When I first went to university, I wanted to be a physician. I failed calculus 1 and did a terrible job. But when I retook calculus 1, something clicked. Once I made it to calculus 3, I fell in love with mathematics. I ended up changing my major to math and graduated last June! So don’t be discouraged, with failure comes success.
As a year 3 math student going into year four, I regretted nothing for failing to make it into engineering and going into pure math. Real analysis is the only thing that made me waver, but overcoming that slope made me see the beauty in math. That utter joy of proving a statement, that sense of accomplishment, I am sure you had the same feeling too. Never regret.
@@zhangkevin6748 I can totally relate, when I studied analysis for the first month and a half I had no idea what was going on then it clicked. It was the best feeling in the world!
@@lorax121323 when I first started my undergrad, I majored in biology and wanted to pursue medicine upon graduation. As a requirement of this degree we had to take calc 1 and 2. I chose to take calc 3 as an elective and then switched my major to mathematics.
So many of my math teachers have told me that if what I was studying was hard at any point, then I shouldn't be in STEM. One college I went to put Dweck's material in the syllabus and the instructor just threw it away, saying you rather get it or you don't. So I appreciate videos like this.
I felt like calculus was hard for me because I didn't truly understand algebra/geometry in MS and HS. Altough I got all A's in MS and HS it doesn't say how well I understood the concepts. Which is one major flaw in the grading systems imo. And to this day I still have trouble understanding basic geometric concepts while I learn advanced math 🤣 so for now I accept geometry as an axiom and try to understand it at the same time. Thanks to your and Grant Sanderson's content you guys have made my life 10x easier and I can't thank both of you enough for letting me keep my love for mathematics
@@DrTrefor I started the most important part of my mathematical journey around 4 years ago with grant's(3blue1brown's) series on calculus. Around 2 years ago i started spending more time on discord and would meet someone who suggested I read Terence Tao's Real analysis and Keith Devlin's An intro to mathematical thinking (Haven't really finished the first one). From there on out I started falling in love with math. And eventually i ended up starting Axler's Linear algebra. And here once again I'd along with what I'd learn in set theory from other sources and about calculus basically helped me change the way I looked at math once more. Wouldn't have been possible without people like you and grant to start me on this journey. Interesting thing I found aboutmany people was that (and I think many others) change how they look at math when they learn abstract algebra
I felt this way I got to calculus 3. I wanted to know why things were true but I wasn’t yet ready for the mathematical rigor required for this yet. I spent way too much trying to get a intuitive understanding of the formulas and be able to visualize all the crazy three dimensional stuff we were dealing with, which wasn’t really getting me anywhere. If I had just learned how to apply the formulas and concepts and called it a day like in calc 1 and 2, I could have saved myself a lot of grief.
This video brought me in tears, you are describing in godly precision what I'm now going through, stuck in that delusion loop hole that made my math skills plummet so hard that I'm getting bad marks on tests, made me depressed and in the "passive learning" mode, taking notes even if I don't understand nothing. And the thing is even my parents are trying to convince me to let down maths and do something else, but I can't even imaging my life without doing maths. This video seriously for me, is a big psychological relief because I'm not the only one who is struggling in the same problem and the solution / advice that you gave in this video. And thank you a lot Mr Bazett!!!!
i went through high school failing everything (60 credits after 4 years) - especially math and physics - then almost 8 years later i decided to go back to college and ended up getting a degree in astrophysics the difference? i was paying for college by working full time at an arby's...worked mornings/classes in the afternoon - and then switched the next semester... it was tough riding from one side of town to the other each day during the winter, but it was important because nobody was going to make it easier for me...when i had 3 finals in one day, i didn't whine - i pushed through remember: it only takes an excuse to do nothing, but it takes a reason to do something
This is why you explain things well. I think a lot of teachers might have difficulty teaching because they learned it easily themselves and have no idea how to explain it to others.
I hadn't taken a math class after high school, after returning to school I struggled and failed pre-calc + trig. I hated math and would cry when I couldn't handle the stress of having to learn it. After a semester of tutoring, I had a solid foundation to move forward. Math is overwhelming when you don't get your foundations right first. I just passed diff-eq with a B. Math is brilliant and beautiful once you get your mindset about it right.
It’s awesome that you point out that those who struggle are not just the ones who feel they are “bad” at math but also the ones who think they are “good” at math! I struggled in early university with the idea that working hard and failing would be too painful… Math, and probably most things, have come easiest for me when I consistently adopt the mindset of “I don’t understand this yet; why not?” Somewhere along the way of doing that many, many times I actually had improved significantly.
@@zhangkevin6748 I wonder if people who are mathematically gifted to grasp things easier also have a hard time when they don't understand anything and how often does that happen...
@@Sentuyashi it definitely does happen. I had one CMO winner in my university math class and it not like they will have to study any less or more than us. He obviously can understand things quicker but in the end everyone gets stumped at least a bit by real analysis. It happens quite often that people get lost in math, unless they are super gifted and even then you can hard work your way through that talent gap. Pure math is all grit and grind, and if you enjoy it a lot talents don’t seem to matter as much. But talent does help a lot.
Not sure if you will see this, but I really needed to hear this. I’ve always considered myself as being bad at mathematics. Though,I’ve never studied, or even given effort. I would say it’s very difficult to say that I’m bad at something that I have t even attempted to try in. I’m going into college for a computer science degree. I’m going to spend the first semester, maybe second, solely focused on improving my mathematics. I’ve neglected the subject, but I’m sure I’ll come to enjoy it. Thank you for this video. I strongly believe I can improve, it would be foolish to think otherwise.
Thank you for talking about this! In my experience as a Lecturer I have found that the single biggest obstacle students are facing is often challenging the belief they have about themselves. This is so true for certain backgrounds that are perceived as "opposite" as Maths or Programming, like Art and Design. And it takes a long time to retrain students to NOT say things like "I am not good at Maths", "I am not good with numbers", "I am so stupid" and so on! So thanks for talking about this! 👏
I came to university being five years removed from highschool where I barely graduated. After years of roofing and working at Target I quickly realized I wanted to further my education as daunting as that may be. I almost failed first year because of requisite courses like calculus and lin alg. I was still figuring out how to balance these courses on top of others required for my major (CS) . I sat in a class and watched a professor scribble on a chalk board trying to figure out what the strange figures meant. It really felt like a brick wall where I too developed an anxiety around these topics. It wasn't a lack of effort but rather how I was approaching things. Circling back to these topics years later, with the help from channels like this one, I have developed a way to learn these topics that worked for me. Not only am I understanding things better, but I have found a way to study things that are difficult to me. Everyone will have a different pace when studying different things and if anyone reading this has struggled and felt like throwing in the towel please take it from me. I am an absolute dummy and I was able to figure this stuff out EVENTUALLY. A few videos a night, scraping online resources and textbooks slowly helped me develop my skills making things easier over time. I still have so much to learn but one thing I have figured out is that you can make it to the moon, even if you have to crawl at the start.
As a Mathematics Major, my best subjects were in Real Analysis, Complex Analysis, Differential Equations, Integral Calculus Transforms, Abstract Algebra and Statistical Modelling. Your video was good. There is a very strong parallel between learning Mathematics and weight training at a gym - correct mindset and positive attitude / discipline.
Wow I needed this, I felt like my calc exam went horrendously and it hit hard! But I’ve been practicing so much since and I’m hoping it begins to pay off for semester 2 with continuation of calculus. Thank you for this :)
Wowww!!!! Thanks a lot prof. So relatable. I was treated as a mathematics star in my high school, and after entering University things changed so much. I got a 55 in linear algebra. Now when I think about it, I feel like I too have this self perception that I am too good at mathematics and somewhere in my head glorify minimal preparation for exams. I'm halfway through my 1st semester, and am glad that I stumbled upon this video.❤
I especially recognize the part about the attitude towards studying for a course and not wanting to fail because of the fear of destroying the confidence in yourself. I'm glad that you mentioned it. Luckily, I've never failed a course when I had studied properly, which confirmed my belief that I was indeed capable of understanding all the topics, given that I'd put in the effort. After years of failing without studying and later more years of making progress and succeeding, I'm currently halfway through my PhD. You never know how it'll go.
As an educator myself, I second this. I absolutely struggled with Abstract Algebra in college. In my experience, hiccups like this can be explained by things like lack of proper prereqs, unexplained notation, ambiguous language, or leaving too much to be inferred by the student. All things that would trip up even the greatest minds. When you realize that, you’re less hard on yourself when mistakes happen. A proper math ego is a big part of a healthy math education trajectory.
That's so interesting that abstract algebra was the course where I really found my love of math, just goes to show there are so many different possible paths!
@@DrTrefor I very much loved the course in fact. But for awhile i was stuck in the pure symbol manipulation phase. I didn’t make analogies to concrete objects (like shape rotations) and that really hampered me.
This is an important message to hear and understand. I got a 4 on my AP Calc BC exam which transferred to a 5 on AP Calc AB. I tested out of Calc 1 and 2 and walked into my first semester of Calc 3. The problem was that I didn’t really have a solid enough grasp of the concepts of Calc 1 and 2 for the difficulty of Calc 3, and because I had always “been good at math,” I showed up my freshman year of college and didn’t really try in Calc 3. I ended up scoring 68% and having to retake it entirely. Learning the material and understanding it deeply is paramount in being successful in future classes that use those concepts. I could memorize stuff well enough to get through AP Calc, but the future classes beat me up because I didn’t build strong foundations.
I think immersion helps a tremendous amount. Math is hard. It's like learning another language. You can't just spend an hour on it here and there. If you're someone who needs to understand math for your degree, try to make a habit of doing math pretty much as often as you can.
