Is any math beyond calculus even useful?

So there's three useful courses in a math degree

>inb4 hausdorff measures are useful

TOPOLOGY

He said useful

>Elementary Linear Algebra

Do Americans not cover calculus at all in high school? Pic related is A-level maths, studied by English 16-18 year olds in Sixth Form or "College" (not the same thing as the American definition of college). Generally a student will start university at 18 or 19, not too long after their A-level results.

It would be strange to have an introductory calculus class at university level, except maybe a brief refresher or something. There are exceptions (access courses for mature students etc) but it seems like US high school is a lot more basic than in most countries.

Graph theory

Calculus (i.e., Real and Complex Analysis), Differential Equations, Linear Algebra, and Statistics are all useful for real scientists. Anything beyond that is just recreational mathematics.

It's an optional course that most high school students who plan to go to university will take their senior year. If they didn't they'll take it their first semester of university.

It is usually offered but it is generally not required.

Differential equations

number theory (elliptic curves) and topology (braid theory) are used in cryptography
teichmuller theory - computer graphics for medical imagery and what not
probability for machine learning
supergeometry for astronomers
math. logic for cs monkeys
analysis on fock spaces for theoretical physicists
knot theory for chemists and biologists
and... and
chaos theory for the pleasure of looking at fractals

America public schools are only for the poor and indigent. That said, the info is taught. 8th grade will be algebra1, 9th grade algebra2/Geometry concurrently , 10th grade trigonometry, 11th calculus 1, 12th grade calc 2. Most plebs will have to have algebra 2 to graduate, but beyond that isnt typical.

Differential equations, linear algebra, Algorithms. *if your a CS or electrical engineer major* other than that the rest is just theoretical shit you'll never have use for. You need to know all the calculus before you can take diffyQ though so I guess you can say calculus is in fact useful.

kys

I'm an Industrial Engineer student and i know:

> Calculus I
> Calculus II
> Dif eq
> Linear Algebra and analytical geometry

Do I need anything else to start reading (and studying, eventually) modern physics?

Obviously i've taken physics I and II (Newton, fuids, Maxwell equations, etc), thermodynamics and other "more engineering" classes like materials science, statics, fluid mechanics, etc

calculus of variations, theory of distributions, differential forms, real & complex analysis, fourier series, measure theory, linear algebra up to tensors at least, differential geometry

2nd year physics student here. We've got most of that covered and physics is still ahead of our analysis classes.

Thanks buddy. I was wondering because most of the physics books i've jump directly to modern physics after Maxwell equations.

Books like Serway, Halliday & Resnick, Sears, Zemansky, etc.

Depends which physics you want to learn really.

>confusing subjects with courses
this is like saying that you understand electrical engineering because you took an intro EM class for bio majors.

It's useful if you aren't a brainlet.

honest question. Is there a lot of math beyond calculus ? If so.. how much ?

It's not a linear thing but there's a lot more math that isn't calculus/analysis than is

All of it really.
Good math majors skip calculus in freshman year.

of course there is, think about it for a minute

it takes students a few weeks / months to finish calculus (usually) and a PhD that does research in mathematics can work for decades, and there are millions of PhDs worldwide probably, or a similarly large number and all they do is study math and publish shitty papers in nepotistic journals

Calculus is just the surface of it. After that, you can either interest yourself in integers and prime numbers (Number Theory), reinvent geometry to make much more complicated, invent complex and never-ending classifications of things (Algebra) or look at how functions behave in general (Analysis).

Even then, there's a lot more to it. Math is very vast.

I'm starting to think that calculus is different in the states and in Norway. Here you take calculus 1,2 and 3 over 3 years if you are taking a degree as an engineer. The calculus 1 book for the first year is about 1000 pages long.

...

