Wikipedia:Reference desk/Archives/Mathematics/2011 August 11

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August 11

Length of a golf shot

Can somebody please check that I did this correctly?

I want to find the distance that my golf shot wll travel.

I'm standing on a golf tee which is 1 metre higher than the surrounding ground.

I strike a golf ball with initial impact speed of 50 m/s at an angle of elevation of 45 degrees.

I work out the time it takes to reach the ground with

$-1=50\sin({\frac {\pi }{4}})t-{\frac {1}{2}}gt^{2}$

With g being 9.8.

I solve for t using the quadratic formula and get a time of 7.24355 seconds.

I substitute this into the horizontal displacement:

$50\cos({\frac {\pi }{4}})7.24355$

to get a total distance of 256.0982 metres.

Is this the right distance? — Preceding unsigned comment added by Thorstein90 (talk • contribs) 01:01, 11 August 2011 (UTC)

The equations look right to me. I didn't actually check that t = 7.24355s is a root, but it seems roughly to fit. Rckrone (talk) 02:29, 11 August 2011 (UTC)

Directions in study

Hello. I've recently completed high school mathematics (as it's taught in Australia, at any rate). Before university begins in March, I'm hoping to work my way through a few textbooks on key branches of pure mathematics, partly as preparation but chiefly for my own enjoyment. I have a copy of Spivak's Calculus, which I plan to finish first, but after that I'm not sure where to go. Areas like group theory, topology, axiomatic set theory, number theory, linear algebra, complex analysis, and the theory of probability are all intriguing to me, but I have no idea which I should pursue first. (This is likely due to a lack of appreciation for the way these branches are interrelated in the big picture of modern mathematics.) I understand there's no "royal road" to learning mathematics, and that my question is very general, but could someone suggest a good initial direction along with related textbooks? Thanks. —Anonymous Dissident^Talk 10:40, 11 August 2011 (UTC)

If you plan on doing pure math, logic and set theory are what you need regardless of your specialty. If you plan on doing applied math, linear algebra is the next thing you need after calculus. But the single best thing to learn, in my opinion, is computer programming, which I believe is where all the important action is nowadays. Looie496 (talk) 20:25, 11 August 2011 (UTC)

Plenty of pure mathematicians do just fine without having studied mathematical logic or axiomatic set theory. Sometimes I wish they knew more, but I'm sure algebraic geometers sometimes wish more mathematicians knew algebraic geometry, so I don't think there's anything special there.

Modern algebra and real analysis are traditionally used to develop mathematical maturity, and complex analysis is a beautiful thing (even if I never use it), so you might consider those.--Antendren (talk) 21:33, 11 August 2011 (UTC)

Since you'd be doing this on your own, you may want to find books that aren't purely academic but of more general interest. One idea might be Road to Reality by Roger Penrose, it's actually mathematical physics but there is a lot of pure math in it. It's not a book to actually finish but to see how far you can get before it gets too difficult. You might want to look at A New Kind of Science as well, again difficult to finish but interesting to browse. Another idea for summer reading is mathematical history and biography, turns out there are quite a few mathematicians who didn't just do math all their lives, for example Bertrand Russell was a philosopher, author and political activist. I found learning to read French and German surprisingly useful for mathematics, it's actually much easier to learn to read a language for math than for normal prose. Though maybe by the time you finish university machine translation will have progressed to the point where this isn't needed. A computer language will also be useful I think, which one doesn't matter much since learning one makes it easy to learn others, and it's the same kind of thinking you need to do mathematical proofs.--RDBury (talk) 21:47, 11 August 2011 (UTC)

Thanks for your suggestions. Is topology something to study after real analysis and an introduction to abstract algebra? From what I've read it's a more sophisticated field requiring deeper knowledge. Can anyone recommend a good textbook for an introduction to abstract algebra? I already have a general understanding of set theory and logic (operations, logical connectives, basic theorems, basic paradoxes, functions and relations), so maybe more of that is not necessary right now, especially since many modern textbooks seem to introduce enough set theory at the start for whatever you're reading about. Doing general reading and learning a programming language sound like sensible pursuits too. —Anonymous Dissident^Talk 23:32, 11 August 2011 (UTC)

This is the point in your educational career where you need to completely forget about the educational model whereby subjects are learned in some fixed order, like climbing a ladder. That's a convenient paradigm for school boards, but does little for you.

