Digging Deep: Unlock Your Mathematics Potential

I discuss the idea of digging deep in mathematics. This will allow you to do well on math exams and it will help you learn math much better. Do you have any advice for people? If so, please leave a comment below.
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Thank you:)

[@CCPlaetean]

You are doing amazing work here. I'm a physics PhD currently undergoing a pretty hard technical pivot to a new field for career reasons, and for the last 6 months your content has been super inspirational for getting through the low points. Your philosophy of perseverence, patience, and discipline is honestly a superpower when implemented correctly. Taking the emotional pain and self judgement out of confusion, and embracing the slow and somewhat stochastic progress is the only way to really do difficult things. It takes a long time to build this mindset and I keep coming back to your vids to remind myself of it, but the effect has been tremendous, and I feel so much more empowered the more I incorporate this. So thank you, and please keep going!

[@studyaccount6969]

in which uni are you doing your phd?

[@AnnieMarie869]

. I'm working through 117 problems on inequalities and set notation right now and so far I have missed 5 out of 51. I missed them because I just didn't pay attention to the problem. That's the main reason I get a problem wrong: just don't read it carefully. Then when I miss it, I make myself go back to do it over and I take more time to read it. Then I can't believe I actually missed it. What he said about just doing math sounds so much like advice to writers about just writing anything on paper until the real writing begins. Working on anything is the point. Its supposed to keep us creative and improve our ability for the moment when we need those abilities. I also suggest watching videos on math you have not yet started to study yet but planned to. For example, I'm watching series of videos on calculus.

[@nadercs2669]

Absolutely loved this video! The concept of "digging deep" really resonated with me. It's true that studying isn't just about passively reading or understanding the material, but actively engaging with it. You've articulated the importance of 'doing the work' so well. It's a hard truth that just 'knowing' is not enough, one needs to actively test their knowledge by doing problems themselves. This is a reminder many students, including myself, often need. Also, appreciate the advice on asking for help when stuck. Keep up the great work! You're making a difference in many learners' journeys.

[@bigbluebuttonman1137]

I remember one time I was reading “A Treatise on Mechanics.” The first chapter had me hooked as I actively tried to see and experiment with the concepts it was discussing, especially as regards senses. This doesn’t have to stop at such books though, it can be done for anything and makes any topic way more engaging.

[@IronAceSUB]

I'm about to take Calc 3 (multivariable) and my first Linear Algebra course this coming semester! This is quite inspiring! Last semester I attempted Calc 3 and Modern Physics but I wasn't doing the homework. I was too hung up on video games and avoiding my homework. This time I'm going to come back strong and work hard 💪😁 ✨️

[@Kapiwolf123]

saying that you're going to do it makes it most likely you won't. Comment and say that you're actually doing it, when you start doing it. Not before.

[@RVM451]

Friend, I failed out of Purdue University three times due to a total inability to grasp Calculus. Calculus was a 5-credit hour class with large Lectures Mon; Wed and Fri & smaller Recitation Sessions led by an undergraduate held on Tue and Thurs. The material was VERY hard for me to grasp. I could BARELY complete my homework on time, though I spent MANY hours on it each week. In fact, feeding the Calculus dinosaur caused me to neglect & fail all my other classes. Tests were two hours long-& at least in the beginning, before I got hopelessly far behind-I felt that I could have passed the test, IF I’d only I had 4 or 5 hours instead of just the alloted 2. #1.} When I came to something in the text that I did not understand, I would halt dead in the water. I would reread that sentence repeatedly. Then I’d repeat the whole preceding paragraph. Finally, I’d start the whole chapter over & over & over again-all the time feeling a sort of agitated frenzy. I thought that it was like building a ladder. There was no way to skip over anything. Only many years later, did I find serendipitously that reading forward of the incomprehensible part can often wield clues to the meaning of what was previously not understood. #2.} I didn’t clearly understand the difference between “Explain” and “Demonstrate.” When I said “I don’t understand this,” I was unconsciously expecting quite a bit of expository prose. The Teaching assistants were given to simply working a similar problem on the board-DEMONSTATING-with hardly a dozen words of EXPLAINATION thrown in. Hey dude! IF I could pick up stuff by osmosis, I wouldn’t have to ask for an explanation… But back then, I was only left unsatisfied without knowing precisely why. I went to see my Professor once. I mean like he had several hundred students in his Calculus class & I was reluctant to bother him. All I recall, is that he observed that I was a very “Brute Force” type of person. This was back in the mid-70’s. Failing out of college doomed me to a horrifying life of working as a low-level manual laborer & even after all these years, I wonder what I could have done differently. Oddly, I have always had a lively interest in the Popular books on Math-Like the Gardner books. Like you, I once had maybe 30-books on Calculus-trying to find one that I could grasp-though I seldom stuck with it any length of time in my self-study. I do wonder though. I did very well in Geometry. They taught us to do a FORMAL PROOF by drawing a line down the center of the paper and every step that we took had to be justified by citing an Axiom; Postulate; Definition or Previously Proven Theorem. Somewhere along the line, Mathematicians came by the curious notion that you could “Prove” things with nothing but a series of Equations. I THINK that if Calculus-and higher Math-was taught like Geometry, that I would have zero trouble grasping it. I always got “A’s” in Geometry.

