Mathematics!!

[GoldLynx]

Fellow Nerds,

 

Join this discussion if you love math and science (but especially math)! Or, if you have a math question, post it here. Math-savvy nerds will get back to you shortly.

Math and science knowledge are essential to completing many tasks. They're like superpowers! From numberphiles to calculus nerds, from physics fanatics to chemistry crazies, this is the place for all STEM aficionados!

 

Let's go crazy!!!!!!!!

[Gainsdalf the Whey]

Just finishing my masters in mechanical engineering. Joining here for the funz of solving math and physics probs for people.

[goodbye_farewell]

Masters in Physics here!

[Ahyar Dreamspark]

B.Sc in bio/chem and M.Sc in organic chemistry here. Nothing too math-heavy, though.

 

I have a love/hate relationship with math. I was rocking it when I was in first grade...to the point where I got bumped ahead to second grade. I liked it when math was easy and everyone thought I was a super star. Easy things were fun to do, and less easy things were less fun. Grade two was tolerable, as was grade three, but at this point I was average at best. There were only four people in my grade (yay, combined classes in a tiny school!) and when long division came around in grade 4, I was starting to feel like I was retarded since all the other kids in my grade got it before I did. Going from academic superstar to being the class dunce was not fun at all, and then I just stopped caring. If I was going to be the class dunce, I'd at least be a funny class dunce!

 

Fourth grade was also the grade where we went from work books that we wrote answers into, to "normal" books where you had to copy the questions into your notebook where you would then do the problems. Fuck that noise--especially for the language classes where entire paragraphs had to be copied. Try getting an overly energetic eight-year-old with an overactive imagination to copy shit for 30 minutes and THEN do the actual woek and see how far you get. Anyway, long story short: I thought I was mentally sub-normal in every aspect from grades 4 to 12. There were several other factors that contributed to this way of thinking, but I won't get into that now otherwise this post will turn into a text wall.

 

Fast forward to 2004 where, completely out of the blue, I thought "I want to go to university and have a nice job where I do science things and help the world!" because I was foolish and ambitious, and didn't want to work in fast food for the rest of my life. I was a D- kid in high school, though, so I had to go register to upgrade some courses at the local community college. LET'S MATH!! And let's chem, and let's physics!

 

The academic upgrading course was set up in a "learn at your own pace" environment, so you had your work book, did your own thing, and went to one of the teachers' desks if you got stuck on a particular question or concept. I got to the first math test and...

 

100% WHAAAAAT!??

 

Maybe it was a fluke? But then the second and third tests also came back with 100%. The realization that maybe I wasn't retarded after all was probably one of the best feelings I've ever experienced. Apparently all I needed was internal motivation, and to be out of the toxic high school environment.

 

I was mostly able to succeed at math in university. The main issue with the program I was in and the way I had split my courses was that I'd do well in a math course, then did no math courses for a term or more, and then would need the math I had learned previously in a new class. Apparently brains and math are like muscles and lifting: and any gains made disappear quite quickly when you stop doing it. I realize now that this is completely normal, but at the time I (surprise, surprise!) still felt like a complete idiot, especially if my GPA was at stake because one's personal worth in academia is tied to their GPA. When I actually had the time to learn math properly, though, I found it incredibly interesting...and fun It just wasn't fun when it had to be rushed or half-assed (or worse, not done at all) because you had a paper and an assignment due the next day and a midterm the day after and you're running on 3 hours of sleep per night the entire week.

 

I probably suck at math now, just because I haven't done it in a while. I know that math can be fun and that it is useful to many things in life, but I just never get around to practicing it. Does a web site exist somewhere that offers casual math practice and teaching or something?

[AugustaAdaByron]

Hello! Joining to stalk the thread.

 

[Girl-Meet-World]

 

 

Going from academic superstar to being the class dunce was not fun at all, and then I just stopped caring.

This is exactly how I feel! In Year 1-6, I was the best in my school. I went to a community school, and my mother really pushed my education. I mean, perhaps finding the answers to the tests she set me was more fascinating than the test themselves, but without her I wouldn't be nearly as intelligent (maybe ). But then I get accepted into a grammar school, where you need to pass a test to get in, and I'm in the comfortable bottom. Okay, i can deal.

