Another math problem! (Not HW)

[ozz]

You didn't happen to sit like, to the front-left of me, did you? <_<

nigga i dont know i was a row from the far left

[Julian]

oh nevermind lol. I have no idea who you are, guess I'll just have to wait

edit: wait, far left as in.. looking from the seats to the board, or the other way around?

[Max™]

Euler didn't even know about the complex form when he wrote it, but yeah it would be less confusing to add in the 0i, but they can also be assumed to preserve the aesthetic.

[ozz]

oh nevermind lol. I have no idea who you are, guess I'll just have to wait

edit: wait, far left as in.. looking from the seats to the board, or the other way around?

as in, near the windows...i was really late and walked across the class while he was talking

[joft]

I'm not sure which edit of my post you saw, because I edited the wording 30 times, but I understand that.

If you know you're strictly dealing with complex number, and that every terms (including the 0 and 1) are complex number...then sure (it's still an ugly notation, but it's correct). However, I'm ready to bet most people think of this 0 and 1 as real number, not complex number. That's why i'm saying this equation is misleading.

but real numbers ARE complex numbers

[Trajan]

Euler didn't even know about the complex form when he wrote it, but yeah it would be less confusing to add in the 0i, but they can also be assumed to preserve the aesthetic.

That's a lie, Euler knew everything.

[Julian]

as in, near the windows...i was really late and walked across the class while he was talking

Can't say that I was really paying attention <.<

Just gotta wait til thursday, I guess

[Kaylia]

but real numbers ARE complex numbers

Why are they complex numbers more than R² elements? Especially when there is a bijection between C and R² .

Again, I've no issue using an equation like this, because it's obviously a complex equation, but I still think Euler's identity is ugly like this, despite what many mathematicians seem to think.

[Woozie]

physics is applied math, somehow i think if anyone's that interested in a subject so heavily rooted in math (which is something they at least like) they won't have any trouble with it

Kinda late, but I just noticed this post. You'd be surprised at how many physics majors suck at math. I took a graduate level math course in the physics department with all graduate students last year, and wow, they really suck at math. To be fair, two of the grad students got their undergrad degree in chemistry and then decided to switch to physics. But they didn't really perform any worse than the people who had a degree in physics (and thus should have known everything in this course before even taking the course. Heck, the fact that this course was even offered to grad students says a lot. We only covered topics that anyone with a B.S. in physics should already know, so the course should have been for undergrads and grads who got their degree in chemistry or something). So far I've only personally met a handful of physics grad students who are half decent in math. I know there are tons of physics majors out there who excel in math, but it seems to me that the ones who suck in math outnumber those who don't.

How can someone be a physicist if they aren't good in math? Yeah, it makes no sense to me either, but it definitely happens a lot.

Edit: Well to be fair, unless your in theoretical physics, math is only a part of what you do (sometimes it's a huge part, some times it's a small part. Depends on what you do). Those chemistry majors are much better suited for the type of research we do here than I am. I mean, the physics department hired me because they needed a mathematician, but they hire much more polymer science and chemistry oriented people than math people. Personally, I don't see why our department doesn't just collaberate with the actual chemistry, polymer science, and math departments instead of stealing their students.

[Ramor]

I suppose I'm noticing more and more what you mean Woozie, I'm in like the entry-level undergrad physics that uses calculus right now ('particles in motion' basically), and I'm utterly shocked at how many people ask the most retarded algebra questions during lecture, not to mention how many get absolutely lost if you throw an integral into any equation, which was supposed to be a prereq to even take the class.

Not sure how my future physics will go, but I'm not too worried. We've already done quite a bit more physics in my diff. eqs. class than we really have in my actual physics class right now to be honest.

Edit: it just really sucks having super shitty group members who get so lost if I try to math my way through things. Take a calculator from the people in my class and they can't do anything. I can do just about all of my calculus calculator free (with a bit of time), most kids in this class couldn't draw a sine graph it seems like.

[Max™]

Physics math is very application specific.

Like knowing enough html coding to be able to adjust the placement or width of a table, but not being able to actually build a webpage with said table in it.

I'm a perfect example of this, the abelian groups thing earlier, it stood out as obvious to me for some reason, but I couldn't even think of how to phrase it like joft did.

