@@pinklady7184 because you can be an better sudoku or crossword solver if you use mathematical thinking properly for solving those puzzles correctly. Mathematical thinking requires using some maths topics like permutations and combinations
sai sreekar I am not so verbal-minded. I have never loved crosswords and I hate them. I am more visual than verbal. I have always loved mathematics from early childhood, but I have spent more time on art than on maths. Now, I am relearning mathematics for the sake of 3D realism in software. I am also learning physics.
@@pinklady7184 then why not try some puzzles related maths, puzzles is not only related to crossword but also there's some puzzles related maths, chess and other things. Are you studying maths in college?
Amazing advice that really resonates with my motto when learning more math/physics in my free time at college: “Don’t let school get in the way of your education.”
I just finished my sophomore year in college as a CS major and just recently decided to double major in math and CS. I have actually been self-studying math for the past year and watching some other random math lectures and videos too, so it surprised me that you brought these two things up in this video. I mainly started self-studying math because I heard certain classes at my university were very difficult or had bad professors, so I wanted to be prepared. During my first semester in college, my discrete math professor randomly emailed me one day suggesting that I double major. I’d never considered it before, but this email planted a seed in my head. I spent the next 2 years thinking about whether I should do it or not. If I didn’t double major, then I’d graduate a year early (3 years total) with a BS degree in CS and a math minor. Double majoring would make me graduate in 4 years total. Math is also hard, but CS comes to me very easily. So I was conflicted on whether or not I should do it. Eventually, I ended up liking this whole self-studying thing, and after doing well in the math classes I’ve taken so far and speaking to another math professor about double-majoring, I decided the double major was worth it. Thank you for this video, it really helped reassure me in my decision. And sorry for my essay lol
Teaching things yourself really does help a lot. I did this myself and knew the material so well that my calc 1 professor actually thought that I had already taken the class before.
Your constant advice and honesty helps more than you know! Acts as a constant reminder to hold myself accountable for learning in class, challenge myself outside of class, and keep things balanced. Also, like the woods as the backdrop, keeps it chill!lol
I'm really disappointed rock climbing isn't on the list. A lot of great mathematicians I know do rock climbing, so it's obviously correlated, causing their excellence :) Thank you for the video.
@@TheMathSorcerer , That environment is perfect for mathematical studies. I use to study math in that environment. I am thinking about doing that again. What is the use of me even bothering? Surely I have no need to pass any tests, get a job, etc. Know what I will do it just for aesthetics. Oh just remember, could help the grandkids.
When teaching yourself, I think it's important to assume that the "student" has a weaker background. For example when "teaching" open mapping theorem, one can assume the "student" is not that familiar with topology etc. Because by doing so, one was forced to have a better understanding of the related topic.
I teach myself mathematics on my days off. I also take the chapter test at the end of each chapter. I must score 70% or higher before moving on in the textbook.
Good luck to you. I remember calc 1 being scary at first because there was so much new content but overtime it got easier. Let me explain, math isn't easy but if you put in the time, things will become better. Make sure to go on RU-vid for math help. There are lots of great calculus videos. My favorite youtubers for math are are professor Leonard videos and math bff videos. I hope this helps and you are going to do great!
Thanks, actually these 3 points make sense in every field.. this why I keep following this channel, even though I am not a math major! Most of your videos are "generalizable, transferable and valid" to be applied on other fields.
oh wow yes you are correct, this is true! I guess this applies to other fields as well:) What is your major again? I think you mentioned it before maybe but I forgot.
@@TheMathSorcerer I am more into the application end. Applied machine learning. A funny thing I do when I read a paper, is that I check the bio of the author. If they come from a math background, this is a BIG warning that the paper will be like gibberish to me :D
All that land behind you, you could grow vegetables and fruits and not bother to go to shops for them. If you have too much, you can share them with family and friends or sell them in open stalls. My late father used to keep a kitchen garden at the back of his shop. Gardening was his hobby.
Great video! I would love to see some longer videos from you. Your five minute videos are great, but longer ones of you talking about these things would be even better.
Yes! Yes! I cannot stress enough how important it is to teach ourselves given the fact that no prof/teacher can make you feel/understand/realise the essence the way you would if you are to teach yourself. And as the saying goes - You can take a horse to the river but cannot make him drink the water! So the charge must definitely be on ourselves. Also, I am learning concepts of Galoi Theory myself, it's fun!
