Tips for Self Studying Mathematics

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In this episode I answer a question I received from a viewer. We discuss self studying and mathematics. Do you have any advice? If so, please leave a comment below.
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Thank you:)

[@mannydossantos9603]

The biggest challenges are self-discipline and leisure time sacrifice. Procrastination and distractions are always constant temptations. Being focused on the achievement goal should suffice.

[@richardphillips2405]

That's a big one, but very true.

[@kevinthompson9953]

Definitely keep notes. I like using plain unlined copier/printer paper and binders to keep them in. By using binders you can add pages, remove pages, and move pages around easily. If you have a lot of notes or subjects, you might try researching the John Locke index method. There is an older book called "Writing the Laboratory Notebook" by Howard Kanare which is helpful for methodologies for general scientific notekeeping, but applies to math and other subjects as well, and is an entertaining read. I have heard many suggestions of keeping notes with other methods, i.e. computer, Ipads, tablets, etc., but it isn't the same. Nothing beats real books and real notebooks. They work anywhere, they don't need batteries, and they will outlast you. Good luck on your self-learning endeavors whatever they may be.

[@gregoryknapen9133]

There is some research that shows that writing things by hand seems to help with retaining information better than alternatives. Writing requires more effort and it is harder to correct mistakes, so you tend to think more about what you are about to write than just typing.

[@forestappalachia6047]

I keep a short journal of what I'm studying. Each day I'll write an entry summarizing what I learned that day in my own words. It is a little more time consuming but it's a good way to track progress

[@douglasstrother6584]

Start with one book and build your notes in a loose leaf binder containing pages 1, 2, 3, 4, 5, 3a (I get 3 now!), 6 ... Afterwards, do a synoptical study on an additional text to understand a different perspective on the same subject.

[@SequinBrain]

This paragraph isn't directly answering the question except in the case of missing something. With either a school where there's a teacher or studying alone, it seems like the goldilocks problem: school goes too fast, self-study goes too slow and as the questioner mentioned, in both cases I wind up forgetting more than I would like. I know this is somewhat to do with my horrible review regimen. But even with a good review schedule, the speed problem seems to still be wrong. My goal is 1 textbook per 6 months, not just 2-3 chapters, but the WHOLE book. Neither schools nor self-study achieves this amount of learning in that time frame. Couple of additions to what you said already: 1. Maybe not the best way, but I use one book for notes and put the name of the textbook and the date when I start a page. Then all the notes aren't scattered all over the neighborhood. 2. Random selection is fun, but for now, I'm focusing on my weakest area and trying to get through just 1 textbook on that subject to strengthen up those weak spots since I'm tired of seeing the same mistakes or having the same issues with every other subject. Again, just some ideas that maybe are done better by others with more skills than I have.

[@MathsScienceandHinduism]

I self studied all subjects including math in school without tutor and performed very well in all the subjects including math. Now I am in college pursuing a math degree.

[@abuhammer7450]

How did you do it?

[@hemrajue3434]

It's difficult to study 3 or 4 subjects by means of self-study. It's better listen to class lectures or watch video lessons. Video lessons are useful in one way that we can rewatch and understand well.

[@what_um_what6690]

There are a lot of shortcomings in trying to learn from watching videos. First, this is not a lecture setting. You can not ask your peer if you didn't catch something, you can not ask questions from professors. There are too many distractions just a click away which are less evident in classes. There are no questions to check the understanding, no assignments, no exams. Video lectures have less engagement of your brain compared to actually reading and trying something in the notebook. One may get an illusion of understanding but can actually be quite far from understanding the topic. We need to dedicate some time to actually sit down go over a topic and try to solve the question. When there are plenty of video lectures available at a click, this becomes difficult to do.

[@christressler3857]

Well, you also don't want to be too random. I have an ultimate curiosity for the blurred lines between algebra, logic, category theory and other foundations. Reading Goldblatt's "Topoi" made me realize just how out of touch I was with algebra, so *within* algebra is random, but I headed to algebra. I have my own reasons for studying algebraic geometry, so I started with Kendig and Jenner. The second should've been easy but I think their format/style kept tripping me up, and not a fan of Kendig, so I went to Garrity et al, superb. Job considerations can also be a guide to choosing. For example, I'm leaning into data analysis, so books on statistics and programming are the only reasonable way forward. I guess what I'm saying is, if there's a subject you're interested in or a career path, you may have to sample some books and randomly pick some maybe before settling.

