A Look at Some Higher Level Math Classes | Getting a Math Minor

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This video goes over some of the extra math classes you can take if you get a math minor. Some of these include...
Graph Theory
Vector Analysis
Topology
Numerical Analysis
Real Analysis
Complex Analysis
Abstract Algebra
Differential Geometry
etc
If you want the full list of classes I show in this video you can click the link below.
Full List of Required Math Classes: catalog.calpoly.edu/collegesan...
Cutting a Mobius Strip in Half (more detailed explanation): • Cutting a Möbius strip...
►Check out my Amazon Store: www.amazon.com/shop/zachstar

[@fyurex8969]

I love math, my problem is i only finally understand the whole concept AFTER the exam when I get a 70%

[@alex73217]

70% is fine isn't it? Our Linear Algebra classes have a ton of people failing. With 70% you'd probably get an A. I am a first semester at college and linear algebra 1,2 and Calculus (idk... 3,4) is required for our comp sci major.

[@inbisibleful]

Yeah this is a good grade still

[@ThymeSoup]

you probably aren't practicing older material enough. I find that if I exchange a majority of my studying time before exams to solving problem sets from some of the older chapters that the test is using I do better.

[@huey1153]

You should work to understand the whole concept of your test subjects a week before the test, and only be reviewing/practicing the week leading to the test. I learned this during my more extreme classes, some concepts are too difficult to just learn a day or two or three before the exam.

[@Tunatunatun]

We all do. Don't ever feel discouraged by evaluations. You've even said it yourself: now you get it.

[@lifebylosh]

How hard was it to reject the line of girls after showing them the Mobius Strip tricks?

[@mr.serenity7203]

i'm dead lol

[@kp8129]

Honestly i would be in that line

[@exobodyfoundation4472]

This actually made a girl crush on me in high school.

[@comradeofthebalance3147]

Trans Tetris oof

[@devlynallin3389]

easily the best comment of 2018

[@d_wang9836]

I have a love hate relationship with math. I love learning new concepts, but I hate it when you think you understand something, and then the next problem throws a wrench in it. Looks like the ones in college magnify that

[@zachstar]

haha I think many people would agree

[@IeagueofIegends]

Figuring out how to remove the wrench is what the actual mathematics is.

[@MrCmon113]

In university, it's all wrenches.

[@kalebbruwer]

That's what progress feels like. The more you know, the more you realize you don't know.

[@bumpty9830]

In some ways, I think the opposite is true. Up through the mathematics I learned in (engineering) undergrad, but especially in high school and earlier, abstraction was mostly avoided for fear of confusion and lost interest. But proper abstraction is exactly the way to keep wrenches out of your math. The wrenches that used to frustrate me ("why is that true?" -> "well, to understand that you need to know more about X,Y and Z") are removed when you see each theorem derived _as a result of axioms/assumptions_. In properly abstracted mathematics, you always know exactly how much you understand, and how much you don't. So, I think there's hope.

[@josephsekavec5232]

Hahahahahaha an ad for antidepressants popped up. They certainly know I'm a math major.

[@subacc8819]

Duh who are you

[@mueezadam8438]

Joseph Sekavec gottem

[@CHROMIUMHEROmusic]

Now that's a bruh moment

[@thehighpriestess2139]

Smae but an ad for pampers came up

[@lilapela]

1:50 "This is intimately connected to what I call the “ladder myth”- the idea that mathematics can be arranged as a sequence of “subjects” each being in some way more advanced, or “higher” than the previous. The effect is to make school mathematics into a race- some students are “ahead” of others, and parents worry that their child is “falling behind.” And where exactly does this race lead? What is waiting at the finish line? It’s a sad race to nowhere. In the end you’ve been cheated out of a mathematical education, and you don’t even know it. " - Paul Lockhart

[@christianvillalobos9814]

I think there are many other reasons why most people who get cheated out of a math education, get cheated. And I think they’re far more apparent than the structure of the curriculum. I like this structure. I’ve learned so much from my classes as a result of this structure outside of simply “math aptitude”. I’ve learned how to be a far more effective student than I could have been without it. through this structure I’ve acquired a baseline level of competence in something. This competence has instilled way more confidence in my intellectual ability. I did kind of view this structure as a “race”, perhaps as a result of the structure, but after maturing a bit I’ve found it to be way more complicated than that because life is complicated. Honestly regardless of structure people are naturally competitive and anyway you try to structure a curriculum some want to be part of the 1% of exceptional students that are “ahead”.