>is there a lot of chemistry beyond gen chem?
>is there a lot of physics beyond newtons laws of motion?
>is there a lot of psychology beyond psych 101

the answer to one of these is no

Obviously the second one, when the base axioms get proved to be wrong, all of modern math and physics will be worthless

Chemistry obviously :^)

>
I've been an engineer for 10 years, never once used calculus on the job, or any math beyond the absolute 5h grade basics for that matter

do you have computers doing calculus for you?

O P T I C S
P
T
I
C
S

But seriously, high precision optics and laser theory require some higher level maths

Guy who fixes people's computer is not an Engineer. Go back home, Pajeet.

NUMERICAL ANALYSIS

literally the best applied math course you can take.

what maths?

might go towards an optics focus in my masters program. I've only used fourier optics in my research really, so I haven't gotten to see the math with quantum optics.

I'm assuming some topology?

Density matrices, perturbation theory, Stokes parameters, fundamentals of QM occasionally

I'd suggest Nonlinear Optics by Boyd for a good read

I'll check out density matrices.

I actually applied for an REU at Rochester and put Boyd on my list of researchers I want to work under. He does some of the same research my advisor and I do in nonlinear optics.

good luck to you then, we need more people researching ways to make better lasers

Depending on the state, district, and school, the math courses available through the school may only go up to pre-calculus, however, at a different school, the classes may go up to calc 2.

Anything above that is typically offered outside of the high school through dual enrollment classes (enrollment in a CC or uni while in high school).

As an American, I feel that students and parents often aren't informed by their schools to even know what options they have for education.

Most public high schools offer AP Calculus AB and BC. Together these are supposed form Calc 1+2, but really it's like a dumbed down version of both that is about a year's worth of material all together

At my *public, small town, relatively poor highschool that would send less than 5 people to top25 schools each year* I was allowed to take calculus AB as a freshman and skip out of BC by getting a 5 on the AP test

People like to jerk eachother off about how european high school is so much harder, but A-levels and GCSE is really not that different from the BC Calculus exam

If you disregard the bottom 50% because it is public and like literally everyone goes there so we cast off that shit--the average student at my school will take Calculus AB maybe junior(3rd) year. Seniors in calculus were regarded as pretty bad at math or slow, and sophomores in calculus were regarded as a bit fast. Everyone I know that went to great schools was taking it as a freshman

Calculus is covered in high school, but it's completely optional. I did very well in every other subject, but always had trouble with algebra and so I think I only got through trig by the end of high school. Math education is much simpler and lower level in the US. There's this self-fulfilling prophecy of math being hated by students, and so students generally hate math which is not conducive to learning it. Good math teachers are also extremely difficult to find and keep, and usually the graduation requirement is only the final algebra class offered at the school. The last math class I took before university was in 11th grade. Had to relearn some algebra and trig at the start of college.

Math education is so poor in the US that I'm surprised we have a functioning economy at all.

I'm surprised no one has mentioned graph theory.

Are you sure? I'm struggling in Calc II right now thinking when I will ever fucking use solids of revolution in life.

...

analysis is the framework for financial mathematics

thanks I appreciate it. thanks for the input also.

real linear algebra is way more difficult than calc

That's an unfair comparison. Real calc (real analysis) is way more difficult than real lineal algebra.

I was talking about 'real' as in reality, not real numbers

Yea me too. Analysis is harder than algebra.

*linear algebra. I don't want to get some fagg upset.

Don't forget A Level Further Maths; Americans are brainlets

IMO analysis is practical while linear algebra is more theoretical with topics like vector space homomorphisms

linear algebra seems like something that should be pretty easy but the way it's presented confuses the fuck out people

>linear algebra is theoretical
If you knew your physics you wouldn't say that. Actually, this is the first time someone tell me that linear algebra is less practical than analysis.

Where the fuck do you go where you learn that shit as a 2nd year?

The University of Internet Lying

CS fag here

>when I will ever fucking use solids of revolution in life
It's taught in calc 2 as just an application of integrals. It's also meant to give some intuition on how you can use integrals to solve weird volume related problems. The main reason why it's so standard is because it's a prelude to surfaces of revolution. Both surfaces and solids of revolution can be used to describe the surface area of an object (which is pretty important when it comes to anything at all that has to do with vectors), without needing to take tons of measurements.

