WHAT COMES AFTER CALCULUS? : A Look at My Higher Level Math Courses (I Took 22 of them).

[@TheBillNye]

I feel flattered that KZbin thought I should know this

[@CHALKND]

Well I'm glad the algorithm threw this at you as well 😅

[@TheBillNye]

@@CHALKND I watched some of your other videos. I wasn’t expecting them to be as high quality as they were. Keep it up!

[@kobebeef1209]

I’m disappointed in KZbin for thinking I’m this competent

[@oliviermadeus9884]

I'm reading calc 1 rn 😭😭😭

[@emmagarcia3048]

well of course, you're Bill Nye!

[@nickcolleran9212]

You know a book is expensive when it's pointed out as expensive in comparison to a bunch of college textbooks

[@TheDbowling]

27$ seems pretty cheap

[@leichen8132]

@@TheDbowling i get books for free

[@CHALKND]

Haha textbook prices change *_a ton_* , especially after new editions come out so it may not be 'expensive' today.

[@humano8975]

@@CHALKND Dude, do you trade? i mean have you try to apply your knowledge on that

[@BaiZhijie]

As someone who never went beyond Multivariable Calculus, this is really great for giving me a glimpse of what lies beyond. Like you've taken me to the top of a mountain and showed me a whole unexplored country. You are describing all the waterfalls and forests and lakes and towns in that country, and I don't understand any of it yet really, but I get a sense that the country you visited is vast and rich, and I like gazing out and thinking about it.

[@adityapradhan4148]

He is wrong! Depression comes after calculus

[@JessieInTheSky09]

@@adityapradhan4148 😂🤣😅

[@coolasf1527]

i sense you good at math

[@翁樂書]

​@@coolasf1527 I feel like the curiosity and wonder that one experiences when just imagining the sheer vastness of maths, that can make anyone with the right amount of desire to LEARN 'good' at math.

[@HemstitchedIrony]

So the answer to "What comes after Calculus?" is suffering?

[@CHALKND]

Unclear 😅

[@taya4818]

i'd say the suffering begins with calc😭i just finished my final

[@brycepowell6639]

@@taya4818 U dont know suffering until you are trying to write rigorous proofs.

[@chelseamensah1732]

@@taya4818 I dont know about you but my calc 1 final was hard as hell

[@alf.2929]

@@taya4818 I disagree. Suffering begins with pre-cal.

[@akankshyamahapatra6352]

Everytime a book hit the floor, my heart jolted.

[@CHALKND]

😅 I’ll keep that in mind next time I think about using books in one of my videos

[@DannyVass]

and a sigh of relief whenever he decided not to throw one

[@fatmamahmoud1306]

Yeah ! I wish he didn't do that 😕

[@ThunderAppeal]

Because youre dumb.

[@SaulNuts]

I appreciate his throwing of textbooks! When I graduate I'm taking the ones I no longer wish to keep for target practice.

[@ricchburglar]

when one completely finishes calculus he/she ascends into the multiverse and loses their mortal selves.

[@tmcche7881]

(he ascends) where, he is the implicit function of (he/she)

[@bluehawkfire55]

mathmaticians dont die. they turn into abstract structures

[@thanhvinhnguyento7069]

lol

[@fvs3189]

As a math major freshman I loved seeing what i will have to study later! Please keep the content going because is so difficult to find great math channels:)

[@CHALKND]

I'm glad you found it interesting/enjoyable! :D

[@Jaysin999]

My best of luckk with math major

[@CHALKND]

Just a tad late on the support maybe 🤔

[@timmydirtyrat6015]

​@@CHALKNDHe's probably just finishing up his degree now, not too late!

[@darkdelphin834]

Actually there are quite good channels with math content

[@kumirei8715]

As a physics student seeing all these fun math classes makes me want to do a math degree after physics

[@CHALKND]

😀

[@plutodagon2385]

same!! I'm a physics student and i started teaching myself analysis and now I think I want to double major in physics and math.

[@IPear]

You guys will be gods, more god than god himself

[@martinnyberg9295]

I did that. 😄👍🏼 Makes me want to go back to my old transcript and count my classes. 🤔

[@jameskoziol8508]

I guest I got luckly with doing a joint Physic and Math degree

[@JM-us3fr]

It might be easier to answer: what DOESNT come after calculus? Mathematics is an incredibly vast subject, and calculus is just one of a couple starting points.

[@josemaria_landa]

I'm a math major as well, so far I've taken: Calculus I Calculus II Calculus III Calculus IV Discrete math I Discrete Math II Intro to programming Linear data structures Non linear data structures Geometry Linear algebra I Linear algebra II Combinatorics Probability I Probability II Statistics I Statistics II Ordinary differential equations I Ordinary Differential Equations II Mathematic Analysis I Numerical analysis I Right now I'm taking measure theory Complex analysis Numerical linear algebra Linear programming Next couple of semesters I'll be taking: Functional analysis Non linear differential equations I & II Partial differential equations I & II complex analysis II Differential Geometry Abstract algebra Numerical Analysis II Classical mechanics I've also taken some other course that aren't that math related like some C.S courses like probabilistic modeling, programming, and language courses It's been quite a ride.

[@CHALKND]

That’s awesome!! And good luck, those classes all at once sound pretty difficult, but also went to a trimester based program (for us 4 classes was considered an overload) so take that with a grain of salt 😉

[@lincolnapollo]

I literally had a heart attack while reading that.