I’m so glad I found this 2 year old video just now, even though I’ve been subscribed for possibly even longer, because it was exactly what I needed to hear. I’ve been very stressed about my upcoming calculus exam, because I can’t seem to focus on reading my Thomas’ Calculus, and instead have been reading Abbott’s Understanding Analysis and Fitzpatrick’s Advanced Calculus. And I’ve been worried that I’m wasting my time trying to really understand what’s going on with the formulae of calculus instead of preparing for the exam. I know I have to practice just the basic computations too, to finish the exam in time, but it’s nice to get some reassurance that learning for the sake of learning is good too. Thanks!
Yes! Especially teaching yourself. I am largely self-taught and, by the time I was able to formally attend school, I was so far ahead that I was able to start working on graduate material as an undergraduate. But I've been absolutely terrible at the 3rd suggestion. (For self-teaching yourself Algebra, I would really recommend Dummit and Foote or Algebra: Chapter 0)
I was interrupted as I started watching this today, so I paused the video. It was at precisely 1:37. When I got back to it several hours later, I found The Professor starring into me with a look of perfectly sincere encouragement. Make a great poster. He is my conscience, cheerleader and Scout Master, and trail guide. I make slow but cheerful progress in Functional Analysis, currently marveling at the amazing number of different statements and expressions and proofs of the Riesz Representation Theorem. I will be 73 in July. BA in Math a long time ago.
I really enjoyed this video, teaching yourself is so so so important. So many people hate math because of bad teachers, and I for one never had good ones. I love math though, and I always will because I taught myself every single year of the youngin' years. The strategy is to watch this kind of stuff when you're learning addition so that it builds up like compound intrest. If you have someone who can actually answer the question, always ask WHY, you're learning trig functions? Well WHY is sin(25°) that random number of all things? How on earth does a calculator figure it out?! Then you get to series, summations, and then Mclaurin/Taylor Series! Now you're like: I know what's happening! I GET it!!! The more you ask "WHY?" at EVERY step, the more incentive you have to learn all that amazing stuff that comes next.
I like this advise. I avoided studying math for years (I was a bio major), but now I'm feeling huge gaps in my knowledge. I have enrolled into undergraduate math courses here in Australia to study over the next year and a half, before I attempt going into an MSc in Biostats. My first course starts in a few weeks, but I have begun studying the content on my own already, and I am quite enjoying doing it on my own. I think it gives me an opportunity to really dig into the parts that I don't understand easily yet.
@@johnclever8813 Stochastic analysis is becoming exceedingly popular in the biological sciences and in epidemiology traditionally. Traditionally, though there may be differential equations or sets of differential equations describing evolution of systems, it was eventually appreciated that perfection is not the norm and thus the popularization of stochastic sets concerning differential equations. For instance, at an instant in time, instead of supposing that the population of a sample will grow to this level due to the previous set of instances as described by an exponential growth, we may instead allow sets of values with appropriate probabilities associated. As an immediate suggestion, for an appropriate discretization e, there is a greater than 0 probability that the population at (t + e) will be equal to the population at t - that is, no growth. Otherwise, stochastic precesses is increasingly becoming overwhelmingly popular in neurobiology and cellular biology due to the classical description of brownian motion. It is perfectly natural to consider biological systems from the perspective of brownian motion. Biology will only see progress with increasingly advanced applications of mathematics and even more so than physics - that the level of mathematics a theoretical biologist should possess is complicated than that of the theoretical physicist. Indeed, mathematical physics saw much more development as opposed to mathematical biology historically because biological systems are much more difficult to comprehend. Therefore, though stochastic processes and stochastic analysis will very likely become ubiquitous in biology, I suspect so will a great diversity of mathematical subfields from harmonic analysis to tensor analysis to functional analysis to algebraic subfields as in group theory, and further in topology, geometry, graph theory, computability and complexity, and so on and on. We simply do not live in an era where progress can be made without collaborations, the biologist, the chemist, the physicist, the mathematician, and the computer scientist will all have to collaborate to see any glimmer of light at the end of the tunnel.
This is really great advice! I started college as a Software Engineering major, but once I took Calculus I quickly decided to also go for dual degree with Applied Math. I'm still not sure what good the math degree will do for me in a software field, but I felt a strong drive to take more math classes because of how Calculus opened my eyes to the beauty of math. I dropped Algebra 2 in high school because I didn't understand why it was useful (nor did I care at the time), and that's where my math education stopped until college. In college I've never had a problem with my math grades because I look for the "why" in my math. Having a deep understanding of why math works makes it much easier for me to spot errors in my work and develop an intuition for whether I am on the right track so I don't waste my time working in the wrong direction. I spend a lot of my free time watching math teachers on RU-vid and it only serves to increase my interest and fascination with math. I'm taking my first junior level class on mathematical proofs next term and I've heard it's very difficult but I'm so excited to learn a new way to understand math. Even if I never make professional use of my math degree, it's constantly teaching me new ways to see the world through the lens of math, and that perspective will stay with me my whole life.
