Is it normal for 13-15 year olds to be doing early calculus?

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Starting calculus at a young age, such as 13, is viewed as early but not unreasonable, especially if the student has a solid grasp of basic math. Many participants in the discussion share their experiences of beginning calculus in their early teens, with some expressing that it can be mastered with the right understanding and interest. Concerns arise about the social implications of advanced math study at a young age, with some suggesting that it might hinder social development. However, others argue that it is possible to balance academic pursuits with social activities and that math can be a fun and engaging subject. The importance of a supportive educational environment and good teaching is emphasized, as well as the need for students to pursue their interests without feeling pressured. Ultimately, the consensus is that there is no "right" age to learn calculus, as long as the student is capable and enjoys the subject.
  • #31
calculus is a great math, gives u a whole new perspective. I took calc 1-3 and diff eq besides 2 semesters of discrete math and a semester of linear algebra. Currently i am taking probability theory and I'm a senior in high school. Whatever keeps you from getting bored it worth it.
 
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  • #32
How are you taking three semesters of calculus and differential equations in high school? Are you attending community college part-time?

- Warren
 
  • #33
i was in the UB gifted math program and that's how i took the 2 semesters of discrete math in by 11th grade year. I also went to them saying i wanted to take calculus so they got me registered for the college, its SUNY at Buffalo. Anyway i took calc 1 last summer and calc2,3 last fall/spring. then linear algebra and diff eq this past summer
 
  • #34
the key issue is whether the topic is enjoyed by the user, not the difficulty.

obviously sdemjanenko is enjoying his experience and the other kid is not.

besides difficulty is all in the eye of the beholder or the skill of the teacher.

anything can be explained in an elementary way by someone who understands it.

there is nothing difficult about algebraic topology if it is selectively presented by some one who likes it.

i have taught euler characteristics to 2nd graders, by handing out cardboard polyhedra and letting them color them, and count the facets.

one of those children, now grown up, is an aeronautical engineer.

there was an 11 year old named lenny eng, in my 12 year old son's summer math class at duke tip. lenny loved pure math and is now a famous mathematician of some kind. But my son wanted to do something else.

actually he enjoyed the well - taught summer program at duke, but when he got home i tried to cram more down his throat than he wanted.

the whole matter concerns extracurricular activities that are enjoyed and self chosen, versus those that are force fed.

unfortunately parenting is not something we all get adequately trained for.:smile:
 
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  • #35
sry i did not respond earlier i went to a college fair today with my friends
 
  • #36
concerning socialization, i don't hang out with friends too much, but that's because there are not a lot of people i find interesting. They are all talking about trivial matters, things that are not current, isn't news or intellectual related. I suppose getting into the right college is the most important thing. Just to meet other people like you. After all, if you are highly talented you can't just expect it to develop, there is some sacrifice.
 
  • #37
It's perfectly OK. I read calculus when I was 12 or so (off my own bat). It wasn't covered in school till I turned 15, but by then I had mastered the basic stuff.
 
  • #38
sdemjanenko, you really need to relax a bit and loosen up some. Not everything has to be intelectually stimulating.
 
  • #39
i read mostly comic books as a kid, and still like them now. i only learned a little calculus for the first time in college, but did not understand it much until grad school. still i have over 500 pages of published refereed research in mathemaics journals, an NSF postdoc at Harvard, dozens of international conference invitations, and hundreds of thousands of dollars of grant moneys. lighten up. there is a lot of time left to do mathematics.
 
  • #40
mathwonk said:
i read mostly comic books as a kid, and still like them now. i only learned a little calculus for the first time in college, but did not understand it much until grad school. still i have over 500 pages of published refereed research in mathemaics journals, an NSF postdoc at Harvard, dozens of international conference invitations, and hundreds of thousands of dollars of grant moneys. lighten up. there is a lot of time left to do mathematics.

I have to say thank you for posting this, this truly is one of the most reassuring and enlightening thing I have heard/read about the field of mathematics for the last two or three days.
 
  • #41
as for socialization, there are other people out there interested in math, I wa lucky enough to meet someone who was very interested in math and physics during my freshman year of high school. There are other people out there who share your interests (alhough it is a good idea to have more to talk about than mathematics).

also be sure that your not pushing yourself because of any pre-concieved notions about what makes a person smart, similarly if your judging conversations to be to unintllectual than you have to ask yourself whether or not your doing that because you have some pre-concieved notions of what smart peopple talk about etc.
 
  • #42
well...as a kid myself...

childhood n teenhood will just go away in an instant...don't push yourself too much, but this doesn't mean that u should get involved in inmorale activities.

follow your heart, but make sure your mind reasons for it.
u can dream but don't make your dreams your master...worst if u become a slave to someone else's dreams.

in the end it is all up to u ...u make the choice ...but also keep your mind open to advices...

for instance, advices of all of these ppl who have replied to your thread...but like what mathwonk said...respect your parents experiences as well...u have to tell it now or never, talk with your parents...

may it be your hopes n dreams come true!

~smile always~ :D

16yr old
 
  • #43
as for socialization, there are other people out there interested in math, I wa lucky enough to meet someone who was very interested in math and physics during my freshman year of high school. There are other people out there who share your interests (alhough it is a good idea to have more to talk about than mathematics).
It is an excellent idea to have more to talk about than mathematics and I can't see how mathematics in some way prohibits one from being talkable in other areas.
 
  • #44
Quote from a friend of mine
"my nephew is 12 and taking calculus"

Response from a mutual friend
"that boy is never going to have a date"

Sadly, my own high school experience bears this out. There was not one person who was taking higher level math (over algebra II) that was actively dating or socializing with the general population of the high school. The people I knew well in the high level math group were almost incapable of talking about normal high school or regular teenager stuff. I was kind of on the fringe between the 2 groups and got along well with both. I may have been smart enough for the high level stuff, but lazy enough to just coast through with C's and b's.

If only I knew then what I know now :).
 
  • #45
Never be afraid to push yourself harder in learning if that's what you're interested in. Schools dumb things down - it is always worth going beyond what an ordinary school can be bothered to teach you - and there will always be someone better than you even then. What you're doing is giving yourself a chance to compete with them.

Oh, and books written for schools are appalling. Throw them in the bin, and get some elementary (foundation/freshman) college books. "Physics" by Hans C. Ohanian is good for the basics - ever so slightly below first year college level. I wouldn't recommend it for actual college work, though.
 
  • #46
wow, i wish i was taught things earlier, your lucky. Then again i was busy messing around with friends, probably wouldn't have had the time to work. ;)
 
  • #47
I didn't take education seriously until I was 17.

It's not a race.
 
  • #48
If you grasp calculus at an early age... you should learn some C/C++ coding to develop physics-based FPS games...then you can reallly wow your friends...or get a job

Also at least your parents are taking an interest into your academic life
 
  • #49
In many Asian countries, you have your first mandatory calculus class when you are 13 - 15.
 
  • #50
Calculus used to be mandatory in the UK at the age of 15...until it was deemed "too hard" and pushed up to be learned at 17 instead. I think everyone should at least be shown some calculus at high school to get an appreciation of the power of maths.

Some of the basic rules of calculus are not as difficult to learn as standard high school algebra.
 
  • #51
if you want a good physics book settle for physics for scientists and engineers, both titles are fine, serway is great as is fisbane
 

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