I push myself up into lower top half in all (except French - but watch as I get an A in that), and I'm doing great. 10 A* to A. Amazing. (lol, sorry). I'm actually fabulous. Then watch as I go to sixth form, and new students come in, and I'm in the top class of maths for the entire school. I'm getting Fs and Ds and one memorable U. I'm breaking. I love maths, but, going from an average of A* to a C is really hard for me, and I have zero motivation for the subject. I used to love it - I was good at it, and thrived from the challenge of these puzzles. Now, when I barely understand the question, and the rest of the class is zooming ahead, the motivation plummets sharply. And I don't even have the reassurance that I'm still in the top class. The other maths groups are all passing me. For a year wide test (for students taking maths), I come second last. Pissed off doesn't even begin to cover it. 

How do I possibly save my love of maths? I still love probability and mechanics (useful as I want to go into Engineering - possibly in Germany), but I'm feeling really negative about continuing it as an actual subject.

I want to do a major minor of Mech Eng and Theoretical Physics, but the amount of maths in my future is making me cry. Help?

 

[Estrix]

OK, I'll post a question that occurred to me the other day when I was driving. If you change the base you're counting by, do you get fewr prime numbers as the base shrinks below base 10 and more as the base expands above base 10?

 

Seems to me that the first part must be true, that there are fewer primes as the base counting shrinks towards base 2, but can't decide about the second part. I think you might just get the same primes by different names lol.

[goodbye_farewell]

OK, I'll post a question that occurred to me the other day when I was driving. If you change the base you're counting by, do you get fewr prime numbers as the base shrinks below base 10 and more as the base expands above base 10?

 

Seems to me that the first part must be true, that there are fewer primes as the base counting shrinks towards base 2, but can't decide about the second part. I think you might just get the same primes by different names lol.

I don't have time to think about this right now, but the question very much reminded me of the Euler Project. I loved working these problems in my spare time...

 

https://projecteuler.net/archives

[goodbye_farewell]

OK, I'll post a question that occurred to me the other day when I was driving. If you change the base you're counting by, do you get fewr prime numbers as the base shrinks below base 10 and more as the base expands above base 10?

 

Seems to me that the first part must be true, that there are fewer primes as the base counting shrinks towards base 2, but can't decide about the second part. I think you might just get the same primes by different names lol.

Damn question stuck in my head now! So, lets think about this question some more. How do we define a prime number in bases greater than 10 since they can contain letters?

 

This led me to so Googling and ran across this... http://mathforum.org/library/drmath/view/55880.html

A prime is a prime no matter which base you use to represent it. On the surface one might think that in Hex you would have 3*5 = 15 as "usual," but it really turns out that 3*5 = F. The example 21 doesn't work too well because it is not prime. The base ten number 37 is better, because it is prime, but its Hex representation is 25, which sort of looks non-prime. Hex 25 is not, however, repeat not, 5 squared.   Okay, enough for examples. The fact of being prime or composite is just a property of the number itself, regardless of the way you write it. 15 and F and Roman numeral XV all mean the number, which is 3 times 5, so it is composite. That is the way it is for all numbers, in the sense that if a base ten number N has factors, you can represent those factors in Hex and their product will be the number N in Hex.      Relating to your question about base 13, the base ten number 13 will be represented as "10" in that system, but "10" will still be a prime, because you cannot find two numbers other than 1 and "10" that will multiply together to make "10". I hope this helps you think about primes in other bases.

[Gainsdalf the Whey]

That's what I figured it would be. Changing the base only changes the symbols used to represent a number of things, but the number of things is still the same. Since the number of things is still the same, you can still either divide it or not divide it into equally sized smaller groups.

 

21 in base 10 and 41 in base 5 still represent this many things:

 

X X X X X X X X X X X X X X X X X X X X X

 

which can still by divided into three groups of this many things:

 

X X X X X X X

X X X X X X X

X X X X X X X

 

No matter what base you use, the factors remain the same, but are just represented differently symbolically in that base. In base 10, the factors are represented by the symbols 3 and 7. In base 5, they are represented by the symbols 3 and 12. But count wise, those factors each are this many things respectivly:

 

X X X

X X X X X X X

 

So basicically, any mathematical property of a number of things is carried through with base conversions, because it still represents that number of things. Any properties dealing with the number of digits and patterns of the symbols themselves (anything times 10 you just add a zero to the end for example) may not carry through, because those are properties of the symbols used to represent a number, not the number itself.

[Estrix]

Glad I had a question that got stuck in some ones head lol

 

Thanks for the answers though, that does makes sense. Prime is a property of the number regardless of what symbols represent it. Can finally get this one out of my brain.