[@CHALKND]

😂😂

[@josemaria_landa]

@@CHALKND my school's also a trimester based program. 4 classes is hell lol. But it's possible

[@CHALKND]

Nope! (But also not sure if you’re asking me or others in the thread here...)

[@vox1962]

I am equal parts fascinated and repulsed by mathematics, I absolutely loathed my courses at university and performed poorly but I love watching the videos

[@a2te45]

Y'all pure math students are on a whole different level. Double-Majored in physics and applied math (and technically minored in Chem, had enough credits for sure but our department didn't award minors. Beyond diffEQ and linear algebra many of my "applied mathematics" courses were counted within my other quantitative courses, so the usual physics major sequence and some of my chemistry sequence. I took modern algebra for a month before dropping it due to just feeling out of league with the other pure maths majors in the class. Very inspiring stuff though and makes me want to independently study much of this on my own now, so ty for the inspiration!

[@hyiux]

What comes after Calculus? Nightmares. That's what.

[@CHALKND]

Times must have been good before Leibniz and Newton 😅

[@karina4692]

😂😂😂

[@manishanand465]

Man u have got to produce more & more of these videos. This is ONE of the BEST, FINEST content I have watched on Math courses & Textbooks that will be useful in undergrad & post-grad.

[@CHALKND]

Thanks Manish! Glad you enjoyed it. Maybe I'll do another one of these one day 😉

[@hmrcyo]

I made it 4 minutes in before I decided I don’t think I’m going to take any more math classes! Thank you!

[@noahgiamei]

The fact that you can remember and articulate the details of all those classes is astounding to me. I watched through the whole video even though it was WAY over my head. A funny idea for the book throws might be to add other sound effects in place of the slams. (Not sure if that's your 'brand', but it might maintain the novelty of it.)

[@CHALKND]

Oh it's definitely not my brand, However, you (or other comment readers) might find this interesting, the sound is not the sound of different books. I recorded the sound of dropping the calculus text book against the board and used that for everything (modified it in some cases) because I didn't actually throw the books onto the chalkboard each time, I threw them into a pile of blankets to avoid damaging them, and then when filming the chalkboard bits, they were lightly tossed into frame. Many of them didn't make an audible sound that would fit with the video's continuity since it would look like I was "hurling" the books onto the board, so I overlaid the calculus textbook sound. Is it a bit jarring, yes, was that intentional, no. 😂😂😂

[@juliusnewman2094]

You nerd. Thanks for not damaging your books. Subscribed.

[@intfxdx]

Engineering physics/science background here. We did about half of these but the order was way different. Your order makes a lot more sense.

[@pharynx007]

literally every class you described here, terrified me. i'm glad the last actual math class i have to take is diff eq. i was considering minoring in math, depending on how many additional math classes i have to take, but i think i will focus on taking extra mechanical engineering courses instead lol.

[@Itzak15]

Just the type of video i've been looking for!

[@CHALKND]

Glad you found it!!

[@reedoken6143]

I think it is pertinent to mention that the curriculum for a maths undergrad degree is *highly* variable based upon the track and uni that you choose to study. Some of the courses discussed in this video were not even available to undergrad students at my uni (looking at you, standalone elliptic curve theory, purely for grad students), and many others were outside of my track for applied mathematics. It's important that those interested in studying maths know that this is not a definitive guide to what you will encounter and you will likely get a better guideline from looking at your uni's college of maths curriculum or speaking with an advisor.

[@michaeldeierhoi4096]

This video speaks to that part of me that didn't take the opportunity to challenge my potential for more advanced courses in college. Years of depression and anxiety stifled me in about every way possible in high school right through my first years in college and beyond as well. Now at 68 and retired I am beginning to explore again what I wished I had had the capacity to do all those years ago. I may be watching more of your videos in time. I suppose the book that interested me the most was fractal geometry.

[@jessicasanchez5765]

@michaeldeierhoi4096 I'm 57, 58 next month and regret not pursuing math. Became a nurse instead which fed us but now I want to go back. This old brain needs to learn a new trick!

[@michaeldeierhoi4096]

@@jessicasanchez5765 I suppose there is still hope for me going back to the higher math too.

[@jessicasanchez5765]

@@michaeldeierhoi4096 Yes! There is!

[@ItsMarenxoxo]

i didn’t understand half the things talked about in this video but i am very intrigued

[@joshuaduplaa9033]

I just finished calc III, i felt so proud of my self. But this video made me realize that I'm just in the beginning of getting absolutely shafted by math. Guess i better bite the pillow.

[@a_smile55]

How was Calculus III compared to Calculus II ?

[@joshuaduplaa9033]

@@a_smile55 calc III felt like going through calc II again but a bit more intense. Expect lots of double and triple integrals and 3d vector stuff

[@brandonbarrales6800]

@@a_smile55 from what I've seen and heard and done from myself is alot of people for some reason find calc 2 harder but for me its calc 3 but what people find hard about calc 3 is the visualizations where as people find calc 2 more difficult in the intuition

[@citizencj3389]

@@brandonbarrales6800 It's the fucking infinite series. The goddamn taylor and maclaurin series. But I never had trouble with those because I LOVE DERIVATIVES.

[@brandonbarrales6800]

@@citizencj3389 to be honest for me infinite series is literally the most exciting part of integration 😁

I love how you throw your books and they make a loud bang. It sort of reflects my mood when it comes to math. I sure love it when I understand it and I solve several problems in a row, but man, when the problems pile up, and you feel like you're on the verge of giving up, DOES IT EVER FEEL GOOD TO THROW THAT SHIT AWAY WHEN YOU'VE MADE IT THROUGH AND YOU'RE EXHAUSTED FROM THE WORK!