Okay understood. I was self taught and basically just followed khan acadamy and played around until I understood what matrices were, how to multiply vectors by them, transformations, etc. Enough for 3D gamdev. Apparently there's a lot more to it.

I loved my Numerical Analysis class.

Off the top of my head: General relativity for GPS.

Ignore trolls

I took calc 1 and 2 in high school and calc 3 my first semester of university

The top students (like 3 per year) even took calc 3 their senior year of high school

Oh and ignore the anti-public-school Betsy Devos shills, this was at a public school.

All of them. Everything you will ever take in undergraduate mathematics has loads of real-world applications.

>Linear algebra
Vector spaces crop up in literally everything, doesn't need to be defended

>ordinary and partial differential equations
used to understand literally every real-life dynamic event.

>probability
doesn't need defense

>real analysis
prerequisite for measure theory which, for one, enables you to study probability on anything but a superficial level, prerequisite for studying fourier analysis on anything but a superficial level

>mathematical modeling
basically the subject of applying math

>combinatorics and graph theory
used in dozens of computer science applications, hardly needs defending

>number theory
all of cryptography relies on understanding number theory

>abstract algebra
if you want to understand tensor products as they're used in engineering and physics on anything but a superficial level, you're going to be learning abstract algebra. quaternions or octonions, as well

>complex analysis
ever opened a physics, EE textbook?

>differential geometry and riemannian geometry
ever open a physics textbook? useful in robotics from what i've heard as well

and these are mostly pure math subjects, as well. even the most seemingly detached, theoretical mathematics is extremely useful in many cutting edge areas.

you see, if your objective in life is to be a basic bitch engineer out to earn money, then yeah, none of this will probably matter, but really neither will you. if you want to be anything important in your field then you'll be better off knowing some of these areas.

but we all know you're just shitposting because you want to get your engi degree with your 3.2 GPA and go earn that totally possible 6 digits starting with as little work as possible.

The fact that you even ask this goes to show you're not gonna achieve anything in life.

have you have heard the term "digital". How about "circuit"?

math is a tool. being specializing in math is like specializing in using a hammer

where as a masterrace physicist is the master of tools, an intellectual craftsmen

>where as a masterrace physicist is the master of tools, an intellectual craftsmen

This 2bh

>Not knowing that Veeky Forums is literally fedora: the board

you will take a course named mathematical method or something similar using a book like the mary boa text. this will cover relevant stuff from upper division math.

even an intro proof based linear algebra is harder than calculus

I want to fuck this pikachu really really hard. Is that normal?

no

yeah

No, it's very ...

...

...

shocking.

define what useful means to you

What are some intro books and mid-tier books on optimal control for an EE?

Books like these will cover relevant material from upper division math courses. You would rarely need a full course in these areas like math majors take. These books are used in mathematical physics - the year long sequence physics majors take. Also engineers take numerical methods a applied version of numerical analysis - so numerics are covered.

amazon.com/Mathematical-Methods-Physics-Engineering-Comprehensive/dp/0521679710/

amazon.com/Mathematical-Methods-Physical-Sciences-Mary/dp/0471198269/

I went to CSUN and we had these ECE classes that covered relevant math methods as applied to common EE situations.

catalog.csun.edu/academics/ece/courses/ece-309/
catalog.csun.edu/academics/ece/courses/ece-455/

Thanks user

>CSUN
>going to a shitty school in the shitty C Uni system

wow m8, no one should take this advice

I went to UC San Diego for my freshman year and did not like it, so I transferred to CSUN.

Like many others I was rejected by CAL/UCLA but accepted by several of the reject campuses.

Well written post. Have a (you).

Maybe, I'll have to see in 4 years

why do you have physics in your math curriculum