What is the Hardest Undergraduate Mathematics Class?
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- Опубликовано: 9 сен 2024
- What is the Hardest Undergraduate Mathematics Class?
In my opinion Advanced Calculus(AKA Undergraduate Mathematical Analysis) is absolutely the HARDEST undergraduate math class a math major must take. Obviously the difficulty of a course is largely dictated by the professor, but in general, I think at most schools, Advanced Calculus is the hardest class for math majors.
If you make it through this class, you can make it through a math degree imo. My class started with like 25-30 people and within a few weeks there were only 10 of us, completely insane!
What do you all think? Is Advanced Calculus the hardest? Please leave your comments and questions in the comment section below:)
The class without a teacher that cares is the hardest.
Wow, sounds like 9/10 of my math classes at college.
@@hegelscat9423 just keep up with the hw and you'll be okay... the work isn't super hard, just explained very awkwardly...
@@SuspiciousFace I got really lucky to have had the math sorcerer as my teacher!
That is really true. In general I agree that Real Analysis/Adv. Calc is the hardest subject but the teacher makes a huge difference.
Absolutely!!
Funnily enough, I got my best grade out of all my math classes in Real Analysis. I will say that the professor was by far the best professor I've had. He really knew how to make the class not just manageable, but actually easy.
that is so good!!
Hi do you have any tips on how to do well in real analysis since I'm finding it really hard to grasp the thinking behind the concepts. I cant wrap my head around all the definitions and proofs.
Professor G! Ive had the pleasure of taking pre-calc with you teaching it roughly 4 years ago. Just know you made me enjoy it (even though I bombed most of the exams but ended up with an A after the final).
I still watch your videos from time to time and I hope one day I can sign up for your Calculus class in the near future if you still are teaching it. You were the best math professor I have ever had and I hope I get an opportunity to learn from you again.
Best wishes,
Z
I took Real Analysis 4 years ago (graduated with BS in Math in 2017) and I just had a nightmare about failing the final exam last night so yes, that's my vote for the hardest class I've ever taken.
Yeah so hard!!
woah scary
Good luck with that. My weird test anxiety dreams didn’t stop until I was about 50, and if I had one tonight I would not be overly surprised. It must be something primal getting dredged up, like a hundred thousands years of early humans waking up in their caves because of a nightmare about being in front of a charging mammoth without their spear.
For me, I thought that Abstract Algebra and General Topology were the hardest. I found that the easiest (but not easy), and the most fun, was Complex Analysis.
Interesting! Yeah many people say complex analysis is the most interesting course you can take as an undergraduate.
A good teacher helps so much with understanding certain topics. You are definitely one of the best (if not the best) professor I've ever had the pleasure of taking classes with!
Thank you!!
I thought the hardest undergraduate math class is Probability and Mathematical Statistics.
My hardest was non-euclidean geometry. I had been out of math classes for four years. Topology was fun. Thanks for your channel!
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The hardest classes that I have took are hands down Magneto Fluid Dynamics and Solid Mechanics. I seriously hate applied Mathematics (espacially the subjects related to physics). Apart from being challenging, the amount of approximations and handwavy logic was deriving me crazy.
Well get used to approximations when you wanna get a job outside academia some time
In the end, math isnt talking about exact numbers since the formal construction of limits and real numbers
Well lucky for me The Math Sorcerer has an Advanced Calculus playlist!! 😁...thank you for sharing your knowledge and passion for math.
You are so welcome!
This may be off topic but could we one of these days get a run down of your library?
Oh yeah good idea sure!! Thank you for the suggestion!!
Nice. Looking forward to it!
Agree. After taking this class, my head was spinning for weeks. I had gotten terrible headaches.
For me it was DEFINITELY algebraic geometry. Trying to wrap my head around schemes as an undergraduate was brutal
I am in advance calculus 2 currently.
I don't find the class harder but there's a lot of bookkeeping in the proofs.