I still say curvilinear coordinates with a properly defined metric would work for the original question, as he wasn't limiting the rest specifically, merely asking for the (0,0) to (1,1) interval to be continuous and equal in length to 1 unit.

[joft]

that's part of what makes math math. even when things seem "intuitively" obvious, proof is still necessary. and that's probably the part of math that frustrates and turns away the most would-be mathematicians, because it's initially very frustrating to have to prove things that are intuitively obvious

[Max™]

Yup, I know I should have been able to point out that all you need is to define the isomorphism like you showed, but I lacked the practical experience to say it.

My head was sitting there beating two rocks together, labeled infinite cyclic and abelian, and I knew they were the same shape but couldn't explain why.... which is why I study math happily, having the language to form these concepts in a provable manner is wonderful.

[Ramor]

It's unfortunate so many people don't like math or choose to not learn it when easily they could. I feel like people are just wanting to do easier majors or areas of study and more and more people are opting out of any sort of critical thinking to take something easy (like psych) which actually is intuitive for the most part and doesn't require much more than a basic latin class to get a bachelors in.

Sigh@society.

[Eliseos]

Kinda late, but I just noticed this post. You'd be surprised at how many physics majors suck at math.

I would say I am not the best at math, but I guess it depends on what you are defining as "suck". I'd say my strengths in applying math to physics lie with purely calculational (according to Firefox, that isn't a word, so I'm making it up and thus showing my weaknesses in English also) problems where I am given enough mathematical information on how to solve it. I am not good at all on proving things (I get lost on how people prove things like the divergence theorem, proving anything in the area of computation theory, or show such and such leads to so and so) on a purely theoretical level. If there aren't numbers involved, I have a higher chance of getting lost somewhere in the sea of greek-letter variables.

Again, it all depends on how you classify suck.

[Kaylia]

Kinda late, but I just noticed this post. You'd be surprised at how many physics majors suck at math. I took a graduate level math course in the physics department with all graduate students last year, and wow, they really suck at math. To be fair, two of the grad students got their undergrad degree in chemistry and then decided to switch to physics. But they didn't really perform any worse than the people who had a degree in physics (and thus should have known everything in this course before even taking the course. Heck, the fact that this course was even offered to grad students says a lot. We only covered topics that anyone with a B.S. in physics should already know, so the course should have been for undergrads and grads who got their degree in chemistry or something). So far I've only personally met a handful of physics grad students who are half decent in math. I know there are tons of physics majors out there who excel in math, but it seems to me that the ones who suck in math outnumber those who don't.

How can someone be a physicist if they aren't good in math? Yeah, it makes no sense to me either, but it definitely happens a lot.

Edit: Well to be fair, unless your in theoretical physics, math is only a part of what you do (sometimes it's a huge part, some times it's a small part. Depends on what you do). Those chemistry majors are much better suited for the type of research we do here than I am. I mean, the physics department hired me because they needed a mathematician, but they hire much more polymer science and chemistry oriented people than math people. Personally, I don't see why our department doesn't just collaberate with the actual chemistry, polymer science, and math departments instead of stealing their students.

That's why I'm taking so many additional maths classes...it was really my weak points, and I felt I was missing too much.

How can you get a physics degree when you suck at maths? You just do it like engineer I guess, figure out how it's done through example, and continue from there. It doesn't lead to a good undertanding of the problems and theories, but it's often enough to pass. I do think it's pointless to do physics this way though, and I don't understand why would anyone be interested in taking physics classes if they don't see the problems with this.

I suppose I'm noticing more and more what you mean Woozie, I'm in like the entry-level undergrad physics that uses calculus right now ('particles in motion' basically), and I'm utterly shocked at how many people ask the most retarded algebra questions during lecture, not to mention how many get absolutely lost if you throw an integral into any equation, which was supposed to be a prereq to even take the class.

Not sure how my future physics will go, but I'm not too worried. We've already done quite a bit more physics in my diff. eqs. class than we really have in my actual physics class right now to be honest.

Problem isn't because they don't understand mathematics. Your understanding can improve if you study...the problem is: if they ask stupid question like this in classes, they probably lack the ability to study on their own, and that itself will hurt their chance greatly on a long run.

