What do I need to know to be ready to take Calculus?

Factual Questions
1

Hello,

Long time listener, first time poster.

As the title suggests, I’m looking for advice on what I need to know to be prepared to take Calculus. I’m thinking learning Geometry, Algebra I and II, and Trigonometry will set me up nicely. Anything I’m missing or are any of my choices not needed?

That paragraph serves as a tl;dr version, but I’m a nerd who tends to be inclined to write walls of text. If anyone is interested in the context, read on.

I am in my mid 30s and dropped out of college after a year my first time. I worked in production, music, theater and video, and built a decent multimedia skillset. I’ve worked at a number of companies that offered L&D programs, and leveraged them to build skills over the years.

I first become a presentation specialist based on strong knowledge of MS-Office. Later I picked up Photoshop, Illustrator and In Design. I learned Avid, Final Cut, Avid, After Effects, etc and put together a nice career around video production specializing in post-production. Not having a degree always felt like it held me back.

About 2 years ago, I got an offer to work at a fairly high-end engineering college. I accepted, and a benefit is free classes. I’ve engaged in a multimedia-based degree with a minor in CS, and have been cherry-picking classes as a non-matriculated student. I went with things that would help my job - animation, motion graphics, digital imaging, etc. Good times. Quality knowledge. Throw Maya on the ‘known software’ list.

But now I’m matriculating in the fall, and will have to take the general ed requirements, including Calculus. I dread math. Loathed it as a high school student. Passed Geometry and Algebra 1 and failed Algebra II. Think I got out of HS without having to take any more math. To be fair, my failure was born of boredom, laziness, and distraction rather than capability. I enjoyed understanding what mathematics can do, and was interested in the general concepts, but not interested in showing my work and repeatedly solving problems. I didn’t do homework.

I’ve recently taken some history of sci/tech classes at this college as well, and I was inspired to learn that all great thinkers of antiquity tended to have a base in math. I particularly enjoyed learning of the sign, legend suggests hung outside of Plato’s Academy, which read: 'Let none ignorant of Geometry enter".

The professors are my co-workers, so poor performance is out of the question, as it will negatively affect my reputation and career. I am committed to learning mathematics - to improve myself, to protect my career, and because it seems like a worthwhile pursuit.

Anyway, I have to play catch up. I’m planning on using Kahn Academy to facilitate my learning cheaply. A google search on 'Calculus prerequisites" suggests I should maybe not worry about geometry. Seems important, though, if Plato’s sign is to be believed. I’m also going to have to take Physics at some point and the CS minor will require a bunch of algorithm business.

Any advice appreciated.

2

Trig, definitely. Memorize as many of the “Trig Identities” as possible – such as 1/sin = cosec, and sin-squared plus cosine-squared = 1, etc. Better yet, try to get fairly good at moving around within these identities, deriving them, etc. The more familiarity you have with 'em, the happier you’ll be.

Also…don’t get discouraged by “epsilon delta proofs.” Ugliest doggone things in the world, but, if you can get through 'em, then it’s easier sledding for a while, and, better yet, you’ll never have to use them again. They are the philosophical underpinning of calculus, and you have to understand it.

(Amusing to note that Charles Dodgson – “Lewis Carroll” to literature fans) didn’t get the infinitesimal calculus! He couldn’t understand how a difference could be made very small but not eliminated. So, this is your chance to show you’re smarter than a professor of maths nigh on to a couple centuries ago!)

Anyway, yes to Trig, Algebra I and II, and Geometry. Geometry was the path Newton used to invent Calculus, but, today, it isn’t taught as a primarily geometric field.

Try to have some fun!

3

If you don’t have a pretty firm grounding of algebra, it will cause you a great deal of trouble in a Calculus course.