7:33 For when you love a math class and had fun all the way through.

[@tylergoodwyn1534]

I am so glad this video exists. Cant tell you how helpful it was

[@CHALKND]

Glad you found it helpful!!

[@Ayaforshort]

This was soooo fun to watch. I wish I had this when I was deciding on a major. I actually had really awesome math teachers my first couple years of college since I transfered to a 4 year school. They did a lot of proofs and thoroughly explained things like what the dx is for. I taught myself Linear Algebra and wish I had taken a class so I could understand the theory better.

[@daisyg509]

I am an aspiring math major in community college but I'm barely going onto Calc 2 and linear algebra and seeing all of this made me nervous because I've heard many times that the math in university is vastly different from the one we do in say, high school, or just simply the "computational" stuff. I appreciate you showing this, as I feel like I don't spend enough time actually researching or knowing more about maths as a mathematics major, but this will make me want to look more into it all.

[@CHALKND]

I wouldn't sweat it _too_ much, before I was introduced to more abstract math and proofs I had a hard time finding resources about mathematics beyond calculus and linear algebra or just didn't know where to look, and the only "abstract math" that I had completed were some geometric proofs during a geometry class in high school. There is definitely a transition period between doing "computational stuff" and more proof oriented work but having a good computational foundation helps (or at least I think it does). If you want more exposure to deeper mathematical ideas and topics, at this point in your mathematical career there are a ton of creators on here that make very accessible videos (mine tend to assume a bit of further knowledge 😕 *but hey, if you want to check them out, don't let that hold you back from doing so* , it might just take a little bit more mental work to get through them! 😅) and a bit of googling will take you far. Also, don't get discouraged by the amount of jargon in some of these resources, even parts of the addition Wikipedia page can feel cumbersome without some exposure to more abstract math. That aside, I'm glad this video was useful in some way and *best of luck with your future mathematical endeavors!!* 😀

[@daisyg509]

CHALK thank you so very much for your reply. I most certainly am gonna subscribe and watch your vids even if I'm completely lost. The point is to have SOME exposure rather than go in completely lost expecting higher math to be like the one I'm doing now.

[@lawrencedoliveiro9104]

Funny, I didn’t too much trouble adapting to university maths versus A-level maths back in the day. It was some of the physics (I did a dual CS/physics major) where I found the going really tough.

[@coltyn2003]

"Diagonalizability" And I thought 'differentiability' was fun to say...

[@emiliecote8248]

On my homework I kept accidentally writing “diagonizable"

[@CHALKND]

😂

[@joondochang843]

Math/Science/Stat Courses I took as an undergraduate after calculus III: (* means a graduate level course) 1. Modern Physics 2. Intro. to Differential Equations 3. Introduction to Mathematical Proof 4. Mathematical Writing 5. Applied Linear Algebra 6. Linear Algebra I: A proof based linear algebra course 7. Applied Ordinary Differential Equations 8. Applied Partial Differential Equations 9. Quantum Mechanics I & II* 10. Mathematical Physics* 11. Special Topics in Fluid Dynamics* 12. Probability Theory*: It was basically a measure theory class with application to probability space and martingales. 13. Complex Analysis I* 14. Functional Analysis I* 15. Harmonic Analysis* 16. Classical Methods of Partial Differential Equations* 17. Abstract Algebra*

[@CHALKND]

Awesome stuff Joondo!

[@athenaapo9746]

Congratulations! That was a well made and interesting video. Also, a Greek I am happy to hear that you take Euclidean geometry as an undergraduate. We are very lucky in greece to have the privilege to learn Euclidean geometry in high school because it such an interesting course.

[@argonwheatbelly637]

My high school gave us the standard substandard geometry. A lot of proof memorizing, and that was it. Over the decades, I've taken the time to read Euclid, and now I'm pursuing reading him in Greek. Subtle differences in the original, but since it math, it still is pretty close. Yeah, not modern, but like Classical vs Ecclesiastic Latin, Greek is proving fun, as always.

[@pstewart5443]

EC Crypto relies on the Rational Points concepts as you stated. It's ridiculously complex, but oddly I recently found not very post-quantum computer resistant. I wondered what came after the difficult math, and I appreciate your sharing even though this is a little late. Kinda wish I had taken more math courses and actually really learned more complex topics of math. As I age keeping these concepts alive in my brain has become extremely difficult and try to be happy with what I can recall after sleep.

[@markkennedy9767]

Real analysis for me was a real trip. Took me ages to get a grip of it but started to like it and got a decent mark in it. I do wonder why people say it's the hardest as it's only hard in its own particular way.

[@CHALKND]

Yeah I agree that it is hard it's own way. At least from my perspective, a lot of the really interesting things in analysis break one's intuition about how things "should work", even when you've had experience with the subject and start to talk about deeper things like Hausdorff dimension, measure theoretic entropy, or the Riemann mapping theorem just to name a few, the analysis can be a bit cumbersome. That's not to say that the same does not happen for other fields of math, Topology is also famous for breaking intuition, and it can be easy to get lost in the details of ideas in Abstract Algebra as you get more specialized but those and other mathematical areas are stereotypically just seen by other mathematics people. A lot of different folks can or are required to take a real analysis course as part of their degree (physics, engineering, stats, IT, economics, just to name a few major areas of people that I have met who have taken it) and so that along with it being one of the first 'hard' classes for those that are solely focused on math can exacerbate the idea that it is the 'hardest'. That might just be my and the experience of others I know, but that is how I arrive at a similar place in thought (at least I think) as my Real Analysis I professor when he said it would be the hardest math class my class would ever take.

