1. take notes 2. do homework early (don't procrastinate) 3. Study for the test (not last minute) 4. Form or go to study groups 5.talk to professors (ask important questions) 6. re-do the homework (work on speed) 7. read math books (his video on math start to finish will give you a general idea on math books) 8. watch math videos (on anything but don't go binge watching, focus on your problems on math topics) 9. at brunt out moment take breaks (remind yourself what you have done and what you are doing, meditation helps too) 10. Go through the struggle and find the beauty of math (think deep about it)

It doesn’t matter what “level” of math you’re at, this is great advice.

Math instructors that regurgitate, almost verbatim-like, on the blackboards what’s already presented in the textbooks are doing the students a grave disservice. The teacher/professor’s principle responsibilities are: to promote enthusiasm, assist with the learning process, provide guidance, stimulate intuition, expose the inner meanings, show the practical applications, teach problem solving skills, and demystify the reasonings and motives behind the mathematical concepts.

Another idea or two: 1. Make up your own homework problems. I got this idea from a book I read (sorry, I forget which one) and it makes a lot of sense. To make your own problem, instead of finding the answer to someone else's problem, forces you to "work backwards" in a sense, which helps deepen your understanding of what's going on. That's the theory anyway. I'm going to be trying this out in the days and weeks to come. 2. Write a math book. OK, OK... not in the sense of something you would expect to publish, or even show anybody. I just mean, take your notes, and rewrite them as though you were writing a book somebody else was going to use to learn from. See also: make up your own problems. This is just another way to force your mind to think about things from a different perspective, and force you to make sure you really understand. As the old saying goes "you don't *really* understand a topic until you've taught it." 3. Get problems from other books besides your textbook. For basically any math topic (especially undergrad stuff) there are books out there with titles like "1001 Solved Problems in X" where X can be Algebra, Calculus, Linear Algebra, Analysis, whatever. Hit up Amazon.com or Barnes & Noble and you should be able to find plenty of sources for additional problems. 4. Related to (3) above, if you Google around you can find class websites from where your class / topic has been taught at various institutions. Many of those will post old exams and old homework assignments (sometimes with solutions, sometimes not). In either case, if you want more problems, or maybe slightly different problems from what is in your book, or what your teacher made up, this is an easy way to get problems to work on. 5. I feel like there should be a 5, but I really can't think of anything else. Uhhhh... "try hard"? I dunno.

Interaction with professors is huge. Absolutely huge.

I think the most beautiful thing about maths is that it is completely man made yet it is a part of nature

I did quite a bit of math in high school (for the purpose of avoiding it in college) and I did pretty well. I remember enjoying pre-calc, but otherwise I considered math to be a necessary evil. Fast forward to now: I homeschool my children and I have discovered a love of math in the process. It really is beautiful, even in the very early stages. I suggested that my husband read Paul Lockhart's books, and he did -- and now he's learning math on his own so that he can go back to college for a mathematics degree. It's so cool to see us literature/philosophy type folks transformed by math!

I wanted to thank you, from the deepest part of my heart, for showing me that math is not only amazing, but fun and a rewarding challenge. I've recently in these past months, have begun to re-teach myself math. And have found a passion for the process of understanding math, not just regurgitating what was taught to me during high school. This humble welder now has aspirations to become an engineer in the years to come. Thank you math sorcerer!

textbook solving questions is super hard

Last year of my PhD. It’s funny that my study habits evolved to much of this advice. The hardest part for me was finding the beauty in the math I’ve done. Especially now with my own research. You really do need to sit back and realize the beauty of how much we know and don’t know.

Sir, after graduation I m learning mathematics from bottom to top In third perception Love from India😊💐 🙏

I'm good at taking notes, but totally suck on going back & reading them later. I like redoing homework or any problems, except it's depressing when the 2nd time it's like I never did it before & for some reason don't remember anything about how to do it. Memory falloff is worse than a final boss fight, it always kicks your ass.

