I love how genuine you are, and I agree with you in that students are not being challenged enough. But at the same time I think that it depends on the context of what the class is (and what the students understand it to be). What I mean is, that usually people don’t try hard in common core classes, and these will have the type of students that don’t know what they want to do yet. One difference between grad students and undergrads is that usually most grad students KNOW that they want to be there and learn and succeed. On the other hand, well, a lot of undergrads are still figuring out what career they want Either way, don’t beat yourself too much, and keep that energy going forward 🙌

I cried when you wrote the limit example. Lol I am so bad at calculus it's actually kind of sad, but videos like the ones you produce give me hope that even though I am really slow at improving my math ability, I feel confident knowing that eventually I should be able to get there. And I managed to solve the limit problem in the video LOL. 10:41

As a freshman undergrad I have had a bit of experience with being taught by graduate TAs, so it's pretty interesting to see the perspective from the other end. Your other videos are also pretty interesting, so thanks for making them

Also I think just the nature of a business calc class will be that a lot of your students aren’t that great at math and they aren’t doing particularly challenging degrees so they aren’t used to a class where they really have to study and practice to understand the material. That’s just my take.

Yknow, math has always come a bit easy to me, so it's sort of easy in some sense for me to say that you're right about undergrads having very easy times in their classes. I took calc 3 last semester, and it wasn't particularly necessary for me to study for it in all honesty. That said, I do think it's important to recognize that there's a lot of factors to consider when you're looking at pushing students harder. One thing is that I think the justification for it might be a bit biased. Like, to me now, something like the chain rule or l'hopital's rule are very simple ideas - and mind you I'm not a math grad student, so I'm sure that they're trivial to you - but I know that when I was in calc I they were absolutely daunting. Calc I especially has a huge learning curve I think, because it's sort of the first class where students need to have some mathematical reasoning skills beyond memorization and application of formulas and factoring techniques and stuff. I remember struggling a lot with the puzzly parts of problems I was given. I guess what I'm saying is that these students, if you asked them, would probably say they feel just as pushed as you did when you were taking the same class; I think the perception that you got pushed harder might come in part because you're just plainly more knowledgeable now than you were then, so the same or similar problems seem much easier to the current you than they would have to past you. Or maybe not, I don't know. I only really say any of that because I helped my little sister a lot with homework over the years, and that sort of thing was a recurring theme - I'd look at her work and wonder how she got so lucky as to get the easy teachers all the time, when really she felt like it was just as hard as I did. Another point is that these are business students lol. Like, you know, I hate to be all pretentious about it, but business students sort of have a reputation for being the major that the party kids go into. In that sense, you have your work cut out for you. But with the kids who are like that, I don't really think it matters how much you push them. They're 19 and away from their parents for the first time, and they're either gonna put in the effort or spend time pursuing hedonism because they can, and that's sort of that. They'll just have to retake the class after they get all that out of their system. But overall, I think your class structure looks great. I can't speak on how you lecture or the kind of homework you give, but I respect being transparent about what's on the exam and making studying as easy as you have for them. If it makes you feel better, my roommate's calc I class had an average of I think 45-55% at the end of his first semester. Mine was an honors college version, and even those kids had averages around 70-75%. I think that for business students especially, you're clearly hitting the mark from an instructive perspective. Anyway, I hope I didn't come off some kinda way here. I don't wanna make it seem like I think I know more than you or anything like that. This is just the perspective of an undergrad student who's right at the end of the undergrad math train, so I'm sure it's biased, but I figured I'd put it out there. I really like the content you put out though, I hope to see a lot more of it in the future.

I'm a third-year physics student and I just wanted to say I love your vids! xD

I'm looking forward for the class I'm teaching, where it's just a Quantitative math class. I also tutor a bunch of different courses, but the course I least like to tutor is Business Calculus. My clients often just do not go to the lectures, don't read the notes/book, and don't do practice problems, but when they go to tutoring they expect me to do the problems for them. I occasionally get a few good Business Calculus clients but often times they have the mentality of "this is my last math class and only need a D- to move on to the other classes". Most of the time I really only get Linear Algebra/Diff Eq/Calc 2 students who genuinely care and makes up for the frustration. Looking forward to just teaching my own course. You're doing great work!