The hardest class for me was graph theory. I feel like the proofs are just out of this world lol
In my case, real analysis was really hard course. When I study math, I’m understanding meaning after making images in my mind at first. But in real analysis to prove those things using mathematical symbol, sign and languages logically was really hard for me.
I think my major was an electronic engineering so I was not familiar with mathematical skills.
Manifolds was a very hard subject. I loved analysis but I did have to watch your videos on Cauchy sequences probably 10 times before I even began to understand it.
Just finished advanced calculus as an applied math major... man that was rough
Totally yes lol
I am glad your channel is growing! That said, you know Advanced Calculus can look like very many different things! You mean, Analysis? I think Complex Analysis or Topology are the hardest but also the most fun!
yeah I mean analysis:)
thank you! I know it's cool to see it grow, I've had it so long and it never grew, it's finally growing a little more:)
@@TheMathSorcerer No, I have been tracking your progress secretly. And you deserve it! Also, it is normal. 3 Blue whom I love has the fancy animations that lure you in so he gets a bit of a wow factor (I don't think he is a better teacher than you or I, I think you're a great teacher.) But otherwise, your growth is normal. Like, Blackpen Redpen took off about 2 and half years ago but he has been making videos since 2012 and it took him six years or more to get to 30K subs. I had a private student I tutored who needed to know what marginal cost is and I don't have a video on it and I shared your video with her. I watched the video first and I thought it was flawlessly executed!
My hardest math class was the one with the hot chick sitting next to me. She was so distracting.
Lol!!!!
You have a thing for Asians, huh?
I watch Nancy Pi just for the math 😀 ruclips.net/user/NancyPi
@@cybervigilante Thank you for this suggestion! I have just watched Nancy Pi and found my focus increased dramatically. So I am unsubscribing here and going over there as Mr. Sorcerer is not as charismatic or compelling, and couldn't be bothered to answer my email.
@@carltoncotter2614 how entitled can you be man. Does he really have an obligation to respond to your email? Don't you think he's busy already?
I had real analysis in first semester and it was doable in second semester I had real Analysis 2 and this was a Corona semester. Everyone I knew failed the first exam. It wasnt like the material was particularly hard we just had everything from manifolds to measure theory, a bit of differntial equations a numerics. This was like 3 classes in one.
sounds really tough
But after real analysis there’s complex analysis... and then foundations of analysis with all the scary measure theory stuff
Yup!
Yeah, I do agree. From my experience, real analysis was a very challenging class. Although, I did farely well in it, the difficulty was nothing to make light of at all. Also for me, abstract algebra was difficult and complex analysis but they seemed very interesting. They were, more enjoyable in a way but still tough. Just from my experience. Real analysis humbled me as a math major 😅
Ya totally humbling lol
Even though for me analysis is one of the hardest undergrad courses, but I would say it depends on professor and student too. The way course is taught makes a difference, also everyone’s brain work differently so yeh it depends on individual.
Ya for sure
I’m taking an advanced intro to real analysis this fall, for me I still think linear algebra is harder compared to at least calc 1 and calc 2 but I’ll compare my advanced linear algebra 2 to my real analysis course this fall and edit this comment in like December.
yeah linear algebra is definitely harder than calc 1 and calc 2 usually
I'm struggling so hard. SO HARD with intro to advanced calculus. I am terrified lmao
Ya that's normal hehe, you will survive👍👍💪💪💪
I wonder why nobody here was thinking of ODE and PDE. I had so much trouble with the methods of characteristic and sturm liouville problems
You are probably right. Theory for PDEs can be excruciating even though not a whole lot (relatively speaking) can be done with theory for nonlinear (it mostly has to be done numerically). However, any class can be made difficult.
yeah any class can be made difficult, that is really key!
Just finished my sophomore year as a math major. Logic has definitely been the hardest class I have ever taken.