[@jjbenavidez6]

Funny I was looking at the course list and thinking "hey this looks exactly like the courses offered at my school" only to find out it is my school lol. Cal Poly stand up

[@hasiumcreeper5384]

Is it just me who wants to take *ALL* of these classes?

[@ijusterik5384]

No, me too

[@arturogonzalez6184]

dude, me too. Is it possible?

[@Diaming787]

Same!

[@Diaming787]

Arturo Gonzalez You could go to mit ocw

[@footage6402]

Sadly wanting or being able to take them are two different things lol

[@ErwinSchrodinger64]

Really enjoyed watching this. I earned my Ph.D in chemical physics 4 years ago. While your video is very informative, I don't think you realize how much abstract fields in mathematics play into chemistry in physics. Graph theory is heavily utilized in attempting to understand covalent bond network in organic chemistry, especially when you introduce molecular quantum theory. Group theory, from abstract algebra, helps tremendously in calculations of electron density of complex molecules. Topology, well, it's used in theoretical chemistry in helping define quantum mechanical wavefunctions assignments to bond types. Matter of fact, part of my research was applications of topological analysis on quantum mechanical wavefunctions.

[@AlchemistOfNirnroot]

Congratulations on ur phd and thesis. Im doing physics and hope to do a phd in a theoretical topic (i have literally no idea which area). is the dover book on intro to abstract algebra a good book? if u havent read it; what would you reccomend as an intro?

[@fernando8246]

I don't know why you'd want calculate the density of an electron and stuff like that for a living but sounds cool

[@RVGENomini]

@@fernando8246 Electron density is how electron dense different regions of molecules are, which allows you to predict their interactions with other molecules of interest. Chemical interactions are entirely dependent on what electrons are doing within systems. Maybe you're interested in curing diseases or making better solar panels, these kinds of things require that you understand electron density of molecules.

[@Syfrim]

Is chemical physics the physical properties of chemistry?

[@Deadmanjacobs]

Isn't the entire electron cloud orbital shapes based purely on quantum mechanical calculations? I got out of O Chem as fast as possible so I could focus on Biochem and Human Phys.

[@prod.winterxphool6227]

Its a real shame that most kids don't ever get to see the real beauty in mathematics. Our school system is so devoid of any of the passion that originally belonged in the subject, that 90% of the population believes math is just calculating numbers.

[@vilmospalik1480]

Eh, how do I put this, most of the beauty of maths comes after a lot of necessary foundational knowledge, and unfortunately a large part of the reason children don’t get to see that beauty is not because the school is bad but because they are genuinely just too dumb to get a good grasp on even those foundations

[@jabarismay]

@@vilmospalik1480lol no it’s because many teachers are garbage in grade school and schools in general don’t take math seriously. Being in that environment sucks the joy out of learning, especially math

[@paulklein8556]