[@michaelfritts7192]

I'm digging deep tomorrow! You consistently rock. Thank you for all your hard work on this channel, it is sincerely appreciated

[@howmathematicianscreatemat9226]

I have discovered that - for myself and my students - the TRULY phenomenal way of teaching maths is exactly the INEVENTOR´s way: leading the students to be able to discover many of the relevant definitions THEMSELVES. Only pointing where they should look and being patient about telling them what to see. Sadly, almost none of our collegues does this approach, although I´m confident many more could than who currently do this. I feel you could do, I believe your current teaching for your students is already awesome. If you apply this suggested method, your teaching can become truly extraordinary! I know it's hard work but it provides - BY FAR - the most value for yourself and your students and you also make our subject orders of magnitude more ALIVE and popular like this! 🙂 Here is an example how I often start the class of showing students how mathematicians create maths: I let them come together in groups and discuss ideas for the definition of a circle, then, after an hour, they usally come up with the following: There are seemingly countless definitions which they then suddenly come up with and the light up like a candle with sparkling eyes: The most symmetric 2-d shape possible The shape that gets the most area for the least perimeter (see the isoperimeter property) All points in a plane the same distance from a given point (drawn with a compass, or a pencil on a string) The points (x,y) in the equation x² + y² = r² (analytic version of the geometric definition above) The points in the equation r * cos(t), r * sin(t), for all t (really analytic version) The shape whose tangent line is always perpendicular to the position vector (physical interpretation) The list goes on, but here’s the key: the facts all describe the same idea! It’s like saying 1, one, uno, eins, “the solution to 4x + 8 = 12″ or “the number of noses on your face” - just different names for the idea of “unity”. Then I usually contnue and let them derive a definition for the ellipse. If they don´t have enough ideas after an hour, I give them the hint that the circle can be used to define an ellipse and that they should think of a way how they can create an ellipse out of a circle You can do this too! 🙂

[@RallyX26]

This is the biggest thing I had to learn, and why I failed calculus multiple times. I could sit in class and pay attention to the lecture and go "Oh this makes sense, I understand how to do this" only to find out on the exam that I really didn't. 15 years later when I was more mature and went back to finish my degree, I nailed my calculus classes, diffeq, linear algebra... Because I learned to dig deep.

[@nerd26373]

We will always support this channel. Your insights have always been incredible.