That is such an inspiring journey; it reminds me of myself. I did fairly well in school in terms of math, but extracurricular math contests were a trainwreck for me. I always loved math and knew there was nothing I would enjoy more than this subject, but my inauspicious career within it has made me doubt myself so many times; seeing you becoming a math professor despite hardship and working hard despite doubts is such a great story man. I am truly happy for you, I know that feeling, especially in math, where you know you love the subject beyond anything, but you doubt your love because you are just not succeeding. You overcame that, and I am so happy for you; I wish you the best of luck and take care. Math is so rewarding yet so harsh, there is no such subject like this.
Professor Bassett, I want to thank you for your insightful explanations and openness in sharing your past. If I may, I’d like to briefly share a similar one: Last year, in year 10 of high school, I walked in to my AP Calc AB class with confidence in other areas of math, as you mentioned here. The first day, though, my teacher (Dr. Friel) tasked us with approximating IROC for real-world situations (word problems, like coffee cooling or car speedometers). While the upperclassmen solved problems quickly, I struggled to see the patterns. Over the course of year 10, Dr. Friel imparted not only formulas for application, but also deep conceptual understanding of calculus ideas to me (as well as those of my classmates who cared to listen). Now, I am taking AP Calc BC as a junior in high school (along with Physics C courses), and hope to take MVC and Linear Algebra classes next year before I attend undergraduate university. I can’t stress enough how much this teacher changed my perspective.
My university didn't have calculus 1, it had math 1 (later 2, 3) it was a mixture of everything. Calculus was included and the pace of the lectures was incredibly quick. Everything was obviously obvious and the professor that was assigned to me didn't take time to explain basic notation. Later I noticed that of the 80 students, only 4 myself included were regularly attending his class. Why? Everyone went to hear lectures from someone else. Of 6 professors that were teaching the course, only 2 did it well. Classrooms of those 2 professors were so full that people were sitting on the floor. None of this was official, students were still assigned to their old professors, everyone was just scrambling for their lives. I figured this out in the fourth week of the course and it was way too late to catch up to anyone. I just stopped going to lectures, taught myself the stuff and barely passed the course. Today I use math and I kind of treat it like programming libraries. I'm not hear to invent it, I'm here to use it. You guessed it, I'm an engineer. And my relationship with math itself? I don't hate it, I just hate that some people are allowed to teach it. P.S. when I say self-taught, that doesn't mean I didn't use plenty of online material. But the thing is, the online material is fragmented, uses different standards and it takes longer to learn this way.
I think maths is like learning how to drive a manual car. Some people are just “gifted” and understand what to do in a second whilst other have to spend hours and hours on the same thing (like how to use the clutch pedal and the throttle simultaneously to make the car move uphill). Personally I was the second type of guy while learning how to drive and also while I was learning maths and now I enjoy driving to my uni where I take classes that require a mathematical knowledge that just one year ago felt intimidating.
Calculus, for me, was for some reason way easier than I thought in highschool. I took AP calc BC as a junior, and soon will be taking calculus iii. One part might be that I enjoyed the learning process, and generally just love mathematics. Another part of it is a) the teacher (mine always showed us proofs and never just said to "accept things") and b) my foundation of algebra and precalc. Great video!
I just recently got my old college calc book (Stewart / Early Transcendentals) and am reading it for pleasure / practice - it's so much better to read it on my own time than being under pressure to pass exams on it. Also really enjoying your videos!
I had very similar experiences in my college days, but math clicked for me the most when I took a leap of faith and took a group theory course. The professor taught it in an intuitive way and really helped me understand the structure of math better given so many different things from all across math can be represented in terms of groups via their symmetries. Anyways great video, and maybe at some point make a group theory video so viewers like me can understand math better through how everything in math connects!
i recommend the book “how not to be wrong by jordan ellenberg.” After reading that, i switched my major to mathematics and it was the best decision i’ve ever made
Wow another fellow math student, I have some questions for you, what field of mathematics interests you the most, for me it’s topology and Euclidean geometry, next how was that journey and that feeling after proofing a theorem all on your own? I wish you the best and good luck 😉
As an upcoming freshman, I decided to go through your (and other) calc 1 course because I was curious of what it was about. When I finished, I was really confused about what going from velocity to distance had to do with area under the curve, why there is a definite, an accumulative, and an indefinite integral but only one derivative, why the chain rule is what it is, ect. I felt like there was a lot of information about how to do calculus but very rarely about the concept of calculus.
Here is one important concept: Integration is a "global" operation -- you need to know how your function f(x) looks like over the entire interval [a,b] which you are integrating over. On the other hand, differentiation is a "local" operation -- for the deriv of f at x0, you only need to know how f(x) looks like on a small interval, say (x0-epsilon, x0+epsilon). Being a "global" operation, you need to supply more information before you can integrate, giving you seemingly many "versions" of the integral, (e.g. [a,b] or [a,x] or [a,infty) ... etc).
It's good that you have these questions. Most students don't care about where things like the chain rule come from / how these important equations are derived. And I think that's a serious problem plaguing students. Students are often more interested in "How do I get an answer for this homework question" (i.e. just googling the question and finding someone's step-by-step answer) rather than actually learning. I see this all the time when I teach intro chem (and even higher level chem). Many students just want the answer without having to think or learn.
ua-cam.com/video/WUvTyaaNkzM/v-deo.html this series helped me a TON when I was first learning calculus, it's way more about the different concepts in calculus rather than doing computations and I couldn't recommend it more
It will tie together when you take physics classes. Like if you have a function for position with respect to time, the first derivative will give you velocity, the next derivative will give you acceleration. And then you can integrate to go backwards. Integration is also useful for finding the area under a curve, like if you wave a weird shaped cup and you wanted to know the volume. If you are just learning it on your own, I don’t think you will get much use out of it, but if you are taking it as a stem class you will be using it a lot in physics and other classes.
Thank you Dr. Trefor. I had the best calculus experience a couple years ago taking Calc 204 with you and it’s awesome being able to keep learning from your videos on UA-cam!
I got pushed back to algebra my 1st year in college, but it (along with some great professors algebra-calc3) really did help build a foundation and appreciation for math. However then covid hit, and now I feel I've lost my momentum, taking ODEs for the 3rd time. Hopefully my refresher/grade boost in calc 1 over the summer will help.
Got started at my engineering degree in 2021 during the pandemic. I went from almost straight As at a pretty prestigious school and having a good social life to not making any connections at uni and not showing up to lectures. We started with calc 2 and I trought I could cram it all in a week... I was so ashamed of how little I knew that I didn’t even show up to the exam. I dropped out later that year. The second start was still kinda rough but I made it trough calc 2, 3, linear algebra, statistics and applied maths. I was dealing with depression and axiety trough all those courses but managed to study them at home, thanks a lot to your videos. Im doing better now and am planning on revisiting some of those courses to get top grades again. Thanks for everything.
I failed Calc in high school. C in Calc 1. B in Calc 2, B in linear algebra. Then, I got an A in Calc 3, modern algebra, and Calc 4. About to get an A in diff eq. It took a lot of maturing for me to get there
@@jacobharris5894 I think multivariable calculus, gradient, and some other stuff idk, us pure math student don’t have calculus 😂 for us it’s called real analysis
@@zhangkevin6748 Oh okay. I’ve heard of that it’s just an unusual name. I’ve only seen it called real analysis or advanced calculus, like at my school. I want to take Advanced Calculus but don’t think I’ll be able to fit it in unfortunately. I already have my math minor and I’ve heard it’s the hardest undergrad math class other than maybe Abstract Algebra. You must not be getting your education in the United States or something because where I’m from even pure math students take three non rigorous calculus classes before real analysis.
Math has always been a terrible struggle for me. I really suck in math. I had to do homework about 8 hours a day. What motivated me to do well was fear of losing money--tuition is far too expensive to just lose. Anyway I graduated with a Master's degree age 62. What was a big "game changer" was taking an online class prior to taking the actual class. It made a HUGE difference so I ended up doing very well in math classes but it took a ton of preparation.
Engineering student here and every single thing you said about yourself was true for me too! You're lovely, so I'm glad to see what I can still become ;)
Thank you for sharing this story & your experience Dr. Bazett! It meant a lot to hear that there are plenty of non-linear paths to a life in Mathematics :) I personally nearly failed Calc 2 my first time taking it in undergrad after thinking I was "good at math" my whole life. After some time away, I took Calc 2 as a Post-Bacc/Non-Degree student and have since taken Linear Algebra, Vector Calculus, Multivariable, with more planned! Which your videos have been very helpful with, by the way, so thank you for everything!
I was in the same situation my entire life since elementary school. Always got bad grades and assumed it was just because I was bad at math and it never worked out for me. I failed pre-calc twice in highschool and one more time in college. When I switched majors to cs from a non-stem degree I panicked because I realized how many math classes I would have to take. I worked my way up to Calc2 and had to drop it because I was failing. I retook it and had a better approach when it came to studying. I treated the class alongside another math class and programming class like a part time job and spent hours and hours practicing problems. I ended up acing nearly ever exam and I then realized that my approach was the issue. Extremely rewarding and I’m glad I made the switch or else I’d probably still have the same mindset. (Possibly have calc 3/physics 2/diff eq’s next quarter so feel free to leave any tips) - You can do it, just make sure to take breaks and look back on the progress you’ve made.
Thank you for sharing your story! I had a similar experience, but with College Algebra & Trigonometry. In high school, the highest level of math I took was Algebra II, and the remedial math I aced my freshman year of college gave me a false sense of confidence. In my sophomore year, I took College Algebra & Trigonometry (skipping an intermediate course due to a conflict), studied for 5 hours daily, and got a 'C'. Luckily, it was the lowest grade needed to transfer into the university I originally wanted to get into, and that summer I spent more time learning math for myself. I took a math placement test during the mid-summer, and somehow, tested right into Calculus I (no precalculus). I lucked out as my professor had an amazing sense of humor and showed realistic applications for the majority of the concepts taught. I felt everything clicked into place and ended up in the upper B range during the first two semesters and my first A during Multivariable Calculus. I strongly believe that my shift in performance was by finding applications and experimenting, which inspired me to do more problems far beyond what was assigned. Now, as a freelance tutor, I do the same thing with my students - teaching by tinkering rather than through the "here's the concept now plug in numbers" approach.