Yes, yes it is!! Also you really cannot rely on someone to teach you, because then you rely on someone else for your own success, not acceptable, you have to make it happen!!!
I can't think of a single famous mathematician who didn't have a voracious appetite for reading math papers, books, and writings. You really have to spend a lot of time with the material, and you need the little hints that come from all the reading will eventually help you. You have to contemplate things for hours and discuss the math with your friends and classmates. This is all excellent advice. It's the exact advice I'd give after my math degree.
Knowing the history and biographies related to a field enriches understanding and reminds us that all of this Math & Science stuff is a human endeavor.
Physics and math books suggestions, I used to think math is not fun but my physics teacher changed my perspective on math and want to learn more, I flunked my math from elementary to highschool thinking I'm bad at maths and now I want to learn more about this subject. Thank to my teacher for opening my eyes he failed me last semester BTW but I learned my mistake and got a B in his class this semester, kudos to your work your remind me of my physics teacher on way of his teaching. Keep up the good work.
What helped me during my math major (especially during my abstract algebra and abstract geometry courses) was solving problems using computer code like Sage Math or R studio. It helped me translate and solve proofs with a deeper understanding. That and it also strengthened my programming skills. I never understood how powerful isomorphisms were until I did this also haha
Apropos your third suggestion, I suggest you watch the RU-vid video from Tibees titled "If you get bad grades, you need better friends." She is an interesting RU-vidr with about half a million subscribers, and lots of STEM course-taking experience. It's 8:43 well spent.
You’re videos are amazing! I’ve been binging a lot of your videos in quarantine and recognized the course code in your video about the hardest exam you ever gave which looks Floridian. Do you teach in FL and did you go to grad school in FL? -Sincerely, an incoming freshman math major at UF :)
Math is a discipline of learning, if it's not the art of learning. Why? The core cognitive requirement is understanding not routine. Understanding necessitates ability to develop a self-taught capacity of breaking down various possible relationships between different math entities. With sustained attention, patterns will pop up, perspectives will flow, and ideas will follow. It's really hard at the beginning to reach this level, but once the habit is acquired with time and perseverance, you become a math guru. And your appetite of learning any math topics increases. So learning for teaching is definitely a central key for being good at math.
Two years ago I decided to award myself a medal in math after completing Cal 3, seriously, a piece of gold or jade or something from a jewelry shop. Now that I'm totally hooked by math and come to know that Cal 3 is not the top of the world but real analysis is, I have to modify my honor code, a degree in math? that's tempting.
I had a old Jewish professor in college, who was just awesome in explaining math. He never used any notes, and it was obvious he himself was really interested in the subject. One thing that I clearly remember that he did (and it seems that all truly great teachers always do) is that he would repeat himself more than once. For example, he would explain a concept, and then, an hour later, he would repeat the explanation under a slightly different angle, and put it in different words. And then, on the next class, he would repeat it again, in a different manner. Than, a few classes later, he might even repeat the same thing again, in yet a different way. Needless to say, I never had a single B in any of his classes - only straight A's.
@@TheMathSorcerer Also he once told us that correctly writing the Greek letter ξ constitutes half of the Calculus knowledge. I remember, right after I heard that I took great pains to learn to draw that letter perfectly, in hopes that I could short-circuit the learning process by half.
Can you do a video on what types of questions you asked your past instructors or how you started talking to instructors? I feel like most of my maths questions are algebra related e.g., in advanced calculus most of the questions were based on algebra... don't really know what else to talk about. I found it easier to talk about topics in my applied classes though e.g., mathematics and cancer was easy to talk about stuff.
By committing to teaching myself, are you mostly getting at the fact that I shouldn't be solely dependent on my professor and the assigned work to learn the material and prepare for exams? Meaning that I should constantly look for other methods of learning the material so that if I don't understand something, I'll keep looking for the answer instead of giving up if the homework and lectures don't answer everything?
Yeah pretty much. I did it mainly because I didn't understand everything that was being taught and I wanted to learn the material well and do good in my classes.