[@missilewhistle5194]

Currently going through a rough time with Graduate Level Group Theory, did all the exercises and gone through all the materials more than once and still barely passed, like bear minimum grade to pass. Will have an opportunity to improve my grade this Friday, but it is soooo frustrating, really feel like I understand all the materials and still i get to the exam and the questions seem to go beyond what i studied, just beyond enough to get me all choked. I kept digging deep and the exams kept telling me I need to dig even deeper, it is so frustrating to feel like you're just not smart enough to come up with the answers to the questions, and after that it's easy to get all confused and mess up even easy questions or just not get all the score in a particular question because, well time is running, and you end up just giving the answer and omitting some parts of the proof to save time and head on to the next problem. Exams are a pain, best one i had was just a conversation like exam where the teacher sat in the room and i had to solve some exercises on the board and in the end it was me and the teacher going over a hard problem together, both really working hard to solve a really hard problem... it felt like doing research and not like the usual high pressure time constrained exam, some problems just take time to solve, and to some more than others, and an exams doesn't really give that flexibility to students, there's no time for mistakes or exploring the wrong paths before getting the right ideias to solve a problem.

[@douglasstrother6584]

After tangling with the lecture notes, problems sets etc., bring your questions to your TA's and Professor's Office Hours (no one shows up anyway), they will appreciate your effort. Organize "Problem Set" parties with your classmates to work through homework problems; this will make you accountable to others and haggle-out the principles of the topic at hand. Do this AT THE START, before you have to recover from a failed exam or course.

[@christopherduvall5325]

Thank you for your videos, I love math about to take Trigonometry in the fall but I'm digging deep into calculus, and I absolutely love it your lectures are a big help.

[@TommyAron]

This is what I needed. Thank you.

[@vampirejs758]

Dude stop being so relatable it's getting scary😂 great video though ❤

[@kenbrashear210]

Thank you very much.

[@bigbluebuttonman1137]

Gonna add onto this; I was doing some pre-calc review, and got to midpoints of lines. I was given the midpoint formula, and decided that I wanted to see what happened if I used it for 3 points that are the vertices of a triangle, which gave me the centroid, reminding me of the video "Journey to the Center of a Triangle." Yeah, it's not that impressive, but it made that section of the book way more fun for what is fundamentally topics that I'm just brushing up on for going back to college. That, and it offered an algebraic connection (midpoint formula extrapolated to 3 points) to a geometry topic (centroids of triangles). I guess statistics since averages were also involved, and was necessary. It's the first time I used a compass, albeit poorly, to check if some lines were actually equal in length. One thing that always helped me with math...remembering the "Facts" about formulas I need to remember; for the quadratic equation, I memorized that there are 2 as, bs, and 1 c, with one b "Dividing" the numerator between the square root and the not square root part, among a couple other things. Stuff like this helps you to play around with the topics, and get a feel for its dynamics and intuitions. Very happy I did this and didn't just pass it up as another curiosity to look for "Later" (which often times means "Never" for me, lol).

[@calculus988]

This is like watching workout videos but not physically training

[@softllamaspajamas]

I’m starting calc 2 for an expedited summer class on Wednesday. Time to dig deep!! Also I’d love to see a video where we can get to know you and your history and interests. You’re super cool and I’d love to know more about you than just the advice.

[@pinklady7184]

I am listening to you, while doing house cleaning. Listening to you is a great pleasure. Thanks.

[@ka.draganova]

Hello. I changed my profession from philology to mathematics. I have bachelor diploma Philology and after I was thinking for long if I like it.. I really missed for math classes (I was at math class in the school, i.e. every day I had math and physics class). So after thinking I said myself "Okay, I need to prepare for exams and just try". Now I have master degree in math (statistics) and learn complex analysis (just for fun and because I like B. Riemman) :) Because of the war in, I left my country and try to figure out how I can manage my life. But I'm still continuing do math almost every. Sometimes I use computer stuff, sometimes I solve problems by hand on the paper. Of course, I had before and I have now some topics, which are difficult for me. When can't solve a problem or when I don't understand the topic, I just say "Now I go to the parc/make tea/see film (put what do you prefer) and then I come back, may be not today, maybe tomorrow". And it works. Mathematics needs time and patience ❤ Good luck!

[@willyh.r.1216]

Yes, math cannot be learned superficially or partially. You have to dig deeper, deconstruct and reconstruct any concept in order to understand and master it. Keep looking for the very fabric of each math concept. Drilling problems without genuine understanding of concept is not effective. Likewise, understanding concept without practices doesn't guarantee success in math. From a math lover.