I got a 5 on the AP Calc BC exam which allowed me to skip Calc 2 at my research university, however despite doing very well in Calc 3 I felt like I might my Calc 2 fundamentals might not be strong enough. So I transferred back to Calc 2. What I didn't know was that the exam was literally the day of me starting and it was in trig substitutions which I'd gotten particularly sloppy at from lack of practice. I wound up starting my first semester with a D‐ on my first exam. 1 year later I almost wound up TAing for that professor in Advanced Calculus. One bad grade doesn't determine your fate nor your aptitude.
I had the problem of active vs passive learning but my main issue was my (undiagnosed) autism spectrum disorder. I went to a really respected sixth form in the UK which is famous for being basically the best state one in the country, but I couldn't function in classes for various reasons (too loud / too many people and I have social anxiety.) As a result I was very withdrawn and passively learning which meant I struggled a lot. I also began to develop imposter syndrome and doubt my abilities in mathematics. To put it into perspective at GCSE I got 8s in maths / further maths and 9s in Physics and Chemistry but in sixth form I was getting C's in Physics and failing chemistry / further maths. Once we began to identify my issues I was fortunately privileged enough to move to a private school, most people there are like your average teenager (it's not some posh place like Eton lol) but the huge bonus was the small class sizes. Immediately I started to improve and while I've still had struggled, the nature of active learning since I was in a smaller class environment means that I'm hoping to get an A* in my one year a level maths, with predicted A* in Physics and History too (we will see based on my maths outcome if I continue further maths.) I've gone from thinking I wasn't good enough and hopeless, to aiming at applying for Cambridge University to study natural sciences :) I still have really bad issues with procrastinating and leaving studying to the last minute which I thought I would have learnt from by now but I am working on it (maybe in a few days idk I'm busy now 🤣)
Hello Dr. Bazett, I only recently stumbled across your channel. I immediately subscribed after watching your Bayes Theorem video. I loved how you detailed everything. This is where my many undergraduate, graduate (Master’s and PhD) professors failed me. Text books, and instructors tend to gloss over the material and leave out small details that just make things difficult. Quickly breaking down a formula and explaining givens when doing proofs should be more important than blazing through the material. Thank you for the awesome material and your presentation style.
Thanks for videos and comments. I am a retired engineer with many mathematical "holes" that remain from university education. I like going through calculus videos, even now that I am retired from a technical engineering career. I went through university calculus in the early 70's... suffering through university calculus with what I and the university called new age calculus teaching methods. I received a C in my calc 1 course. I went back to my HS calc instructor and asked him to help me with my university calc at the end of my first semester. He commented that I should need no help as he had already taught me the Calc 1 curriculum in HS and that I had had no problems latching on to it. I felt the university did more to destroy my calculus ability than to nurture it. Thus went Calc 1, 2, and 3. I did find the series and DE class to be interesting (possibly more app oriented) and more personalized. Anyway your classes and comments here are of great help from a ''hey so that is calculus" viewpoint for me. Well done. I finished my math department coursework by taking and thoroughly enjoying a Complex Analysis course. For me complex analysis contains a most beautiful mathematical language of calculus methods that are clearly and concisely defended.
My experience is not about calculus but STEM subjects in general. In 9th grade i remember struggling with monoms and polynoms and now, in my freetime, (i'm going to 11th grade) i study rocket science and astrophysics. Why? It's interesting, and i'm not afraid of admitting my limits, but i saw that with dedication and sweat you can get on a high level. For example i already learned derivates, i'm at good point with integrals and i know, as i said, a lot of stuff about rocket science. My passion was genuine, i just found the right teacher that of course didn't teach me these things, but she created the base for this.
As a teacher of mathematics in the equivalent of a high school in Britain, I often did an informal survey of students who joined my classes. The vast majority of students were at age 13 were put off mathematics. It made me keen on developing enthusiasm for the subject as a priority to develop mathematical skills.
Interestingly I was part of a study of mathematical education where a follow-up ten years later was carried out and interestingly my students were the ones that had the most positive response to mathematics still ten years later.
I'm counting my days in High School now but the fewer days I've left, the more I am thankful for taking calculus course as one of my elective. For the record, I was also considered pretty decent at math and have always found math quirky but kind of fun. However, as soon as the calculus actually hits, it hits HARD, more than half of my class dropped out of it. I can't express how much I have struggled to get to the place I am now, and I still consider myself very much a beginner! Or at least to this very day I still can't solve a complicated integration or differentiation without a couple of trial and error, sometimes, I am totally defeated too! BUT! I always know that I am not falling behind, and at least I can sometime do them, and that's very crucial for my morale! Not to mention the things you can achieve with calculus are so much fun and worth it. What I am trying to say here is that math and especially calculus are hard but they are absolutely worth it. And hey! If a brain dead high schooler like me can do it, so can you! Or, look at it the other way, if you are struggling, so are your classmates, so chill! Take a break if you need to, that helped me a ton!
...Good day Dr. Trefor, I am glad to see by your inspiring video that you're doing pretty well! When confronted for the first time with the Definition of the Derivative, it felt like I was passing through a portal leading to a world of limitless possibilities, both infinitely large and small. Similar to going from childhood to adulthood. Thank you very much for sharing your valuable experiences with us and for your unwavering commitment to education... Take good care, Jan-W
I hit that wall in Abstract Algebra and figured that, despite being a math wiz growing up, I was just stupid after all and dropped the math major. I still managed to graduate with a stem degree, though many years later I've never had a job that used it. At some point I went back and learned some Abstract Algebra, and it's a really interesting subject. I just wish I had had a mentor or anyone to talk to about how I was feeling about math to have help put me in a better direction. At least there are good videos like this for students today.
I failed Calculus before you !! ... and I'm still working on getting better at it. Hi Trefor, Your vector calculus lectures have been very helpful over the past 7 weeks, my exam is tomorrow. The UA-cam algorithm, being what it is, has been pushing me to watch your "failed calculus" video for some time, so I finally did and I agree entirely with experiential learning. Your early math experience is similar to mine (not mentioning hiking and canoeing). I failed my first university calculus course but got 80% second time around, but that was in 1976, now in my retirement I'm a second year computer engineering student in Montreal interested in understanding AI and I turn 66 the day after my exam. Abstract algebra here I come.
2:25 : literally my entire university career. I actually thought to show how good I was at all of this, the least amount of work done would show I only needed little time to study. After university, I basically knew nothing useful since everything I crammed in for exams, instantly got forgotten. So I had to spend a year after uni to reteach my self everything that I didn't fully learn when I should have.
After I took up calculus at first semester, I was discontented and deeply frustrated by the non-rigority of the teaching material (I didn't have this idea in my mind back then, I just felt confused and everything seemed haphazardly made-up). The university was trying to get through the material as fast as possible, because the tools of calculus were needed for other courses. Then I had the luck to receive a very good and rigorous introductory real analysis textbook from a math professor (from another institute). That was an enlightening experience for me and made me love mathematics, for the same reasons that the prof in the video mentions at 08:46. No more feelings of mindless symbol juggling with handwavy justifications and "abuse of notations". And just learning about the history of calculus about how long it took to develop to the level of rigor that mathematics demands really was a humbling experience, and put my struggles into perspective, and made me less self-judgemental.
Something similar is hapemning to me. I felt like my understanding in calc was only intuitive and everything was so fast ,explenations were poor, theorems were not proved,and exams didnt actually grade ur knowledge only ur ability to calculate (i call it do numbers) , i felt like all was made up in my physics degree. I was so sad bc i wasnt liking the degree i have dreamed about. But luckly , next semester my Linear algebra was abstract and well connected most of the results/formulas/theorems we used prove. I knew where the formula came from , why a particular thing was definned that way , everything seemed more natural !! Thanks to that class I realised that I really enjoy math , that I can understand abstract things if they are connected ina logical way , that im not that bad at proofs. And the most important thing, that I should be in a math degree bc it naturally fits how my mind works. I went to talk with the head of studies of mathematics in my uni . Now i cant wait for September to start my math degree.
ha! I do actually want to do this, I have an idea of a very visual/intuitive twist that helps to ease how we discover proofs. Not 100% sure yet though:D
@@DrTrefor Yes that would make all the difference. Like I can write proofs for exercises, but I always need a handy list of other proofs/books in front of me to write them. I can promise you it will make many self-learners happy if you do so!
I sucked at maths in school and I labelled myself as math hater. Later on when I did really well in Physics and actually learned more maths through physics than math textbooks. i think the problem with me was fixed mindset which in turn set in due to fact that maths taught to me was too abstract, no theoretical context, no conceptualization, teacher would go straight to the end of the chapter exercises and start tampering with numbers. But physics taught me some theoretical context and concepts.
I often worry that sometime in high school or early uni I just suddenly “got bad” at maths. I think the reality is just that life got more complicated. Generally I don’t do well in exams regardless of how well I understand the topic, so I’ve been demotivated, falling back into that fixed mindset idea. Being aware of it and noticing myself going down that path is really important, and this video helped remind me of that.
really hope i can improve to be a successful engineer in the future. putting in the effort is hard af but i gotta get used to it I did actually fail calculus. The second time around i understood it a lot better
I'm in my 4th year now and struggling so much recently. I've been repeatedly thinking that I chose the wrong major and wasted tons of money and time. I'm constantly calling myself down and really creating a negative headspace. There's probably little I can do to salvage this semester, but I won't give up, and I'll be taking this advice sincerely to heart for the next semesters. Thank you Dr. Bazett.