@acceptableconvo

10 ай бұрын

As a fellow tutor of business calc students, I feel you. For me, the challenge is that I believe business calc, depending on the professor, can actually be a harder class than regular calculus I. For one thing, most of the time the class doesn't really dive into the "why" so much as the "how," which was why I was actually surprised that Struggling Grad Student gave a proof for the product rule in his class. Students are sort of expected to learn these processes of derivatives and integration without really understanding fully why they're doing it or what the purpose is. They sort of just get a list of equations and are told that, "if you're trying to calculate the marginal cost you need to take the derivative of the cost function using a memorized rule." And students in business calc, at least where I tutor, are not required to take precalculus, which is a course that builds a lot of grit and problem-solving skills that students need before they try to tackle a topic like integration which is so open-ended in its approach. Even if a student doesn't really remember anything from precalculus when they get to calculus I (which is like 90% of students if we're being honest), they leave the class having experience using a bank of techniques (unit circle, special triangles, graphs of trig functions) that they can think through to choose the best approach to solve the problem at hand. A student fresh out of college algebra, on the other hand, is used to memorizing techniques to solve problems and doesn't really have the problem-solving skills necessary for interpreting, say, the slope of a tangent line or a limit, or trying to determine an outside and inside function properly in order to do the chain rule. Not only that, but they're also expected to learn some business mathematics at the exact same time as they're learning the calculus, which means that the course actually covers more material than a standard calculus I class. I think the business calc class at the college I tutor at actually teaches integration by parts sometimes, which students in calculus I don't even cover in the curriculum. So it's more material, some of the material most math tutors can't even help with unless they happen to also have a background in finance or have taken business calc for some reason, and the students don't have the same maturity and understanding as the standard calc I student. Together, this makes the class very, very challenging, contrary to most students' belief that it is an "easier calc." My college even calls it "brief calc," which is a horrible misnomer, in my opinion.

love these videos man

Im an undergrad EE student. I absolutely agree that your undergrads really should be doing more. I’m pretty sure you’re a good teacher and I think you have more than reasonable expectations for your students. These kids nowadays, especially business majors, are for lack of a better word quite lazy. The problem you showed is something I was doing in high school. I really think it’s up to the students’ genuine desire to learn the material that makes or breaks them.

I am a high school student taking AP Calc BC in high school. I do well and I love it. This test was more than reasonable!! I feel bad for you, I’d appreciate you a lot as a mentor or teacher!

I LOVE your videos! ^_^ I ain't that great when comes to math, but I do enjoy Calculus a lot!

@PhDVlog777

Жыл бұрын

Thank you! Calculus was my favorite math class as an undergrad. I wish I could go back sometimes

Hi man, i discovered your channel llike 3-4 days ago and it's made me love maths. I've always been an under 50% test grade - 15/20 in report card type of lad but you opened my eyes to the world of maths and i've recently begun paying more and more attention to class. Thank you so much.

Sitting here 2 hours into my analysis 1 homework. Yes calculus and proofs are different, but I agree the jump from calculus to "advanced" math classes is crazy. Advanced classes are extremely "stimulating" whereas I got all a's from precal to cal 3.

@saymyname5942

Жыл бұрын

I really struggled getting A's in my math classes, hopefully I won't struggle too much going forward 🥴🥴

That is totally different than what I was thought back in the days. The sample problem you have shared in your video was an easy one that we usually had to solve in 11th grade. To be honest I did not expected to see such big differences between generations.