@@vilmospalik1480 You could not be any more wrong. Yea sure there are people who are generally not fit IQ wise to digest advanced mathematics. I was not one of those people. I excelled in real world math like physics and chemistry. Simply because I could visualize and understand things more. Algebraic theorems start to get more abstract when you take algebra 2 and up. This is where most people who are interested in science and math get stuck. Somethings are intuitive and easy to spot right away. Others not so much. I had a horrible teacher that sucked the soul out of me when it came to math. So much that I went from an A+ student to a C student on the cusp of failing. She was mean, old, bitter, didn't like any questions, and forced you to come in during lunch to get help. She also was argumentative and pushy. It really trained me to put my head down and ignore math and try to get by from the book. Now years later I'm deep in a stem major and have taken multiple math courses that I originally thought I could not do. Teachers can easily make or break math. It's just the nature of the topic. It can be dry and rigorous. If you don't inspire people with historical stories and intuition on how problems were overcome then you might as well play music and let people sleep. My goal is to become an instructor that inspires people to get into math. Not one that pushes people away and gatekeeps calculus because "Some people are just too stupid".

[@lichh64]

Sometimes you are just sitting there solving math, and thinking about how beautiful it is.

[@hectorsalamanca9483]

And difficult too

[@dantefalls2156]

Dollar store?! Take it easy with the insults, man. I don't make engineering money, yet.

[@ireallylikehuskies9472]

Dante Falls I READ THIS RIGHT AFTER HE SAID THAT LMAO

[@michaelpisciarino5348]

0:49 Calculus and Linear Algebra 1:53 Math is a Ladder, Then A Tree 4:37 Geodesics, Differential Geometry Complex Analysis 6:02 Numerical Analysis 7:48 Abstract Analysis And Pure Mathematics 8:43 Topology Topologically The Same 9:13 The Möbius Loop 13:03 14:15 Engineering Computer Science

[@pepega3055]

I am 98% sure you wrote this, so in future when you will come back, you will know where to go. Actually, I'm freshman and I would like also to timecode everything important. Thank you, bruh!

[@mathincrease.3906]

Is there any best book for this high level mathematics?

[@SaiTeja-ge3lv]

Damn

[@kaladin783]

I love how you portray college as an opportunity to pursue your passion for knowledge and expand your horizons, versus just going to get a good job on the other side. That’s how college should be, and if you don’t think that way you’re probably better off going into a trade, which is probably financially smarter anyways.

[@prorangerr]

Why am I watching this? I struggle with algebra lol.

[@tombkings6279]

Wow

[@JuanRamirez-qf1qr]

No shame! It just takes practice!

[@bumpty9830]

Because your curiosity is not limited by your current state of knowledge/ignorance. [edit] Unlike, for example, "My beautiful and amazing Princess."

[@MybeautifulandamazingPrincess]

I hate math and have difficulty with it too, and I dont care about it

[@orca3894]

it's never too late

[@neverbackdown1918]

This is SO COOL. I like math and I’m ok at it, but this makes me want to learn some of these classes. Job well done.

[@narata1541]

Awesome video! This brings back sweet (and equally frustrating) days while I studied for my major in physics and my minor in mathematics. I really enjoyed calculus 3, linear algebra (I remember it being easy, till the second half of the book when it got into 4 dimensions. ACK!), and complex numbers. Haha, I remember sometimes doing math that was really complex (for me anyway) that at the end, I had no idea what the answer meant. Anyways, keep up the great work and I wish all you math majors and minors the best! :-)

[@StEvUgnIn]

I like the way, your videos now follow a red line from the conclusion. You said instead of taking technical courses like DSP in senior year, you would have taken some physics or high level math courses and you now take the time to explain what it is about

[@MrBlindGames]

I do not excel at maths but this is amazing. Makes me want to study more and more! Thank you for that.

[@foresightmystery9845]

The mobius strip was the first time my mind was blown! 4D analysis is crazy

[@renjia3504]

Yeah bout to start studying math

[@Koisheep]

@@metachirality nice vihart reference

[@tausal1]

You deserve way more views. Amazing video as always. Keep up the work! 👍

[@roygalaasen]

I think the world needed this video!

[@steliostoulis1875]

Waited a long time for this. Thank you

[@2010RSHACKS]

This is bullshit. The school he used as an example is absurd and unique. Most colleges will have those MINOR requirements as their end goal MAJOR requirements. The stuff he says is for a math major are graduate school courses...