That can be so rough! Being caught in the middle of a hard semester where it feels like everything goes so poorly so easy to get in a really negative head space about it. Good luck next sem!
As someone whom graduated as an engineer in the past year, I chalk this up to my 'engineering mindset' but I feel like i'm the opposite of you when it comes to learning via definition-theorum-proof verses Computational fluency. With the way my mind worked, the fact that a mathematician or a textbook could prove the formulas and operators worked was important, but at best I wanted to see that evidence once just so any failings in the formula/operator (and why they fail in specific cases) were kept in mind, as I dived into the application, since it was the fact that calculus could be applied to projects and mental scenarios is what drove my love and engagement with math, to the point where I once dove into Combinatorics so I could build a spreadsheet that could tell me the probability of rolling towards the middle with a combination of dice since that related to the tabletop game I was playing. Granted, I knew this about myself since I took Geometry in either middle or high school, and avoided the heavy proof-based classes like the plague in later highschool and college like Linear algebra an any form of advanced geometry. On a separate note, just want to say, found your channel like 2 or 3 days ago and I've enjoyed your math discussion~
I emailed my prof. cause I wanted some advice on how to study math. I've passed two calculus courses with hard work and some pity. For my third math course I want to study it in a different way. He emailed me back saying that it was too late and the only thing he could do was answer to question about the course not about the study methods and strategies. I do believe that everyone could do anything with the right attitude in the right way.
My daughter, 33, was not happy with her command of mathematics. So, she asked me to teach her. She has been learning for two years and she is proud she has been able to apply what she learned to her job, supervision of technical translations.
OK, this is super werid and a bit crazt, but I swear to god that was my mentality coming to University. I have to work as little as possible to show my talents, it's sooo crazy. From 1-3 minutes, that literally was my highschool and first 2 year of university. Thank you for sharing!
May you like the following: By employ mathematica, we have the following algorithm for solving Riemann Hypothesis: 1. Compute the contour of inverse zeta function over a closed path (without singularity); 2. The resulted complex value NOT equals to zero implies the existence of zeta roots; 3. It may then be expressed by Euler product decomposition & determines all zeros; 4.We may then extend the squared closed path by analytic continuation (& regularization) for the whole zeta critical strip. 5. Any residue value not equals to zero may indicate a singularity nearby. (Ref: Terry Tao PhD, USA & Zeta Maths) In fact, for both of the residue and contour, the integrated values is either zero or not may constitute a philosophy.
Can you do a video about surviving grad school/Ph.D. programs? Like course work, finances, work/life balance, sharing your story, or other ideas I'm not thinking of.
My first introduction to the calculus happened when I was in highschool. My school book (NCERT) was so good in it. Without having a teacher (actually i had a teacher but her contribution in class was ignorable) i solved every single problem of my book without taking any help from outside. I wasn't believing myself that is it me doing these problems? I love mathematics but I'm physics major. Edit: BTW I love mathematics because of you and 3Blue1Brown. Thank you.
It amazing how I am actually in the same path of the journey. I was excellent in math in school but university math gave me anxiety and I was avoiding it as much as I could. Only recently during my PhD I fell in love with math again (credit to 3Blue1Brown) and improving my methods of learning to get better. This video will help a lot of student like me who lost their way to find their way back.
I failed every single math class except for geometry in high school. I failed algebra 1 and pre calculus and didnt finish algebra 2 . In about 30 days I start my first college algebra class and I'm truly excited.
This is such a great opportunity to reset. My advice is just to be really on top of thinking about your own learning, and asking "am i falling into old bad habits" or whether what you are doing is really effective. you got this!
@@DrTrefor thank you that really does mean a lot! I've read a lot since then, and I do believe that it's all about the growth mindset, to be open to new ideas and like you said to be on top of my own learning. Heres to the future
It was at abstract algebra when I figured that I prefer computational math (applied math) than abstract math (pure math). I loved mathematics my entire life and I wish I majored in math in the beginning. Thankfully, I earned a Master's Degree in Applied Math. What you stated is true: math is not a spectator sport. Even to this day, I have to practice all the time.
I recall in 2nd year -- the integration by parts and by partial fractions -- which could be a challenge on hour examinations. You had to learn "substitution" and know your functions well. John Fish 's video channel (a c.s. major now just graduated from Harvard) has some interesting videos on learning a few years back -- look for " a day of calculus" on the channel
I am in the first year of a Masters in Mathematics and I failed 3 classes, topology, representation theory and cohomology theory. I had a very weird year because of covid and I could not study full. I feel very disappointed and the classes felt extremely hard all of the sadden… I have re-exams all of the august, but it seems that it will be impossible to pass all of these courses at ones :(
It is so hard when other life things happen. And that is a lot! You might want to speak to advising/supervisor if there is any way to stretch those re-exams out so you can genuinely learn some of the content again.
I was extremely good at mathematics and physics and somehow for some reason I ended up as a physician. I still cannot remember why and when it happened. I’m still planning to go back and do physics after I’m done specialising. It sucks that I’m still required to do 3 years for a BSc in physics and cannot accelerate it in the UK.
I am a graduate student who is going to be a teaching assistant in the computer science department and I failed an object-oriented class as an undergraduate student. I changed the way that I was trying to learn to program. My skills are good now, but I am still learning and making myself better.
Please please make more math motivation videos like this .I would also like to know how you got through Real Analysis ,Thank you so much for this video ,it would be awesome if you make more videos like this similar to MathSorcerer .
I am an Engineer, I never found Calculus to be difficult, I loved it and got straight A on Calc I, II, III and Diff. Eqs. But I absolutely struggle in probability courses, it was difficult for me to make sense of it.
I dropped out after getting a low C in calculus 1. Years later, I went back more mature and got A's in calculus 2-4. I always liked math, but I didn't think I had to work at learning when I was younger. I wish I learned that lesson earlier.
My first exam was 50 % as well. In the end I made my master in mathematics with disctinction, because I was so much willing to learn maths. The 50 % in the first exam motivated me so much that I started reading the proofs, which I did not do before.
Dear Dr. Trevor, please create some videos related to how to research in math. I have graduated from university as one of top students from mathematics department and I’m really want to research inorder improve my skills for the sake of getting my master.For that matter,please consider creating videos about it. Thank you
I have a similar story to share. I am currently a Math undergrad. My first year was exclusively online, and so I did not do Calculus 1 and 2 in a completely honest manner, if you know what I mean. However, classes are no longer online - and, even though I thought I was a fraud and would perform badly at Calculus 3, I did really well: 9.1/10. It was really intense though.
I subscribe your channel and others like it because of my love for mathematics, each time wishing I had people like you in my beginnings. Once upon a time, I was told that I wanted to run before I could walk, I wanted to be original before I knew anything, yet that was how I understood and reproduced the concepts they taught. One even said, “stupido”. They couldn’t explain anything well enough for my simple brain to understand. Today, I am a publishing solid-state and condensed matter physics professor with worldwide collaboration. One former professor even asked to join my collaboration (I did not reply).
Time pressure is my biggest struggle. I am a single mom and I work while taking full time classes. I’m about to take my summer calc 2 exam on Friday. I want to be the best of the best and get the highest grade and I just haven’t.
You said something so true; “mathematics is beautiful” And beyond that, it is so useful. As an engineer, yes we use tools to help us. But the understanding behind those tools is worth a hundred times more. At my office, i can almost assure you, I’m the only who does integrals or derivatives. Which makes me sad. BC i feel there’s a loss of learning, of understanding. I’ll use the software, but I’ll do my own double check to make the software agrees with me! And at the heart of every engineering software, is, of course, beautiful mathematics.
Motivation is always the key factor, the drive. No matter what , if one is not interested or motivated to do something, better to avoid it. Your students may have problem with basics of calculus, you are having problem with Fekete's conjectur etc.. But without trying these challenge s there's 0 chance to concur the obstacles
I have a similar case. Disliked math during middle school because of the kids I used to hang out with. At the last year of high school I fell in love with math and I am absolutely obsessed with it.
Abstract algebra was the course that made me fall in love with mathematics too! And I had been an English major. Abstract algebra changed my life. I still found calculus difficult, though.
When I first went to university, I wanted to be a physician. I failed calculus 1 and did a terrible job. But when I retook calculus 1, something clicked. Once I made it to calculus 3, I fell in love with mathematics. I ended up changing my major to math and graduated last June! So don’t be discouraged, with failure comes success.
So many stories like that!
As a year 3 math student going into year four, I regretted nothing for failing to make it into engineering and going into pure math. Real analysis is the only thing that made me waver, but overcoming that slope made me see the beauty in math. That utter joy of proving a statement, that sense of accomplishment, I am sure you had the same feeling too. Never regret.
@@zhangkevin6748 I can totally relate, when I studied analysis for the first month and a half I had no idea what was going on then it clicked. It was the best feeling in the world!
I thought physicians didn't need to take any math courses besides Statistics.
@@lorax121323 when I first started my undergrad, I majored in biology and wanted to pursue medicine upon graduation. As a requirement of this degree we had to take calc 1 and 2. I chose to take calc 3 as an elective and then switched my major to mathematics.
So many of my math teachers have told me that if what I was studying was hard at any point, then I shouldn't be in STEM. One college I went to put Dweck's material in the syllabus and the instructor just threw it away, saying you rather get it or you don't. So I appreciate videos like this.
why the f would anyone do that that fucked up
Many of them are insecure, so they take it out on the students.
Every teacher I’ve had has been supportive.
I felt like calculus was hard for me because I didn't truly understand algebra/geometry in MS and HS. Altough I got all A's in MS and HS it doesn't say how well I understood the concepts. Which is one major flaw in the grading systems imo. And to this day I still have trouble understanding basic geometric concepts while I learn advanced math 🤣 so for now I accept geometry as an axiom and try to understand it at the same time. Thanks to your and Grant Sanderson's content you guys have made my life 10x easier and I can't thank both of you enough for letting me keep my love for mathematics
So glad we have been able to help:)
@@DrTrefor I started the most important part of my mathematical journey around 4 years ago with grant's(3blue1brown's) series on calculus.
