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

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.

Yeah this is a good grade still

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.

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.

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

i'm dead lol

Honestly i would be in that line

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

Trans Tetris oof

easily the best comment of 2018

haha I think many people would agree

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

In university, it's all wrenches.

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

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.

Duh who are you

Joseph Sekavec gottem

Now that's a bruh moment

Smae but an ad for pampers came up

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”.

No, me too

dude, me too. Is it possible?

Same!

Arturo Gonzalez You could go to mit ocw

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

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?

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

@@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.

Is chemical physics the physical properties of chemistry?

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.

Dante Falls I READ THIS RIGHT AFTER HE SAID THAT LMAO

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

@@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

@@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".

Wow

No shame! It just takes practice!

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

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

it's never too late

And difficult too

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!

Is there any best book for this high level mathematics?

Damn

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...

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.

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.

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.

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

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

Yeah bout to start studying math

@@metachirality nice vihart reference

Too much theory not enough application

@@huey1153 what? they ARE applying the theories

I will!

best comment award. please come pick

honest

As in crippling anxiety or excitement?

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

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

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.

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

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

@@umartheguy4612 exactly

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

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

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.

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

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.

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

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.

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.

Same!

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.

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

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

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.

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

Sorry I had myself at a wrong age lol

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

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.

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 RU-vid creator 3blue1brown has amazing videos on just about everything (my favorite is the one on Fourier analysis). Or maybe pick up a textbook online

@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.

Acid Plug If you don’t understand what’s going on, see the professor during office hours. Math is hard, but it’s like learning the piano. When you start off with learning the song twinkle twinkle, you think it’s really hard but eventually you move onto learning harder songs and think playing twinkle twinkle is easy. Keep it up and work hard and you’ll be looking back at college algebra as easy! Good luck!

Izzy Explains thanks

Definitely go to office hours if you struggle with math. But I also want to point out something else that a lot of students seem to do. They tend not to _think_ when doing math. They view it as a very algorithmic process where you just have to memorize a bunch of random stuff and repeat it. That's not a good way to do mathematics. You really need to think about what's going on and what everything means because everything in math _makes sense_ - there's a reason _why_ everything is the way it is. Sometimes that reason may be too complicated for you to understand, but most things you encounter should be in your grasp as soon as you see it. You'll definitely need to learn some things on your own, but if you are really struggling with a concept, ask _why_ something happens. Here's an example of something that confuses people: graphical transformations of functions. Let's say you have a function f(x). It's generally not too difficult to see that f(x)+2 shifts the graph of the function _up_ 2 units, and that f(x)−2 shifts the graph of the function _down_ 2 units. But what about f(x+2) and f(x−2)? Most people initially think that f(x+2) should shift the graph of the function right 2 units, and f(x−2) should shift the graph of the function left 2 units, but it's actually the exact opposite: f(x+2) shifts the graph of the function _left_ 2 units, and f(x−2) shifts the graph of the function _right_ 2 units. Most students at this point are content to just memorize that: if you change the inside of a function, it does the opposite of what would happen when you change the outside. But if you want to understand math, don't be content with just knowing this information: try to think of _why_ this is true. So what you can start to try is to look at some simpler functions that you kind of understand. Like f(x) = x. It's a nice line passing through the origin with a slope of 1. Now look at f(x+2) = (x+2) (replacing x with x+2). Now try to graph this function next to f(x) = x, and notice how it is shifted 2 units to the left from f. Now look at f(x−2) = (x−2) (replacing x with x−2) and try to graph it next to f(x) = x and notice how it is shifted 2 units to the right from f. And maybe try a more complicated function like f(x) = x^2 or f(x) = |x|. Try graphing each of these and then try graphing the versions where you replace x with x+2 and with x−2. A nice way to sketch a graph is to try a couple different x-values and find the corresponding y-values and plot all of those points. And after plotting these, maybe you'll start to get a sense of why this is true in general. The point here is that f(x+2) and f(x−2) are technically new functions, right? So let's treat them like new functions. Rename f(x+2) as g(x). In other words, g(x) = f(x+2). Now, for example, if we plug in x=0, we get g(0) = f(0+2) = f(2). Or if we plug in x=5, we get g(5) = f(5+2) = f(7). And no matter what value for x we plug into g, we get that its input is 2 numbers to _the left_ on the number line for the same output on f. So you've shifted f to the left: you get the same output as f, but 2 units earlier! And similarly, let h(x) = g(x−2). Plug in x=0, and you get h(0) = f(0−2) = f(−2). Or plug in x=5, and you get h(5) = f(5−3) = f(2). And no matter what value for x we plug into h, we get that its input is 2 numbers to _the right_ on the number line for the same output on f. So you've shifted f to the right: you get the same output as f, but 2 units later! What you notice here is that g(x) = f(x+2) and h(x) = f(x−2) is that you're affecting the _input_ value of the function. So you could think: If I start with g, how can I get _back to_ f? What do I have to plug into f in order to get the same value as g(3)? Well, notice that g(3) = f(3+2) = f(5). So you need to plug 5 into f in order to get the same value as plugging 3 into g. So notice that in order to get _to_ f _from_ g, you have to shift two units to the right. So in order to go backwards _to_ g _from_ f, you have to shift two units tot he left. So that's the sort of thing you can do if you don't understand something in math. Try a few examples and really think about _why_ things are true. Try thinking backwards too (like what I did at the end there: instead of thinking about what you have to do to get from f to g, think about what you have to do to get from g to f). If you can figure out the reason on your own, you'll really remember and understand it much better! But sometimes it's really tricky to think in the "right way" to make the reason clear. That's when you can ask in office hours or ask someone else who may understand the topic. Yes, this is time consuming, so you won't be able to do this for every topic. But if you want to understand math, this is the sort of process you should strive to do as much as possible.

MuffinsAPlenty thank you sooo much by the way and for taking the time to type all of that.

Honestly I think the main issue with math is that children are given problems and not much real world applications to it. I had the same issue in high school but once I started taking physics everything started making sense to me. And once I started calculus in college I went in a bit confused from precalculus but I felt that calculus just made everything easier to understand.