[@manybuckets969]

I’m a CS student and It’s all calculus : ( *cries in java*

[@chawza8402]

dunno man I only take calc twice and haven't actually use it on the next semester... until you found backpropagation on Neural Nets. other than that, haven't stumble it again

[@jesng7770]

same. I will take Linear and Discrete Math soon. 😂

[@AVVideo247]

Taking calculus as a C.S. student is mainly about improving problem solving skills and your ability to understand complex theory’s and problems. It’s not about using calculus in the future but about the problem solving skills you learn along the way. In the most basic sense it’s a filter class that colleges use to weed out students who either aren’t dedicated enough or don’t have what it takes to make it through the upper level C.S. Classes.

[@spencerrr9878]

@@jesng7770 Those are actually useful / used all the time in CS tho so they make sense. I loved my Discrete class and am currently taking Linear Algebra rn

[@vivi-fe5rj]

@@spencerrr9878 How difficult was discrete for you in comparison to say - Calculus II? I know courses and universities vary, but I'm still interested. I will be taking discrete in the spring, and am gearing up for Calculus II finals right now. :)

[@pinochet3698]

Ten years ago, I was a very precocious child. I was the only one of my peers so interested in physics or anatomy or higher math and other abstract thought in elementary school. My academic zeal may have faded slightly, but I'm glad to see my youtube recommendations age with me. I especially appreciate the covering of complex topics that I will either not delve deeper into, or not study deeply for many years. I'm not so presumptuous as to call myself a modern Renaissance man, but I definitely have such vast, disparate interests, and such a hunger for an accurate depth of knowledge and experiences, that it would be impossible for me to satisfy my curiosity. That can't stop me from trying.

[@mrbunnyjr]

Thanks for the list! Very comprehensive and great descriptions. I will use this as a reference to guide my self study in mathematics (many free courses online bc degrees are very expensive!)

[@ulissemini5492]

I understood everything until 2:45, I've got a journey ahead of me! great video :)

[@ulissemini5492]

update: now I know everything up till 6:35 :))

[@dustingibson4087]

I graduated from a lower tier university, but all of my math professors were passionate wonderful people who cared deeply about their students. My undergrad math was much lighter: * Calculus 1 - Derivatives and integrals * Calculus 2 - More integrals and infinite series * Calculus 3 - Calculus 1 with an extra variable with vector stuff on top * Linear Algebra - Matrices, transformations, systems, vectors, eigenvectors * Differential Equations - ODEs. Solving differential equation in different forms. Laplace Transforms * Mathematical Structures - Proofs, set theory, functions, and some topology. * Programming in Mathematics - Kind of like Numerical Analysis course without a lot of theory. * Real Analysis 1 - Mostly did series, more set stuff, and measure theory. * Real Analysis 2 - This felt like going back to Calculus I and proving stuff we learned from there * Geometry - 90% Euclidean geometry learned in HS but all proofs. 10% interesting non-Euclidean stuff. * Probability - Discrete probability and continuous probability. * Statistics - Confidence intervals, error, random generating functions, linear regression, and ANOVA * Combinatorics - Counting. Combinations permutations, binomial theorem, some algorithmic stuff * Graph Theory - Coloring, planarity, min/max flow, pathing, and hypergraphs. * Abstract Algebra - All groups: cyclic, subgroup, ablein groups, isomorphisms, permutations, etc Math related * Formal Languages - Regular grammars, pushdown automata, turing machine, and chomsky hierarchy * Algorithms - Asymptotic analysis, master theorem, divide & conquer, greedy method, dynamic programming. * Database - Professor was a huge theory nerd. About half course on relational algebra and theory. Graph theory was my favorite course. We were lucky enough to have a distinguished professor who made tons of advancements in graph theory. My least favorite was Geometry. Most of the course was rehashing from high schools days. The non-euclidean stuff was far more interesting, but we didn't get to it until the very end :( The most difficult for me was Real Analysis 1. It was by far the largest difficulty curve spike to overcome.

[@stevenwilson5556]

I went more heavy into Statistics, R, and computational mathematics in my undergrad than you did, and less into analysis, topology, and differential equations. Good video thanks for sharing.

[@Indeedjj]

Good work! I wanted to take combinatorics but it wasn’t offered my graduating semester. Neat handwriting... I could never lol

[@CHALKND]

Thanks! 😀 Also can confirm the handwriting takes a while lol 😂. I was never a fan of combinatorics in undergrad, but I've been learning more about it recently and I have to admit there are some really cool ideas that come from combinatorial arguments!

[@ofarinas]

This video excited me to get my Masters in Math upon retirement, like I wanted to do at one point before I began tutoring part-time instead! I'm a graduate Electrical Engineer, but Math is my passion. Thanks for sharing!

[@CHALKND]

I'm glad it peaked your interest in mathematics again! Thanks for watching! 🙂

[@i_sulfat]

i dont know why i’m even watching this, i’m still in high school :/

[@ulissemini5492]

same :D

[@argonwheatbelly637]

It's like I'm reliving college. Yep! And now I work with teaching my daughter arithmetic, and my son how to count and group. Math is a language, and I'm ensuring my children can speak it. It's funny, but when you pull the first book off the top after the Calc book, I KNEW it was a Linear Algebra book by the...shape. Yeah, I don't know why, but they have a "look" about them. Too cool! Great video!!