Around 2 years ago i started spending more time on discord and would meet someone who suggested I read Terence Tao's Real analysis and Keith Devlin's An intro to mathematical thinking (Haven't really finished the first one). From there on out I started falling in love with math. And eventually i ended up starting Axler's Linear algebra. And here once again I'd along with what I'd learn in set theory from other sources and about calculus basically helped me change the way I looked at math once more. Wouldn't have been possible without people like you and grant to start me on this journey. Interesting thing I found aboutmany people was that (and I think many others) change how they look at math when they learn abstract algebra
I felt this way I got to calculus 3. I wanted to know why things were true but I wasn’t yet ready for the mathematical rigor required for this yet. I spent way too much trying to get a intuitive understanding of the formulas and be able to visualize all the crazy three dimensional stuff we were dealing with, which wasn’t really getting me anywhere. If I had just learned how to apply the formulas and concepts and called it a day like in calc 1 and 2, I could have saved myself a lot of grief.
@@jacobharris5894 calculus 3, smh, another physics student. JKJK, wow I totally understand your struggles man and I am glad you overcame them
This video brought me in tears, you are describing in godly precision what I'm now going through, stuck in that delusion loop hole that made my math skills plummet so hard that I'm getting bad marks on tests, made me depressed and in the "passive learning" mode, taking notes even if I don't understand nothing. And the thing is even my parents are trying to convince me to let down maths and do something else, but I can't even imaging my life without doing maths. This video seriously for me, is a big psychological relief because I'm not the only one who is struggling in the same problem and the solution / advice that you gave in this video. And thank you a lot Mr Bazett!!!!
HOLY SHIT SAME
all STEM students need to hear this
Thank you so much @sedthh!!!
i went through high school failing everything (60 credits after 4 years) - especially math and physics - then almost 8 years later i decided to go back to college and ended up getting a degree in astrophysics
the difference? i was paying for college by working full time at an arby's...worked mornings/classes in the afternoon - and then switched the next semester...
it was tough riding from one side of town to the other each day during the winter, but it was important because nobody was going to make it easier for me...when i had 3 finals in one day, i didn't whine - i pushed through
remember: it only takes an excuse to do nothing, but it takes a reason to do something
This is why you explain things well. I think a lot of teachers might have difficulty teaching because they learned it easily themselves and have no idea how to explain it to others.
I hadn't taken a math class after high school, after returning to school I struggled and failed pre-calc + trig. I hated math and would cry when I couldn't handle the stress of having to learn it. After a semester of tutoring, I had a solid foundation to move forward. Math is overwhelming when you don't get your foundations right first. I just passed diff-eq with a B. Math is brilliant and beautiful once you get your mindset about it right.
It’s awesome that you point out that those who struggle are not just the ones who feel they are “bad” at math but also the ones who think they are “good” at math!
I struggled in early university with the idea that working hard and failing would be too painful…
Math, and probably most things, have come easiest for me when I consistently adopt the mindset of “I don’t understand this yet; why not?” Somewhere along the way of doing that many, many times I actually had improved significantly.
Then you realize math is so unending and so beautiful that it is ok to not understand sometimes lol
@@zhangkevin6748 I wonder if people who are mathematically gifted to grasp things easier also have a hard time when they don't understand anything and how often does that happen...
@@Sentuyashi it definitely does happen. I had one CMO winner in my university math class and it not like they will have to study any less or more than us. He obviously can understand things quicker but in the end everyone gets stumped at least a bit by real analysis. It happens quite often that people get lost in math, unless they are super gifted and even then you can hard work your way through that talent gap. Pure math is all grit and grind, and if you enjoy it a lot talents don’t seem to matter as much. But talent does help a lot.
Not sure if you will see this, but I really needed to hear this. I’ve always considered myself as being bad at mathematics. Though,I’ve never studied, or even given effort. I would say it’s very difficult to say that I’m bad at something that I have t even attempted to try in.
I’m going into college for a computer science degree. I’m going to spend the first semester, maybe second, solely focused on improving my mathematics. I’ve neglected the subject, but I’m sure I’ll come to enjoy it.
Thank you for this video. I strongly believe I can improve, it would be foolish to think otherwise.
Thank you for talking about this! In my experience as a Lecturer I have found that the single biggest obstacle students are facing is often challenging the belief they have about themselves. This is so true for certain backgrounds that are perceived as "opposite" as Maths or Programming, like Art and Design. And it takes a long time to retrain students to NOT say things like "I am not good at Maths", "I am not good with numbers", "I am so stupid" and so on!
So thanks for talking about this! 👏
That mindset is so influential!
I came to university being five years removed from highschool where I barely graduated. After years of roofing and working at Target I quickly realized I wanted to further my education as daunting as that may be. I almost failed first year because of requisite courses like calculus and lin alg. I was still figuring out how to balance these courses on top of others required for my major (CS) . I sat in a class and watched a professor scribble on a chalk board trying to figure out what the strange figures meant. It really felt like a brick wall where I too developed an anxiety around these topics. It wasn't a lack of effort but rather how I was approaching things. Circling back to these topics years later, with the help from channels like this one, I have developed a way to learn these topics that worked for me. Not only am I understanding things better, but I have found a way to study things that are difficult to me.
Everyone will have a different pace when studying different things and if anyone reading this has struggled and felt like throwing in the towel please take it from me. I am an absolute dummy and I was able to figure this stuff out EVENTUALLY. A few videos a night, scraping online resources and textbooks slowly helped me develop my skills making things easier over time. I still have so much to learn but one thing I have figured out is that you can make it to the moon, even if you have to crawl at the start.
As a Mathematics Major, my best subjects were in Real Analysis, Complex Analysis, Differential Equations, Integral Calculus Transforms, Abstract Algebra and Statistical Modelling. Your video was good. There is a very strong parallel between learning Mathematics and weight training at a gym - correct mindset and positive attitude / discipline.
I don't feel bad for failing calculus but I learned such a big thing about it and I am grateful about it. I can improve, we can improve. 💜
Wow I needed this, I felt like my calc exam went horrendously and it hit hard! But I’ve been practicing so much since and I’m hoping it begins to pay off for semester 2 with continuation of calculus. Thank you for this :)
Wowww!!!! Thanks a lot prof. So relatable. I was treated as a mathematics star in my high school, and after entering University things changed so much. I got a 55 in linear algebra. Now when I think about it, I feel like I too have this self perception that I am too good at mathematics and somewhere in my head glorify minimal preparation for exams. I'm halfway through my 1st semester, and am glad that I stumbled upon this video.❤
I especially recognize the part about the attitude towards studying for a course and not wanting to fail because of the fear of destroying the confidence in yourself. I'm glad that you mentioned it.
Luckily, I've never failed a course when I had studied properly, which confirmed my belief that I was indeed capable of understanding all the topics, given that I'd put in the effort.
After years of failing without studying and later more years of making progress and succeeding, I'm currently halfway through my PhD. You never know how it'll go.
As an educator myself, I second this. I absolutely struggled with Abstract Algebra in college.
In my experience, hiccups like this can be explained by things like lack of proper prereqs, unexplained notation, ambiguous language, or leaving too much to be inferred by the student. All things that would trip up even the greatest minds. When you realize that, you’re less hard on yourself when mistakes happen. A proper math ego is a big part of a healthy math education trajectory.
That's so interesting that abstract algebra was the course where I really found my love of math, just goes to show there are so many different possible paths!
@@DrTrefor I very much loved the course in fact. But for awhile i was stuck in the pure symbol manipulation phase. I didn’t make analogies to concrete objects (like shape rotations) and that really hampered me.
This is an important message to hear and understand. I got a 4 on my AP Calc BC exam which transferred to a 5 on AP Calc AB. I tested out of Calc 1 and 2 and walked into my first semester of Calc 3. The problem was that I didn’t really have a solid enough grasp of the concepts of Calc 1 and 2 for the difficulty of Calc 3, and because I had always “been good at math,” I showed up my freshman year of college and didn’t really try in Calc 3. I ended up scoring 68% and having to retake it entirely. Learning the material and understanding it deeply is paramount in being successful in future classes that use those concepts. I could memorize stuff well enough to get through AP Calc, but the future classes beat me up because I didn’t build strong foundations.
I think immersion helps a tremendous amount. Math is hard. It's like learning another language. You can't just spend an hour on it here and there. If you're someone who needs to understand math for your degree, try to make a habit of doing math pretty much as often as you can.
I agree with this comment. It's also maturity or focus. As I'm getting older, things I didn't understand when I was younger, make more sense.
That is such an inspiring journey; it reminds me of myself. I did fairly well in school in terms of math, but extracurricular math contests were a trainwreck for me. I always loved math and knew there was nothing I would enjoy more than this subject, but my inauspicious career within it has made me doubt myself so many times; seeing you becoming a math professor despite hardship and working hard despite doubts is such a great story man. I am truly happy for you, I know that feeling, especially in math, where you know you love the subject beyond anything, but you doubt your love because you are just not succeeding. You overcame that, and I am so happy for you; I wish you the best of luck and take care. Math is so rewarding yet so harsh, there is no such subject like this.
Professor Bassett, I want to thank you for your insightful explanations and openness in sharing your past. If I may, I’d like to briefly share a similar one:
Last year, in year 10 of high school, I walked in to my AP Calc AB class with confidence in other areas of math, as you mentioned here. The first day, though, my teacher (Dr. Friel) tasked us with approximating IROC for real-world situations (word problems, like coffee cooling or car speedometers). While the upperclassmen solved problems quickly, I struggled to see the patterns. Over the course of year 10, Dr. Friel imparted not only formulas for application, but also deep conceptual understanding of calculus ideas to me (as well as those of my classmates who cared to listen). Now, I am taking AP Calc BC as a junior in high school (along with Physics C courses), and hope to take MVC and Linear Algebra classes next year before I attend undergraduate university. I can’t stress enough how much this teacher changed my perspective.
