My Self Study System

[@DrTrefor]

What are your favorite self-study tips? And don't forget to check out https:/brilliang.org/TreforBazett for one way to support self-studying math:)

[@HighlandHellboy]

In this day and age of chatgpt, I use it to self study all the time. I would avoid just randomly asking things. Instead upload the pdfs and/or textbooks you are already currently using and ask it to only use the sources uploaded. Doing this turns it into a way to interact with the source to verify and check your understanding. Don't get it to work out problems unless you've already tried, but if there's no answers to problems, it also becomes a semi-reliable way to verify your answers.

[@Hotrob_J]

​@@HighlandHellboy "semi-reliable way to verify your answers" is not something I'd consider useful. Something that gives you mostly correct information mixed in with some wrong information is dangerous, particularly when it's difficult to figure out when it's right or wrong.

[@Hotrob_J]

Also, is that link right? I think you may have made a typo in the domain.

[@ClaytonMurzyn]

Hammer out questions mainly. Read the chapter and supplement with youtube video for explanations and visuals. But it always happens to me where I "think" I get it. But after enough questions you actually get it. You make many connections and everything falls into understanding. I'm amazed at how much it seems like you need to remember. Once you actually understand it feels like it all makes sense and you don't have to memorize anything.

[@loquaciouslizard59]

Seek multiple explanations for any given subject. Some will have more depth than others, others will make more or less intuitive sense. Beyond that, determination.

[@henrikthehun]

I'm a math major at my community college. I 100% agree that you still have to practise and put the effort in, no matter how passionate you are about the material or intelligent you are, putting in the work and practise is what pays off. I've learned this the hard way a few times

[@zachhaberler3903]

I think its important to also note that self-study can be very iterative. A book or topic you approach at one point in your self study may illuminate some things based on the interest and questions you bring to it at that point...revisiting the same topic or book at a later stage of self-study will illuminate different things or will help you realize that you only understood them superficially before (or not at all). Iteration is part of the journey.

[@MarleneWalker-su8ku]

Very underrated comment, and it's a beautiful thing when it happens.A wide selection of books is excellent in this regard.

[@whitb62]

I believe that mimicking the structure of a college course is extremely helpful when self-studying. For example, try to watch the same number of lectures/hours of material (if available) as you would if you were attending a real course, complete as many homework problems as as you normally would (usually from a cheap/used textbook), and simulate test preparation. My school provides past exams from several years back for many math courses on their department website. When self-studying, I try to master these as if they were mock exams, just like I would when in an actual class before a test. I'll even make quizzes out of lecture problems, mastering these as well. And you're completely right about structure. It is vital when self-studying as it gives you a form of accountability that is hard to replicate without grades and a professor.

[@Luke_Robbins]

Doing calc 4 in electrical engineering rn, and you are the best for obtaining that additional intuitive understanding that I don’t always extract from my textbooks or lectures. Love your videos! Best on KZbin, there’s a lot of KZbinrs I watch. You do the best job, along with 3b1b.

[@FlorianProck-Schauer-j2k]

you're absolutely right, the most I learned about Differential Geometrie or Topologie was out of beeing curious and triying everything on different problems that I asked myself, not by simply following a Script or Book. Curiosity and Practice is the best way to learn and also the most fun one.

[@keithdow8327]

Thanks!

[@DrTrefor]

Thank you so much!!

[@ISuperI]

5:32 this is such an important and reoccurring problem that I think not a lot of people think about. Math is not a game of just contemplation, you _must_ do exercise regularly if you want to really cement the thoughts in your head. I say this because I see a lot of people that, either watch the lectures resumes or just read the textbook, but omit the exercise part and then wonder why they can't understand the topics later and get stuck (I also had this problem too). Another thing: try to do all the exercises of your textbook, regardless of how hard or -trivial- easy they are, *do it* to make sure that you are effectively learning. And, if you don't understand, go back to where you could.

[@Idyll_Insomniac]

Perfect timing. Firstly, you and Prof Leonard are my go to guys to watch, you manage to describe the material in a way I just 'get'. I'm currently studying a Bsc Mathematics from an online distance learning university, so self-learning. I'm in my final academic year but barely passing. Honestly I can not remember most of what I have learned prior to now. I still have to go back and relearn stuff I have already covered like basic differentiation/integration techniques. I follow some online lectures here on KZbin, currently on Calculus 3 and enjoying them. But my uni mainly just uses their own textbooks which I struggle learning from, I'm much more auditory/visual. So close to the end but still contemplating giving up, of which I have done before at uni so do not wish to do a second time. I have just lost all motivation, especially whenever I associate learning with this uni. I have tried just learning from external resources then using that for my assignments etc. but got marked down for not using their specific methods/procedures so gave up on that. I will definitely be giving this video a rewatch or two to take some notes. All the best

[@kenanz7613]

Hi Trefor, I just wanted to say thank you so much for all the work you've done and continue to do over the past years teaching calculus, discrete mathematics, and more. I'm a computer engineering major and I don't think I'd have the grades I do now without you. You explain so many thing perfectly and encapsulate it to where I think anyone can understand it, and you do it seamlessly.

