Study, Lift, Hydrate

I have realized that one avoids studying because one is afraid of the challenge ahead and procrastinates accordingly. It is good idea to break that challenge into humiliatingly small parts and start there.

0) Embrace your ignornace. We all have to start on Square One, wherever that might be. 1) Skim through the entire book, cover to cover. There's usually interesting stuff in appendices and so on. 2) Eliminate distractions: phone, computer, watch, etc. Carve-out a place to concentrate. 3) Write things out on paper: definitions (think of examples and counter-examples) and draw doodles, pictures, etc. that will help you visualize a concept. 4) Get going. See (0).

Hy i'm nadim, thanks for the advice, its really cool to see people that help me to grown, i think that from now and up i need to grow up mentally and physically, i needed a strong motivation, thanks for all the support, not for only you sorcerer but for all the people that helped me ❤😊

there's no set way to study. trial and error to see what works for you is the best way to study. part of studying is understanding your mind, thought process, and understanding of the topic. the only thing that can really determine success more than anything else is effort

As an engineer with many years of experience here are some words of advise. 1. Be easy or patient with yourself, don’t ever feel defeated. 2. Learning is a process in itself. Every learning process has a start and an end. 3. Celebrate your successes. 4. Move on when you get stuck, but come back. 5. Use as many books or references to learn a difficult topic. There is no best reference on anything. 6. Start and finish your homework before they due to reduce stress. 7. Ask questions.

A long time ago I got to meet the great John McCarthy and asked him how he went about reading a new paper. His advice was basically the same - read it once to get the gist, then go through over and over, writing down things he didn’t understand and working through them. Sometimes, he said, he’d have to read a paper five times to finally get it. Even the best of us have this problem and your advice was great.

Nadim: I’m sorry that you’re going through that. Depression and poverty are two extremely difficult challenges. It’s a good sign that you want to improve. Those who want to improve generally do. It’s likely that you’re improving and you don’t realize it. Improvement frequently feels like confusion. It’s when people are confident that they know everything that they are in trouble. Hang on. Hope is a major asset. Best of luck and be kind to yourself and others.

My central problem with studying (math & math-heavy fields) is the extreme oscillation between obsession (up to compulsiveness) and avoidance (usually manifesting as procrastination). I'm aware of the fact that it essentially has nothing to do with math itself (and/or other related fields), but it's the one thing that is most affected by it.

When studying Mathematics, we need to know that haste makes waste. If we try to understand every process of proving the theorems, to follow the solution of every example, and to understand the logic of them, then we have the fastest way to learn.

When I study mathematics via KZfaq videos, I turn on the closed caption and literally write down everything the teacher is saying verbatim. Afterwards, I go back over what I've written down and rewrite it in a more organized manner. It does take me a while to do this, but I've learned so much and retained a lot of the information.

this is what I've been doing for so long thanks to my mom. she's a housewife with political science degree but she is so good at mathematics and analytical thinking generally. Here is her highlights: -write things down and do any science with pen and paper -read things out loud for subjects that need memorization One of the things I like to do is to have a huge notebook for first time studying a subject then making summery sheets for exams, these sheets are super helpful for your finals since you don't need to waste so much time relearning things and give you time to start working on problems, also add some reference in those sheets for hard topics like "go back to page x in text book/notebook. Focus more on understanding lecture than busying yourself taking notes during them, if you study on youtube you can finish the video or a section of the video then writing everything on the screen down and take the notes told by the tutor these tips might sound basic but I regret it every time I become stubborn and miss them

Combining hard studying with causal reading is a great strategy.

I suspect that few are truly worthy of the title of sorcerer. In your case, I think the title is well-suited. You are a great mathematician with a kind and compassionate heart. -You make me want to be a better mathematician.

Honestly, if u study, it's nice to be able to keep track of your progress and have clear goals set up for yourself. What worked for me was inventing a language/learning journal since i study more than 1 subject. For each week and each subject, i set up a single goal (finish 2 chapters, for example) plus the approximate time i can spend on it. Then, after each session, i write down what i did, where I need to still improve/what do i need to do the next time, and i include the hours i spend studying. On the last one i like to make some yearly/monthy graphs depicting my overall score. Seeing me improving on the amount of self-study i achieved keeps me motivated :)

Mental Health is also important, without a clear mind you wont be able to focus and do math efficiently. He said that he is depressed, since hes only 13 i assume that unhappiness with his current situation would fit better. Nadeem if you are reading this, stay strong. Take that pain and convert it into effort. Study hard, become good at maths and all those problems will go away, it will just take a little bit of time. Remember there are always people who are in a worse situation.