[@lse123polis]

What i discover with the whole information we get over the internet, is whatever you read a blog article, or a chapter of a book/textbook, or a tutorial, or watch a video tutorial or else watching in KZbin, is to do just after these tasks a PRACTICAL WORK about this subject, like, write a blog post, or write a coding task like a web page or small program in your skillset programming languages or may a whole website or a whole program - just something go and do, something practical, also you can record a video about this, and put it in KZbin, alternatively you can take your notes, and do this as soon as possible from the time you did the initial reading... You can also do a project pertinent like build a home gadget like a home web/NAS server this should require some more involved by more reading or more watching on the subject... home this helps!

[@Humble233]

Great video! I would add what also helps me is asking questions as I read. Like you, I find picking a topic a random helps me think about a something deeply. I stop and try to think about what I am learning and jot down questions to myself

[@hhoudrouge]

I think it might be good idea to start only by two subjects then increase or decrease the number of subjects according…. It also could be helpful to look to courses in some university and just follow their syllabus…

[@abhinandanmalhotra8519]

This will help me a lot. Thanks Professor !

[@2501-yite]

I'm taking this dude's advice and it's actually freaking working! I just gotta keep the momentum going

[@21ruevictorhugo]

I’m guessing that the reason you didn’t have to take notes to learn programming was that you learned it by doing it. That’s certainly how I became a programmer. The same strategy works for lot os other things. Say you’re studying algebra. Well, your book, or videos or whatever you’re using will go from beginning to end using what you learned and then adding to it. Do what you did with programming. That means use the mathematics. You can’t learn anything without doing problems. If you want to,learn to play the clarinet, you can only learn by playing the clarinet. Taking notes won’t make you learn anything. Notes are useful at reminding you to think about something, but then you have to go back, read your notes and do whatever it is the notes are about. The only way to learn to drive a car is by driving a car. The only way to learn *anything* is to do it. That’s especially true of mathematics. Once you’ve learned algebra you can move on to calculus, then to more advanced topics. Each one will,build on what you already have learned. And you’ll remember it from the fact that you’ll be using it.

[@gaurangagg]

Amazing! This is very helpful advise.

[@lightwishatnight]

Thank you. Love your work. You've taught me so much, and made my life better. I wish you the best.

[@noam65]

Generally, at least when I attended school, the course generally followed the same order as the text book. I'm a different type. Over the decades, the subjects I've studied followed my passion and interest in a subject. I would acquire and read several to many books on a topic, often scouring the bibliographic entries, to see the sources the author used, and would read some of those books also. Often, I would annotate inside the books that I owned, copy that to index cards, and write final form notes from that. I used to kero those in binders. Some of those are in digital format now. I wish I had been more discipline and rigorous about more taking, from when I was young. There are now books on that subject also, and youtube videos about how to take notes, annotate your books, organize, etc. Little of which was known or available to me in my youth.

[@noam65]

Keeping notes is a great thing. I keep notes with individual books, noting down the pertinent info about the text, like a bibliographic entry. I copy those notes into a subject binder. Keep an indeed of subjects and their sources.

[@cassandraandrade3274]

Considering that I finished the semester of my college, I just want to thank you for providing these math-related videos as it has helped me not struggle with math as much and has given me confidence for a math placement test that I had difficulty preparing to self-study on, you've been a lifesaver for me! 😁

[@genghisgalahad8465]

Amazing Go-To List!!

[@tethyn]

Good advice as always. Notes or proofs need to be written down and filed in some way that makes sense for the learner. I feel random learning is only good when you have a foundation of mathematics; otherwise you can be easily lost in what you are reading and do not know where you are going other than the chapter/section heading. The key is to reflect about what you do or do not know about a subject so you know how to progress.

[@donaldmickunas8552]

There are note taking systems that allow you to develop a Personal knowledge management system. There is software specifically for this like obsidian where you can take notes and link them in various ways. You can also tag your notes. I’m doing a version of this now because my memory isn’t good.

[@MysteriousSlip]

In my self study, I have found it to be useful to have two topics which do not have much dependency on each other (though if the prerequisites overlap that can be good). This way after you spend a while on one, and start to get bored with doing the same types of problems for a while, you can switch to the other and have a different type. This gives some variety and makes your brain feel like you are doing something 'different' which gives a new kick of motivation. So lets say you are studying mutlivariable calc, and you have a 'single variable' style intro physics book. They both have the same prerequisite (single variable calc) but they do not depend on each other and are presenting problems in very different ways. There are many situations where this can come up, and not just with math. But in this way I feel the two topics reinforce each other, while offering something fresh.

[@tavapaschos3136]

I homeschool my daughter. She does get math instruction from an outside source but as a homeschooler your advice to just pick a book and work with it resonates with me. Picking a book at random (when you don't know what else to work on) tends to lead you to picking the next book as a response to whatever you picked. So you do find yourself on a pathway. My math study is extremely hit or miss but at this point in my life that's what it is going to be. However I feel I have learned so many things that are valuable to helping my daughter as she goes through a more structured progression of mathematical study. Kudos on your channel. Your videos always provide valuable knowledge and/or insights about math and/or the learning process in general!