[@Petch85]

At uni, one of the things i learned was how much I learn by teaching others what I just learn. When someone else ask you a question you quickly realise that you don't fully understand it yet. Also we did a lot of rapports and coming up with a good structure and a good angle to use in a report for writing down what you have learned, proof reading etc. At the end I understod the material much more. Another thing I always do when I am trying to learn something new is to take my time on all the side quest. Not just answer the question as intended. If you know more than one way to solve the problem, try more than one and pay attention to the differences. If it is an equation maybe plot it, change variables and make other changes. See what happens. Always check if your result is correct if at all possible. If you need to find x, put your result into x and check that the equation works as intended. If it is about real things in the real world try to imagine it. Does your result make any sense, does it seem reasonable? Maybe think about what happens at the limit, upper bound, lower bound etc. When does the assumptions break down. How fast do you have to throw the ball before the wind resistance becomes very relevant. Think about other situations where you could uses what you are learning. It all helps with the understanding of the problem. I think of it as looking at the same thing, but from different angles and distances or tricking my brain to pass nearly the same thing through it again. It helps with understanding and understanding makes is easier to remember.

[@ShrinjoyPatra]

Just started university doing Physics and your videos have been extremely helpful in helping me get a much deeper understanding of the maths content that I learn so that I don't have to rely on any rote learning. Definately going to use these tips to help me get more consistant with my learning.

[@DrTrefor]

that sounds awesome!

[@camrouxbg]

Trefor, this is such a fantastic video! I am teaching grade 9 math this semester and, while it isn't as complex or detailed as upper-level maths, it is challenging for students. I am always encouraging my students to practice, and I regularly make the analogy to sports (they look at me like I'm from Jupiter when I do that). One of my goals this semester is to work on that spaced repetition with them. They may think they're being assessed only on one outcome, but it is also looking at outcomes they've previously worked on and assessed. I really like your five-step system, and I'll certainly adopt it for myself when studying something new or even reviewing something I've not looked at for a long time. Cheers!

[@Hotrob_J]

Thank you - I'm looking to start doing this. I loved math in school, but I never learned how to study so hit a wall in Calculus 2 when I couldn't immediately intuitively grasp the concepts (and the undiagnosed adhd didn't help). I'm not prepared to leave my career and go back to school for 6-8 years to get the masters in theoretical physics I've wanted since I was a kid, but I still want to study for myself so I can better appreciate the beauty of mathematics.

[@guruji75]

As a high school teacher, studying graduate level mathematics keeps me humble and reminds me what it is like to learn with fresh eyes. Many textbooks are not great for self learning as they don't provide the motivation for why a particular topic or matters. They are often quite rigorous or terse in their development of ideas which I find challenging when self learning. The other challenge I have is how different parts of mathematics connect with each other - is there a preferred sequence of topics??? For example could the study of topology, Riemann spaces, differential geometry, tensors, Lie groups or Clifford algebras be done in any order and what is the prerequisite knowledge to have before tackling these topics.

[@Budgeman83030]

I recently bought a college algebra textbook, a pre calculus textbook, geometry and trigonometry textbooks, and I found the exact same calculus textbook I used in college back in the mid eighties. I’m just bouncing between them depending on my mood

[@cutenot]

Wow, I really needed this right now. Sometimes I feel dumb going back to the basics or focusing to much on certain details but this has helped me see that I am doing something good. Thank you!

[@rorolonglegs4594]

I love the production quality!!!

[@MelodiCat753]

Great video, but I will say that for people with ADHD, they may not be able to form habits like others can, and that's okay. We often benefit from deep explorations and then a break. It's not as consistent as most neurotypical people's patterns, but we still make great connections and become strong at our passions! I really loved how you emphasized connecting topics together. Since October, I've been using Obsidian for my math note-taking partly due its great LaTeX support but also because I can literally link math topics together, allowing me to see ideas and techniques that travel between disciplines. That cross-thinking really helps you remember a subject far greater.