 

Although Gainsdalf's comment up there about "symbols used to represent the number, not the number itself" leads down some almost metaphysical rabbit hole. Although I suppose it must be true that numbers and the symbols that represent them are separate things.

[AugustaAdaByron]

Although Gainsdalf's comment up there about "symbols used to represent the number, not the number itself" leads down some almost metaphysical rabbit hole. Although I suppose it must be true that numbers and the symbols that represent them are separate things.

 

That would be the difference between numbers and numerals! 

 

[Oramac]

Wow.  So I'm not even close to on par with all y'all.  I don't understand half the crap in this thread.  

 

That said, I do like math that applies to things.  I have a B.S. in Automotive and quite enjoy figuring numbers as they relate to mechanical operation of engines and things.  Finding a way to cram more fuel/air into an engine and bump up the torque/horsepower numbers is always fun.  

 

Course, it's not quite as much fun as using the extra power to shred some tires.......

[Gainsdalf the Whey]

Wow.  So I'm not even close to on par with all y'all.  I don't understand half the crap in this thread.  

 

That said, I do like math that applies to things.  I have a B.S. in Automotive and quite enjoy figuring numbers as they relate to mechanical operation of engines and things.  Finding a way to cram more fuel/air into an engine and bump up the torque/horsepower numbers is always fun.  

 

Course, it's not quite as much fun as using the extra power to shred some tires.......

 

Wish I lived in an area where it would have been worth it to go automotive. I find the mechanics so interesting. I went basic ME and have all the basic stress and thermo theory, but we never actually studied any actual mechanical systems.

[Oramac]

Wish I lived in an area where it would have been worth it to go automotive. I find the mechanics so interesting. I went basic ME and have all the basic stress and thermo theory, but we never actually studied any actual mechanical systems.

 

It's definitely worth checking out.  Hell, with the stuff you posted already, automotive math ought to be a cakewalk for you.  The numbers can get really small though sometimes, especially in transmissions with .0001" tolerances.  

[Gainsdalf the Whey]

It's definitely worth checking out.  Hell, with the stuff you posted already, automotive math ought to be a cakewalk for you.  The numbers can get really small though sometimes, especially in transmissions with .0001" tolerances.  

 

I've dealt with that on and off with some hydraulic systems. The manufacturing processes get pretty cool with those tolerances.

[Maj. Bloodnok]

This whole thread has me singing Tom Lehrer songs.

 

Specifically "Lobachevsky" and "New Math".  :-)

[goodbye_farewell]

It's definitely worth checking out.  Hell, with the stuff you posted already, automotive math ought to be a cakewalk for you.  The numbers can get really small though sometimes, especially in transmissions with .0001" tolerances.  

You think that is a small number? Take a Quantum Mechanics class    Better yet, check out the big numbers in Astrophysics!

[Estrix]

This whole thread has me singing Tom Lehrer songs.

 

Specifically "Lobachevsky" and "New Math".  :-)

"It's not the answer that matters as long as you understand the theory" I love Tom Lehrer!

 

Thought I'd post another interesting idea I read awhile back, written by Paul Lockhart. Basically he suggests that there is no good reason for a circle to be composed of 360 degrees, and for all other angles to be calculated as parts of 360. This division is essentially historic and unnecessary.

 

Instead he suggests that 1 would be a better degree reference for a circle, and everything becomes a fraction of 1. And for regular polygons this seems to work pretty well: Corner of a square 1/4, corner of a triangle 1/3, corner of an octagon 1/8 etc.

 

This also allows you to easily create patterns with polygons (think Moorish tiling) because you know the shapes always fit together as long as the joining corner equal 1.

 

I think it's a pretty neat and simple idea. Wondered what everyone else thinks?

[goodbye_farewell]

"It's not the answer that matters as long as you understand the theory" I love Tom Lehrer!

 

Thought I'd post another interesting idea I read awhile back, written by Paul Lockhart. Basically he suggests that there is no good reason for a circle to be composed of 360 degrees, and for all other angles to be calculated as parts of 360. This division is essentially historic and unnecessary.

 

Instead he suggests that 1 would be a better degree reference for a circle, and everything becomes a fraction of 1. And for regular polygons this seems to work pretty well: Corner of a square 1/4, corner of a triangle 1/3, corner of an octagon 1/8 etc.

 

This also allows you to easily create patterns with polygons (think Moorish tiling) because you know the shapes always fit together as long as the joining corner equal 1.

 

I think it's a pretty neat and simple idea. Wondered what everyone else thinks?