[@anniesizemore3344]

I kept track by writing in my math books. I know what I need in help in math based on what I do poorly on when I'm doing the exercises in the book. My math books are where I keep my notes. Look through math books I'm working through and you see where I filled in answers to the problems. You see where I wrote comments like "pay closer attention to signs'.

[@ShaheenGhiassy]

Spaced repetition is the best way to persist memory for the long term. If you’re serious, using software like AnkiApp or similar would work to ensure you didn’t forget anything (assuming you took the time to input the info) P.S:I’m not affiliated with any of the AnkiApp type programs out there

[@mcjedi2123]

Why not use Obsidian? Creating simple cross linked notes written in markdown with mathjax for math expressions.

[@gaurangagg]

Wonderful -- that makes it easier to form cross-linked notes and infinite combinations of bullet notes are possible through it. Unfortunately not everyone knows about Obsidian or how to use it extremely well for making high quality notes.

[@encapsulatio]

Please make a video fully dedicated to mathematical logic and what books you recommend, from the easiest to the most advanced mathematical logic books.

[@richardphillips2405]

I would like to ask a question that brushes up against your video on self-study. It has to do with what can you do if you don't understand something or if the author makes a statement that does not fit with other things that you have learned. One example was when I took trigonometry. It was taught that the cosine of a positive angle or the cosine of a negative angle is positive. Yet, the sin of a positive angle is positive and the sin of a negative angle is negative. So what does the really mean? I had and still have trouble with logarithms especially when you start raising them to a power or exponent. What I did there was I watched several KZbin videos on logarithms and exponents, read some books, and practiced switching back and forth between exponents and logarithms. I guess I wore a grove in my brain so that I can do it, but I have to think and process the data. Another area that I am having trouble is understanding with angular rotation. I don't understand Oeler, but I know how to change e raised to an imaginary value to the trigonometric form and then solve for x and y. I am wanting to use this information in order to understand complex impedance that you would find in transmission lines and antennas. I think that the problem is that I have incomplete knowledge in a lot of different subjects that you need to know in order to understand a topic. So my question is how to find out what you need to understand first before trying to learn a certain topic and how to organize yourself to achieve your goal of understanding something. By the way, I wish to thank you for this video.

[@Swangorapofficial]

Legend 🧟‍♂️🧜‍♂️

[@sverrirjensson9772]

May be not read several books at time read just two or even one then you should stay focused.

[@HilalAhmad-yu7qt]

I have been watching your content for so long now. Plz make a video and suggest suitable mathematics books for international mathematics olympiads from start to finish!

[@jidrit999]

can you review Geometry by serge lang

[@valeriybaibossynov2690]

I was thinking the same but then I find out notion , it is so great for notes

[@subhayanghosh2677]

I would like to learn BA/BSc graduation level maths which I could not explore in my college days very well. Shall I enroll in online or distance courses or self study would be fine? I get 2 hours daily free time so in a week 14 Hours and I am poor at math. Please help me by answering.

[@scatteringparameters.4167]

Help me too

[@swa227]

Hello, Professor, I want advice from you. Sorry if I find mistakes, because I use the translator. When I solve math problems, such as factoring algebraic expressions, in the middle of the solution, I find myself forgetting some steps and leaving it behind, and blocking my way with the solution, although I know very well the steps, but I forget them during the solution. Really, you are my role model. I hope that Advice me for this problem I hope that you will answer me because I really want your advice, because most of my mistakes are like this, I mean, like I forget the steps despite my knowledge of them

[@oooltra]

If you were stranded on Bora Bora with a beautiful girl and only three math books which would you choose?

[@TheMathSorcerer]

LOL will have to think about this one! I googled Bora Bora, WOW! What a cool place!

[@douglasstrother6584]

Spending time with both is "work-life" balance.

[@SteveSpears-Kuhlah]

I got 7 College Algebra books... Blitzer, Schuam's, REA, Nazari, Demystified, McGraw-Hill, and Dummies. They all have weaknesses. Only 2 of them have coverage of Function Inverses. I prefer not to be dependent on KZbin. Any thoughts?

[@aryansrivastava727]

Research more books and explore more

[@muhammadmotivation5723]

the conclusion here is we must struggle for reach our dream through out a map

[@oooltra]

Why study anything? AI is here. Learn plumbing or bricklaying or elder care. Good luck.

[@lightwishatnight]

Because math is far more than those 3 things you describe. Math is the language of the universe.

[@1vootman]

I was following Professor Leanord on YT...a plug for him because he's a fantastic teacher. I followed his courses through differential equations. It's free also!