[@russellreisinger4541]

Pick up a pencil! Yes! Agree 100% That's it. Put down the dumb-phone and get a pencil or get to a whiteboard. In my humble opinion. Not just for math...but for almost anything.

[@madonobel]

Hi, I am 45 years old man from Egypt, North Africa, I've missed college for long time and would ask you If you may design a Mathematics Pathway/Syllabus with suggested Timetable for adults or elder students, as if I were in community college or as self study effort, someway between a hobby and dedication, considering busy work days, conserving your same concepts of study more to get any thing is better than doing nothing, thank you for great efforts explaining books and topics to us.

[@WhishoMH]

Really thanks! I'm on calculus 1 right now

[@miroslavkalousek9410]

There is a relation between multiples of 3 and 7. I try explain : it is about digit in ones order. Example: 0,3,6,9,2,5,8,1,4,7,0 this is a sequence of ones digits of multiples of numbers 3 and 7. Characteristics of that sequence is: numbers are added or subtracted by number 3 and if you look better numbers are added and subtracted by 7. Next holds that every number in this sequence has unique position in every period of multiples. From that implies to every simple digit I can paste certain multiple of 3 and 7. Example: 24,14 or 7,27 or 15,35 or 28,18.

[@armyoftwo13]

I took calculus 1 a few summers ago, I literally failed the 2 out of the 3 exams. I dig deep into my notes and homework, and I passed the class! And it was the best overwhelming feeling of satisfaction, if I can do it, you can too, good luck to all on your journey.

[@guilhermefranco2949]

I feel just like this, to be honest. I recently completed a first course in Real Analysis, the teacher really wanted us to become machines solving problems in easier ways, it is not like this is always bad, but considering how hard can this course be already, all extra difficulty not always pays off. I know I probably didn't dig deep enough because some other colleagues were getting things right and knowing stuff I was not aware of, details that slips in a class or maybe some property that is more general than what we're seeing that is underlined in the examples. But I'm glad I got it done, I know now I can focus and dig even deeper next semester. Thanks Math Sorcerer!

[@petredraghici8705]

Thank you for all your hard work you are a great motivator. Can you please make a video about what parts of math are most useful for computer science and coding? I am learning to code right now and I would like to know what type of math exercises I can do to increase my coding skills. Thank you again.

[@miroslavkalousek9410]

Did you know that you write multiples of number 3 in column from 0 to 30 then Look from bottom number 30 to upper number 0 and aim eyes to ones part of that column. You can see that digits in ones in order from bottom to up are ones part of multiples of 7. Try it in paper and pencil.

[@meninpursuitofpurpose3331]

Can we calculate something simple, for example, the permutation(s) of a hologram/holograph of a whale [in motion] on a basketball court?

[@Number6_]

The man is right most of the problem is not doing the questions assigned. Turning up for class is about 5% you may get some tips or insight. If he is working example that is a plus. If that is all you do it is a fail. You got to understand the chapter and do the assigned. Going to class on top. That is digging deep.

[@user-ng4oz6xq9u]

Hello everyone ..digging deep is important. I'm in grade 11 and I flopped on a whole euclidean geometry section in my recent mid term.I was focused on other sections and I thought I could just wing the geometry portion.I didn't dig deep enough ,and all of the geometry was problems we tackled in class

[@methandtopology]

I would really suggest you look into a hair routine for type 2 or maybe even type 3A hair. It really wants to curl but you are not taking care of it properly, I bet if you used a proper shampoo (sulfate free) and conditioner your hair would transform. The top layers which are exposed are particularly dry. Not an expert but would definitely recommend you look into it.

[@trim1180]

I'm digging deep and ended up with the best grade in my math class, im working on somewhat harder material but i feel like im still bad at math, that i can sit trough a what seems later a trivial problem with trivial solution for hours and i still sometimes altough rarely do dumb mistakes.

[@abdulwahabalwahbi8661]

Hi the math sorcerer I watched your videos and it was informative and great I really appreciate what you put thank you I want your advice I’m gonna apply next year to undergraduate program in engineering but I’m 24 years old and I’m far from HS so where I should I start in math to be good in math and to be ready for engineering major how many hours should I put daily to get good and understand math concepts correctly and with confidence to take the SAT and apply.