[@VanessainSTEM]

Totally unique- Love your humor haha! Can you do a ranking your math classes video?

[@CHALKND]

That sounds possible😉

[@PasserbyP]

That was wonderful, i was only able to take up to multivariable calculus and second year linear algebra so i was really curious what came after thanks for this video. Looking forward to the post grad version!

[@lawrencedoliveiro9104]

1:05 I still have some of my university texts, too. Though not that many.

[@skrux9707]

I really enjoyed watching this, the layout is great. Congratulations dude!

[@ashishKjr]

I was waiting for the textbook that you used for Axiomatic Set Theory since you've made few videos on Axiom of Choice, Zorn's Lemma....

[@CHALKND]

Haha I had done things with set theory in College; but they weren’t through a particular class :D

[@japtracks4709]

Hi, I have taken set theory, and you should try the books of Rosen, Epp, and Modd

[@sthetatos]

I dont like Set Theory but one of the best books for learning is Alexander Abian's book.

[@andescosmico3016]

I will take the way this man throws the books. It is delightful.

[@CHALKND]

Well thats a new take on past me chucking books

[@leocomerford]

9:36 Harmonic oscillators are supposed to be weirdly ubiquitous in physics, right? I guess that might explain the focus. 21:20 As a (sort-of) programmer I'm glad you enjoyed Sipser! I assume it's a lot more basic than most of your other undergraduate maths classes were? 22:50 It's remarkable that fractal visualisations are so famous and so familiar by now that people talk about fractals as the maths behind the images rather than the images as visualisations of the mathematics ...

[@CHALKND]

9:36 Yup it was one of the classes that physics majors were able to take for their major so the assumption was that a majority of the audience had some physics prior. The ultimate “theorem” of the class explained how the universal oscillator equation was an ODE that could describe any given harmonic oscillator (or something like that I haven’t touched ODE’s much since other that the Fourier series class where some review was done.) 21:20 Actually no, the class was considered one of the hardest CS/Math classes at my undergraduate institution. While I was there it was taught by a CalTech PhD who had some research interests in Tiling complexity. So instead of strictly following Sipser and proving that SAT was NP-Hard (at least that’s what I think he uses) and using that to prove other problems were NP-Hard we proved that a Plane Tiling problem was NP-Hard and then used that to prove SAT and others were as well. He pulled in a lot of other weird constructions as well and kept the class well rooted in math despite the majority audience being computer science oriented folks. So, with all the other weird math that I did, in all I would say it was on the higher end of the upper middle quartile of difficulty. 22:50 I would say that the math is necessary for describing the visualization since there are MANY issues with the word “Fractal” being a rigorous term and the math does a much more accurate job of describing how the image is so. Fractal Geometry has been around the block at this point as an area of math (Felix Hausdorff introduced his version of dimension in 1918) and still many mathematicians either avoid the word fractal altogether when talking about them or use it as a buzz word to inspire interest. To give an ever imperfect analogy, using the math behind the “fractal” images is much like how if you would see the color blue and want to define it, the only way is to communicate what color you are experiencing is by giving them the exact wavelength.

[@shadowofchaos8932]

For me it was Statistics and Large Probabilities as a Senior in High school.

[@imnotdaredevil3714]

im not sure why why YT is showing me this after graduating from economics when all i learned was i am not as good in math as i thought i was

[@CHALKND]

Unclear to me too. It just takes practice. Math being the it

[@paqap]

Understanding nothing but still watching the video fully invested

[@XavierMacX]

As a stats person who gets made fun of by math peers, yet usually outclasses them (at least in analysis), it sounds like Feller's probability texts would've been more your style. Thank you, and great video.

[@XavierMacX]

Also, Jun Shao's math-stats book is the one we used during grad school. An intense semester only got us halfway through, and you may enjoy that one much more as well.

[@CHALKND]

Cool! Thanks XavierMacX! I’ll have to check those out, I’ve been looking for some more stats/probability stuff recently :D

[@XavierMacX]

@@CHALKND Feller is expensive to find... um, legally, haha. But totally worth it. Enjoy, and you have a new fan! :)

[@somnathdash4428]

You deserve much more subscribers. The level of work do on your videos is mind-blowing. Excellent content. Just subscribed

[@adeeb1787]

Man/Woman does a doctorate in both Physics and Maths. The power is over 9000

[@NerBarbaro123]

@@Speed001 and people say money dont buy bhla bhla....

[@rivierasperduto7926]

My discrete math 2 course at my community college was basically just graph theory and a little bit of algorithms. Very much geared for CS people, but I wish I learned more about it. I might take another class while I get my bachelors in CS. I'm debating about getting the math BS because after calc 3 and linear algebra I knew it was only going to get harder from here and for me those classes were pretty hard. Almost all my classes for my associates degree was just me learning from teacher notes and not really using a textbook. Those classes were also heavily proof based and extremely rigorous. I had a single test for linear algebra that would have been about 80 pages of work had I chosen to do all of it but I couldn't.... I managed 56 I think. I like the way you described things so I subscribed. Thanks for sharing. I do hope you take graph theory because for me it was my most interesting subject in math.

[@KMMOS1]

I want to know how much math "after calculus" could come "before calculus." In other words, if calculus were not "universally" used as a flunk-out filter, a masochistic masticator, and a pupil purifier for professorially-preferred progeny, what would a math curriculum look like if the courses that can be taken without calculus first were encouraged to be taken and enjoyed?

[@yorch802]

everything that you can find in mathematical olympiads for example.

[@jameschen2308]

Quite a way with words, sir/ma'am.