I would like a video titled “The 10 things you’re doing correct in math and should keep doing”

Take notes, take notes on the notes you took, rewrite the notes you took and make them look super nice, then get a blank piece of paper and act like you're teaching your notes to an empty audience. This got me from a 45 my first time taking calc 3 to a 99 in differential equations. I also love how you talked about study groups. Pick up a tutoring gig at your school (even if you aren't 100% confident on your ability) and you'll see the more you teach it the better you get at it yourself. I also love

I've been studying math on my own for a couple years now and I'm from a medical background. Your advice has been very helpful for me preparing for applied math graduate study. Keep up the good works!

All very solid advice. One thing I would add is don't overdo it on how many courses you're taking. One semester I took seven math courses and ended up failing two, getting a D on one and doing average in the others. The next semester I did only three courses, graduate level math courses, and got A's on all three. One of the A's was a course I failed the previous semester. Reducing stress, not overextending yourself and giving yourself plenty of time makes a huge difference. This isn't a race. Best to give yourself a work load that is sustainable rather than to burn out and feel defeated. When you put all your focus into a single course and ace its exam, that feeling is infinitely better than to take three courses and get an average or worse grade. Your morale matters.

the first suggestion that I would give to any math (and STEM) student is to stay with the problem for a while (the amount of time will depend on the level of the problem). write it down on a piece of paper (even if it is a computer science problem), don't waste your time staring an screen and sit down in a park/beach/forest with a couples of beers and just enjoy the problem, I also use my whiteboard and write a problem for a couple of days but give yourself a time limit and then look the solutions (if there is ) you will learn a lot after milking your own brain and then read other people's solutions. The second suggestions in case you are preparing tests and exams is to work on the similar problems using the real exam time given for your professor, it is painful I know but somehow you learn more thinking on your own than preparing with a different time criteria. My English sucks (I learned it from a book hahaha) greetings from Santiago de Chile

For math and CS I highly recommend the MIT lectures online (though maybe not if you are just starting to learn a specific subject). They are usually high quality and it gives you a boost of confidence when you can understand what is being taught. That said, there are many great math channels that aren't MIT (this one included!).

As an addition to why it is a good idea to start early is that you permit yourself to get stuck and struggle, which makes it a lot more bearable. Plus, it allows the problem to "solve itself" in the background, allowing for moments of reflection during idle moments that sometimes come with key insights. :)

I like the redo idea, not just for homework, but in exams, too. When you finish a paper, go over it again to ferret out careless mistakes, my personal bugbear.

I prefer listening to what the Professor says and make photos of the blackboard. When i'm home, i go through the photos and take my own notes in my own order. Often there are either arguments that are missing (or trivial for the Professor 😂), or arguments that are clear for me so i can skip them or i don't like the order in which he presents it. This works best for me personally

True words, final year PhD student here , visualization helps me I think it’s important to learn to write code .

At many levels we lack motivation to do maths. Your advice is really helpful.

Your mic sounds brill. Crystal clear, podcast-level audio!

With regard to the procrastination thing, based on behavioral theory in psychology, that's simply a species-independent response to a fixed reward schedule, as you have fixed times when tests happen and when you get your reward (grade/points) so frantic maximal work tends to happen just before.

I'm an engineer so I did a lot of maths. I want to add that when I was in college all the way to post graduate studies, I did about all of your advice. Number 8 watch maths videos was out of question simply because there was no youtube when I was a student! I just want to stress that no. 4 is important. I always advise my son to do this. BUT you have to be careful about who the students are and how many they are. I found out that three or four is the best number. More than four is chaos and the group turns to chatting and laughing. Four is fine if they all are at the same level of seriousness. Two could be the best if they are both motivated. A group helps because: 1. You listen to a different method of proof and a different way of looking at things. 2. When you explain a problem or lesson to your colleague, you find yourself engraving the lesson in your brain and you surprise yourself by coming up with solid arguments to this lesson OR finding out that what you're trying to explain is simply guesswork or wishful thinking or not rigourous enough! Don't underestimate number 9. Taking a walk outside is surprising helpful, but don't forget to take a small notebook with you to quickly write down an idea that comes to you. I would like to add: 11. Do past papers. These show you what the university wants from you and what to expect. I hope this helps the young mathematicians. And thanks to the Maths Sorcerer. I wish I had a sorcerer when I was a student!