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Modular Forms for sure
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I'm from Germany, so I'm not really sure what "Advanced Calculus" actually means. For me personally, Analysis III was the hardest undergrad course. It's climax was the generalized Stokes theorem formulated in the language of Cartan calculus, and of course everything was based on Lebesgue integration. Generally speaking, I think what makes real analysis so hard is the (psychological) tension between the intuitive notion of a continuum and the attempt to grasp it by means of a logic that has an inherently discrete nature.
Honestly I found Combinatorics to be the most difficult for me personally.
To an extent I agree I took that class my final semester as an undergrad
Yes, analysis is usually to be more abstract/difficult than other entry high math subjects. So, I agree but I'd like to add a few points:
A lot depends on the course difficulty level. Even topology can be given in a simplified form just like abstract algebra. On the other hand, even elementary math can be presented at a higher, more sophisticated level. *The higher the level of rigor and the more material the course delves into, the more advanced it is, i.e., elementary math can also be very advanced* A good example is _College Geometry_ by Artshiller-Court which is about plane geometry (circles and triangles). That said, the difficulty normally should go something like this:
(1) elementary algebra (incl. matrices and determinants) + plane geometry
(2) solid geometry
(3) calculus I and II
(4) analytic geometry (part of calculus nowadays - no separate course)
(5) ODE
(6) linear algebra
(7) calculus III/IV (also called _advanced calculus_ and sometimes _vector calculus_)
(8) abstract algebra
(9) probability theory
(10) complex variables
After that (not necessarily in a very coherent order), more advanced branches follow, like PDE, analysis, statistics (Stats is always rote-learned by stupid people, although folks can't understand stats without understanding probability theory but who cares!? They don't understand probability theory anyway), differential geometry, topology, advanced linear algebra, functional analysis and so on.
But once again, overall it also depends on how advanced the treatment of a subject is. I mean linear algebra can be more difficult than analysis; calculus I and II can be more difficult than complex variables depending on how advanced or dumbed-down the material is. If we take a look at _College Geometry_ by Artshiller-Court, we see that the true math, even elementary, is not easy; it's not some stupid template rote-learning. But students do exactly that - they do problems via templates = by rote-learning only. What's more, a regular math teacher (99% of them) doesn't have a single math bone in in his/her body! What's worse is that students are encouraged to take dumbed-down classes and not to follow some natural order of difficulty or math material order. It is heinous when students are encouraged to skip elementary algebra and geometry and take Calculus or Statistics right away. That's how math education is destroyed. That's how every advanced instructor/professor in college is from India or China unless he/she teaches a dumbed-down course. I've just re-read Lockhart's article on math education titled _Mathematician's Lament_ and he deserves a lot of kudos for exposing the situation. Of course, some of his examples and arguments are extreme and far-fetched. For example, I'd rather compare math with physics or chess than with music or painting. Yet, the gist of his invective is spot on.
i had an awesome professor for advanced calculus which im really grateful for
My second year Calc was a second year in analysis. It was calculus on manifolds. It was the most time wasted course since we did not had any vector calc or regular topology background. It was all theory and everything is proved up to the context of lebesgue measure zero with partition of unity, tensor products, differential forms on chains, proof of change of variable formula in lebesgue measure zero and generalized stokes theorem. We had to know how to prove all of them for the final.
Wow hardcore
But Calc II is probably the class that made the most students cry
I completely agree. I failed that class twice before passing it and earning my math degree. In that class, most students are first exposed to what real math proofs are like. It was really hard because there are no templates for how to write a proof. One of my professors said that writing proofs is a
"form of art"
Yeah it's so tough I agree. I struggled so much also. It really is a game changer
I liked real analysis. We used Principles of Mathematical Analysis by Walter Rudin. Books like that are worth retaining in one's library. Rudin's Real and Complex Anaysis is great for complex analysis. However, Churchill, Remmert, and Ahlfors have excellent texts also. Churchill's Complex Variables and Applications is great for practicing working out integrals and sometimes understanding a detail in a proof that is difficult to understand in Rudin's Real and Complex Analysis. I divert to complex analysis because I love it too. In real analysis I often look at other books but I usually go back to Rudin's Principles of Mathematical Analysis as the best source. Whereas in complex analysis I often find each book has its own particular strengths.