[@hemrajue3434]

Coordination with professors is a good approach. They may advice you how to prepare for the test. Even today i fear tests even though study for hours.

[@e-thernglee]

How would you reccommend reviewing notes? Most of the time, I read through my notes a few times and tell myself that I understand a theorem or proof, but when it comes to an exam, I am not able to apply the theorem where its needed, or write a proof that is similar to one that is in my notes. Thank you.

[@brunodonadelli9004]

Olá, sou brasileiro e venho vendo alguns de seus vídeos. Acabo de comprar um dos livros de cálculo que você sugeriu. Obrigado. Um abraço

[@pallaskedisiCokiyi]

Hey Math Sorcerer, what do you think about the antinet zettelkasten? Would it be worth for math training and learning?

[@nox5282]

As say this cause I’m the same, stop ask for permission and just try it! As you learn a math concept or deepen knowledge in, try to capture the easence on one or more cards, key is it should be useful without external references

[@pallaskedisiCokiyi]

@@nox5282 I started and it is going really really well, do you index your cards meanwhile you take the notes or after?

[@gauravbansal2438]

I also face problem in writing proofs

[@Himanshu631x2]

Sir i just given the test and score 22 out of 40 after doing so much hardwork doing extra side books but this score just giving me so much depression

[@arashaghamaleki1716]

In my opinion, every math question has a map. Students should be able to recognize this map and find the connections and expansions between the map of the question and what they have already studied.

[@metalwing1232]

Had an abstract algebra final last year in the fall, 6 questions 3 hours sounds east right??? Nope, Question two was left blank for 1 hour and 30 min, I kept going back and forth after completing other problems because I just couldn’t even get a start, but finally I glanced down at my notes we could bring and I almost jumped out of of my seat, one small line in my notes sheet gave me just an idea and with like 15 min left I solved it and Whent holy crap! Keep the pencil moving don’t give up!, I’m taking real analysis this upcoming fall so I’m starting my practice studying with proofs, any tips from people?

[@husky5912]

Please make a video on Field's medalist winner 🏆

[@allaeibgaming2164]

How to buy second hand books

[@reyaanmazhar1422]

Hey Dear sir I am from India , a btech first year student. I am working hard on mathematics to get better marks even better to enhance my coding skills but Why i am making silly mistake from last 3 years. Due to this i couldn't cracked 😢 IIT.

[@psybranet]

Hey Math Sorcerer. Are you a professor? If not, you'd make a great one

[@dumbfrog123]

Digging Deep = work hard and study more (extra materials)?

[@Kapiwolf123]

Do you mind me asking what you do for a living? Besides revenue from your KZbin Channel? What kind of work have you done with Mathematics? Sincerely, Pawel

[@entropy59122]

I just NEVER work hard, I ju REALLY want to but I can't. So I came here in hopes of improvement

[@julienarpin5745]

Imagine the love of your life paid for your college so you could be with her in another country. Imagine you came from poverty and know that only squalor awaits if you fail to make the most of the gift. When you will do anything to fight against returning to that broken home in your home country, you will fight hard enough to graduate. Believe me.

[@entropy59122]

@@julienarpin5745 I can't imagine that sorry, I've always felt like I've been different or mentally challenged or autistic but no one will listen, I don't want to just graduate and I'm a girl btw I want to do great things. I remember that when I was a kid I hated math and I always cried when I didn't understand it. I start crying when I make a mistake I kid you not. Idk I'm scared to work hard because what if I fail?