My university didn't have calculus 1, it had math 1 (later 2, 3) it was a mixture of everything. Calculus was included and the pace of the lectures was incredibly quick. Everything was obviously obvious and the professor that was assigned to me didn't take time to explain basic notation.
Later I noticed that of the 80 students, only 4 myself included were regularly attending his class. Why? Everyone went to hear lectures from someone else. Of 6 professors that were teaching the course, only 2 did it well. Classrooms of those 2 professors were so full that people were sitting on the floor. None of this was official, students were still assigned to their old professors, everyone was just scrambling for their lives. I figured this out in the fourth week of the course and it was way too late to catch up to anyone. I just stopped going to lectures, taught myself the stuff and barely passed the course.
Today I use math and I kind of treat it like programming libraries. I'm not hear to invent it, I'm here to use it. You guessed it, I'm an engineer.
And my relationship with math itself? I don't hate it, I just hate that some people are allowed to teach it.
P.S. when I say self-taught, that doesn't mean I didn't use plenty of online material. But the thing is, the online material is fragmented, uses different standards and it takes longer to learn this way.
What you’re saying about how a fixed mindset can go both ways is so true! I can really relate to what you said about thinking you’re good at math!
I think maths is like learning how to drive a manual car. Some people are just “gifted” and understand what to do in a second whilst other have to spend hours and hours on the same thing (like how to use the clutch pedal and the throttle simultaneously to make the car move uphill). Personally I was the second type of guy while learning how to drive and also while I was learning maths and now I enjoy driving to my uni where I take classes that require a mathematical knowledge that just one year ago felt intimidating.
Calculus, for me, was for some reason way easier than I thought in highschool. I took AP calc BC as a junior, and soon will be taking calculus iii. One part might be that I enjoyed the learning process, and generally just love mathematics. Another part of it is a) the teacher (mine always showed us proofs and never just said to "accept things") and b) my foundation of algebra and precalc. Great video!
Congratulatons, Prof!!! Godspeed!!!
I just recently got my old college calc book (Stewart / Early Transcendentals) and am reading it for pleasure / practice - it's so much better to read it on my own time than being under pressure to pass exams on it. Also really enjoying your videos!
I had very similar experiences in my college days, but math clicked for me the most when I took a leap of faith and took a group theory course. The professor taught it in an intuitive way and really helped me understand the structure of math better given so many different things from all across math can be represented in terms of groups via their symmetries. Anyways great video, and maybe at some point make a group theory video so viewers like me can understand math better through how everything in math connects!
i recommend the book “how not to be wrong by jordan ellenberg.” After reading that, i switched my major to mathematics and it was the best decision i’ve ever made
come back to youtube, we miss you
Oh wow I didn't know you switched to Math.
Edit: I've watched your Computer Science videos
yooo tren black you should give more advice for a poor guy like me
Wow another fellow math student, I have some questions for you, what field of mathematics interests you the most, for me it’s topology and Euclidean geometry, next how was that journey and that feeling after proofing a theorem all on your own? I wish you the best and good luck 😉
As an upcoming freshman, I decided to go through your (and other) calc 1 course because I was curious of what it was about. When I finished, I was really confused about what going from velocity to distance had to do with area under the curve, why there is a definite, an accumulative, and an indefinite integral but only one derivative, why the chain rule is what it is, ect. I felt like there was a lot of information about how to do calculus but very rarely about the concept of calculus.
Here is one important concept: Integration is a "global" operation -- you need to know how your function f(x) looks like over the entire interval [a,b] which you are integrating over. On the other hand, differentiation is a "local" operation -- for the deriv of f at x0, you only need to know how f(x) looks like on a small interval, say (x0-epsilon, x0+epsilon). Being a "global" operation, you need to supply more information before you can integrate, giving you seemingly many "versions" of the integral, (e.g. [a,b] or [a,x] or [a,infty) ... etc).
It's good that you have these questions. Most students don't care about where things like the chain rule come from / how these important equations are derived. And I think that's a serious problem plaguing students. Students are often more interested in "How do I get an answer for this homework question" (i.e. just googling the question and finding someone's step-by-step answer) rather than actually learning. I see this all the time when I teach intro chem (and even higher level chem). Many students just want the answer without having to think or learn.
ua-cam.com/video/WUvTyaaNkzM/v-deo.html
this series helped me a TON when I was first learning calculus, it's way more about the different concepts in calculus rather than doing computations and I couldn't recommend it more
It will tie together when you take physics classes. Like if you have a function for position with respect to time, the first derivative will give you velocity, the next derivative will give you acceleration. And then you can integrate to go backwards. Integration is also useful for finding the area under a curve, like if you wave a weird shaped cup and you wanted to know the volume. If you are just learning it on your own, I don’t think you will get much use out of it, but if you are taking it as a stem class you will be using it a lot in physics and other classes.
@@Chemasaurus I totally agree! How have you been able to encourage students to try to learn the concepts, in your experience?
Thank you Dr. Trefor. I had the best calculus experience a couple years ago taking Calc 204 with you and it’s awesome being able to keep learning from your videos on UA-cam!
Cool! Thanks for sharing:)
I got pushed back to algebra my 1st year in college, but it (along with some great professors algebra-calc3) really did help build a foundation and appreciation for math. However then covid hit, and now I feel I've lost my momentum, taking ODEs for the 3rd time. Hopefully my refresher/grade boost in calc 1 over the summer will help.
As a self learner the content that you provide is very helpful for me
Prof you are helping thousands of students with your efforts
Thanks a lot
Glad to hear that!
Got started at my engineering degree in 2021 during the pandemic. I went from almost straight As at a pretty prestigious school and having a good social life to not making any connections at uni and not showing up to lectures. We started with calc 2 and I trought I could cram it all in a week... I was so ashamed of how little I knew that I didn’t even show up to the exam. I dropped out later that year. The second start was still kinda rough but I made it trough calc 2, 3, linear algebra, statistics and applied maths. I was dealing with depression and axiety trough all those courses but managed to study them at home, thanks a lot to your videos. Im doing better now and am planning on revisiting some of those courses to get top grades again. Thanks for everything.
I failed Calc in high school. C in Calc 1. B in Calc 2, B in linear algebra. Then, I got an A in Calc 3, modern algebra, and Calc 4. About to get an A in diff eq. It took a lot of maturing for me to get there
That is quite the progression, well done!
What is Calc 4?
@@jacobharris5894 I think multivariable calculus, gradient, and some other stuff idk, us pure math student don’t have calculus 😂 for us it’s called real analysis
@@zhangkevin6748 Oh okay. I’ve heard of that it’s just an unusual name. I’ve only seen it called real analysis or advanced calculus, like at my school. I want to take Advanced Calculus but don’t think I’ll be able to fit it in unfortunately. I already have my math minor and I’ve heard it’s the hardest undergrad math class other than maybe Abstract Algebra. You must not be getting your education in the United States or something because where I’m from even pure math students take three non rigorous calculus classes before real analysis.
@@jacobharris5894 I go to Waterloo so it’s a bit different. First year I don’t think we even learned calculus it’s mostly geometry and contest math 🤣
I needed this video to get through a homework assignment today. Back on track!
Math has always been a terrible struggle for me. I really suck in math. I had to do homework about 8 hours a day. What motivated me to do well was fear of losing money--tuition is far too expensive to just lose. Anyway I graduated with a Master's degree age 62. What was a big "game changer" was taking an online class prior to taking the actual class. It made a HUGE difference so I ended up doing very well in math classes but it took a ton of preparation.
Engineering student here and every single thing you said about yourself was true for me too! You're lovely, so I'm glad to see what I can still become ;)
Thank you for sharing this story & your experience Dr. Bazett! It meant a lot to hear that there are plenty of non-linear paths to a life in Mathematics :) I personally nearly failed Calc 2 my first time taking it in undergrad after thinking I was "good at math" my whole life. After some time away, I took Calc 2 as a Post-Bacc/Non-Degree student and have since taken Linear Algebra, Vector Calculus, Multivariable, with more planned! Which your videos have been very helpful with, by the way, so thank you for everything!
I was in the same situation my entire life since elementary school. Always got bad grades and assumed it was just because I was bad at math and it never worked out for me. I failed pre-calc twice in highschool and one more time in college. When I switched majors to cs from a non-stem degree I panicked because I realized how many math classes I would have to take. I worked my way up to Calc2 and had to drop it because I was failing. I retook it and had a better approach when it came to studying. I treated the class alongside another math class and programming class like a part time job and spent hours and hours practicing problems. I ended up acing nearly ever exam and I then realized that my approach was the issue. Extremely rewarding and I’m glad I made the switch or else I’d probably still have the same mindset. (Possibly have calc 3/physics 2/diff eq’s next quarter so feel free to leave any tips)
- You can do it, just make sure to take breaks and look back on the progress you’ve made.
Thank you for sharing your story! I had a similar experience, but with College Algebra & Trigonometry. In high school, the highest level of math I took was Algebra II, and the remedial math I aced my freshman year of college gave me a false sense of confidence.
In my sophomore year, I took College Algebra & Trigonometry (skipping an intermediate course due to a conflict), studied for 5 hours daily, and got a 'C'. Luckily, it was the lowest grade needed to transfer into the university I originally wanted to get into, and that summer I spent more time learning math for myself. I took a math placement test during the mid-summer, and somehow, tested right into Calculus I (no precalculus). I lucked out as my professor had an amazing sense of humor and showed realistic applications for the majority of the concepts taught. I felt everything clicked into place and ended up in the upper B range during the first two semesters and my first A during Multivariable Calculus.