@nolanalexander8696

Жыл бұрын

Perhaps it has something to do with the course name "Business Calculus", perhaps it is calculus for economic department, thats why the problem is more simpler or "easier". And also perhaps he just "fast think" some problem to give an example, since he surely cannot give real exam questions on video :)

@mihaihuluta2427

Жыл бұрын

@@nolanalexander8696 I apologize, hopefully I did not offended anyone.

@nolanalexander8696

Жыл бұрын

@@mihaihuluta2427 I think you did not offend anyone. However, I think I really want to address the habit of seemingly "compare" between what we have in the past (which often we thought as more difficult) and what people had today which we judge as "easier". One possible explanation for this is perspective. We already learnt Calculus, knew its niches and difficulties, and so when we saw people striving to understand and getting perhaps more innovated method to learn, or more concise material, we tend to think that is more easier, which in fact, no. I learnt Calculus way back during my undergrad, and forget much of it, until I need them again for my masters degree, and I had to relearn everything. The method are helping, but the difficulty of getting "Calculus main idea" are still there.

@mihaihuluta2427

Жыл бұрын

@@nolanalexander8696 Sound reasoning, thanks for pointing it out ;).

@mrmaaf1443

Жыл бұрын

I'm in 12th grade right now and my math class could probably answer that problem too

I discovered your channel a day ago and I really enjoyed it! Great work. Keep it up :flame: 🔥

Grate work 💪💪...i like pure mathematics... Helpful video..l

I wonder how COVID has affected the level of knowledge that incoming undergrads have.. because I know that (at least in Canada), online school has caused a lot of grade inflation in highschool and so a lot of students that shouldn't be getting accepted into certain programs end up getting accepted anyways. In general I hear from other teachers that the "quality" of incoming first years has been decreasing each year for the past 3 or 4 years (lower averages, etc.)

@PhDVlog777

Жыл бұрын

I would say a similar situation has happened in the US. I also think the standards all across the board ( high school and colleges) have diminished. Some say it is because students complain too much but idk

Channel growing fast 👍

I remember a lot of people in calculus 2 class were there because they needed the credit for other majors and had very little interest in math. Towards the middle of the semester the professor seemed to get frustrated with how little people were trying and started giving us a concept on the test and then we could pick from a list of 10-20 questions to solve and show we could do it. For example, question #1 might be integration by parts and there was a list of 10 options to pick from but you just needed to pick 1 and solve to get credit for the question. Still, I don’t think the test scores really improved but it was hard to blame the professor because you knew that concept would be tested in advance and had many opportunities to show you knew how to do it on the test. I think the professor gave out a good amount of low final grades, which I thought were well-deserved given how forgiving this system was...

Those complaining about the difficulty of this course need to realize its business calc. I am sure the engineering calculus class is more challenging.

@mikuculus3720

Жыл бұрын

I’ve seen this in a calculus for stem majors course, it’s like the first problem given. They get much harder but you start somewhere.

I’m not in the US but I did this kind of maths in high school. The jump from high school to university was quite big for us with the latter being almost more theoretically based and not just doing calculations the whole time but most of us adapted and many of us got A’s at the end of the day (albeit the standard for an A where I live is only 75%)

Hi Grad Student, hope you are in good health, and stay in good spirit! I really like your video, perhaps for next development, you can arrange your desk, lol. Its the same as my desk as a grad student. Like your genuine content. I wonder how you are doing in teaching. Perhaps it would be interesting you make some content about teaching math. Good luck, man! Hope you are surviving and succeeding in your studies!

As someone who went to community college and is now going to a state-school, a lot of the courses at the 4-year school are less rigorous than the CC courses. I think that has to do with the CC transferring students out to the best schools in the area and needing to meet those requirements in order to fulfill transfer agreements. I've also noticed that the quality of professors at the 4-year school is lower than that of the CC. Personally, I think that has to do with the fact that many CC professors don't have tenure and often care significantly more about teaching since it's their only job as opposed to what the professors at my 4-year are responsible for doing.