[@julienarpin5745]

@@entropy59122 failing isn’t actually a problem, it’s the direction that people think failure means they’re headed. It’s better to fail a thousand times and still make progress. As a kid I was placed in math 4 years ahead of my peers but I hated it so badly I stayed in the same class until my peers caught up. I’m a programmer now so I just learn the math concepts or learn it enough to do it just once so I can write a program to do math in the future. Math is about connections and how they change, which you can gain wisdom for from other angles like literature. Ultimately school and grades aren’t the determinants of intelligence or creativity. I know what you mean about feeling different as I was simultaneously ahead and behind in many ways compared to other kids. But those feelings may be forgotten once you graduate and continue on with life. People are dumb but embracing our own potential for failure also lets us accept the overall pitfalls of humanity. We are all trying our best and that’s enough. Just work to ignite your passions and see beauty in these concepts. You know plants follow fractal patterns right? And that the networking laws that govern things like plants also govern how people and societies grow? Math is beautiful and that’s all you need to learn to be a good student.

[@nox5282]

Let me introduce you to pomodoro, set a timer for 25 minutes and get sterted

[@entropy59122]

@@nox5282 I'll try

[@Lurch150]

I did well on math tests, but I never learned anything. School does not teach you math, even if its a math class. Math textbooks are written for professors, not students.

[@mokamoka9048]

I mentioned this before I was taking calc3 so the professor provided exam review. So my mind told me this first exam is easy based on review 😂😂 so I kept ignoring the review 😂😮 I did some of it and I failed the exam 😂😢😢 it was my first experience. Man I felt I'm an idiot 😂😂. However, the problem is my next classmate I believe Vietnamese he's always getting 100 which made harder for me 😮😮😅. Never believe when your mind tells you this easy you can do it 😮😮 mind deception 😂😂isn't Ellison 😊

[@dominikriegler]

I once went to a course for A-Level maths. The teacher kind of gave us a really difficult homework. The homework was: Curve sketching of the function: f(x)= ([1/3]x^4)-([2/3]x^3)-([x]^2)+x+2 The fraction always stands in front of x, so it's NOT 1 over 3x^4, but it's (1 over 3) times x to the fourth power. First thing to do, was to take all the derivatives (f') (f'')(f''') or (f1)(f2)(f3) I did that and I got: f1(x)= [(4x^3)-(6x^2)-(6x+3)]/3 f2(x)= (4x^2)-4x-2 f3(x)= 8x+4 and as a fun one f4(x)= 8 The second thing to do, was to do the integration by parts in the first function: ∫f(x)dx= ∫((1/3)x^4-(2/3)x^3-x^2+x+2)dx which was (x^5/15)-(x^4/6)-(x^3/3)+(x^2/2)+(2x) Note: the /number term divides the whole x^n So x^5/15 means (x to the fifth) all divided by 15, and NOT( x to the 5/15) which would be (x to the 1/3). After Integrating and getting things together, it is: x/30(2x^4-5x^3-10x^2+15x+60)+C Then I wrote the Definition for the first function and got: D=R Then, there was the tangent line to find the equation for: t(x)= f'(a)*(x-a)+f(a) taking f(2), because the number without any x was 2 before ∫f(x)dx= ∫((1/3)x^4-(2/3)x^3-x^2+x+......2.......)dx The 2 between the dotted lines is meant. f'(2) gives us -(1/3) f(2) gives us 0 so in that case by setting up the tangent line (y=kx+d), d=2/3 The tangent function for x=2 is y= - (1/3)x+(2/3) That was the normal question. By curiousity, I got further and calculated the rest of the zero-Terms or zeros, by doing polynomdivision by (x-2). I looked it up on the internet and got the info, that by doing (x-x0), you get further zero-Terms, so I did that. I got (1/3)x^3 -x -1 Then I got the obvious 2 zeros N1=([(squareroot of 5)/2 +3/2]^(1/3) + 1 over (squareroot of 5)/2 +3/2]^(1/3) | 0) which is approx.( 2.1038 | 0) and the obvious N2= (2|0) That should have been it for the zeros, but I calculted it further by transforming the equation into R= (q/2)^2+(p/3)^3 I used Cartano Tartiglias formula, which states that if R>0 then there are 1 reele and 2 complex solutions R=0 there are 3 reel solutions where 2 fall together R

[@niraj7616]

7:20 When you forget your wallet at home

[@musonobari2560]

Second comment 😀😀🤘🏽👋🏽

[@petergreis]

Proofs…. 35 years and counting, still suck at doing proofs….😅

[@BrainDonors]

First