I'm currently learning trigonometry using Mckeague and Turner. Your videos guide me on what book to use to self study.

My advice for studying for exams is review well ahead of time and once you are comfortable with a certain concept try speed running a few problems and check your answers for any small mistakes and correct them. During exams time is scarce and its important to not waste any this strategy has definitely been the difference between receiving an A or B for me.

Thanks for the tips, Sorcerer! I’m going into my Calculus finals next week. I’m feeling sharp, feeling good; I get one page of notes per test - let’s go! Wish me luck!

I always appreciate your input! I enjoy the Feynman technique in understanding the material more fully in an encapsulated way. Your point on writing it down is an excellent way in doing such and creates strong mental models/data structuring in the mind! Thank you for adding to the learning community as a whole Sorcerer! Cheers!

Please keep uploading...we want more videos...these pieces of advice are damn helpful.. thankyou so much sir

My mans getting huge!

This is the type of channels that i like!!!

Together with my dad, we are both located in Poland, were thinking what is your take on Polish based mathematicans. Have you every encountered any, or books written by some of them? Are they recognized in the US? On the second note, I want to thank you for the enthusiasm you spread in your videos. Math was always triggering anxiety in my mind, almost always I felt notion of being lost, even tackling basic concepts. With your videos, I bough first books and started to learn math from very scratch. With that move I started freeing myself from fear and felt joy of learning math. Now I see that fear of math was only the outcome of untackled things in my life. Once I started learning again, I see that my mind is at peace. It might sound bizzare, but I do believe that going back to unresolved stuff can be very liberating for ones mind. So with that, I want to thank you for all you do in YT's space. Marcin

1- Active Recall : Read things until you have committed them to memory. 2- Space Repetition : In intervals, read again until things are committed to memory. 3- Interweaved Learning : 3- Study connexe things that will reinforce your learnings. For maths, yes, you do indeed need to practice. But you also need to learn the properties of different concepts as well as there definition. This in turn will help you come up with solution. Welcome in the frustration of not knowing as it is part of the process. Be revisiting things you thought you've already mastered, you will discover nuances and will thus grow. Search websites as some offer apps/formulas you can plug your problems into to obtain the solution. This will help you with those pesky little even number problems... And always remember the words of Miyamoto Musashi : "It may seem difficult at first, but everything is difficult at first." Last but not least... It will never become easier; you will simply have become better ;) Hope this help, wish you the best :)

Noting where you got the information from is also part of studying. When I was writing my book on the meaning behind the academic hat in the early days, I struggled because I did not 'note' where I got some information, and it took me forever to find it again. Thank you for your KZfaq channel.

My personal way to study is to wake up early in the morning ( bc you won't be excited to do anything if you wake up late and I say that from a personal experience ) and at night before each morning I make a list of what I'm gonna do next day ( I use notes app on my phone YOU don't need a journal !) Then I start studying like I'm a teacher and actually I'm a totur for engineering students so, I feel like I'm playing a game not studying I use small board to make me feel I'm really a techer I take breaks of course ...but the most important is the PLANNING a day before ❤

Excellent advice. I use the method of overall reading of the complete text, studying the examples. Taking a short break, and then going back over the material. Helps with Calculus--still it's a hard slog. Understanding comes slowly.

I typically do understand everything the first time, but I can't remember it without a bunch of practice, and I absolutely cannot pay attention and write notes simultaneously - that totally tanks my comprehension.

Hey Math Sorcerer, I'd just like to say thanks for the great videos, talks, book reviews, etc. You're a nice, caring, intelligent guy who just wants to help people learn, and I think that's hard to find in modern times unfortunately. I hope all is going well in your life, thank you for the videos and awesome algebra course; I am currently using it to tackle my MAT 1033 (Intermediate Algebra) class. I have always struggled with math and dropped out of college when I was 19 because of medical bills and I also just didn't know what I wanted to do in life so I didn't care about any of my classes. I was broke, depressed, and felt like a failure. (This was 2018-2023) Fast forward to the present, I am back in school, just finished my first semester back with a B in both my philosophy and logic classes. Despite my lifelong struggle with math, I am pursuing a degree in astronomy and astrophysics because I just love the mysteries questions about life we just don't know the answer to. Thank you again for your great, helpful, and inspirational content. It really helps out academically and mentally.

