video.
Thank you!
Grande
:)
Proceeds to reflect the figure against a line and gets the solution immediately
Me:
-watch the video
-try to see how I got the resolution of a problem
-can't actually do it because I figure out I actually write problems around a single sheet of paper
-realizes why the teacher gets mad at me for disorder in maths and physics exams.
Jokes apart great and underrated video.
How to reflect in maths
Hello I have a question, when Do you think someone is good at math bad or mediocre. Or is this question impossible to answer? Thank you for your time
lol i doing proof induction right now
Anyone know what the sorcerer's name is ? I hope it's falcor the high Mathzard
I'm junior highschool and i want to be better in math
Awesome 👍
First word of the video answers the question. #ggg
hehe yup:)
What type of math topics should I learn in order to become a cryptographer?
I took a grad level course on cryptography once, it seems we used a lot of number theory and stuff. Best way, find someplace to take a course on it! not easy though to find I think:)
Thank you for the advice Math Sorcerer. I will look into that.
I like this omg
👍
@@TheMathSorcerer can u help me with my math. I reflected like u said and yet I still don't get some parts
I tried reflecting on the imperial system, it got colonized.
👍🏻👍🏻
:)
Instructions too clear, I'm a mathematical genius now.
I have no Idea what any of this means. No idea what a Proof is. I thought Math was just memorizing formulas and processes.
I’m really old now & only had the basic required high school level math classes back some 40 years ago, and that’s how it often seemed to be taught - a mechanical, memorized process.
I realized even back then even at the most simple beginner level that understanding a little not only saved lots of memorization work but also kept me from getting confused.
You’re definitely not alone!
You should reflect on your day before bed.
not sure why you always call yourself "average"... you think faster, deeper and more abstract than the average person. You might have been average as a student but certainly not in comparison to the general population. The things you discover I only see whe dealing with students with IQs>110.