[@Tunatunatun]

I certainly enjoyed the high-level descriptions of these vast and nourishing mathematical realms. Given my electrical engineering and physics academic background, I've already dwelled upon most of these topics in varying extents and definitely agree with the approach and the examples. This is a really great guide for scientific newcomers to get a hint on what their preferred niche is. Much appreciated Zach, and I'm certain this single piece alone will do wonders for many undergrads. Kudos^2!

[@Gorilla_Chaos]

I’m barley passing calc 1 Why am I here.

[@xyzxyzuvwuvw7633]

that topology tutorial was so cool haha

[@joeyGalileoHotto]

It's interesting that Discrete Math isnt shown. That's required for CS Majors at my school.

[@zachstar]

That's what the proofs class was for us (although computer scientists did have their own discrete math course just for them). I did multiple videos on discrete math so didn't go into much depth on it.

[@mzg147]

At my university, math students also don't have Discrete/Combinatorics required, but cs students do. Well, it's a part of math that is probably more important to them than to us.

[@eduardorivera508]

Duuuude I had to take that class a second time to pass. Maybe it was my professor but screw that class. Though, I can see how one can get nerdy on combinatorics and I found problems involving Fibonacci numbers quite fun too.

[@BHaller5]

I fucked hated that class. God bless I managed to get a C my first goaround

[@cdsmetalhead99]

Joseph G. Hotto That's what Graph Theory and Combinatorial Math are...

[@spacetimemalleable7718]

Excellent video!! Enjoyed it immensely especially on the Mobius strip - Wow just blew me away. Thanks!

[@TheSolidheroes]

Great enjoyable teaching and I really appreciate the enthusiasm and joy you bring to difficult subjects thank you 🙏🏾

[@xyzct]

Zach, consider doing a video on some of the awesome books that give great overviews for math enthusiasts, such as _Mathematics: Its Content, Methods, and Meaning._ These types of books can be great stepping stones to more involved texts.

[@BriTheMathGuy]

Nice information. The world needs more math majors (minors). Have a great day!

[@user-or7ji5hv8y]

Great video! Really great explanation. Wish I had this when I started my journey.

[@martinkunev9911]

5:10 Differential geometry is quite useful in computer graphics. 8:00 Abstract algebra is applied in cryptography as well.

[@jake_runs_the_world]

love the content bro!

[@crystaljeffbabeeey]

all of this math seems so interesting. i'd love to be able to study it one day. too bad i am currently failing high school maths lol. but oh well, i'd like to improve so i could one day tackle these kind of topics.

[@douglasstrother6584]

Integral Equations: Fourier & Laplace Transforms, Green Functions, etc. These are used a lot to solve PDEs (Jackson's "Classical Electrodynamics"!) and model systems rather than differential equations.

[@llawliet2310]

in my undergrad I was a double major in psychology and mathematics and was floored by the amount of mathematics I saw in my senior level psych classes when learning about cognition and robotics/ artificial intelligence (things like fourier series, graph theory, game theory, group/ set theory, category theory, number theory, and a lot of abstract algebra)

[@huey1153]

Too much theory not enough application

[@delgande]

@@huey1153 what? they ARE applying the theories

[@raph009]

Analysis classes have made my lab reports a lot more rigorous cause I learned how to build up from what I had and deduce stronger conclusions. Making links between results and the discussion part was a lot easier after this, although I failed one of them and cursed them all the way through X)

[@vifair3623]

I've always been strong in math and will be attending university this fall for Mechanical Engineering. However, I have not exactly loved math until recently. In our school system, we do not learn how to find the area under a curve in calc until university. So, I asked a teacher at my school with a major in mathematics about it and he gave me a great textbook to learn it from after a brief example. At this point, I had never gotten involved with calc yet. So I taught myself Lim of functions, derivatives and finding area under a curve. This may sound boring but learning it all was actually somewhat beautiful. I went through these subjects in 2 weeks, in comparison to the 5 months our school would devote a 75-minute class to every day. Because I enjoyed being able to do things that seemed almost out of reach a few weeks earlier. And now I am considering a minor in mathematics once I go to university so that I can learn to love and understand more of math!