[@reversicle212]

This is such a good video OMG insanely helpful PLEASE post more videos similar to this one! Especially ones regarding problem solving in math, how one should go through a textbook, etc.

[@DrTrefor]

Problem solving, oh yes! That's a great idea.

[@callmedeno]

One thing I had to watch out for was the very heavy 'contextual expertise' you get what doing a particular math textbook. It's like when nearly all the questions are necessarily following a very particular exposition, you drill a bunch of problems and it feels like it has become easy so you fool yourself and think you understand. But really, without the active thinking it becomes a kind of rote when the questions are all on that same topic. It feels like it might be optimum to do just a very small selection of exercises from each section, and go through the book twice, versus once where you aim to cover most questions. I know it sounds obvious, but I find often times the knowledge has been shallow and only connected to a certain presentation.

[@violetsweet1660]

My self-study curriculum has been focused as much on CS and writing code as mathematics in and of itself, and one advantage of that, I believe, is that creating one's own version of some mathematical structure as a struct/class/collection of functions etc. in a programming language is often a great way to gain practical/computational familiarity with that structure. Python specifically is a great language for, if nothing else, playing around with numbers. Of course, I do this alongside writing proofs and doing textbook exercise problems, usually with good old pencil and paper. If I have any self-study advice it would be to keep and obsessively fill lots of notebooks. Also: buy a nice compass and a ruler and construct a big scalene acute triangle, then find its four classical centers and Euler line.

[@DrTrefor]

Ya I really think the interplay between math and coding is so powerful

[@capnbug]

I tried self studying over the winter break but failed hard lol. I got overwhelmed by getting stuck on problems in a single section, to the point where i felt like i wasnt progressing at all. I was planning on structuring daily practice problems like "do 2 easier problems from the new section and 1 hard problem from the one i finished up" per day or smth like that. I asked people if that made sense on some discord and they said no. Your thing on assessing yourself really validated my initial thought lol. Maybe ill try doing extra self study this semester

[@DrTrefor]

To me that reads as the gap between where you currently are and the difficulty of the problems you were trying was (perhaps only slightly) to big. Like for instance, I've noticed students who try calculus but their algebra skills are the real problem, something like that. So what I might to do is try to assess yourself authentically on the slightly easier content that comes BEFORE whatever you were trying to tackle, see if there are any weaknesses there and then return. Marathon not sprint:)

[@callmedeno]

I think it would be great (if you haven't already) to actually show your experience of going through a new a chapter yourself where you kind of do a commentary on all your thinking in a particular context as you grapple with new concepts. Almost like a reference to people new to learning from textbooks can reference and see the reality. As a self-studier who has now become somewhat competent, I find there are still times when I open a new book or chapter where I get the daunting feeling, the difficulty finding the most relevant things, when to think and when to just go to exercises etc. I just think it would be extremely informative and motivating for people to see how (hopefully) slow it is going through a couple of pages. Even though I know math isn't like other books, there's still a part of my brain at least that feels inadequate by how long it takes to really absorb new concepts in math even though as I said it may just a few pages of text.

[@DrTrefor]

Ya actually that kind of deep dive learning something new kinda together would be a cool video, I’ll think about that

[@authorpathak]

i love him more then my girlfriend

[@DrTrefor]

:D

[@goofy_walking_pluto1218]

😂

[@alex_ramjiawan]

*than.

[@solaris413]

is it bcz of the rainbow "Pi"?

[@amrsaied8696]

I just came for math, these things are everywhere right now. ​@solaris413

[@pre-universitygeometricalg5862]

Extremely helpful. I'm promoting it (and your entire channel) in our LinkedIn group.

[@DrTrefor]

Thank you so much!

[@Naaaja-ld]

Hello Dr.Trefor, do you think that the journey in university is more like a journey of doing self-study?

[@jursamaj]

Much of my learning thru the years has been totally unstructured diving into knowledge, just for the joy of learning things. Growing up in the 60s-80s, we had 2 version of Encyclopedia Britannica at home, plus yearly update books. I'd read or skim most of the update books when they came in, and it was never unusual to see me on the living room floor with half a dozen volumes of the encyclopedia open, as I followed cross-references. In college, I took calculus 1 & 2 in 1 semester, and mostly learned it from reading the book, rather than from the professor. He was… not very good. I got invited to study session, not because I needed the help, but to help the rest of the class pass.

[@GottfriedLeibniz5]

Thomas's Calculus is the top notch book for me.

[@amritsagarkar7899]

Hi, Can you put a video a explaining whatever u said here in a more detailed fashion so that every category of student can get benefit of it. What u said seems like an ideal one case.