Ya definitely worth keeping those books , those are all classics imo, excellent books !!!!
what university did you do you bachelor/ master/ phd if you don't mind me asking ?
also when you say advanced calculus do you mean like analysis ? like sequence limit theorem differentiations properties of real numbers and all because my school " advanced calculus" is just a multivariable calculus class with no proof just calculus in 3 dimension and people at my school said analysis is the hardest course ?
I am actually taking both at the moment, and I agree analysis can be a bit tough the first time that is why during the summer i read all the chapter of the analysis1 and now that I am actually taking the class I struggle i seems to be able to grasp the ideas way better and actually became one of my favorite class I am taking at the moment even more than computer science courses, and before that I used to be scared of anything proof related and abstract stuff but now i gotta say I find it really interesting my point is to any student that plan to take this course if you could go over by yourself before it actually start it would be way more interesting and easier to go over it again in class with an actual professor
yup I mean analysis:)
awesome advice!! totally agree!
Too broad a question for a straight forward answer. My algebraic structures course was taught using the framework of category theory, my math logic course taught model theory and Godel's theorems. Veteran professors tend to have some academic freedom when developing upper division courses, so they can make classes as abstract as they like.
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Yep; Analysis was a hard class, and I felt Analysis II to be a bit easier (got a better grade in it too). I also thought upper-level linear algebra to be not as hard as Analysis I or II. If I were to choose what the hardest math class I've taken was, it'd be one of these three: Introduction to Mathematical Analysis I, Intro to Modern Algebra & Number Theory, or Introduction to Complex Analysis (was also the math class I did the worst in, got a D).
Just gotta say W totsuka pfp.
Honestly, I’d say if combinatorics/prob theory. I had an easier time in analysis and abstract algebra.
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For me it was tensor analysis, took it in 4th year mechanical engineering
I am gonna be taking 3 big pure math classes all in one semester next year
- Advanced linear algebra (To my knowledge it is to linear algebra like what advanced calculus is to calculus)
- Abstract algebra
- Advanced calculus
Wish me luck
You know based on this video, I spent my summer preparing for Analysis. I would suggest this to anyone who is taking it.
very nice!!!
I don't know, it feels like you can make a math course arbitrary hard. By now my hardest Math class was elemantary number theory. Not because of the content but because my professor just didn't cared that much. The hardest content i encountered was maybe Commutative Algebra. But i like algebra so that is fine. I still have one year left in undergrad and i might take algebraic geometry and that looks really hard.
Oh for sure, it can be made hard, totally agree!
Totally agree! It's the only subject I've repeated the course...
What about functional analysis?
I got a B+ in undergrad Advanced Calc but an A- in Point-Set Topology. Topology was way harder but I put tons more time into it.
Very nice
Advanced Calculus was a nightmare for me. It took me around 7-8 hours just to finish a homework (I kid you not, the assignment was filled with notations that I never saw in undergrad at that time and grueling integrals). Luckily, the TA was chill and graded extremely leniently. I managed to get an A- in the class.
I kinda disagree. I've not got the time to do analysis yet but yeah i think it's awesome! I began Terry's book after seeing your review.
Algebraic Geometry I was the hardest math class I did. But I guess it's not an undergraduate class. The coolest class (but quite technical) was Foundations in Representation Theory, which was a dedicated introduction to Category Theory and Homological Algebra.
I am a mathematics student from Brazil, still in de middle of the course. Until now, the hardest was Abstract Algebra, but Mathematical Analysis is still to come.
Awesome:) Will be interesting when you take it to see what you think of it:) Both are hard but it's very different.
@@TheMathSorcerer I imagine. Keep on posting videos, please, I love your channel! It is easy to tell that you really love Mathematics!
@@jv_pessanha thanks will do!!
Stochastics is hard too but I think that it would be considered a graduate class.