[@christianlagua6787]

Today i start the pure math career, I'm very excited about this opportunity and your video gets me a major idea about career

[@DrLol07]

For mechanical engineering, differential equations and matrices should be a must, understanding how those two work will make some of your upper division course a breeze

[@frootube5662]

Idk why but my heart beats 100x faster when I come in contact with math

[@akshat_shukla00]

As in crippling anxiety or excitement?

[@baronvonbeandip]

Excitement, of course. Gotta pump blood to my... organs.

[@marverickbin]

I graduated in computer science, but fell in love by engineering maths. I took diff. eqs., Fourier analisys, complex analysis, numerical analysis. However, I had to take also number theory, graphs algebra for computer science degree. I realized that I have only few disciplines to get a math major.

[@Aniket7172]

i love this channel so much, i regret not finding it sooner

[@douglasstrother6584]

"Complex Variables" by John W. Dettman is a great read: the first part covers the geometry/topology of the complex space from a Mathematician's perspective, and the second part covers application of complex analysis to differential equations and integral transformations, etc. from a Physicist's perspective.

[@MalamIbnMalam]

You are the best man!

[@gonzalezm244]

Alright! I’ve been waiting for this

[@369951369951]

Thanks for the video... Came at a good time for me!

[@kchannel5317]

Good video I love the visuals. If I had the time and the brains to take all these classes I would.

[@fanimeproductionst.v.3735]

4:46 Say that again for the flat earthers in the back who didnt hear you.

[@Mr_Gspot]

best comment award. please come pick

[@liamgauvreau]

honest

[@ariusmaximilian8291]

Hi, please do a video about physics and its subfields please!

[@zachstar]

I will!

[@michaeledwardharris]

Cool demo! I guessed incorrectly. You're one of my favorite math teachers. Thanks!

[@lesterdavepaguio4680]

I’m majoring in math and minoring in computer science. Thank you for this informative video as to what extra classes I need to take in terms of math and computer science together to be needed for my future job, which is cryptographer.

[@Mateo-kf1ud]

hey if I want to become a data analyst, should I major in math or computer science?

[@Lemurai]

No lie, having a minor can’t hurt, getting my nursing degree and having a Chemistry minor and taking Calc 1-3/physics (NOT required) for nursing out of curiosity, it helped me secure a slot in CRNA school. When my admissions counselor did the interview, he was like my, my, you certainly are an ambitious one sir! lol! I only took those classes because I love science, nothing else, had nothing to do with climbing the career ladder. I do despise folks like that however, because they don’t care about anything, to include the job they are paid to do.

[@ChickenChipotleSandwich]

ill comment just to make videos like this a fraction more popular on youtube

[@subtlegestures]

I love your channel! ❤️

[@worldedit8784]

Your videos help me a lot

[@ccuuttww]

even u are not studying the above subject I recommended linear algebra, caculas and statictics since we have utube, Udacity and open course anyone can learn any Maths subject very easily

[@levibeam100]

Well. They have the resources to learn it. Just because you have resources doesn’t mean you can completely understand it

[@Gonthor1000]

I perform adequately in mathematics, essentially, "pure math". Invariably, I struggle to apply this material to real world problems. As an engineering student i'm considering switching to mathematics. Does anyone else struggle with this? Any advice on switching from engineering to pure mathematics? Thank you and great video!

[@hughjazz4936]

I don't know about switching majors and what challenges you might face but prepare for a nasty surprise when you finally get your maths degree. I got one of those and I got so frustrated looking for jobs that I became a freelancer. Unless you'll stay in academia you will not have a lot to do with pure maths at all. Most of the jobs I applied for actually wanted a programmer and the other 10% could be done with basic maths skills.