[@RobertSmurda]

What’s ur problem with calculus lol. It’s not very hard.

[@KMMOS1]

Many schools unnecessarily force students to take calculus before allowing them to take other courses of more interest or utility to the students. For example, number theory, linear algebra, and even discrete math may have been given calculus prerequisites without mathematical necessity to the curricular detriment of students who may not be engineering or natural science students. Herding hundreds of freshmen into Calc I every semester may keep the math dept's service credit-hours high, and other math professors happier to have calc survivors in their classes, but many students are ill-served by such restrictions of their curricular time, sub-optimal coursework choices, and extra financial costs.

[@Brien831]

@@KMMOS1 calculus is merely an introductory course not because it is used to weed out bad students but because it is the easiest non proof based class that is still helpful in university. Maybe Set Theory or abstract Algebra would be better introduction in terms of usefulness but they are a lot harder and would easily scare of many more. Calculus is on the border between school maths and uni maths. Actually where I live my first semester in uni was real Analysis. 80 percent failed that class. Count yourself lucky if your professors still go over calculus and dont dive into real analysis instantly. I think all of europe just does not do calculus in uni and expects it as a prerequisite from A levels.

[@kevindecara9237]

Very helpful for knowing what I need to study beforehand. Thanks.

[@CHALKND]

(Edit July 31 2020): I've had a handful of requests to go through and list out the books that are in this video. For the physical books, I have gone ahead and added links in the description to where you can find them. Thanks for making this one of my most popular videos!! I really do appreciate the support 😃 === I know it took me a while to give my answer to "What comes after Calculus?" but if you want to see me talk anymore about the topics that come up in this video you can let me know here!!! (Also, really thinking about rating these classes based on my reluctance to throw them books lol :D )

[@erre2823]

Can you please do entire courses compressed into 30 min, or something like 3B1B's Essence Of Calculus series

[@CHALKND]

I have a few ideas in the works that would be similar to this; but I haven’t nailed down the format that I want to do it in.

[@CHALKND]

Hey Bruno! 👋 I went to Carleton College, it is a small, well-regarded, liberal arts school in Minnesota.

[@CHALKND]

Oh gosh that’d take a while 😂. I believe when I produced this video I tried to keep them in chronological order. There are a few that overlap near the end, but for the most part they are in the right order. I did not take them in order of difficulty though so that’s another thing to keep in mind.

[@readingRoom100]

@@CHALKND for differential forms, was that pile of paper lectures notes or a textbook? If it's a textbook, do u have an amazon link for it? I couldn't make out the title

[@deepmistry3114]

CHALK, I never knew of your existence. I do now. You deserve my subscription and a real hard tap at that bell icon.

[@klong9269]

Diffy Q's Kicked. My. Ass. So glad to have finished out the series with a C- (Mercy pass)

[@paulcohen6727]

I got an A in it but I can't remember any of it and need to do a complete review. Then, I'll probably forget it again.

[@rebecca3647]

I'm a math/computer science double major with a couple of math-related minors. Beyond Calculus 3, these are the math classes I've taken at my college: 1) Foundations of Mathematics: my college's intro to proofs class 2) Mathematics of Finance: covered accumulated values and present values of certain cash flows, loan balances, sinking funds, basically a lot of introductory financial math topics (shocker) 3) Linear Algebra: pretty much exactly as described in this video 4) Algebraic Structures: covered things like groups, rings, isomorphims, homomorphisms 5 & 6) Mathematical Probability & Statistics I & II: covered probability/statistics topics with applications of integrals and derivatives. Both courses used the same textbook, with Prob & Stats I covering the first half and Prob & Stats II covering the rest 7) Advanced Calculus I: basically what this video called Real Analysis. This was my hardest and least favorite required math class. Ew. 8) Game Theory: covering zero-sum games with pure strategies and mixed strategies, bimatrix games and Nash equilibria, linear programming, and some additional topics (I'm still taking this class) 9) Life Contingencies: the contingent versions of the topics and formulas in Mathematics of Finance, almost always contingent on "living" or "dying". (This class is also hard. I'm about to switch it to credit/no credit.) This upcoming fall, I'm taking one more math class, Ordinary Differential Equations I've also taken/will be taking some additional statistics courses since that's one of my minors. These include: 1) Statistical Computing: R and Python programming 2) Linear Regression/Time Series: simple and multiple regression, regression transformations, and learning Minitab And in the upcoming semester, I'm taking Regression Analysis, which is a level above Linear Regression/Time Series

[@cesareangeli6653]

Being Italian, there is one thing that I always find strange: we have no calculus. If you need calculus, you'll get real analysis. Also, maths is always proof-based for people who really need it (physicists as myself, mathematicians, engineers, etc...). Also, scientific subjects practically never have required readings.

[@Hamppuapina]

Watching videos on other countries' education is so confusing. I had to take maybe 6 of these in my BSc in engineering in Finland. Like what are the future mathematicians studying here?!

[@cesareangeli6653]

@@Hamppuapina I know people that study maths in my university and they have 3 geometry courses (which includes Linear algebra, they cover 5 semesters), 2 abstract algebra courses, 3 analysis (but they cover 5 semesters), general physics, 3 mathematical physics courses, etc... in the Bachelor's. Very different ahah

[@user-zh1ih]

@@cesareangeli6653 so cool! What year are you in? I‘m from Switzerland and I wanna study mathematics and Italian (I have a B1 Italian) but first I wanna spend a couple of months in Italy can you recommend me any schools or any city that is safe to go to by myself?