Could you talk about the hardest math classes are based on perspective? Like which math classes are the biggest jumps in knowledge based on the prior class in the progression of math? I would be interested to know. For instance going from algebra 2 to precalculus algebra was difficult for me. However precalculus algebra to precalculus trig seemed to be easier
Real Analysis I and II (or as he say Advanced Calculus I and II) is ONE of the hardest classes an undergraduate can take. Id probably take a proofs and logic course before taking that class. But you typically do A LOT of epsilon and delta proofs in that class.
That many people agree that advanced calculus is the hardest class is a clue to the likely truth that more people are under-prepared to take the course. Given the commonplace observation that too much, and often the wrong, material is jammed into prior calculus classes with insufficient time allowed for students to comprehend the depths and interrelations of the material, it should be no surprise that a proof of concepts calculus course should be hard.
Here's a curriculum reform idea for you. Separate the engineering calculus service courses, with their heavy emphasis on problem solving, and light load of proofs, from another calculus series that does less problems, and more proofs, at a more leisurely pace to allow comprehension and understanding. Require this course as a prerequisite for advanced calculus, and deny entrance to the engineering course students who have not taken it. Likely the result will be happier and better prepared math majors, engineers who are oblivious to what they are missing, and graduate math profs who don't have to watch so many students writhing in agony as a result of their inadequate preparation.
You know that's a good point. I think back when I took it, and I already had calculus 1, 2, 3, linear algebra, two proof writing classes, and maybe even some PDE's. It was still hard. If I would have had some "Michael Spivak-like" Calculus based courses it woud have been easier I think.
Real Analysis is the Hardest, because of it’s highly lengthy and detailed proofs.
I think some schools call it real analysis
I respect this guy, I failed this class. He’s definitely smart.
What do you think is the hardest math class for a phd student?
Depends on the teacher for sure, they are all hard!!
Math Major here, I agree. Real Analysis is the hardest!
Yes totally!
I just finished taking Adv. Calc at Rutgers for the 2nd semester in a row and Ohhh boy, This class is a doozy. The easiest was right out the gate, Laplace transforms. Simple and straight forward. Then, a deep deep dive into Matrix calculus, far more advanced than the linear algebra class I took (surprisingly) considering linear algebra wasnt a pre-rep for this class. Then, again another straight forward topic Fourier series! Then, Heat, Wave and Laplace equations... Our professor put a 2 spatial 1 time dimension heat equation problem on the final, yea we all just skipped that one. Then, Polar and cylindrical coordinates for those 3 equations... and lastly, Fourier Integrals and Fourier Transforms. Safe to say, least favorite class in my entire degree of engineering.
Lol sounds so hard
@@TheMathSorcererCauchy-Euler just doesn't click with me. Everything else is fine.
idk I kinda thought those algebraic topology/geometry was way harder than calculus.
I hate solving bessel equations using frobenius method because i always mess up a minus sign somewhere😥..... Please tell me if there is a substitute for it
Functional Analysis was the hardest for me
Abstract algebra because the professor started with rings. We didn’t do anything related to groups until the end of the course. I had to take the class twice. I decided to pass with a D so I could graduate. Abstract algebra is the only math course I failed.
Wow starts with rings ,hardcore
Idk, I thought real analysis was pretty darn hard
isn't real analysis and advanced calculus the same?
@@lemyul lol
Unbelievable! In India we study advanced calculus at age 16-17, i request you to take a look at some IIT JEE ADVANCED maths papers, you'll be shocked to see how much pressure we go through
oh wow! Yeah I looked at the JEE it's insane. At what age do people take the JEE , is it before university?
@@TheMathSorcerer yes, before University around the age of 16/ 17ish
Wow
@@TheMathSorcerer JEE is taken after completing 12 years in school
So what is Advanced Calculus? I've taken Calc III at my community college but I assume that's not it but I've never taken abstract or linear algebra so Calc III might not be it then.