I usually had several books for each class too. This way I could get more than one explanation. I guess near the beginning of my math education I realized that it was super hard and that I couldn't rely on someone else to teach me everything. If you rely on someone else then your success depends on that person, and that's no good. Good comment❤️
@@TheMathSorcerer Yeah that all makes sense! I recently had like a realization that I have so many other resources at my disposal to succeed (RU-vid, tutoring sites, other books & people, etc). In the past, I found that I would get tunnel vision and always forget to look outside of the lecture material and required book from my professor because I just assumed all of my classmates were passing with just those things. It took me a while to realize that I have the power to look elsewhere. Thanks!
What can I do as an undergraduate in order to pass my classes with good grades. I am bailing out of university due to some problems I have had, therefore it is hard to continue. Can you make a video on specifically undergraduate failure and how to come out of it. I have many classes that I need to pass and the allotted time that I have given myself is two years to pass with good grades all the classes that I haven't passed. So I think that the video could focus on failure in undergraduate classes and how to come out of it with good grades. I have lost 2 years of university because I was in a very dark place. I still am but now I am motivated to finish these two lost years in the 2 years that I have ahead.
I will make a video on this! Some tips/ideas, 1) believe in yourself, this is key, if you know you can do it this helps 2) realize that this is it, you failed once , now is the time to succeed You got this my friend!! Good luck to you:)
Try bookfinder.com, you can get some(not all) older books for less than 10 dollars. I get all of mine there because it searches multiple websites. Although often I do have to pay more than that hehehehe.
I wish grades didn't matter My past grades and current gpa don't reflect my current skill set but are based on ruined semesters when I didn't didn't know what I wanted to do and didn't know I was smart enough to succeed. I am finishing my associates this fall for a transfer degree in engineering. Haven't taken a course in four years but my gpa will not reflect the studying I have done in that time... My last math class was Intermediate algebra. I got a D. I have a dozen notebooks covering precalc, calc 1 and 2, and physics. Starting calc three now. I found I learn much easier on my own. I now study math as a hobby. But my gpa will not reflect this. It will raise as I complete the rest of the degree but will still look bad on paper 😢 I will have fun trying to get accepted to any college for a bachelor's lol
yeah but the thing is most of the time you dont have time for extra self learning.. like i wish i could but, how do you keep up with what you already need to learn in class + extra self teaching?
Oh I know, that's always the issue. It's so hard, especially when you are taking really hard math classes. I usually did most of my self study in summer semesters since those were lighter, and also during holiday breaks.
I think as one gets older, one realizes to become a self-learner. I think college education is more valuable after one has experienced years of life after high school.
I would use tons of different books, it was a struggle but eventually(not always) it would click. Honestly sometimes I would give up and later when I came back to it, that's when it made sense.
Hey, I've got a bit of an unrelated question. Recently, I ended up getting a B in my math course (the course was essentially the Swedish equivalent of calc 1) and it felt like there was quite a big gap between the two highest grades. As a result of this, I've gotten quite paranoid that maybe I'm not smart enough to actually get an A in my upcoming course. This brings me to my question; is it possible to get a B but then just remain stagnant at that level, even with maximal effort? I'm asking because I've kind of developed a phobia of that happening.
Getting a B is awesome but you can do better I'm sure. I had plenty of B's and then was able to get A's in much harder courses. I wouldn't worry about it, it's one class:)
it does, I used to study very early in the morning, now I just read whenever I feel like it:) Since I no longer have the pressure to take courses it's much easier for me.
@@edwardgaming466 if you struggle with math it could potentially be a weakness/technical gap in your math foundation eg. High School Math like algebra, trig and geometry fundamentals and basics,(math is extremely cumulative and concepts build on each other sequentiallly) the other issue could be that your math practice, trying using spaced repetitions when trying to absorb math concepts and procedures, this gives your brain time to form it's own understandings of the math problem and how it works....Good Luck!
I started when I was 35 and now going in to my second year. Really fond of abstract algebra and find that the proofs are quite intuitive when you get the gist of things. Usually one thinks about does this satisfy the definitions of what you want to proof.
@@TheMathSorcerer seems quite right. My doubt was in the direction of if you just read a bunch of different sources or read the obligatory material in advance so you already know when you get to class. Thanks!
Thank you for your very valuable words. I would also encourage to use math.stackexchange.com as a further extension of advice #1! P.S: try to look at the camera lens as if you're addressing it. This way, it would seem like you're really talking to us! :)