I did my undergrad engineering math series at a California CC. They were brutal, as were the Physics and Chemistry departments. 80% failure/drop rates were the norm. Moved up to the CS system to finish out my undergrad and was appalled at the (laughably low) competency of my fellow students who had come through completely through the CS system. Tough call what to do about it. I hate to advocate for ruthlessly weeding out the non-hackers, but I can tell you there are engineers out there in the world today who I wouldn't trust with the dumb end of a pencil.

When I had to learn to factor in algebra in high school that was a dead end for me!

I think it would be beneficial for professors of math courses at the university level to take a teaching methods class much like those who go into secondary education do. The response to poor performance being cutting/simplifying content is unnecessary seeing as you said the level of difficulty doesn’t have much effect on the grades on the class. The issue must be outside of the difficulty of the content.

At my college the calc exams had a 60% average and that was considered normal by the professor, but I think they were slightly harder than how youre describing yours. Probably not much more difficult though. High school doesn't prepare students for uni math imo

I'm currently studying MSc Mathematics in the UK, on track to get the grades to apply for a PhD. I've been discussing with my advisor about moving to America and undertaking my PhD there. The primary reasoning for this would be that I want to teach Mathematics more than I want to do research. I'm trying to gather as much information as possible and your channel is a valuable resource. Regarding teaching, what kind of topics would you typically expect to teach at a level such as yours? And do you expect to begin teaching further topics?

Totally unrelated to the topic, but man you have a really relaxing voice! Reminds me of an old friend I used to study with before he left to go abroad to teach English

@PhDVlog777

Жыл бұрын

Lol thank you very much!

that the same thing when I went for Grad School(Grade or Teach). you can teach as a master student(only calc and below). anything else higher up, you need to pass the Qualifying Exam(we called it the GQE). and thats how my school GA becomes a thing.

I think it is great you are able to teach while being a grad student. You are still young and it is well worth the investment. It is apparent you enjoy math and teaching it.

I’m not a math major nor do I plan on going to grad school but I love your channel😂 keep it up

for an undergraduate math student who wants to study analysis in the future i guess this is a good channel.

I think there is a good idea to learn some math subject iteratively (it is like developing software). Let's take Calculus : "Calculus for business" ===> "Calculus book by Stewart" =====> "Calculus book by Spivak" ====> "Real analysis".

Can you please make a video about your recommendation for young mathematicians, and how to get to research in math. I think it would help us, undergrad students. Thank you for your videos.

I learned calculus 1 the summer before i took the class in fall. I didn’t learn everything but it was enough where the class seemed easy. But math usually came easily to me, non-proof writing math that is lol. I took calculus 1 that was for engineers and I think they pushed us because obviously we’re going to use it a lot. I still didn’t find it too difficult. But being a STEM student we like math. I don’t think business majors like math. I BET they barley passed their college algebra course and that’s why they are struggling.

Why my professors are always in "hardcore mode" whenever they are having an exam...

@PhDVlog777

Жыл бұрын

Me too bub lol

Weird seeing how the undergraduate US system differs from the UK system. In the UK admissions to university programs are based pretty much entirely on merit and all programs cost the same. We also start rigorous mathematics right away and don’t really do any other subjects once we’ve started. In the first year students would probably do abstract algebra, analysis, probability, differential equations, programming, linear algebra. But we don’t have that breadth of knowledge I guess since university is entirely specialised from the beginning.

Its interesting that these problems are still inside german school math classes in like 11th grade (in a normal math course, not even a special thing).

I was a math major/graduate in the 90's. I just remember that course grades were based only on 2 items: 50% midterm and 50% final. The prof would provide problems to do, were never collected. You had to take initiative (ask q, go to office hours,etc) if you wanted homework feedback.

This is crazy cuz I’m a biomedical engineering PhD student and there’s no way we could teach a full length course on like biotransport or something. You guys are nuts

It seems like there's a lot of students that breeze by classes, but I have a lot of trouble getting good grades. I love math, but I'm not a good student.