[@cesareangeli6653]

@@user-zh1ih I'm in the "sixth" year: Bachelor's in physics and Master's in Earth System Physics done and I'm now in the first year of PhD in Bologna. As for cities, it depends: if you want to study here, just go to the city you want to study in. Otherwise, if you just want to live a couple of months, pick some big city (Milan, Bologna, Florence, Rome...) which are both full of "italian things" but also very accomodating for tourists. Also, travelling by train is fairly easy and common, so be sure to visit areas around. Obviously this particular time is not really the best, I have to admit

[@user-zh1ih]

@@cesareangeli6653 wow that‘s great keep it up I wish you all the best! And yes I know ughh but we‘ll see how it goes!

[@syedmohammadabdullah]

This was the most helpful video ever. thank you

[@mahlizam412]

Lmaooo I’m using the same linear algebra book I’m taking it this semester and honestly I needed help with understanding so I also got “Linear algebra done right” but it wasn’t required for my class

[@michaelkruse3536]

"Linear Algebra" by Stephen H. Friedberg, Arnold J. Insel, and Lawrence E. Spence (fourth edition) is what I used in my linear algebra class and it was an AMAZING textbook if you ever want to check it out. I found a free pdf of it online when I took the course

[@0xggbrnr]

I love this video format so much. Great video.

[@likestomeasurestuff3554]

#4 suprised me, in Germany "real analysis" is the way calculus is approached in Uni from the first Semester onward ... and in my opinion rightly so. Sounds like you learn a lot of stuff heuristically over there.

[@CHALKND]

At least I can't fully speak to the university Calculus experience here in the US since I ended up placing out of those courses when I got into undergrad. High school calculus here in the states definitely felt like it relied more on formula memorization in place of rigorous/proof based explanations. I'm sure I will have a better understanding once I TA for or teach a Calculus course here soon once grad school things start to ramp up.

[@kejtos5]

@@CHALKND The US system is weird. How does "university" and "undergrad" differ in this context? Here (it is similar in Germany), when you finish high school, you go to university, which is usually (e. g. medicine is not divided and is a 5 years program) divided into 2 parts - bachelor and master. You firstly study bachelor (almost always 3 years) and then you continue on to do master (almost always 2 years). So when I see "undergrad" I automatically assume it is the first stage of a university.

[@miles6875]

You have an awesome spirit. Subscribed and looking forward to future content

[@Thomas-yf1ve]

so there are like 3 or 4 classes after calc, and then 15 dedicated classes to proving the specifics of the others

[@zaza8870]

I live in england and I just graduated with my BSc in mathematics. We share most of the fundamental courses like linear algebra, differebtial equations and complex analysis (real analysis wasn’t available for some reason lmao). I didn’t expected most of our modules to not overlap which was a nice surprise. I got to do a lot more applied modules such as fluid dynamics, quantum mechanics, tensor analysis. I even had modules related to coding, stochastic processes and metaphysics. I’m rather surprised you didn’t study group theory but i envy the fact you got to do topology since it wasn’t an option where i studied.

[@UniquelyCaptivating]

dude stop throwing books ,respect them geeeezz!

[@waynelast1685]

that was my thought too but I think he is asserting his dominance over his math books LOL

[@alphago9397]

Yeah, I felt bad for those books through the whole video.. lol

[@yurii6080]

Every time i accidentally damage or fold one of the pages of my math books, I go full psycho mode because i want to keep them in a good state

[@malawigw]

no wondering pages are falling off

[@amyx231]

I loved calculus. I wish I could go back to college some days. I’d love to go back to those halcyon days. Sure I sometimes was hungrier than I wanted, but…less stress when your work was to study and the actual job was just food money.

[@amardily]

Lol I had Otto Bretscher as my linear algebra professor...I will reserve my opinions about him 😂

[@masonbarnett4713]

Getting into calc 3 in the spring looks like a bright future ahead!

[@rolandoarodriguez6672]

Thanks for this. I just got accepted to UC Davis for math and thinking of pursuing it. Or mechanical engineering at a maritime academy. not sure yet

[@CHALKND]

No problem, glad it was helpful! Either way, those both sound like pretty cool opportunities.

[@hammadumar4082]

I love your classical teaching style

[@metatron4890]

So what advice can you give for a undergrad when proving proofs becomes a dominant part of the course?

[@CHALKND]

That’s a really good question that probably should be a video in itself. Right off the top of my head though understanding the properties of the object you’re working with is vital to proving stuff about them, so knowing definitions is extremely helpful, but that’s not all one needs when doing proofs. I’ll have to work more on an answer to this!! Thanks for the question I really appreciate it 😁

[@metatron4890]

@@CHALKND no problem. I am thinking about studying math, but I am worried that I might not be able to do well on the highly abstract and logical part of math. I am trying to study philosophical logic to test my ability in abstract thought.

[@CHALKND]

I also looked into philosophy when I was a bit worried about my ability to abstract ideas in mathematics. I would definitely say that philosophical abstraction has a lot more freedom and can be much more difficult due to the subjective nature of some philosophical structures. At least with math and concrete philosophical logic (think Gödel) the definitions and axioms/postulates in some way motivate to at least the basic abstractions of those core logical and mathematical objects and that’s one reason I enjoy math more than philosophy too! But that’s only just my two sense 🤓😅

[@nada3131]

I just found this and I want to tell you that this is really awesome content, really helpful! I think you should definitely make more! Thank you!

[@CHALKND]

Thanks Nada! I'm glad you thought so. I've got more things planned but I'm taking a brief vacation (last week and this week) from KZbin to get settled after moving. So there should be new things coming out here soon!!!