Tip #0 which all good students practice, especially if they enjoy or are interested in the subject, READ AHEAD. Better than Tip #7, is practicing the process or auditing ahead the next class. For example, if you know you are taking Real Analysis next term, then sit in on the class in your current term. Do not stress over taking notes or doing homework or taking exams. Enjoy attending the lectures like watching a good movie. Use the break/vacation time to study ahead. Better struggling through Baby Rudin during the summer months at your own pace than stressing having to do it all in a single go while striving for an excellent outcome.

I finally made my room not suck to live in after a decade and a half. Sometimes it's being not in filth that changes things I think.

Re-doing homework is a real good one. “Repetitio est mater studiorum”

doing all this requires so much time, that's why Im struggling: I dont want to do all homework problems over again as I want to be able just to solve exercises not learn them by heart The same applies to proofs seen during the lectures That's what I hate about maths (at my university) We aren't allowed to have any notes for the exam and I don't know how to study efficiently for an exam like this as I don't like learning by heart

When #10 happened to me it kind of blew my mind. I didn't expect I would ever see math as beautiful. Math Sorcerer helped me keep going until I could see that. Thank you!

Found primarily math a blast quite literally since I got into precal in my comm college. Decided I’d do it as primarily a “player” while, at most, secondarily a “student”. Like just for the sake of itself. Got messaged I got awarded a pure math cert this year and am a class away from an applied btw. I am “multi-majoring” in the sense I am doing it at least one at a time, though more like I don’t exclude any subject. Not just “math” per say.

Nothing else to add except that you must don't even know how much your content gives both motivation and inspiration to study not only mathematics but for me also my ancient greek and latin classes ! Thank you !

I only recently discovered your channel. My graduate and professional work in cyber security have brought me to strive to get others to implement the message covered in many of your salient points in this video. I thank you for your content, and the energy you bring generally to teaching, but also in mathematics itself. Is wonderful.

Great video, sir. I wish I had had you for a professor! My freshman Calc book was by Bonic. One of the great features of the book is that there are accompanying notes by Bonic's students who comment about the struggles and insights they have had while taking his course in prior years. For a student like me who has always been afraid of math it was wonderful to be able to relate to the other students' experiences.

This is an excellent list. I am a first year physics grad student and I do some of these (take notes, go to office hours, finish my homework before the tests, watch math and physics videos), but some of the things on here genuinely hadn't occurred to me. The big one for me was your point about redoing the homeworks. I review/reread my homeworks before tests, but I don't usually actually redo those specific problems, and I don't know why, because doing that makes so much sense now that you say it. I am going to start doing that now, so thank you for the studying help!

My favorite technique was to read the sections in the book days before the class. I would find different books and read the same same section. You’ll find authors say things differently and one author might click better.

Thank you for your advice! Another thing that increased my performance in math is doing my math homework early, not worrying about mistakes. On the next day, I would redo the most challenging problems and then compare my answers. By revisiting the difficult problems a few times, I would end up getting most of them right eventually.

I love this channel. I found it days ago and makes me feel like I'm not stupid in maths and makes me feel like I have the chance to be better with maths and more. It is not my motivation channel is my reflexion channel. Thanks for exist sir

Thank you, Professor. I got a long way to go but will get there by doing what you suggest in this video.--God willing.

Great video, packed with lots of good advice, and applicable to anyone studying anything. As a self learner I suffer from the isolation you mentioned. I don't have a peer group of others around me to talk to. I supplement this with online forums which are a great help (if a little scary at first). I did spend some time training people in technical problem solving skills years ago, and found, as you said in the video, that by teaching you get to know your subject intimately. I use that experience by preparing and presenting a lesson on the module, subject, concept I have recently learnt. I video it and then I watch it, writing down any questions I might have had as a student. Then I switch back to the teacher role and answer those questions. This approach has made a huge difference to my depth of understanding. Some times I go back and teach previous lessons again. It feels weird at first, but it is very effective. Thanks for all the effort you put into this channel, there is one self learner out here who genuinely appreciates your help and encouragement 🙏

Me throwing all my energy into "finding the beauty, deep thinking" and often getting struck by the harsh reality of my lack of technical & problem solving skills ... I should grind this harder ...