Upper part goes to 1-2+1=0, lower part goes to 0. 0/0 = infinity. Qed.

13:43: took AP Calc Ab in 2020-2021. The exam was more difficult than the course, but I found them both to be easy. I took Calc 2 in community college. I found the course to be easy, except for series, to which I only got an 80 percent average, but otherwise, I thought it was easy. Calc 3 I also took in community college and it was the most difficult one for me. The homework were the hardest parts, but the exams I found easier. Either way, I was left with a B average in Calc 3, which was a bummer for me. Besides those, I found the hardest course was US history (because I am bad at memorization) and University Physics 1 (the homework was again the hardest part, and the exams have their occasional curve balls).

I think the best way to grade exams like this is to not punish for silly mistakes up to 2 marks, then you can take marks off for negligence.

I assume the low-level difficulty is because its a class for business majors? All of the topics on that exam are things that I learned during 10-11th grade.

My first encounter with calculus was the book "Applied calculus" by Berresford and Rockett. The calculus concepts are given in a very simple way and there is no trigonometry in the book.

@PhDVlog777

Жыл бұрын

That is the text I use for my course lol

@meteor8076

Жыл бұрын

@@PhDVlog777 Ohh really ? mine is "brief applied calculus" 6th edition, I bought it used for a few dollars )) I actually enjoyed it very much, it contains a lot of exercises and there are solutions at the end. Ideal for self study. The authors even added a separate chapter for differential equations!

@PhDVlog777

Жыл бұрын

@@meteor8076 I use the seventh edition to teach from

On the comment at end about maybe going too easy on the undergrads; I think it makes a world of difference that you’re teaching math to a class of students who probably don’t want to be learning calculus. At the same time, math grad students do want to learn more math. So now imagine, even though you’re already a math grad student, how well would you do if all of the sudden you were in German literature class? I gotta imagine you’re not going to be giving it your all, in spite of being a grad student. You’re probably going to try to just get by so that you can spend more time on what matters… to you. Yet, the German lit instructor might make similar comments about your performance as you do about your business calc students. Point is, as much as we might want our students to excel in our classes, if the subject matter doesn’t matter to them, then demanding more out of them may not have the desired effect. Personally, I hated and really struggled with most of my classes outside of STEM, even though they were very easy. Making them harder wasn’t going to make me try harder, it would have made me drop the class and look for the next available easy A.

@audxc

Жыл бұрын

I understand your reasoning here. My disagreement would be that if you start an undergraduate class you should should have the ability to do well if you try and put effort in. I think doing the homework without chegg and going to class will get most students a B average. Now that being said I am similar I had a semester with one math class during undergraduate and it was my worst semester. I still liked going to class and listening to what the professor had to say. I had the opportunity to make A's in all those classes, and I did not complain about my grades because it was own doing. Edit: I think if students value education more than just a means to an end then the average student would do better.

Have fallen in love with your channel (eat dinner to it!) I am a CS student, but I loved my Calculus 1-3 class here at my University. I have heavily floated the idea of getting a 2nd Bachelor's in math while I do my CS grad program. If I don't, I'd still like to study college-level math. Do you think a second degree for Math is a good idea?

@horiuchiworld

Жыл бұрын

I'm taking double major in CS and math. It's kinda nice

@rampage14x13

Жыл бұрын

I'm in grad school for CS right now, and I did both CS and Mathematics for undergrad. It definitely helps to be comfortable or at least experienced with more advanced math.

@PhDVlog777

Жыл бұрын

It depends on what you want to do with it. In general I would want a degree in a subject that I planned to do something with like teach math or do research. But if you love the subject then getting a degree in it is time well spent.

Business calculus isn't supposed to be hard. That's incomparable with calculus for mathematicians. My experience were 70% failing and me getting my worst grade in uni. My experience was also people dropping out after several years. And my experience was my dumbass taking probability theory without having any clue about topology or measure theory and understanding about 1/3 of the class.

interesting how for you 50 people is a lot in a course, for the first year courses here have 1k-2.5k people

Which university are you in?