My only problem is being consistent i can study 4 to 6 hour a day during my semester exams even 10 hours depending on the difficulty of subject before the day of exam but on regular days it becomes impossible no matter how hard i try If only i was able to study 6 hours everyday with no distractions and complete focus.

1:43 I say first do a casual reading and then careful reading. By casual studying first, you learn the surface level information, which seems like a waste but you are priming your mind for the subject you will be learning. Take a break for some time (it up to you) and start studying in carefully. Since, you have casually read the subject, your brain will have an idea of what you will be learning. This is called Priming or Pre-Study. If you want to know more you can search about it on KZfaq or look for the research papers (I watched the entire video and realized you said the exact same thing)

Writing is really useful, especially for reworking the proofs yourself, coming up with examples and counterexamples, summarizing chapters and sections, and rephrasing and expanding on sentences that could be confusing. I am a slow writer though, so I prefer studying from PDFs and annotating the PDF with highlighted comments, and underlining important keywords/sentences. This has the added advantage of making reviews much simpler because the annotations act as memory hooks allowing you to race through a page by navigating the annotations.

Free paper advice: many offices have misprints or prints that they will not use ever again, so many times they throw them away, but you can go and ask if they can give you those papers because most of the times they only use one side, so you can write on the other

Actually that was beneficial for me. While I understood that concept of kinesthetic learning and have always applied it to learning languages I never considered using it for math, or to the extent that you’ve described. Thank you.

Write notes like someone else has to read and study from them example they will be used in a published citation. Helps keep you explanations clear and concise, also helps identify gaps in understanding, if you can't explain it to yourself, it probably merits looking iver again.

Good luck on your math class, Nadeem! You'll do great if you stick with it!

5:30 ChatGPT or similar tools could be helpful to generate answers to problems where the book doesn't provide them.

I'm not sure about math specifically, but I'm reading a fantastic book about learning in general - "Make it stick - The science of learning". Great information in that : self testing, space retrieval, interleaving, variation, and elaboration. Well worth a read.

The other thing you can do is once you've looked at something a couple of times try and teach it someone else. If you have siblings then try it on them. Teaching, even if you don't know very much, will help you learn.

Tough get you going, Nadine. Be sincere, and the day with help may just come. And no good dream ever die.

I was in the same situation of Nadine when I was a teenager. Don't give up Nadine!♥️ You can do it! 😊💪🏻 P.S. you need of a clever plan. Fix a goal and follow the math sorcerer advices. 😜

What about every time you open a mathbook, you start reading stuff like this: "Let f(x) represent a set of real numbers,{ a+b=c} where the absolute value of c depends upon the increase of a with respect to b, minus the value of the set of intermediate real values Y, so that a+b/Y and c/Y = f(a+b) and f (Y)". I mean this sort of abstract stuff is why people hate math! Combine this with the fact that textbooks provide a few crumbs of examples, and then give you a hundred exercises, 99% of them which are not found in the examples, and you have to come up with some creative reasoning to even solve the problem. This is why math is hard!

Because most of what I study now is on a computer, one technique I've used to thoroughly learn something is copy and paste the section of text into a notepad file then parse through it. When I go through it, I make sure I can understand everything the author is saying in a passage, then I ask myself if there is a briefer or clearer way to express that in words. Most of the time there is, so I basically edit what the author wrote, then do what I think is a better job, or at least it somehow "feels" better when I read it. In the process of doing that, the thoughts of what the author talks about begin to gel more and I'm satisfied that I captured all that was said. Thanks!

It's well established at this point that both *simply* re-reading or writing (copying) information are pretty much useless, not mentioning being a time sink that makes students think they're actually learning. Writing things down and re-reading are only okay if they're a part of an effective learning system.

The whole bit about writing down “everything” is so validating to me, I had been writing down everything my entire mathematical career until my final year of undergrad which was during the peak of the pandemic. I found out we had take home exams for everything and I got complacent and my grades tanked. Thankfully I was still able to get into my Masters program, and I’ve been writing everything down ever since, it just feels so right (grades also went up but the real gift was my experience with math being repaired)

100% agree, I’m doing this in my Physics course at university. the first read is made by me listening to the professor in the class, later I go back on the video he uploaded and I take notes stopping the video and taking all the time I need to solidify the notions

The most efficient way for me to pass my calculus classes was the 100 exercise and their answer sheet in each chapter I was doing 100 exercises and with their details answer sheet . But first u need to understand property and theorems and then try to apply exercise that apply them directly so that u can understand them. Cuz theorems will let u understand what’s possible in mathematics and not , then try to do 100 exercise with gradual difficulty in each chapter with their answer u should pass any class in maths in worst case scenario. Form an electrical engineer.