[@nada3131]

CHALK That’s great to hear, look forward to them! Have a nice vacation and settling in 😊

[@RedStone576]

depression come after calculus

[@hannahgreidanus6450]

I'm a kinesiology major looking to pick up a mathematics minor, and this makes me really excited!!! (I've just done calc 1 and 2, and I'm working on linear algebra at the moment). Thanks!

[@michaeljohnmagistrado1166]

Why would you throw your books like that. I even wrapped my books in a plastic cover....anyways, nice content.

[@aidenstern5254]

I just download them as pdfs off of libgen unless i really liked the book and think ill use it often

[@edjrage7745]

I print multiple copies and throw all of them at once. The number of copies is proportional to the suffering the book caused me.

[@pinklady7184]

I am back listening to you and taking notes.

[@qwerty-gc8tn]

How were you able to learn greek that fast?You know the correct orthography of the name eucledian and how to put the correct emphasis and diacretics in ancient greek!?! All that in 4 months?

[@ianhubbard641]

He said he taught himself calculus over the summer bro, I think he’s just a god at learning

[@CHALKND]

Learning all day everyday 😅 But no, I overloaded my course work and, when I couldn't overload, audited ancient Greek courses during my Freshman and Sophomore years of college so that I could read Euclid in the original at some point before I graduated. I also had some background in modern Greek as well so that knowledge did not all accumulate in 4 months time.

[@andrewdemos1]

You are a hero

[@CHALKND]

I'll make sure to wear my glasses when I go out into the world.

[@dillbourne]

What's the book you used for Differential forms and Vector Calculus? I'm studying physics in grad school (year 1) and I feel like that would be an extremely useful topic to become very familiar with.

[@colin8923]

I'm just going into Calcus next year for my senior year of highscool, yet I watched this entire video. Did I understand it? No. Did I enjoy it? Yes.

[@leonmasuda8443]

How did you self-study for Multivariable Calculus??

[@CHALKND]

You're the second person to ask so I guess I really do need to make a video on it! 😅

[@leonmasuda8443]

@@CHALKND Yes please :)

[@guanchengzhu7749]

I just finished my second year taking multivariable calculus and ODEs and I gonna take topology in the summer. In the third year, I'm going to take group theory, real analysis I, PDEs, intro to combinatorics, complex analysis, rings and fields, intro to number theory, differential geometry and maybe one or two courses in classical geometry, in total 9 or 10 courses. I'm very excited about those, feels like stepping into the realm of mathematics.

[@ethanbottomley-mason8447]

That sounds very similar to my third year at UofT.

[@jasonsmith8548]

Bruh you shouldn't be throwing books like that. Books and knowledge are a privilege.

[@tannerross75]

I really enjoyed partial differential equations and fourier series, also learned about perturbation theory in that class which was very fun!

[@shadon_official2510]

Me when he pulled out the calculus textbook and it wasn’t Stewart’s 🥺🥺

[@shadon_official2510]

And then it also wasn’t Antons linear algebra 😠

[@strugglingP6student]

Really fun video and so informative! Thanks a lot from Philippines

[@Ddos2212]

Please don't throw the books like that.

[@pandabearguy1]

I'm an Actuary student on my last semester now and I have taken the following courses (numbers indicate the semester) 1. Calculus I Introductory statistics Philosophy 2. Calculus II Linear Algebra Statistical methods 3. Calculus III Stochastic Processes Introductory programming (in python) Accounting and business economics 4. Differential equations Inference theory Macro economics 5. Finance and investing Generalized linear models Numerical methods Introductory data analysis (in R) 6. Monte Carlo methods Life insurance mathematics Bachelor thesis (Bayesian Regression using STAN) 7. Risk theory (general insurance) Advanced Probability Theory (this was hard) Algorithms 8. Arbitrage theory in continous time (finance theory) Databases and modelling (SQL) Applied statistics (advanced) 9. Machine learning Stochastic processes (retake for grade improvement) Finance theory (exam only for grade improvement) Master thesis (Spline regression in generalized linear mixed models) 10. Life insurance mathematics (for grade improvement) Master thesis (Spline regression in generalized linear mixed models)

[@JaspreetSingh-zp2nm]

You need lot of imagination to do maths

[@CHALKND]

Topology and Complex analysis definitely put some strain on my imagination for sure. 😅

[@earendilthebright5402]

My favourite math unit in undergrad thus far has to be non euclidean geometries and topology. It was so interesting to look at math so different from subjects in analysis, linear algebra, math techniques etc. Complex analysis did my head in, I cant tell you how many late nights I had staring in bewilderment at the residue theorem lol

[@azharlatif6228]

Why this guy keeps throwing Books around?He needs trearment and those who made this footage should be interened in a mental asylum for the safety of others present in the room .

[@CHALKND]

My audience of ghosts and spirits in the room were appalled Its comments like these that tell me and the youtube algorithm that I should do it again 😊 thanks for your engagement!! Every bit helps!

[@owieczkanapolu7327]

It's just that a couple of us struggled with differential forms, and to hide our embarrassment, we've reached inwards to the place where emotions arising from the aerial displacement of your math literature reside. What can we do?

[@hawima4853]

I love math and this made me to take all this courses ..thanks a lot 💚💜

[@mhenderson5305]

Sorry, I can't respect someone who treats their books like that.

[@1flybyguy]

Whateva, he can do what he wants.

[@konekosamvs3264]

Awesome video! I really enjoyed it!