Oh god not me at 10:45 using L'Hopitals rule instead of factoring

@PhDVlog777

Жыл бұрын

Honestly, if one of my students used LHopitals rule, I would just give them an A for the course lol

A pure mathematics specialist teaching business students maths. Sounds like a disaster waiting to happen.

@topercaker2646

Жыл бұрын

They probably think that calculus is a conspiracy to make them fail lmao.

@Barneyboy-uw3ux

Жыл бұрын

@@topercaker2646 well why tf can't mathematicians use helpful examples with meaningful variable names... Especially when it comes to teaching those who don't have that much of a maths background. I only ever had one good maths teacher, cause he actually gave me the confidence that I could do it. Instead of just shoving a bunch of random equations in my face and then acting surprised when I can't do a partial derivative. There is a big difference between challenging someone and just messing with them so they can fulfil their fragile ego because they know more maths than the average person.

@topercaker2646

Жыл бұрын

@@Barneyboy-uw3ux Not sure what you mean, it's unfortunate that you had bad teachers but the guy who did the video gives you full credit on quizes despite making mistakes and I would assume gives plenty of examples on how to solve problems during his lectures.

@MrCmon113

Жыл бұрын

Pretty normal for mathematicians to give maths courses to non mathematicians.

@thepruh1151

Жыл бұрын

@@Barneyboy-uw3ux Consequences of generalisation. If I told an economist derivatives only work for marginal cost, his only intuition of derivative would only be that it works well with that example. However, if the topic is generalised, and then specified, it provides larger insights to the student. That's what my maths teach did so not all mathematicians aren't helpful

Undergrads have a lot going on in their lives... serious psychological issues, some are probably trying to earn a living, and many don't want a degree in the first place because they believe it's useless and nowadays there are many other ways of earning money. Pre-university courses in America are very easy, but the problem is that these students have been spoilt since kindergarten! Once you've been spoilt and made lazy for 12+ years, it's very hard to get rid of that.

@PhDVlog777

Жыл бұрын

Spoiling students has probably contributed a lot to what we are seeing today. But I also feel that my generation was spoiled but the situation is not the same

@ILoveMaths07

Жыл бұрын

@@PhDVlog777 Yes, there is a huge difference in the way students behave, even with a small age gap. I was born in 1990, and during my BSc, I found most students behaving maturely and responsibly, even the ones who weren't particularly bright. However, I cannot say that about students born in 1995... and I could see the stark difference at university. I think it's technology and the lack of old-fashioned social interaction... That really changes people.

You're somebody who has been passionate about math for your entire life, took a lot of math classes in school, dabbled in college math, did a math master's and is doing a math PhD. Compare that to the average business major, whose experience in math is suffering through it during high school while hating it and doing the bare minimum to pass, and who did a business major because it's a common major to do if you're not too sure about what to do or don't like humanities and hate math, physics and the like enough to not go for a science major. Calculus is likely one of the last courses you want to take, you don't like math and math doesn't like you back, and chances are you will barely use it in the real world (seriously, you mention business majors needing calculus in their daily lifes, that's not true for the vast majority of them). Would you be motivated to push yourself in this subject? If you only look at it from your perspective (oh, this and this is so easy, how can students get it wrong, they're so lazy), you're just projecting your own feelings about math onto the subject and onto what you believe the students should be able to do. Just my two cents as a Economics (which is very similar to Business, at least in my country) graduate who did awful on calculus and algebra.

this is kinda sad... the way you explain your frustration when students don't get what you are trying to do. The way you talk In the video makes it seem you did almost everything you can do to help the students. Im an undergrad student and a lot of students still struggle with basics. I major in IT and there's basically only 2 courses required that are related to math (statistics and discrete math) and i see students struggle hard because they don't go to classes or just wing it every test/exam they get.

You are very woke.....spell out the truth