I'm in probability course this semester and ironically the thing I struggle the most with is combinatorics. Usually I try to draw the problem and visualise it, but i have so little understanding of this topic that i almost always get the pictures wrong :c. I will try out the writing method, maybe it will turn out to be helpful.

Hello, i just want say thanks to you, because your videos are the best way for me learn math and conversational English. I might do some mistakes in the text, so don't pay attention to it 😅

Thanks mysterious math man.

All these prescriptions are wrong and right at the same time. It may work, it may not, only you can figure it out. Everyone wants somebody to tell them what to do. Be the one that doesn't know but moves forward. Getting stuck is good, that is when you "get" to figure it out for yourself. KZfaq is a godsend. Watch all the different views on a particular subject, one is bound to work for you. If it doesn't you "get" to be the one who figures out another way to approach it. Life is good, you are awesome, go get it!! BTW Math Sorcerer is amazing ;)

Thank you sir!

I like to pretend i'm teaching it to somoene, if i can t do it, then it means i don't understand it myself. Thank you for your great advice..

To me I think ma thematic is problem solving. So in order to understand all the concepts, definitions, theorems, ... and their properties, I have to solve a tons of problems. Problems force me search all the prior knowledge to find the suitable one for the problems. Some very hard problems require deep understand multiple theories in order to solve it so they can make links between these concepts.

My instructor said we wouldn’t be given credit unless we did 80% of our hmwk. I have been so stressed I cracked my tooth from grinding my jaw. The new era doesn’t give us books and the computers don’t allow us to pass a question and move on if we don’t get the question right. It’s super defeating. I thought I was going to bomb on my trig test today but we will see. I hate controlling teachers. Just let me learn without the ptsd. It’s not cute and they always have a psychotic grin on their face. Not you ofc, you are like Kermit the frog if he were human and a math sorcerer! I mean that with deep respect and admiration, very few bits of my life have been light hearted 🐸 🧙‍♂️ ❤

Study less, more often would be my advice. By this I mean study every day possible even if all you have is 20 minutes. Personally I have a limit how long I can study for it's around three hours. after that my efficiency and effectiveness drops drastically. Every time finals come around I think oh I'll just study all day for the next few days and I'll be good. All day rarely exceeds 3 hours for me and then I think awe why didn't I study this over the course of the symester.

"Alain Connes - How a Mathematician works" is a good advice for learning mathematics as well !

Another good advice i can give is: By time, look back at your accomplishments. See where you startet before lets say one year ago and where you are now. You will get that stronger consciousness of your progress and you will realize that you can achieve everything you want.

If i get stuck in any trig question, I google to look for any algebraic identity that i might have missed and then apply it and it works mostly. When that doesn't work, i ask AI to teach me that one problem and then proceed to solve the rest on my own.

Apply things that you are learning to somthing you already know. 👍

Great video, it helped me out a lot. Thanks from Brazil!

In addition to writing everything on the paper, I'd say it's important to break down what you're writing. There's times when you don't understand how the problem is being solved. In those cases I like to write it and focus on finding what doesn't make sense to me and actually trying to understand it. When I finally understand it I try to explain it the best I can in the paper, circling what I need to emphasize or whatever I feel like doing. That way you not only memorize and learn, but also discover where you're lacking and explain it so that if you're studying it again at some point (because re-reading is also important to consolidate something) you'll now be able to understand it easily and fast cause of your own notes and explanation.

Nice table! It's amazing how many ideas you can pull from such a compact drawer.

Very wise and helpful advice, thank you very much!

Hope the mans feels better and thanks for the tips.

sometimes it feels Awful ...How do you study for 2 weeks straight... when you are depressed worst part is, i know i could have done it. It was easy. I know i had the potential. this just makes failing...10x more...hurtful. because, i can't get myself, to start, anything.

Blessings to you sir and to young Nadeem! Love listening to these uplifting talks!

One thing that's helpful for me, I don't know about anyone else, is to read out loud and talk to myself as I'm solving a problem-the only downside is that some people might think you sound like a serial killer while doing it.