Your enthusiasm transfers, it was a real dose of motivation to renew my efforts! Great tips!!

You actually inspire me to like math and appreciate the value of the work that goes with it. I am so proud of myself though. I wasn't good at math at all and never had the confidence for it. But now I'm learning and actually enjoying it just for the sake of learning.

thank youu very much, i will keep this advice until my last breat, and i pray all this tips and advice truly use in my life :)

Beautiful solutions! Yes, that’s what it’s all about, isn’t it. Math is absolutely beautiful. Thanks so much for this video.

Sir all of your points are very relevant and truly very helpful. I was a below average student but in the last one and a half year I self taught myself and worked out my problems.Today I not only feel confident but also realised how beautiful this discipline is.Because of my poor score in high school I was not able to get a major in Maths but downloaded pdf and purchased books to learn the courses .Now I am also preparing for my entrance examination for masters in maths , your videos act like a guide for me. Definitely would like to meet you in person one day and have a mathematical discussion. With love and respect from India.

I'm doing my SAT soon so my key takeaways from this video will be 1. take notes from all the videos and books I'm learning from, putting it in a way I can understand, 3. study for the test (of course) 4. study groups!! 6. Re-do homework, basically all the questions I did, especially the ones I got wrong in, 7. read math books probably on topic but also anything I'm curious in, 8. watch math videos...which I'm doing currently, lol, just trying to immerse myself in math for once, and 9 & 10 is very nice advice for me to remember through the tough times :) I always thought I wasn't a math person but lately I feel like it's time I change that. You can agree with me that Math can be mastered by anyone and I want to get into that mindset so I can have a hopefully bright future. Thank you for this video!

Thank you for the advices! I'm learning math mainly alone by self study and I very rarely get to talk to someone about it (I'm not yet in university, I'm 17) so I find it hard very often to keep the motivation high. I feel like I will re-watch this video when I will need some motivation (and practical help of course).

Great video! Thanks a lot! I think your advices are useful not only for all Math students, but also for ALL students (Physics, Chemistry, History, Geography, etc).

The deepest mathematics have symmetry and beauty to itself.

I can feel another math course coming up - the official start date will be October. The course, Fluid Mechanics, is with the Open University and as the material content is readily available I could/should begin now to prep this and any of the background I may need. One thing about notes and exam questions I think is a good idea is to add your book references to your notes, in case you need to retrace your steps.

I'd say this advice is really a commandment (10 commandments to do well in Math)! Thank you very much, Professor.

great advice man your videos do motivate me t rock my classes in this sem thank you buddy

Love, Love, Love These Suggestions!!! Thank You, Very Much!!! I’m A Mother Of A College Freshman! She Is A Dual Degree Engineering/Art+Design Major’s Student! Math Has And Is A Challenge For Her, But She Has A Passion For Engineering And Art, So She Has To Complete A lot Of Mathematics For Her Degrees! I Love Listening To Your Videos And Sharing Them With Her! I Believe That You Are Helping Her Think Differently About Math! Thank You! She Is Working Really Hard To Pass And To Understand Her Calculus Course’s! Thank You, Very Much, For Sharing Your Expertise!🤗🤗🤗

Another idea too : One day i was reading "Understanding Analysis", When i learnt the definition of limit, i start thinking why we need a rigorous definition? isn't limit just a phenomenon of "Tends to"? And i start thinking back what i have learnt, axiom of completeness, nested interval property, etc..... and i find out why we needs ε-δ, its about completeness of real numbers, and we described it with ε and δ. So the another advice is trying to "Think more", these are some question appeared in my brain while i am reading books : "Why we need this theorem/lemma/etc..., is it solved some problems?" "Is the converse of this theorem is true?" "How this definition connect with something we learnt before?" Then you will become stronger, and can develop your own understanding on mathematics.

You are the main motivator why i haven't quit self studying math. Currently i m at the end of algebra 1 (began from pre algebra 2,5months ago), i don't understand math fluently and its struggle at times, but i wish that i ll grasp math as a language one day. Thanks for motivation!