[@umartheguy4612]

Yeah that’s because pure maths rarely has applications in irl problems

[@usagi8234]

@@umartheguy4612 I think mathematics is applied in irl but it's usually elementary level.

[@bhartiyacreature4950]

@@umartheguy4612 exactly

[@kuldeepparashar7266]

Excellent knowledge 🙏🙏

[@firstname4337]

this was a fantastic video thanks very much

[@SunnySyde]

Even though I received my undergrad in Math many years ago I was curious to hear what you would say about Game Theory, the course which caused more pain and suffering than any other math course I ever took.. you almost made it sound pleasant for that half a second, but don't be fooled fellas haha.

[@sk5213]

Oh my god I completely relate to how you feel with profs and geometry lol

[@VidhathShetty]

Damn this inspired me to learn topology 🙏🙏🙏 thank you Zach.

[@naut_nigel]

I wish I watched this video before or in the middle of my college career! I'll make note when I start my masters. :) Thanks!

[@izzyexplains8620]

I think this video did a good job of separating the proof classes from the applied class, however I’d just like to point out that all of the applied classes are based on rigorous proofs and at the graduate level include proofs. Therefore, depending on the school, an applied class the video listed may be more proof based. For example, most universities’ topology classes are very proof based. Also, I think this university’s math minor is very proof light. Most schools require at least intro to real analysis, and proof classes require a very different set of skills than applied math classes. I know several engineers who thought it’s only three/four classes more for a math minor and take analysis and then drop their minor. So if you’re an engineer, take the proof courses seriously.

[@2010RSHACKS]

You're full of shit. Most schools do not even OFFER real analysis. That is grad school shit. At least in america, those "minor" reqs are major reqs at most schools, with the addition of abstract algebra

[@izzyexplains8620]

nothing First of all, there is no need to be rude. Real analysis is a requirement in almost every math major (with the exception of some liberal arts colleges that shouldn’t even offer a math major if they are not going to require any actual math) and most math minors. I can send you the requirements for my school’s math major and minor if you’d like and I have looked at dozens of other schools’ requirements and I can send you theirs as well. Real analysis is not “grad school shit” and if you don’t know what you are talking about, you don’t have to be rude to people who do.

[@2010RSHACKS]

Dude, I have a fucking bachelor's in mathematics!

[@izzyexplains8620]

nothing so do I and I’m a PhD student. It takes all of two seconds for anyone reading this to google math BS requirements or math minor requirements.

[@2010RSHACKS]

First several school major requirements that popped up in google after searching for: bachelor's in mathematics requirements. math.arizona.edu/academics/undergrads/requirements/mathematics catalog.unc.edu/undergraduate/programs-study/mathematics-major-bs/#requirementstext catalog.unc.edu/undergraduate/programs-study/mathematics-major-ba/#requirementstext www.sas.rochester.edu/mth/undergraduate/ba-requirements.html coursecatalog.syr.edu/preview_program.php?catoid=3&poid=807&returnto=253 catalog.buffalo.edu/academicprograms/mathematics_ba_requirements.html mathstat.umbc.edu/files/2014/04/advising-Math-BA.pdf mathstat.umbc.edu/files/2014/04/advising-Math-BS.pdf At first glance, only one of these schools even offers an analysis class. They almost all follow the standard curriculum: Calc 1-3, Differential equations, Statistics, Linear algebra, Abstract algebra, intro to CS + electives.

[@smug8567]

I had been to school most all the time, and could spell, and read, and write just a little, and could say the multiplication table up to six times seven is thirty-five, and I don't reckon I could ever get any further than that if I was to live forever. I don't take no stock in mathematics, anyway.

[@johnchestnut5340]

I was introduced to the moebius strip in a magic, math and illusions book. "Make the strip. Now try to draw a line down the middle. The "edge" is "twice as long" as before joining the ends.