Topology is not a single subject, but a bunch of them. It's a good idea to learn some general topology (also called point-set topology) at the same time as real analysis. In fact you can't really do real analysis without at least a little bit of it.

On the other hand, you probably should have a decent background in real analysis before you try to tackle the topology of manifolds. At least the elementary notions of measure theory. But once you have enough to follow what is being discussed, whether you learn about manifolds before you go deeper into analysis is a matter of personal preference and goals. --Trovatore (talk) 23:40, 11 August 2011 (UTC)

Okay. I guess my desire to find a "ladder" is related to the desire of understanding how all these fields fit together in the big picture. I assumed that studying some of the main fields in a certain order might help me grasp the general layout of pure mathematics, but perhaps it's naïve to think you can gain that understanding without many years of experience in an assortment of areas. —Anonymous Dissident^Talk 23:46, 11 August 2011 (UTC)

You could perhaps use the book "Real and Complex Anaylys" by Walter Rudin as a reference book. This book is practically self-contained apart form the very elementary stuff (things like definition of limits, derivative, Riemann integral, uniform convergence etc. etc.). Studying directly from this book may be a bit difficult, because new topics are directly used in quite advanced ways and you may then want to go slower. But then you can just study that topic from another textbook. Count Iblis (talk) 00:56, 12 August 2011 (UTC)

I second (third, etc.) the suggestion to learn at least one programming language. I taught myself to program in junior high (back, ahem, before this newfangled Windows OS). It is the single most useful skill I have: I used it several times in grad school to design mathematical models and simulations, and I've had at least three occasions at my current job where I was literally the only person who could delve into an antiquated program written in some god-forsaken language (i.e. COBOL) and figure out what it was actually doing. The language you learn isn't important, since they all work the same general way (except for AI languages like LISP or Scheme). I learned in C and C++, and I've never programmed in either after high school: but in my current position I've worked with Visual Basic, COBOL, and PL/SQL, and I was up to speed in a week at the most.99.100.92.26 (talk) 06:29, 12 August 2011 (UTC)

I don't know if the op is still reading, but ditto on computer languages, not least because people tell me in science, if you want a PhD, they tend to tell you what needs to be done, and you have to decide whether you are willing to do it. It can't work that way for geniuses, but for the rest of us, maths is sooo much better at undergrad level (up to honours). Computing allows you more freedom. That said, one of my favourite maths books for general enrichment and a practical introduction to the deeper rigour of mathematics is Schaum's outline of Topology. Schaum's books are great for maths, because they dive straight in. You can read theory later to fill in the blanks, but maths is about doing. My other favourite is An Introduction to Mathematical Reasoning by Peter J. Eccles. It doesn't cover much that you wouldn't already know, but it helps guide you to writing neat mathematical proofs, showing the scratch work alongside the finished product. One of the books I would take to the moon, alas, if only someone would send me there ...It's been emotional (talk) 04:35, 14 August 2011 (UTC)

physics

1.a ball of mass m1 and block of mass m2 are attached by a light weight cord that passes over a frictionless pulley of negligible mass. The block lies on a frictionless incline of angel q.find the magnitude of the acceleration of the two objects and the tension in the cord? 2.a projectile is fierd up an incline(incline angel q) with an initial speed v1 at an angel q1 with respect to the horizontal (q1>q). (a)show that the projectile travels a distance d up the incline,where d= 2v1squarecosq1sin(q1-q) the all over g cos squareq — Preceding unsigned comment added by 213.55.90.6 (talk) 18:12, 11 August 2011 (UTC)