I strongly believe that my shift in performance was by finding applications and experimenting, which inspired me to do more problems far beyond what was assigned. Now, as a freelance tutor, I do the same thing with my students - teaching by tinkering rather than through the "here's the concept now plug in numbers" approach.
I got a 5 on the AP Calc BC exam which allowed me to skip Calc 2 at my research university, however despite doing very well in Calc 3 I felt like I might my Calc 2 fundamentals might not be strong enough. So I transferred back to Calc 2. What I didn't know was that the exam was literally the day of me starting and it was in trig substitutions which I'd gotten particularly sloppy at from lack of practice. I wound up starting my first semester with a D‐ on my first exam. 1 year later I almost wound up TAing for that professor in Advanced Calculus. One bad grade doesn't determine your fate nor your aptitude.
Thanks for sharing!
I had the problem of active vs passive learning but my main issue was my (undiagnosed) autism spectrum disorder. I went to a really respected sixth form in the UK which is famous for being basically the best state one in the country, but I couldn't function in classes for various reasons (too loud / too many people and I have social anxiety.) As a result I was very withdrawn and passively learning which meant I struggled a lot. I also began to develop imposter syndrome and doubt my abilities in mathematics. To put it into perspective at GCSE I got 8s in maths / further maths and 9s in Physics and Chemistry but in sixth form I was getting C's in Physics and failing chemistry / further maths.
Once we began to identify my issues I was fortunately privileged enough to move to a private school, most people there are like your average teenager (it's not some posh place like Eton lol) but the huge bonus was the small class sizes. Immediately I started to improve and while I've still had struggled, the nature of active learning since I was in a smaller class environment means that I'm hoping to get an A* in my one year a level maths, with predicted A* in Physics and History too (we will see based on my maths outcome if I continue further maths.)
I've gone from thinking I wasn't good enough and hopeless, to aiming at applying for Cambridge University to study natural sciences :)
I still have really bad issues with procrastinating and leaving studying to the last minute which I thought I would have learnt from by now but I am working on it (maybe in a few days idk I'm busy now 🤣)
Thanks for sharing!:)
Hello Dr. Bazett,
I only recently stumbled across your channel. I immediately subscribed after watching your Bayes Theorem video. I loved how you detailed everything. This is where my many undergraduate, graduate (Master’s and PhD) professors failed me. Text books, and instructors tend to gloss over the material and leave out small details that just make things difficult.
Quickly breaking down a formula and explaining givens when doing proofs should be more important than blazing through the material. Thank you for the awesome material and your presentation style.
Thanks for videos and comments. I am a retired engineer with many mathematical "holes" that remain from university education. I like going through calculus videos, even now that I am retired from a technical engineering career.
I went through university calculus in the early 70's... suffering through university calculus with what I and the university called new age calculus teaching methods. I received a C in my calc 1 course. I went back to my HS calc instructor and asked him to help me with my university calc at the end of my first semester. He commented that I should need no help as he had already taught me the Calc 1 curriculum in HS and that I had had no problems latching on to it. I felt the university did more to destroy my calculus ability than to nurture it. Thus went Calc 1, 2, and 3. I did find the series and DE class to be interesting (possibly more app oriented) and more personalized.
Anyway your classes and comments here are of great help from a ''hey so that is calculus" viewpoint for me. Well done.
I finished my math department coursework by taking and thoroughly enjoying a Complex Analysis course. For me complex analysis contains a most beautiful mathematical language of calculus methods that are clearly and concisely defended.
My experience is not about calculus but STEM subjects in general. In 9th grade i remember struggling with monoms and polynoms and now, in my freetime, (i'm going to 11th grade) i study rocket science and astrophysics. Why? It's interesting, and i'm not afraid of admitting my limits, but i saw that with dedication and sweat you can get on a high level. For example i already learned derivates, i'm at good point with integrals and i know, as i said, a lot of stuff about rocket science. My passion was genuine, i just found the right teacher that of course didn't teach me these things, but she created the base for this.
As a teacher of mathematics in the equivalent of a high school in Britain, I often did an informal survey of students who joined my classes. The vast majority of students were at age 13 were put off mathematics. It made me keen on developing enthusiasm for the subject as a priority to develop mathematical skills.
Interestingly I was part of a study of mathematical education where a follow-up ten years later was carried out and interestingly my students were the ones that had the most positive response to mathematics still ten years later.
I'm counting my days in High School now but the fewer days I've left, the more I am thankful for taking calculus course as one of my elective. For the record, I was also considered pretty decent at math and have always found math quirky but kind of fun. However, as soon as the calculus actually hits, it hits HARD, more than half of my class dropped out of it. I can't express how much I have struggled to get to the place I am now, and I still consider myself very much a beginner! Or at least to this very day I still can't solve a complicated integration or differentiation without a couple of trial and error, sometimes, I am totally defeated too! BUT! I always know that I am not falling behind, and at least I can sometime do them, and that's very crucial for my morale! Not to mention the things you can achieve with calculus are so much fun and worth it.
What I am trying to say here is that math and especially calculus are hard but they are absolutely worth it. And hey! If a brain dead high schooler like me can do it, so can you! Or, look at it the other way, if you are struggling, so are your classmates, so chill! Take a break if you need to, that helped me a ton!
...Good day Dr. Trefor, I am glad to see by your inspiring video that you're doing pretty well! When confronted for the first time with the Definition of the Derivative, it felt like I was passing through a portal leading to a world of limitless possibilities, both infinitely large and small. Similar to going from childhood to adulthood. Thank you very much for sharing your valuable experiences with us and for your unwavering commitment to education... Take good care, Jan-W
Thanks for sharing!
I hit that wall in Abstract Algebra and figured that, despite being a math wiz growing up, I was just stupid after all and dropped the math major. I still managed to graduate with a stem degree, though many years later I've never had a job that used it. At some point I went back and learned some Abstract Algebra, and it's a really interesting subject. I just wish I had had a mentor or anyone to talk to about how I was feeling about math to have help put me in a better direction. At least there are good videos like this for students today.
I failed Calculus before you !! ... and I'm still working on getting better at it.
Hi Trefor, Your vector calculus lectures have been very helpful over the past 7 weeks, my exam is tomorrow. The UA-cam algorithm, being what it is, has been pushing me to watch your "failed calculus" video for some time, so I finally did and I agree entirely with experiential learning. Your early math experience is similar to mine (not mentioning hiking and canoeing). I failed my first university calculus course but got 80% second time around, but that was in 1976, now in my retirement I'm a second year computer engineering student in Montreal interested in understanding AI and I turn 66 the day after my exam. Abstract algebra here I come.
2:25 : literally my entire university career. I actually thought to show how good I was at all of this, the least amount of work done would show I only needed little time to study. After university, I basically knew nothing useful since everything I crammed in for exams, instantly got forgotten. So I had to spend a year after uni to reteach my self everything that I didn't fully learn when I should have.
Your suggestions are the best. I share your videos with my students.
After I took up calculus at first semester, I was discontented and deeply frustrated by the non-rigority of the teaching material (I didn't have this idea in my mind back then, I just felt confused and everything seemed haphazardly made-up). The university was trying to get through the material as fast as possible, because the tools of calculus were needed for other courses. Then I had the luck to receive a very good and rigorous introductory real analysis textbook from a math professor (from another institute). That was an enlightening experience for me and made me love mathematics, for the same reasons that the prof in the video mentions at 08:46. No more feelings of mindless symbol juggling with handwavy justifications and "abuse of notations". And just learning about the history of calculus about how long it took to develop to the level of rigor that mathematics demands really was a humbling experience, and put my struggles into perspective, and made me less self-judgemental.
Something similar is hapemning to me. I felt like my understanding in calc was only intuitive and everything was so fast ,explenations were poor, theorems were not proved,and exams didnt actually grade ur knowledge only ur ability to calculate (i call it do numbers) , i felt like all was made up in my physics degree. I was so sad bc i wasnt liking the degree i have dreamed about. But luckly , next semester my Linear algebra was abstract and well connected most of the results/formulas/theorems we used prove. I knew where the formula came from , why a particular thing was definned that way , everything seemed more natural !!
Thanks to that class I realised that I really enjoy math , that I can understand abstract things if they are connected ina logical way , that im not that bad at proofs.
And the most important thing, that I should be in a math degree bc it naturally fits how my mind works. I went to talk with the head of studies of mathematics in my uni . Now i cant wait for September to start my math degree.
I felt your story really resonated with me for my first year calculus class going into college.
Will be waiting for your Abstract Algebra course!
ha! I do actually want to do this, I have an idea of a very visual/intuitive twist that helps to ease how we discover proofs. Not 100% sure yet though:D
@@DrTrefor Yes that would make all the difference. Like I can write proofs for exercises, but I always need a handy list of other proofs/books in front of me to write them. I can promise you it will make many self-learners happy if you do so!
I sucked at maths in school and I labelled myself as math hater. Later on when I did really well in Physics and actually learned more maths through physics than math textbooks. i think the problem with me was fixed mindset which in turn set in due to fact that maths taught to me was too abstract, no theoretical context, no conceptualization, teacher would go straight to the end of the chapter exercises and start tampering with numbers. But physics taught me some theoretical context and concepts.
I often worry that sometime in high school or early uni I just suddenly “got bad” at maths. I think the reality is just that life got more complicated. Generally I don’t do well in exams regardless of how well I understand the topic, so I’ve been demotivated, falling back into that fixed mindset idea. Being aware of it and noticing myself going down that path is really important, and this video helped remind me of that.
really hope i can improve to be a successful engineer in the future. putting in the effort is hard af but i gotta get used to it
I did actually fail calculus. The second time around i understood it a lot better
I'm in my 4th year now and struggling so much recently. I've been repeatedly thinking that I chose the wrong major and wasted tons of money and time. I'm constantly calling myself down and really creating a negative headspace. There's probably little I can do to salvage this semester, but I won't give up, and I'll be taking this advice sincerely to heart for the next semesters. Thank you Dr. Bazett.