Thanks a lot ❤️ -from Nepal

I think some of the best advice you have given here is to form study groups and being almost a tutor for the students. The only thing you need to realize is that you yourself have to be correct. If you relay the correct information, it will aid you in creating building blocks of knowledge - which will help you in areas of math beyond the current topics studied in your class. Also forming bonds with professor is actually the most important part of being in college. You never know if you are going to find yourself also becoming a professor in that university because they recommended you to teach there. Fellowship in a math program is awesome.

Thank you for the insights and motivation!

Reading math books and watching videos has definitely increased my performance !

I think that what boosts the first advice is the extra time reviewing and understanding what one wrote in the notes

Great advice, indeed. I would add that you need to watch your attitude. Many times I’ve struggled and struggled without any breakthrough. Then, I take a break and look at my attitude. I find that a relaxed, playful attitude helps the most. I’m also sensitive to times when my frustration, aggravation , and weariness start to build. That is when I take a break and chill. I can’t count how many times I’ve done this and I get a breakthrough when I come back. I’m also an advocate for daily review. Taking the time before class starts to review notes and homework makes a huge difference at test time. The more often you are exposed to the material, the more you will remember. Doing this takes a lot of pressure off when it’s time to study for exams.

This is the best and most concise advice I've heard on math success. Thank you. Prof!

I feel like this video rejuvenated my energy and mindset… thank you 😁 im going to make this world a better place

Personally, I stopped taking notes when the material got difficult for me (diff equations and calc 3) especially since the professor posts the notes, it helps me understand better when I put all my focus on the lecture and kind of force my brain to remember since I have no other choice lol. I completely agree with doing the homework early, taking breaks, and study. It is also so nice to talk about mathematics and hearing others talk about it really helps a lot and it just feels good. Talking to professors is great, when I did not know something in class or about the homework, helps a lot. As for redoing the homework, I would not redo it but I would get more practice problems, I believe I tried that once but since I already knew the answer and process it felt like a false sense of knowing, like I knew how to do those problems but not other ones. I have never read math books but I have recently become interested in it. Breaks are so important in my opinion, I take one once a week at the very least, you just think so much better especially once you are burnt out.

Hi Prof Math Sorcerer, you are a key source of inspiration and encouragement for us, the struggling university students. We are immensely thankful.

Thanks for all sorcerer, you have helped me a lot.

If you have the time, get another highly regarded book on your topic, read the corresponding section as you come across them, and do that book's problems as well. For algebra, I had Grove, Hungerford, and Lang. For real analysis, I had Rudin, Folland, and Royden. For complex analysis, I had Rudin, Ahlfors, and Conway. For topology, I had Massey, Munkres, and Hocking and Young. For geometry, I had Spivak, Stoker, and Bishop and Crittenden. Algebra was 1 year while the others were 1 semester. What I did might have been overkill, but it worked for me. And I'm an applied guy.

Wonderful advice. Really enlightened me on what i did wrong this year. Hope to use this for the next

Thanks for the advice

Brilliant video, thank you so much!

Thank you so much for all the advice. 😍

You are awesome ! Your videos help me not getting frustrated in learning

My problem with taking notes; I can take notes or I can pay attention to class. I am very good to remember tidbits in verbal communication but I cannot write and listen at the same time. In math I solved it by writing down the theories / methods and paying attention at the examples. That helped a *lot*. Also, #11: Help your classmates! This forces you to repeat your knowledge and reinforce what you already know.

Thanks for brilliant advices!!!

I remember when I was doing an integral homework and my solution was sec(t), and I thought its wrong, so I worked on it for 1 hour more, just to realise that sec(t) is equal to 1/cos(t), which WAS the good solution for the problem. So I can say, the 10th advice really hits hard, even if this was only my first semester. I hadnt really studied this type of math before, so everything was new, and I felt depressed, but now, Im fine, with only 1 final exam left (which is from calculus 1).

thanks for the information

When I was 14 I totally lost confidence in my Math abilities. The teacher at the time was writing very fast. At first I tried to write them as much as I could with lots of errors and try to read them from home. It totally failed, my tests results were quite bad. I was writing badly and could not even work on it later. So I gave up. I joined the back of the class and stopped writing anything except the main formulas, perhaps a couple of lines per lesson in my agenda. On the next exams something strange happened, my result improved. Not wanting to lose it I kept my no notes rule. After a few weeks I became one of the only person who would even interact with the teacher. Before long I became the best in the class. Later in university I had extended my no-notes rule to all the subjects. In France not many people do not take notes during lessons and very few with good results. The teachers were often surprised when they were giving me my first results. I did work with other students. I totally agree on this with you. Especially for me who did not have any note, working with other was helping everybody including me. In fact I agree with all you said apart from the writing notes part. My rule: Take notes if you can. If you can't then don't take notes and listen.