[@PaulHoskins-t2c]

Professor Bazett, I have wolfram alpha. For future content could you please explain how the wolfram app does integrals with double substitution. Also, can wolfram app do double or triple integrals?

[@PaulHoskins-t2c]

Professor Bazett, I believe students suffer from mental atrophy because of alcohol or pot. The memory curve is e^(-x) or worse because of bad habits.

[@noobifest2413]

This seems so similar to inquiry-based learning, which I plan to implement in my studies. How long should I study for those subjects, though? I'm trying to build a multi-faceted approach where I use a variety of techniques to study, yet it's hard for me to find structure in my routine.

[@DrTrefor]

If your constantly assessing, you’ll figure out the time needed based on how the assessments go

[@aragajamishra8323]

Hi Sir, can you please share how to be more productive and manage time during phd to finish it on time.

[@DrTrefor]

PhD is a marathon not a sprint. I sometimes struggled at this, like I'd pull a crazy late night and work until 4am knowing I had a supervisor meeting the next day and didn't feel prepared. But then I'd sleep in and doing nothing the entire day AFTER the supervisor meeting. Lol. So when things worked for me it was about having a really solid daily routine and habits that split between 1) things I HAD to do (like teach a tutorial) 2) things directly related to my PhD work and 3) all the tangential things liek seminars and reading papers that are still important. Need a balance of all 3 so usually i'd carve out chunks in each day for each.

[@kapoioBCS]

I fully self study algebraic geometry in the past. It was simultaneously the worst and best day of my life. Nothing else has make me feel more stupid and lost before. And I am a PhD in string math 😢😂

[@kapoioBCS]

I still feel that I don’t really understand very basic stuff 100%

[@krishna396]

Sir please teach financial maths 🙃

[@algirdasltu1389]

Do you have a similar book on calculus? Preferably multivariable/vector, although, some of my calc 2 needs polishing.

[@DrTrefor]

No, but check out the CLP series from UBC. Free and open source and good.

[@wjrasmussen666]

I have a few books on proofs that I have collected since Covid. I am going to study one of them this year.

[@DrTrefor]

Awesome!

[@wjrasmussen666]

@@DrTrefor I have chosen to start with The Book of Proof by Richard Hammack.

[@technicly.]

I just watch your videos!

[@funkycatglasses01]

Nice piano 🎹

[@DrTrefor]

Thanks 🔥

[@MikeFazedMuch]

Make your own definitions and theorems list.

[@DrTrefor]

Ya I think that's a great idea

[@fframemrl]

i want to learn math because i am 18 and i dropped from school when i was 15 wasted these days, and i realised if i realy try to learn, math book with "EXERCISES" is MUST thing that basically teaches me how important the instructor is, but nowadays we have ai chatbots, but the biggest problem is, i can't choose a source any advice?

[@fframemrl]

i am no pro at past 8th grade basic wuadratic equation

[@amritsagarkar7899]

Hi can you suggest some nice channel who discusses how to self study graduate physics

[@DrTrefor]

I don't know, but I think at the graduate level it would be about finding professors (as opposed to youtubers) who are posting full lectures for their graduate courses as opposed to the more pop physics stuff from people like veritasium

[@SEVIT_gamer]

Assalam alaikum teacher, thank u for ur videos, just love it!!

[@DrTrefor]

Glad you are enjoying them!

[@sedthh]

Professor, you should do some collaboration with other math / science channels or guest appear in podcasts to boost your views.

[@DrTrefor]

That’s a great idea actually, any favourites I should reach out to?

[@matejcataric2259]

​@@DrTreforSteve Mould or Dr Peyam. Greetengs from Croatia,love your stuff!

[@sedthh]

@DrTrefor 3blue1brown, Tarek Said, Matt Parker, Tibees, Sabine Hossenfelder, Steve Eigensteve Brunton For podcasts, you can go for the ones that have little to do with maths, and share ideas like you do here + how you also struggled and how people often give up after a topic that they can't get their head around, thinking they are bad at maths. I would also try Neural Network related channels because many students want to learn stats and calc for the sake of machine learning. Good luck!

[@kapoioBCS]

@@sedthhNOT Sabine

[@imeprezime1285]

​@@sedthh Tibees and Sabine 😂? I guess Dr.Trefor doesn't want to become a clown

[@mr.misbah7577]

Hey Trefor, Do you support LGBTQ+?

[@Caio-Ann]

hey , what about a phyton playlist ? @Dr. Trefor Bazett

[@DrTrefor]

ooh, I might! I'm not yet enough of an expert in my opinion, but would be fun to work towards.