That can be so rough! Being caught in the middle of a hard semester where it feels like everything goes so poorly so easy to get in a really negative head space about it. Good luck next sem!
As someone whom graduated as an engineer in the past year, I chalk this up to my 'engineering mindset' but I feel like i'm the opposite of you when it comes to learning via definition-theorum-proof verses Computational fluency. With the way my mind worked, the fact that a mathematician or a textbook could prove the formulas and operators worked was important, but at best I wanted to see that evidence once just so any failings in the formula/operator (and why they fail in specific cases) were kept in mind, as I dived into the application, since it was the fact that calculus could be applied to projects and mental scenarios is what drove my love and engagement with math, to the point where I once dove into Combinatorics so I could build a spreadsheet that could tell me the probability of rolling towards the middle with a combination of dice since that related to the tabletop game I was playing.
Granted, I knew this about myself since I took Geometry in either middle or high school, and avoided the heavy proof-based classes like the plague in later highschool and college like Linear algebra an any form of advanced geometry.
On a separate note, just want to say, found your channel like 2 or 3 days ago and I've enjoyed your math discussion~
Thanks for sharing!
I emailed my prof. cause I wanted some advice on how to study math. I've passed two calculus courses with hard work and some pity. For my third math course I want to study it in a different way. He emailed me back saying that it was too late and the only thing he could do was answer to question about the course not about the study methods and strategies. I do believe that everyone could do anything with the right attitude in the right way.
That was a sad reply from your instructor. College instructors can teach the subject, but rarely teach you how to study.
My daughter, 33, was not happy with her command of mathematics. So, she asked me to teach her. She has been learning for two years and she is proud she has been able to apply what she learned to her job, supervision of technical translations.
OK, this is super werid and a bit crazt, but I swear to god that was my mentality coming to University. I have to work as little as possible to show my talents, it's sooo crazy. From 1-3 minutes, that literally was my highschool and first 2 year of university. Thank you for sharing!
Right?! So obviously silly when you say it out loud but we've both totally been there
May you like the following:
By employ mathematica, we have the following algorithm for solving Riemann Hypothesis:
1. Compute the contour of inverse zeta function over a closed path (without singularity);
2. The resulted complex value NOT equals to zero implies the existence of zeta roots;
3. It may then be expressed by Euler product decomposition & determines all zeros;
4.We may then extend the squared closed path by analytic continuation (& regularization) for the whole zeta critical strip.
5. Any residue value not equals to zero may indicate a singularity nearby.
(Ref: Terry Tao PhD, USA & Zeta Maths)
In fact, for both of the residue and contour, the integrated values is either zero or not may constitute a philosophy.
Can you do a video about surviving grad school/Ph.D. programs? Like course work, finances, work/life balance, sharing your story, or other ideas I'm not thinking of.
oooh I've got a LOT of stories from that time, maybe I will make a vid!
My first introduction to the calculus happened when I was in highschool. My school book (NCERT) was so good in it. Without having a teacher (actually i had a teacher but her contribution in class was ignorable) i solved every single problem of my book without taking any help from outside. I wasn't believing myself that is it me doing these problems? I love mathematics but I'm physics major.
Edit: BTW I love mathematics because of you and 3Blue1Brown. Thank you.
Ey jee ❤️
It amazing how I am actually in the same path of the journey. I was excellent in math in school but university math gave me anxiety and I was avoiding it as much as I could. Only recently during my PhD I fell in love with math again (credit to 3Blue1Brown) and improving my methods of learning to get better. This video will help a lot of student like me who lost their way to find their way back.
I failed every single math class except for geometry in high school. I failed algebra 1 and pre calculus and didnt finish algebra 2 . In about 30 days I start my first college algebra class and I'm truly excited.
This is such a great opportunity to reset. My advice is just to be really on top of thinking about your own learning, and asking "am i falling into old bad habits" or whether what you are doing is really effective. you got this!
@@DrTrefor thank you that really does mean a lot! I've read a lot since then, and I do believe that it's all about the growth mindset, to be open to new ideas and like you said to be on top of my own learning. Heres to the future
Thank you for this. As I am about to get into electrical engineering courses. I needed this
It was at abstract algebra when I figured that I prefer computational math (applied math) than abstract math (pure math). I loved mathematics my entire life and I wish I majored in math in the beginning. Thankfully, I earned a Master's Degree in Applied Math. What you stated is true: math is not a spectator sport. Even to this day, I have to practice all the time.
I recall in 2nd year -- the integration by parts and by partial fractions -- which could be a challenge on hour examinations. You had to learn "substitution" and know your functions well. John Fish 's video channel (a c.s. major now just graduated from Harvard) has some interesting videos on learning a few years back -- look for " a day of calculus" on the channel
I am in the first year of a Masters in Mathematics and I failed 3 classes, topology, representation theory and cohomology theory. I had a very weird year because of covid and I could not study full. I feel very disappointed and the classes felt extremely hard all of the sadden… I have re-exams all of the august, but it seems that it will be impossible to pass all of these courses at ones :(
It is so hard when other life things happen. And that is a lot! You might want to speak to advising/supervisor if there is any way to stretch those re-exams out so you can genuinely learn some of the content again.
I was extremely good at mathematics and physics and somehow for some reason I ended up as a physician. I still cannot remember why and when it happened. I’m still planning to go back and do physics after I’m done specialising. It sucks that I’m still required to do 3 years for a BSc in physics and cannot accelerate it in the UK.
I am a graduate student who is going to be a teaching assistant in the computer science department and I failed an object-oriented class as an undergraduate student. I changed the way that I was trying to learn to program. My skills are good now, but I am still learning and making myself better.
Please please make more math motivation videos like this .I would also like to know how you got through Real Analysis ,Thank you so much for this video ,it would be awesome if you make more videos like this similar to MathSorcerer .
If people like this video I was thinking of doing a little series on my journey up to professor for sure!
This video is extremely valuable with rich insight. Thank you for this.
Stokes' Theorem (the generalized one) is the most beautiful theorem in all math!
Thank you for the video.
Wonderful video as always Dr. Bazett
i'm like really good with algebra and trignomentry, even inverse. This helped alot for me in understanding calculas quicker.
I am an Engineer, I never found Calculus to be difficult, I loved it and got straight A on Calc I, II, III and Diff. Eqs. But I absolutely struggle in probability courses, it was difficult for me to make sense of it.
Thank a lot. I think this is not just about Maths but any topic.
I was depressed after my jee but I will improve
This year I will have a growth mindset and get cse in iit r
I'm so stoked to see that shirt!
Lol well played
I dropped out after getting a low C in calculus 1. Years later, I went back more mature and got A's in calculus 2-4. I always liked math, but I didn't think I had to work at learning when I was younger. I wish I learned that lesson earlier.
My first exam was 50 % as well. In the end I made my master in mathematics with disctinction, because I was so much willing to learn maths. The 50 % in the first exam motivated me so much that I started reading the proofs, which I did not do before.
Dear Dr. Trevor, please create some videos related to how to research in math. I have graduated from university as one of top students from mathematics department and I’m really want to research inorder improve my skills for the sake of getting my master.For that matter,please consider creating videos about it.
Thank you
Great suggestion!
I went to college as a mid twenties adult and I had to retake Algebra 2. So when I got to trig and calc 1 I was really invested and appreciated math.
I have a similar story to share.
I am currently a Math undergrad. My first year was exclusively online, and so I did not do Calculus 1 and 2 in a completely honest manner, if you know what I mean. However, classes are no longer online - and, even though I thought I was a fraud and would perform badly at Calculus 3, I did really well: 9.1/10. It was really intense though.
Amazing, well done!
I subscribe your channel and others like it because of my love for mathematics, each time wishing I had people like you in my beginnings. Once upon a time, I was told that I wanted to run before I could walk, I wanted to be original before I knew anything, yet that was how I understood and reproduced the concepts they taught. One even said, “stupido”. They couldn’t explain anything well enough for my simple brain to understand. Today, I am a publishing solid-state and condensed matter physics professor with worldwide collaboration. One former professor even asked to join my collaboration (I did not reply).
Time pressure is my biggest struggle. I am a single mom and I work while taking full time classes. I’m about to take my summer calc 2 exam on Friday. I want to be the best of the best and get the highest grade and I just haven’t.
Good luck! Sounds like you have a LOT on your plate, so if it doesn't go exactly the way you hope, be kind to yourself:)
8:36 Yeah, Abstract Algebra really can be that beautiful. Overall, it is my favorite mathematics topic that I have studied as an undergraduate.
very well considered video, especially the awareness of extra curricular commitments of students
You said something so true; “mathematics is beautiful”
And beyond that, it is so useful.
As an engineer, yes we use tools to help us. But the understanding behind those tools is worth a hundred times more. At my office, i can almost assure you, I’m the only who does integrals or derivatives. Which makes me sad. BC i feel there’s a loss of learning, of understanding. I’ll use the software, but I’ll do my own double check to make the software agrees with me!
And at the heart of every engineering software, is, of course, beautiful mathematics.
Motivation is always the key factor, the drive. No matter what , if one is not interested or motivated to do something, better to avoid it. Your students may have problem with basics of calculus, you are having problem with Fekete's conjectur etc.. But without trying these challenge s there's 0 chance to concur the obstacles
Totally, and motivation is super tricky to cultivate!
I have a similar case. Disliked math during middle school because of the kids I used to hang out with. At the last year of high school I fell in love with math and I am absolutely obsessed with it.
Abstract algebra was the course that made me fall in love with mathematics too! And I had been an English major. Abstract algebra changed my life. I still found calculus difficult, though.
Such a great course!
Respect 🙏🏾