I’ve shared my story on here before about being 37, back in school, and having to start at Math098, basic Algebra. I’m now taking Calculus and doing quite well, thank you. I can attest: the struggle is beautiful. It’s a test of the mettle that requires me to pull up all kinds of things that’ve just been laying dormant inside. The only thing comparable to it that I’ve experienced was my time in amateur boxing as a young man. It’ll show you what kind of person you are.

Reading up a short introduction or essay is a great idea to utilise those boring waiting times. Gives you time to reflect on what you read as well.

Greetings professor!, great advices!... thanks!

One place where math books and videos fall short is giving sufficient (or any) motivation for the particular definitions that arise in an area (e.g. the (formal) definition of a topological space). Why is it defined this way and not another? What's the idea behind this way of defining the object? What aspect of the informally-described idea is being captured by the definition? I think expositors need to pay way more attention to this problem. And, yes, I know that the way to "understand" the definition is (possibly) to plough through the theory, and that an informal discussion may not capture all the nuances of the definition, but a decent motivation/justification of the basic definitions can greatly help the student, by giving them at least a direction to be going in. (A good example is Fraleigh's motivation, in his abstract algebra book, for the axioms of a group. He could have gone further, though, and given an outline of the whole "project" up to the insolvability of the quintic, say. I think a well-written chapter describing in outline how "the drama is going to play out" would have been seriously helpful, like, e.g., the following short video: kzfaq.info/get/bejne/b8eFpredp9DXoHk.html)

I am a self learner, but I am certainly going to try to adapt the classroom advice to my situation of learning. I am learning through books and searching KZfaq and the internet in general for help on concepts I am struggling with. As for the beauty part I have been working through Euclid's Elements in the evenings just for the enjoyment and even a dummy like me can understand it at least at a surface level.

Valuable advice sir much needed : )

Thanks Math Sorcerer, im learning calc 1 from you rn

Thanks for your motivational videos

Thank you!

I'm following your advice--or at least trying to. Every day I try and take on a new type of math 'set'--a little algebra here, a little calc there, some geometry when the mood sits, and a little trig over there. This approach is to make it so the formulas in the physics and engineering I'm trying to learn don't all look literally like Greek to me. But the main thing I'm trying to do is PRACTICE. Take some old scratch paper, find some problems--with instructions how to do them--and then do them, and repeat them. Change it up a little bit, check my work, recheck. . .in an attempt to get a logical--almost intuitive--grasp of what's going on. Shit. . .even looking at math and science meems helps. Point is, I've learned more math--and become more confident and understanding of it--in the last six months than all my time in high school and college. And I KNOW I still don't know a thing. But the fact that I've learned this much gives me urge to carry on more. Thanks for your insight!

Great advice!!! and inspiring ! Thank-you so much !

Awesome advice deep from heart. Very well said.

Very much valuable video. Sir has put his all years of valuable experience into this video.🙏🏼

This video is for me as well 👏👏👏♥️♥️♥️ Thanks.

Good Advice. Personally I never studied the night before a test, I made sure all my studying was done days before. I did this to avoid the stress of discovering I didn't understand a certain key point. I also never discussed exam answers when leaving the exam room, the exam was behind me, out of my mind, and I needed to focus on my next exam. Also, it's only by doing many many problems that you get useful insights and revelations on a subject, university problems rarely are solved in sequence a-b-c-d-e they usually require some sort of "hook" or deeper insight especially those that allow you to elevate your score "C" or "B" to an "A"

Big Thank You

I really hope I get to appreciate math like you do. I feel like I'm so far behind.

always or mentor in math. Thanks math sorcerer!

We need a bookshelf tour!

Your channel shares traits with math. Beautiful endeavor

Thank you ❤.