How To Self-Study Math

in this video i'm going to show you how to actually study math i'm going to give you a step-by-step process that you can follow so you can sit down and actually learn some mathematics and it really doesn't take that long if you follow these steps you'll be able to study smart and make effective use of your time step one is to gather your supplies so for the purposes of this video i'm going to show you the things that i've been using whenever i do math this is a really good choice for a pencil these are ticonderoga pencils and they're really good quality so currently this is the pencil i use and it's pretty awesome i'll leave a link in the description by the way to all the supplies i use in case you want to check them out if you're one of those people who likes to do mathematics and pen then this is an incredible one i've known a lot of people who are engineers and physicists and they tend to use pen and they tend to produce a lot of really correct mathematics personally i prefer pencils but if you're a pen person this one's pretty incredible although it is a little bit pricey of course everyone needs a sharpener and i like having one that's pretty good this one doesn't use batteries so i can take it with me so if i decide to do math outside i can take it outside and it doesn't require any electricity or anything like that one of the most important components is of course a timer so you can use this to time your sessions which i highly recommend this is a really simple one that works great and it uses one double a battery of course you can't do math unless you have something to write on and this is paper notice this paper doesn't have lines the reason i use paper with no lines is because the smartest person i ever met used paper with no lines and i thought maybe that's making him better at math so i started using paper with no lines and ever since then i have been hooked so you've gathered your supplies you have either a pen or a pencil a timer a sharpener and some paper that you're comfortable with and it doesn't have to be these i would just recommend using what you prefer if you prefer a mechanical pencil get that remember you want to be as comfortable as possible when you're working on math the next thing you want to do is pick a quiet location you can see here the room that i'm actually in is very very small and very secluded and it is extremely quiet so try to find the quietest spot you can so you can sit down and be productive if you can't find a quiet location to study then try to find a place where you can go that is a little bit more quiet consider college libraries or even public libraries those are usually pretty good places to go study the next step is a really fun step and it's picking a book and this is a step that you might get stuck on my advice is just pick a book and go with it if you can't make a decision just grab one of your math books and start reading it now i've got a lot of books here as you can see we've got some calculus advanced calculus vector analysis combinatorics more calculus differential equations linear algebra more differential equations real analysis number theory some abstract algebra some multi-variable calculus some real analysis some topology a little bit more calculus and some trig so all kinds of choices and for the purposes of this video i'm actually going to pick one of these books and i'm going to show you how to study because this is such a popular book and it is so widely available and it is so widely used by colleges and universities all over the world i've chosen this one this one is calculus by james stewart and it is the fifth edition this is a super thick book that people use to take calculus one two and three in colleges in the u.s and in canada once you have the book you have to decide what section you want to read my advice is to pick something that you want to read so something that is interesting to you but at the same time you want to pick something that is going to push you a little bit you want to study something that you really haven't seen before or something that you feel uncomfortable with you want to push yourself into that uncomfortable place so that learning actually takes place after all the whole point is to actually learn something now it's time to set the timer i like to set it for one hour i feel like one hour is a good amount of time to study most subjects and then you just get started so you start reading the book you notice that it gives you the definition of the hyperbolic functions so the first thing you want to do is make sure you know that definition so how do you do that well the best way to do that is to actually write down the definition and you want to be able to write it down without looking at the book for example the hyperbolic sine of x or sinch x is going to be half the difference of e to the x and e to the negative x so you take e to the x you subtract e to the negative x and you divide by two the hyperbolic cosine is going to be the average of e to the x and e to the negative x so you take e to the x you add e to the negative x and you divide by two and for the rest of them if you noticed in the formulas they're very similar to the trig functions so you can go on from there and fill in the rest of the formulas for your hyperbolic functions if you find yourself having to look at the book you want to start over and do everything without looking at the book until you know the definition's cold as you continue reading the text you want to work through all of the examples for example here you notice they give you the hyperbolic identities and they have a proof of one of them so maybe prove the one they do but do it on your own without looking at their solution and maybe do a couple more just for practice then you continue reading the text and doing all of the examples that you can not everything will make sense and that's normal and you want to just work through it and try to understand as much as you can from the examples that are given in the book once you get to the exercises you should feel pretty good about yourself because you made it through the entire section at this point you should start doing as many problems as you can in a book like this you'll have answers to most of the odd numbered problems which really helps one thing you will notice in most math books is when you get to the problems at the end of a section you're going to find problems for which there are no examples in the book so you wonder how am i supposed to figure those out well that's when you have to go back to the section and try to find information that you can use to help you solve those problems if you still can't figure them out it's okay books like this have tons of problems and some of them are harder than others and if you're wondering why the author didn't include examples of every single type in the book it's because then the book would be insanely huge so they have to pick and choose what content they present in the book so now you're done studying you should feel good about yourself you got a lot done and this is the last step it's to reflect reflect on what you did reflect on how meaningful your time was you just took an hour of your life and you learned a lot of mathematics if you like you can keep your work you can buy a hole puncher and put it in a binder you can stack it up in a big stack or you can throw it away whatever you like as the day proceeds you're going to find yourself thinking about some of the math you did maybe there was some points that you found confusing and you might feel a little bit confused and i really think that's normal when you study math and when you read a math book you're not going to understand everything you're going to have moments of confusion and those moments of confusion should motivate you to study more next time one of the great things about self-study is you can study whatever you want so the next time you have a study session you can study something completely different if you didn't like the book that you were using you can get a different book math books are so cheap you can get books at really good prices and the really good thing with math books is they contain so much information for example this book here has enough material to teach you calculus 1 calculus 2 and calculus 3. in fact if you went to college and you took all three courses calc 1 calc 2 calc 3 you probably wouldn't even cover all the material in this book in fact i pretty much guarantee it there's just so much content in a book like this if you're wondering which book to get my advice would be to get as many books as possible a lot of times you'll pick up a book and read a certain section from that book and it won't be very good and then you pick up another book and it's a little bit more clear for example here we have two differential equations books but they're very very different this is the one by edwards and penny and this is the one by zil and they do have some similarities but this one covers a lot of topics that this one doesn't so by having a wide selection of books that's really going to help your self-study journey hopefully this video has given you some ideas on how to have better study sessions and learn math on your own i hope this video has been helpful good luck and take care

Channel: The Math Sorcerer

Views: 1,942,993

Keywords: how to learn math, how to self study math, math, self study, learn math

Id: fb_v5Bc8PSk

Length: 8min 16sec (496 seconds)

Published: Fri Aug 12 2022