I would say I am not the best at math, but I guess it depends on what you are defining as "suck". I'd say my strengths in applying math to physics lie with purely calculational (according to Firefox, that isn't a word, so I'm making it up and thus showing my weaknesses in English also) problems where I am given enough mathematical information on how to solve it. I am not good at all on proving things (I get lost on how people prove things like the divergence theorem, proving anything in the area of computation theory, or show such and such leads to so and so) on a purely theoretical level. If there aren't numbers involved. I have a higher chance of getting lost somewhere in the sea of greek-letter variables.,

Are you sure we are talking about physics? There is literally no number in physics, it's just an orgy of greek letter.

[Woozie]

I would say I am not the best at math, but I guess it depends on what you are defining as "suck". I'd say my strengths in applying math to physics lie with purely calculational (according to Firefox, that isn't a word, so I'm making it up and thus showing my weaknesses in English also) problems where I am given enough mathematical information on how to solve it. I am not good at all on proving things (I get lost on how people prove things like the divergence theorem, proving anything in the area of computation theory, or show such and such leads to so and so) on a purely theoretical level. If there aren't numbers involved, I have a higher chance of getting lost somewhere in the sea of greek-letter variables.

Again, it all depends on how you classify suck.

Well, the best (only) way to learn proofs is by doing them.

How far are you into math? (I'm assuming you're in calc 1, 2, or 3. Correct me if I'm wrong). If you've only taken calculus, it's not that unreasonable for you to not yet be used to proofs. Most calculus or differential equations classes aren't focused on proofs because most of the students there aren't even math or physics majors. So the teachers typically just make sure that if they give you numbers, you can give the the correct answer back (which is also a number). They don't force you to learn proofs. That's probably why you're really good at giving the numerical answers to problems but are unable to do proofs or more abstract calculations involving symbols instead of numbers.

The only way you're going to become familiar with proofs at this point is if you make an effort to learn the proofs in your books on your own (since the teachers aren't going to go through them or force you to learn them). You'll also want to do the homework problems that says "prove [statement]", even though your teacher probably doesn't assign these. Of course, I don't expect every math and physics major to do this because being a student is a busy occupation and you don't always have time to do all of this extra stuff. So I don't blame anyone who's in modern physics and calculus 1,2, or 3 for not being good at proofs. If anything, I'd want to blame the professors for not teaching or showing proofs, but I can't really blame them either because half of their students don't need or want proofs.

You get exposure to derivations on calculus-based physics, which can be similar (or in some cases, the exact same thing) as math proofs, but that level isn't very rigorous in what they do (or they classify the rigorous stuff as "optional", just like they do in calculus).

In physics, it's not until you reach Classical Mechanics (the jr level stuff) that you become required to use proofs or proper derivations. Once you reach this level you'll never again see a problem where the questions and answers are numbers ever again. Ever. Almost every question is deriving or proving something. I can't even remember half my fundamental constants anymore because I rarely use numbers lol. A few months ago someone asked me what planks constant was, and I answered "h bar", completely forgetting that it actually stood for a number

As for math, at my school, it's not until linear algebra where math professors force their students to learn the proofs. Then, right after linear algebra, we have to take Fundamentals of Advanced Mathematics (we call it "FOAM"), which is really just a class on how to do and understand rigorous proofs, as well as an introduction to higher level mathematics and using symbols and set notations and such. If you're interested, the book we use is

A Transition to Advanced Mathematics

Nothing in this book is too high for you to understand at your current level of math (it doesn't even use calculus). And this book will get you very familiar with mathematical proofs. At my school, it's a prereq for virtually every higher level class, and it's probably one of the most important and useful math courses I've ever taken.

The math classes you take after FOAM are similar to physics. Virtually every question is a proof.

For me it was a little different. I taught myself calculus, so I just read the book front to back, and went through every single proof, so I got somewhat familiar with proofs. I also did almost every problem, including the ones that are proofs or derivations. Then my H.S. math teacher found out I taught myself calculus so she had her husband (a math professor) come to my high school once per week, and he made sure I was learning the proofs and derivations instead of just remembering formulas.

So what I'm saying is that as long as you aren't asking questions about stuff you should already know (like the people in Ramor's class), I don't consider your level as "sucking" (well, unless you're like a senior or a grad student or something).

Are you sure we are talking about physics? There is literally no number in physics, it's just an orgy of greek letter.