[@trimmien]

i went from only being able to do very basic algebra equations (like barebones) 4 weeks ago , and now i’m headed into algebra 2 and trig in my rush to linear algebra i gotta say, math is pretty damn cool

[@suleb1]

That Möbius Strip demo has me feeling smart because I guessed both questions right... but then also because I got it right it also doesn’t feel major 🧐

[@wazarter1586]

Now i'm motivated to study math xD

[@themoribundapathetic4530]

Same!

[@bishnumishra1590]

Me too! I just got major in mathematics in university just by luck. I had not zeal to study it. But Zach Star has changed my mindset.

[@MariaFernandazz]

this makes me so excited

[@matheuscardoso1]

Another great video!

[@kevinstreeter6943]

It is refreshing to find an engineer that sees the beauty of math.

[@usmanzafar4751]

Electrical Engineering does that. It did the same to me. It is awesome to see how mathematics manifests in something tangible and physical applications that follow from it.

[@vapenation7061]

i’m in 10th grade and all this seems terrifying.

[@pspppe]

My school actually has 2 other computer science related math courses logic and computability, and computational complexity. Both courses deal with defining proof systems and computing the efficiency of algorithms. Logic and computability also goes into specifics about logic programming, aka the foundation for artificial intelligence. I would recommend taking those courses for other people in computer science looking to get a math minor.

[@bibekbasnet7374]

You are a star of Topology.

[@Diaming787]

There is just too many to learn 😅

[@eriks9505]

Can you make a video about FEM (Finite element method)?

[@bowlofsoba]

Thank you very much for sharing! Could you please talk about what real analysis and abstract algebra studies? Thanks!

[@skifast_takechances]

So at 5:35 I saw you talking about the proofs to some of the trig identities inclusive of the sum and difference identities. I just took precalculus (so I'm still quite low level math) but in class we actually proved the sin and cosine sum identity using a triangle inscribed in a square where one corner of the triangle is also a vertex of the square. Hence, we have angles α, β, and 90-(α+β).

[@brucen.3602]

you should do a video on actuarial science

[@realmadru394]

Bruce N. I wanted him to talk about combinatorics so bad 😢

[@letsseewhatwecanlearn9242]

I honestly cheated in Algebra I in eighth grade, and I harmed myself from there. Once I realized how many foundational skills I did not know, I decided to study my algebra foundations. I’m now in Pre-Calculus, and I love the class. Math is fun once you change your perspective and think of math as a game with rules you have to follow.

[@A_ldo..]

Im in 8th grade right now, my teacher signed me up for advanced next year and i dont think i’ll survive lol.

[@sqrtof-1]

Glad to see I'm not the only 8th grader watching this. I am in my 8-9th grade summer break right now. I took Algebra 2 and Precalculus (at same time) and didn't do the homework for Algebra 2 because I was so busy in Precalculus, but in my school this year there was a new grading system which didn't count homework and no points were taken off on late (In my highschool, it would just be the regular grading system). I am planning to take Calc BC for freshman (because I want to learn about infinite series). I'm not sure if I'll do good, but I've always had a passion for math, biology and chemistry. Any tips would be nice

[@robinchoo5481]

Great video!

[@Jesuschrist-oy5xz]

if anyone was wondering about the 32g 6g jug one, what i came up with was filling the 32 with 5 6g scoops, for the last scoop to fill it all the way save the excess now you start with a 4/6 filled 6g or 4gs now empty the 32g and fill it was the 4 and another 6

[@bolufakayode5528]

It’s going to cut evenly in half (just a broad guess )

[@synckid]

what about the math necessary for quantum computing?

[@juliuspleaser4675]

This video gave me a really pleasant nostalgia over how unintuitive higher knowledge always feels at first…I love that reality gets more wild the more sense it comes to mKe

[@SuperSaltyFries]

We use abstract algebra in my undergraduate EE research dealing with cryptography.