• As stated above: "If your question is homework, show that you have attempted an answer first, and we will try to help you past the stuck point. If you don't show an effort, you probably won't get help. The reference desk will not do your homework for you." --Kinu ^t/_c 18:19, 11 August 2011 (UTC)

1.a projectile is fierd up an incline(incline angel q) with an initial speed v1 at an angel q1 with respect to the horizontal (q1>q). (a)show that the projectile travels a distance d up the incline,where d= 2v1squarecosq1sin(q1-q) the all over g cos squareq — Preceding unsigned comment added by 213.55.90.6 (talk) 18:25, 11 August 2011 (UTC)

See the header: "If your question is homework, show that you have attempted an answer first, and we will try to help you past the stuck point. If you don't show an effort, you probably won't get help. The reference desk will not do your homework for you." -- kainaw™ 18:31, 11 August 2011 (UTC)

a ball of mass m1 and a block of mass m2 are attached by a light weight cord that passes over a frictionless pulley of negligible mass.the block lies on a frictionless incline of angle ɵ.find the magnitude of the acceleration of the two objects and the tension in the cord — Preceding unsigned comment added by 213.55.90.6 (talk) 18:35, 11 August 2011 (UTC)

Asking more homework questions will not increase the likelihood of any of them being answered. -- kainaw™ 18:39, 11 August 2011 (UTC)

My advice would be to think about the forces acting on each object. Drawing diagrams may help. --Colapeninsula (talk) 10:13, 12 August 2011 (UTC)

math class

What's a better/easier course to take, Intro to Calc I or Linear Algebra 1? — Preceding unsigned comment added by 174.5.131.59 (talk) 22:24, 11 August 2011 (UTC)

What's better, ice cream or cheese? The question is more or less unanswerable as posed. Depends a lot on your goals and approach to mathematics.

One thing I can tell you is that introductory linear algebra is an incredibly easy subject, if you're willing to actually think just a tiny bit, as opposed to memorizing. If the only way you know how to approach a math class is via memorization (this unfortunately describes all but a tiny fraction of first-year university students) then you'll have a rough time in linear algebra.

In some sense it's the first abstract mathematics that most students ever see, and they're just not used to it. If they'd just let it be what it is, they'd be fine, but they insist on trying to make it something else, and it doesn't work. --Trovatore (talk) 22:40, 11 August 2011 (UTC)

If you intend to do much maths in the future, then you're going to need both. Neither particularly depends on the other, so it doesn't matter what order you do them in. If you don't intend to do any more maths, then calculus is more useful in other fields (linear algebra is extremely useful in all sorts of areas of mathematics, but I don't think you'll learn much in a course called "Linear Algebra 1" that would be useful on its own outside of mathematics). --Tango (talk) 23:46, 11 August 2011 (UTC)

I agree with this, except for the last parenthetical remark. Just a little bit of knowledge about coordinate system transformations from linear algebra turns out to be very useful for a lot of computer graphics applications, for example. Regarding the original question, it depends very much on the way the courses are taught. Intro to Calc is probably intended for non-math majors, so it might not be too rough. If the Linear Algebra is meant for math majors, it might include a lot of proofs, which could be a bit of a shock if you're not used to that. 130.76.64.116 (talk) 00:27, 12 August 2011 (UTC)

I stand corrected. I spent some time trying to think of a direct application of linear algebra and couldn't find a significant one. Somehow, I'd forgotten about computer graphics. Thanks! --Tango (talk) 10:11, 13 August 2011 (UTC)

OP here, sorry the course is "Introduction to Calculus I". I don't think Introduction to Calculus is meant for non-math majors, since it's been said to have a high drop-out rate :o

But I'm more interested which one will make it "easier" to study the other. — Preceding unsigned comment added by 174.5.131.59 (talk) 01:06, 12 August 2011 (UTC)

At that level they're going to be pretty much independent. Calculus won't help you at all with linear algebra. Linear algebra won't help you with calculus until you get to differential equations. --Trovatore (talk) 01:54, 12 August 2011 (UTC)