This is so true. This is what I mean when I say you'll never see numbers again once you reach a certain point. But you will be able to say your ABC's in Greek easily.

[Eliseos]

Are you sure we are talking about physics? There is literally no number in physics, it's just an orgy of greek letter.

For my modern physics class this semester, I'd say 75% of the problems are calculation based. We just got into quantum mechanics about a month ago, so right now we're doing things like calculating the probability of finding some particle in an (in)finite potential well given such and such psi function, the quantum number of some electron given certain parameters, etc.

Well, the best (only) way to learn proofs is by doing them.

How far are you into math? (I'm assuming you're in calc 1, 2, or 3. Correct me if I'm wrong). If you've only taken calculus, it's not that unreasonable for you to not yet be used to proofs. Most calculus or differential equations classes aren't focused on proofs because most of the students there aren't even math or physics majors. So the teachers typically just make sure that if they give you numbers, you can give the the correct answer back (which is also a number). They don't force you to learn proofs. That's probably why you're really good at giving the numerical answers to problems but are unable to do proofs or more abstract calculations involving symbols instead of numbers.

I'm taking Vector Analysis this semester, which is the extension of Calc 3 into more in depth problems of vector derivatives, integrals, Green's Theorem, Divergence Theorem, and Stokes' Theorem (And I guess Curvilinear Coordinates at the end). So "fourth" semester of calc, plus a class on advanced engineering mathematics (matrix manipulation, differential equations, etc). I've actually learned more about differential equations in my Circuits and Modern Physics classes this semester then I did when I was taking the actual classes on them, using your example of some people learning better by example.

I suppose you're right too, the more proofs I can "prove", the better I'll be at them. I guess I should clarify that I can (for the most part) understand proofs already given to me, as long as it's not too rigorous in detail (meaning that they don't use or specify certain concepts that aren't at my level of math education). I just usually have no idea where to start a proof that I have to do for homework or an exam.

[Woozie]

For my modern physics class this semester, I'd say 75% of the problems are calculation based.

Trust me, things are going to be very different next semester and every semester afterwards. Modern physics is the last class with calculation based problems.

Apparently "afterwards" is not a word either.

[Kaylia]

This is so true. This is what I mean when I say you'll never see numbers again once you reach a certain point. But you will be able to say your ABC's in Greek easily.

I wish it was true for me. My brain still read most letters in english/french (nu = v , mu = u...etc). It doesnt really cause any problems when I do equation by myself, but when I'm trying to explain equation to other...it can be quite a mess.

I've been working on this for a bit, but it's really hard to kill the habit.

As for math, at my school, it's not until linear algebra where math professors force their students to learn the proofs. Then, right after linear algebra, we have to take Fundamentals of Advanced Mathematics (we call it "FOAM"), which is really just a class on how to do and understand rigorous proofs, as well as an introduction to higher level mathematics and using symbols and set notations and such. If you're interested, the book we use is

I really wish we had a proper introduction to linear algebra before quantum mechanics. We went from the retarded easy linear albegra classes in college (9 years ago for me), to the introduction of operators, eigenvalues, complex conjugates and hilbert space.

While none of these are particularly hard to calculate, we still skipped one or two classes worth of mathematics that give a meaning to these concepts. Hell, even now, 2 years later, I still have trouble to tell you what an eigen value is.

For my modern physics class this semester, I'd say 75% of the problems are calculation based. We just got into quantum mechanics about a month ago, so right now we're doing things like calculating the probability of finding some particle in an (in)finite potential well given such and such psi function, the quantum number of some electron given certain parameters, etc.

Tighten your seatbelt, because thing will change drastically next year. Introduction to modern physics is still application of known equations. Once you reach classical mechanics, electromagnetic , quantum I and II ...you won't see a real number again. If you see a number, it probably mean you programmed a numerical solution using maple, mathematica or any programming language, but that is in itself a whole new problem. Looking back at it, I don't remember last time I've done "physics" in quantum mechanics. I was probably in a better place to talk about energy level, spin and particles 3 years ago, than I am now.

Kinda offtopic, but I'm always amazed how old physics is. Classical mechanics is 300 years old, electromagnetics is 200 years old, quantum mechanics is 100 years old. It makes me feel bad to struggle on equations that were solved by people 300 years ago...You won't find any domain that age as slow as physics and mathematics