Hi, I'm in uni and I have engineering courses with relatively basic math (basic trigonometry and algebra) but for me, it's still hard because I have no depth in the field of mathematics. I can tell by comparing the way I can form complex analyses on other topics in my head and visualise them in depth, whereas with math I keep asking questions that end up going on tangents besides the scope of the course and I get stuck often. I'm trying to study and I'm realising two things. I generally want to learn and actually understand things (I know sometimes it's better to move on and you'll understand later but with me everything is unclear) and for me to actually learn would take a lot longer than one semester so it's hard to be ready for exams. And the second thing with math specifically, it's so complex that I notice some things are calculated and some things are just memorised information. Most students I know usually cram and memorise just to pass, but I can't really do that either. I guess my question is, how to deal with this duplicity? How much should I try to understand and calculate and how much should I just memorise? I remember when I was a kid and "learning" the times tables, we used to just memorise them, and sure it's useful, but there's so much else I don't have memorised and I don't really understand how or why. I keep getting stuck in the same place because of it. What is your opinion on this, if it makes any sense to you at all?

Getting up close and personal with this one

Nice video as always. I was wondering if anyone in this comment section could suggest me a platform to publish my proofs and exercises in order to get some opinions on that. Thank y’all in advance!

Here's an approach that I've found often works for math (and related subjects): After that first casual read, try to solve problems. There's a good chance that you won't know, or at least won't know well enough, everything you need to know to solve a problem. So then go back and look at the formulas, theorems, examples, etc. with the goal of figuring out what you need to know to solve the problem.

How do you study for something you don't understand

A+ advice, thank you!!

Studying keeping you big as hell 💪

@TheMathSorcerer You shared good advice with great tips which are indeed valuable to young beginners. Thanks for sharing

math sorcerer Thanks a lot for making this video and I've been searching for study realted videos, finally I've got one.

thanks for great advice!

At 13 nobody knows how to study. 😅 At 30 everybody gets tired of studying. At 13 you have 15 more years of learning how to study. My advice, no worries and take it one step at a time. Read and practice in a safe place (your school?). Focus 1 hour per day and it should get you through...elementary school? If I understood correctly...

Sing 'Stars' man!

Thanks so much for your videos they help a lot

Hi mate, just watched the video and i will give your advice a go! I have never practiced writing down carefully what I am hoping to learn in a comprehensive way, I have always just taken small notes to save time but I have noticed my learning is not as great as I would like it to be. So saying that, hopefully this advice helps! Thanks!

Aww man. It's so easy to just draw diagrams and do fundamental problems with a pencil. I had a hand injury, which makes drawing, writing and such slow at best and painful at worst. 🥺 It also caused an association with physical pain with math. So, there are many avenues for avoidance.

I pray God helps Nadeem in his poverty and his doubts.

Thank you for this video. Also, just wanted to point out the ghost "orb" at 1:55. Whoever that was still wants to learn how to study, even in the afterlife.

Hi math sorcerer . I'm a math student. Do you have any advice for me to study linear algebra? As we are going further into details some proofs are getting harder especially those that involes matrices (where you need to put indices everywhere.. and it become unreadable)?

As a JavaScript engineer. I can say next. If you don't have talents like me, i must work in 1000 time harder and more, if others really talent developer go home in tame, cause their job is done and completed professional, i must stay at work and do the best as i can, to stay in shape at that area, to be good developer. I should sacrificing many actions to be better developer. And that my way. Hard work -> gym 3 day per week (20-30 min) -> eat (don't track macro, only calories) -> sleep (only 5-7h and that very low for me). Only at this pattern i can beat this. I like programming, but unfurtunatly thats olny way for me and many others people. We must sacrificing huge different actions, for being pro in only one shit !

Thank you for the tips that' really worked for me.❤

math is really hard it takes effort, grit and imagination to understand concepts and metaphors.

Please talk about studying while having ADHD.

Casually Reading , Reading with pencil about things you are confused , write everything down when you don't understand , solve as much as possible that is homework

I’m 34 and still scared to understand math due to the fact how my dad treated me by whooping me just to learn…..Now I have a daughter that’s 10 years old she’s teaching me math….my kids mothers is a math teacher so just imagine how good in math my kids are

Wizard!! I recently started your college algebra course on udemny. The purpose is to refresh my math before I start graduate school in the fall.for financial analysis. Would you say college algebra (in addition to statistics) would be the best use of my time in preparing for this graduate program? I figure algebra is a base that's used in most higher level mathematics.

We appreciate your insights. Keep working hard.

could you possibly do a review of "advanced engineering mathematics" by dennis g zill? I'm wondering whether this is a viable alternative to buying a book on differential equations, linear algebra and complex analysis, respectively.

Im in the second half of a Discrete Math course trying to wrap my grey matter arround partial orderings and such. Pain indicates growth ;p

Salute.

Love

Hola profe. 👋😀