Question on Calculus for a middle schooler

Awesome that your son loves math. I completed the typical HS and College math courses required for engineering. I skill that I employed was to go through the textbook prior to setting foot in the classroom as I needed to see the material multiple times to learn it well and get an A. I did have trouble teaching myself higher math from the old textbooks though.

I'm sure that today's course material is easier to follow. One college math course I found really helpful was "Technical Math 2". I'm not sure if it still exists as a course as I experienced it, but it involved some very fun and detailed math. One course that I hated (I think it was called linear math) involved arrays and matrices, I was instantly bored with it.
 
The one thing I learned about Calculus early on (and found it to be quite true) is this - The Calculus is easy, it's the Algebra that kills you. My Calculus I professor kept reminding us of that from the very first lecture.

Calculus can be thought of as being the rules and methods of dealing with numbers and math. One follows the rules & methods and creates an algebraic equation to solve.

Good luck to your son!
 
I thought the trig was the hardest to grasp.

In my opinion you should get your kid interested in electronic circuits. Op-amps and comparators. Why? You can build differentiators and integrators, which is the stuff of Calculus. Plus, at that age he'll get to learn the supply catalogs, so he'll pick up how to design circuits with commonly-available components.

To me, all the math was very dry without someting to apply it to. Also, it was a bit scary to see how many people hadn't the foggiest idea what were commonly-available components.

Plus, underneath it all every component has physical properties. Not many of them matter to beginner circuits. As one progresses in circuit design the physical properties become important.
 
This is fascinating and I hope he goes far with it.

I am a product of the math deficient generation of the 60’s when the schools went from old math to new math. Even basic algebra became a stumbling block for me.

If the opportunity arises he should meet with someone in a field that uses complicated math.
 
Good evening,

He loves Khan Academy a lot as he has told me that it is a very thorough site and well done.

He loves Physics and Chemistry. Wants to be a Physicist for a career field. He can balance chem equations, but I do not know if that is on the easier side of things as I am chemistry illiterate. Strangely enough, he idolizes Issac Newton and has pictures of a scientist on his wall who killed his own cat in an experiment named Schrodinger. ha!
Those are great goals and I am a Newton fan as well. The history of science is often as interesting as the science itself. The changes in thinking and perspective.

In the meantime - Astrophysics is a fascinating field...

Just sayin'
 
Your son needs to be proficient in trigonometry before starting calculus. It may be useful to study pre-calculus to review the important concepts of algebra 2, trigonometry and geometry before starting calculus. You'll find more information in a Google search
That's what I was thinking myself; Algebra II and Trig are the primary prerequisites for Calculus I. Geometry's sort of a side-line math course that doesn't really build on, or much tie into other math courses at the high school or college level.

I also would have him hold off on physics until after he's had Calculus. I took non-calculus physics in high school and it was a total pain; all sorts of wonky summations and goofy stuff was required, because so much of first semester physics is integrals and derivatives, i.e. calculus.
 
My kids used the schaum series of books for their AP courses. There cheap and include lots and lots of example problems, which is what he needs. I 100% agree he needs to absolutely master albegra and geometry and also pre-calculus which is more or less a combination of the two before he jumps to calculus. One of mine did and had little problem with calculus. The other did not and struggled.
 
Best book ever:

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I took Algebra I in 8th grade and then skipped straight to Geometry. I think that's where I went wrong. I was loosing grasp of it in Algebra I and the Geometry was like another language. Those are the only two math classes in your list that I have completed in the public education system.
Pretty sure our curriculum in NJ in the late 90s was:
-pre algebra
-algebra
-geometry
-algebra 2
-pre-calc
-calc

Starting in 7th grade if you were so inclined.
 
Pretty sure our curriculum in NJ in the late 90s was:
-pre algebra
-algebra
-geometry
-algebra 2
-pre-calc
-calc

Starting in 7th grade if you were so inclined.
We had an Integrated Math 1 and 2 that were supposed to fall in the Algebra 1 and Geometry area but I can’t remember where. I needed 3 credits to graduate so Algebra 1, Integrated Math 1, and Geometry got me there. With being bussed to another school an hour away for automotive technology my junior year there wasn’t time to take a 4th math class.
 
Hi Guys,

I have a 12 year old 7th grade son that is very much obsessed with math. Pretty much what he does in his free time.

He has self taught himself Algebra 1, 2 and Geometry from used high school textbooks and workbooks I purchase for him.

He still has Trig to start.

He is wanting me to get him some Calculus books so he can begin working on that.

I am math illiterate to be quite honest and I have never taken calculus.

He did request workbooks on "Logarithms and Exponentials", not really sure what those are to be honest. LOL

If he has a firm grasp of Algebra 1, 2 and Geometry is there any reason he can't self study calculus or will that be the course he actually will need someone to walk him through it? I want the little guy to achieve all he can, but will spend money and hire someone if I need to.

Thanks guys
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From.what my dad has told me and he is a math major Calculus 1 is a building block that won't make sense till later math. A tutor might not be a bad idea if he wants to jump into higher math. Maybe finding things that correspond. I'm not a math person, but when I took statistics my senior year it was much more interesting when we discussed things like Airlines calculating the number of people who don't show for a given flight. And yes there are people that do that.
 
First, I think it's great he's focused enough and driven enough to study and learn all this on his own. He will go far. It may have been mentioned and I missed it but another resource is free online classes from major institutions like MIT, Harvard etc. You'd have to do a search to see who, if any, offer calculus or any other subject(s) he's interested in but I periodically see promos for them. Not knowing where you are, there may be something available nearby as well that offers auditing classes at no charge. That might lead to finding/meeting a professor who would take an interest in a young math prodigy and offer mentorship. Good luck.
 
Young kids these days can take those courses and get credit for them. So when they graduate from high school they already have a bunch of their college credits.
 
I think calculus is conceptionally very easy to understand as far as derivatives and integrals, especially when viewed from a geometric POV of slopes and making small little rectangles under a curve and multiplying their LxW and adding them all up. Once you get into differentiation and integration with derivatives and anti-derivatives, the fundamental theorem of calculus, chain rule, partial differential equations, etc it gets a little more complex. But, honestly, if he brought himself this far, there's nothing all that much more difficult than what he's already taught himself.

Good for him...a solid understanding of math will always help in life. I don't know if this is still true but 20 years ago Wall Street was the number one employer of newly minted physics PhDs. Actually, it makes sense - they're just people who can apply math to very complex problems.
 
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XB_Fan,
Below are two typical rational functions that a student might be asked about in a differential calculus course. More specifically, they will be asked to identify all points of interest for each of the rational functions. Both of the functions can be quickly graphed on the x-y plane using algebra. The first rational function requires no calculus whatsoever in order to identify all points of interest. In contrast, the second rational function has two points of interest that will require a bit of calculus in order to correctly identify. In my opinion, students that are unable to quickly graph each of these rational functions using their algebra skills could benefit from some additional algebra education prior to starting calculus.
Belker

Rational function #1: y = x^2/(x^2-1)
Rational function #2: y = x^3/(x^2-1)
 
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