It's basically proof based calculus, so like calculus but you prove everything
Algebraic Topology
For me abstract algebra was horrific. Real analysis was tough but algebra was a nightmare.
I haven't taken that class. I am an Applied Math major.
Cool! I did pure math. Do you have to take it still?
I bailed out of a masters degree in applied math because the condition for getting a scholarship was to get an A in real analysis during the summer classes.
My school doesn't have a class called "Advanced Calculus". Somehow I find the concept of "Advanced Calculus" very vague. I would argue people should just call it "Real Analysis" lol.
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Abstract algebra is hands down the hardest because it's just too abstract
interesting:) yes it's very abstract, extremely!
professor, linear algebra is the hardest for undergraduates in China. Because the coursebook is poorly edited. Could you please recommend a few good coursebooks ?
Statistics was hard and it was hell.
To me nothing can beat differential geometry in the case of being hard in undergraduate level!
I concur with you.
:)
I’m an undergraduate maths student and I’m taking Real analysis this semester . My exams are so close
By advanced calculus do you mean real analysis? In my advanced calculus class we’ll learning about manifolds on differential forms
Abstract algebra seems too difficult for me... actually real analysis was one of the easiest lessons to pass
Oh wow that is so different than most people! Actually when I wasjn grad school it seemwd that most of the internetational students were better at analysis, but not as fond of abstract algebra. Coincidence maybe though👍
I would imagine that differential equations would probably be the hardest class.
If you did well in Calc I and Calc II, you should be in good shape. The only Calc III concept that is needed in a standard Ordinary Differential Equations course is knowing how to take partial derivatives, for determining whether or not a differential equation is an exact differential equation. There is some Linear Algebra in a Differential Equations course, as well, since you have to compute eigenvalues and eigenvectors for solving systems of differential equations.
Linear Algebra is definitely trickier and harder (on the theoretical side of things, but computationally, it is easier than Calculus and Differential Equations).
Topology if given. I had trouble with linear algebra.lt didn’t make any sense
Yeah I also had trouble with my 2nd linear algebra course, the proof based one. I struggled. I did much better in abstract algebra. I had the same teacher for both classes too, so it wasn't the teacher, but it was the subject and/or me.
I don't think advanced cal is the hardest boss, Topology is spanking me so hard right now.
Ya that is hard for people! Maybe it's becauSe I took it my very last semester after having taking sooo many other math classes
Is Advanced Calculus equivalent to intro to Real Analysis?
Multivariable calculus
I find statistics much harder than calculus because it not straightforward at all.
Did you mean real analysis or calculus on manifolds by “ advanced calculus”. Calculus on manifolds is the hardest class at my college but it sounds like you might be talking about real analysis
Real analysis 👍
This makes me even more pissed that I graduated accidentally and never got to take AP calculus in highschool.
But what is the hardest branch of math?,is it calculus?
Is advanced calculus the same as multi variable calculus?
Calculus was split into 4 quarters in my college calculus a,b,c and d
Usually no, usually it's like real analysis, so it's proof based calculus
Partial differential equations is our hardest course.
I'm a first year, and I'm taking Calc II next year, are there any tips you could maybe give me to survive? I mean besides doing exercises
Maybe start learning calc 2 now. If you do that it will help a ton!
What about prob theory
I mean the jump from high school
When you say Advanced Calculus, what exactly do you mean? At my school at least, there is a sequence of Real analysis courses that start at the beginning, and work all the way up to measure theory. Was there a particular course you had in mind as the hardest one, or just that type of sequence? What material is covered in the one you are thinking of?
Real analysis
But as an undergrad we didn't get to measure theory
What are the current topics in research --- that are close to Elementary Mathematics?
What about Math 55
Math class is the hardest with the teacher with the thickest accent.
Is advanced calculus the same as real analysis?
Yup! Now there is measure theory which is also called real analysis, but most of the time advanced calc is real analysis, esp at the undergrad lvl.
What's the most interesting math class?
Now that is a great question!!! Totally depends I guess😄
Any ideas?
Abstract Algebra