 

I'll stick with the radian     Super easy to work with and lots of built in conveniences.

 

Oh, and the 1 based system you are describing is referred to as a "turn"

[Gainsdalf the Whey]

Wouldn't the inside angle of a corner of an equilateral triangle be 1/6 of a circle? And that of an octagon would be 3/8. Not sure I'm tracking the math.

Sent from my iPhone using Tapatalk

[Oramac]

You think that is a small number? Take a Quantum Mechanics class    Better yet, check out the big numbers in Astrophysics!

 

Haha.  Well, yes, that's true.  But I was talking about numbers that are actually used in real mechanical devices right now.  Naturally there are smaller numbers, but it's pretty tough to measure .0000000001" with a micrometer.  

[insanity]

OK, I'll post a question that occurred to me the other day when I was driving. If you change the base you're counting by, do you get fewr prime numbers as the base shrinks below base 10 and more as the base expands above base 10?

 

Seems to me that the first part must be true, that there are fewer primes as the base counting shrinks towards base 2, but can't decide about the second part. I think you might just get the same primes by different names lol.

You'd have the same number of primes, no matter which way you go. Infinite... :-)

[GoldLynx]

B.Sc in bio/chem and M.Sc in organic chemistry here. Nothing too math-heavy, though.

 

I have a love/hate relationship with math. I was rocking it when I was in first grade...to the point where I got bumped ahead to second grade. I liked it when math was easy and everyone thought I was a super star. Easy things were fun to do, and less easy things were less fun. Grade two was tolerable, as was grade three, but at this point I was average at best. There were only four people in my grade (yay, combined classes in a tiny school!) and when long division came around in grade 4, I was starting to feel like I was retarded since all the other kids in my grade got it before I did. Going from academic superstar to being the class dunce was not fun at all, and then I just stopped caring. If I was going to be the class dunce, I'd at least be a funny class dunce!

 

Fourth grade was also the grade where we went from work books that we wrote answers into, to "normal" books where you had to copy the questions into your notebook where you would then do the problems. Fuck that noise--especially for the language classes where entire paragraphs had to be copied. Try getting an overly energetic eight-year-old with an overactive imagination to copy shit for 30 minutes and THEN do the actual woek and see how far you get. Anyway, long story short: I thought I was mentally sub-normal in every aspect from grades 4 to 12. There were several other factors that contributed to this way of thinking, but I won't get into that now otherwise this post will turn into a text wall.

 

Fast forward to 2004 where, completely out of the blue, I thought "I want to go to university and have a nice job where I do science things and help the world!" because I was foolish and ambitious, and didn't want to work in fast food for the rest of my life. I was a D- kid in high school, though, so I had to go register to upgrade some courses at the local community college. LET'S MATH!! And let's chem, and let's physics!

 

The academic upgrading course was set up in a "learn at your own pace" environment, so you had your work book, did your own thing, and went to one of the teachers' desks if you got stuck on a particular question or concept. I got to the first math test and...

 

100% WHAAAAAT!??

 

Maybe it was a fluke? But then the second and third tests also came back with 100%. The realization that maybe I wasn't retarded after all was probably one of the best feelings I've ever experienced. Apparently all I needed was internal motivation, and to be out of the toxic high school environment.

 

I was mostly able to succeed at math in university. The main issue with the program I was in and the way I had split my courses was that I'd do well in a math course, then did no math courses for a term or more, and then would need the math I had learned previously in a new class. Apparently brains and math are like muscles and lifting: and any gains made disappear quite quickly when you stop doing it. I realize now that this is completely normal, but at the time I (surprise, surprise!) still felt like a complete idiot, especially if my GPA was at stake because one's personal worth in academia is tied to their GPA. When I actually had the time to learn math properly, though, I found it incredibly interesting...and fun It just wasn't fun when it had to be rushed or half-assed (or worse, not done at all) because you had a paper and an assignment due the next day and a midterm the day after and you're running on 3 hours of sleep per night the entire week.

 

I probably suck at math now, just because I haven't done it in a while. I know that math can be fun and that it is useful to many things in life, but I just never get around to practicing it. Does a web site exist somewhere that offers casual math practice and teaching or something?

Congratulations on your success!! There is a website that offers exactly what you're looking for. I've used it in the past to brush up on statistics. You can practice all sorts of problems from any type of math. Guess what?? I can't remember what it's called! I will let you know when I think of it.

[GoldLynx]

Masters in Physics here!

:-O *bows in respect*

Seriously, that's awesome.