[@Lorch95]

i am really confused, i've never seen a math lecture without proofs, even in something very applied like numerics. How in the world would you go through a class in Calculus (let alone 3) or linear Algebra without being able to proof even the simplest of statements? isn't the point of those classes to proof statements in Calculus and linear algebra? I mean what do you learn instead? Also someone studying Physics for example would also need to know about proofs and technical stuff to be able to survive right? how does that work?

[@MrCmon113]

Where I'm from everyone in a technical field has to do proofs at the very least in the basic maths classes.

[@blazeinhotwings]

Lorch95 at my university classes that are not proof based still show the proofs in class to explain how something work but the students themselves don’t have to write proofs and the in class proof are usually less formal

[@Darticus42]

Lorch95 demonstrating how theories are used and why they work (or giving a special case "proof" that shows it is true) doesn't often require actually formally proving it. In Calculus in my uni at least, it's more of the former as a formal proof class is not a prerequisite and proving a lot of calculus theories supposedly involve higher level math. Though I suppose one could make the argument that the solution to *any* mathematical problem is a proof, formal or not.

[@Vapor817]

my calculus 1-4 classes leaned more towards mechanically calculating expressions involving derivatives and integrals, usually through real-world applications. we would either need to demonstrate or simply assume that statements were true, formal proofs were few and far between

[@patbateman69420]

Pure Mathematics (algebra/topology/geometry etc.) is pretty boring for me personally. But I'll be honest, it's partly because it's difficult. Applied Mathematics is way more interesting but that's because I enjoy applications of Differential Equations, Fourier analysis, Boundary Value Problems etc. (Analysis).

[@khamisi__6378]

I def learned something new. Thx

[@daniellfraga7322]

thank you grassmann for telling me the dimension of an intersection vector subspacd

[@floidsoda5470]

Yeah let's watch this when I had to take geometry a like 4 times

[@evenightshade565]

I am on a maths journey at 37 years old at pre-calculus, liner algebra and calculus level I want to study more advance maths topics after khan academy calculus's subject, I also use cosmo learn and youtube, I want to start when I am now but after calculus 3 does anyone know any advance, really advance pure maths, advance or higher pure maths topics I really want to get into it, because I am into physics now.

[@evenightshade565]

Sorry I had myself at a wrong age lol

[@redaabakhti768]

I am also studying myself math for fun I finishieed undergrad abstract algebra and galois theory have some topology and finishing measure theory my next goal is differential geometry I m proving everything I do

[@AlqGo]

Seriously, people have got to stop saying "Calculus 1, 2, 3, etc". In the pure field of Mathematics, there's just Calculus. The topic is never divided into "1, 2, 3" nonsense. That's just a system used by schools and colleges to organize their subjects. No such grouping is used in the pure field of Mathematics.

[@Darticus42]

Look at the class descriptions of universities, they spell out a lot of the topics math students learn within each class, their names alone might be enough to research more on your own. As for resources that help understanding post-Calculus concepts, the KZbin creator 3blue1brown has amazing videos on just about everything (my favorite is the one on Fourier analysis). Or maybe pick up a textbook online

[@AmazingStoryDewd]

@Steven Lee I don't think it's ever to late. My dad got his degree in electrical engineering at 34. Then he went on to get his masters. And you know what? He did just fine. It's never too late.

[@haweater1555]

Mobius strips are often used in fabric ink ribbon cartridges in the old dot matrix printers.

[@fightwithbiomechanix663]

Additionally in some cases mobius strips are used in belts for drive systems. This is becasue they have one side and can provide uniform wear (material removal of a surface due to friction).

[@christianmarin6267]

10:32 dis how CVS be making they long-ass receipts

[@ipodtouch470]

"Saved you a trip to the dollar store"😂

[@mathematicalninja2756]

i took a step further and majored in maths along with cs.it opens up s lot of opportunities

[@altuber99_athlete]

Topology is also used in circuit analysis and power systems analysis