4

Here are some questions for you, taken from memories my days as a Calc I TA:

[ol]
[li]Do you understand what a function is?[/li][li]Do you understand what it means for a function to be invertable?[/li][li]Do you understand the real line? The difference between the rational numbers and the reals?[/li][li]Restricting the scope to functions from real numbers to real numbers, do you understand, in general, how to plot such a function on an x-y Cartesian plane?[/li][li]Given a plot of an invertable function, can you sketch the plot of the inverse of that function?[/li][li]Given the plot of a function y = f(x), can you sketch the plot of y = a*f(x), y=f(x) + b, y = f(cx), y=f(x+d), and y=1/f(x) for known quantities a, b, c, and d??[/li][li]Can you sketch plots of the following functions, including labeling axis-intercepts and extrema: sin(x), cos(x), tan(x), exp(x), ln(x), x^n, 1/x^n?[/li][li]Do you understand exponents? Polynomials?[/li][li]Can you recognize and plot the equation of a line in it’s various forms (e.g. y = mx+b, (y-y0)/(x-x0)=m, &c)? Can you identify the axis intercepts given such equations?[/li][li]Given a quadratic polynomial, ax^2+bx+c, can you find its roots, minimum/maxiumum value and location of that value?[/li][/ol]

Those were the kinds of pre-calc activities we’d do before getting down to it. If you can answer “yes” to all of those, you’re probably golden for Calc I.

5

Each layer of mathematics is pretty much just doing the layer below it. So, first you learn your numbers. Then you learn arithmetic, which means making the numbers dance. Then you learn algebra, in which you use arithmetic to solve algebra problems. And then you have calculus, where you use algebra to solve calculus problems.

So if you’re terrible at algebra, calculus is going to be a horrible slog, because everything you do in a calculus class is applied algebra and trig.

6

Plato’s been dead for a long time. You will need to know some basic geometry–in particular, you should know the formulas for the area and perimeter of some common shapes–but you don’t need a detailed knowledge of geometry for a first semester calculus class. Algebra and trigonometry are much more important.

7

That’s all greek to me (zing!). Thanks for the confirmation and warnings.

Thanks, that’s helpful. As I’m teaching myself, I can move on as soon as I’m comfortable with principles - not a slave to a book or the pace of a class. That list sounds like it will help to set milestones.

I was terrible at Algebra because I never really wanted to try. I’m convinced that I am capable of learning it all, and coming to understand, enjoy and leverage mathematics.

We’ll see how that works out. . .

8

This was what my research suggested, Geometry not that important. I’ll look at those formulas at the very least.

Any suggestions on order to tackle these? I was thinking:

Geometry (even if narrowed focus)
Trig
Algebra 1
Algebra II

If I recall, that’s the order it went in High School.

9

You can probably tackle algebra and geometry in either order, but Trig requires a solid knowledge of both, and should definitely come after the other three.

10

You mentioned never wanting to study much math, but you think you are ready to tackle it now. How many hours a week do you think you can stand studying math? Since you’ve already passed Algebra I, are you planning to start now with II, or take I again to brush up? You might very well need to take I again if it’s been a while.

I have an Associate of Science degree in math. I studied and practiced something like 20 hours a week outside class to get there (and that was just the math classes).

> Geometry (even if narrowed focus)
> Trig
> Algebra 1
> Algebra II

You absolutely need to have Alg. I and II first before Trig, since Trig is largely just a specialized application of algebra.

You definitely need to know as much as possible of each level in order to get anywhere at the next level. As you get into Calculus, you will see that all the Algebra and Trig textbook authors knew where it was heading, and their choices of topics to cover was not arbitrary. EVERYTHING (almost) in ALL those courses comes back to haunt you in calculus!

It’s not like, say, History, where you can take U. S. History 1-A (beginnings to Civil War) and 1-B (Reconstruction to Present) in either order.

I have a theory: The grade you get in any level becomes the limit of what you can do thereafter. If you get a B in one class, you will have a hard time ever getting better than a B in any later class. If you get a C, you will be stuck a C math student. The things you don’t know, that cause you to get anything less than A++++ will bite you ever after.

Is your ambition to become a really good math whiz, or just to get through the classes with your ass intact? If you really want to excel (and even if you don’t), it will be helpful if you study all you can, well beyond the text and the class material, at every level.

There is much debate these days (that is, for the last 40 years at least) that classes are getting more and more dumbed down. I think that’s true. About 10 years ago, when I when back to school for that math degree, and then tutored it, I went to the Math Chairman’s office and chewed his ass up one wall and down the other for the shit-f*ing dumbed-down Alg. I book they were using.

It proved to be a very amicable conversation. (Surprise!) He fully agreed with me, saying that they chose that book because it was the least dumbed-down they could find. We had a good long chat about how dumb math teaching has gotten, compared to how it was Back In The Day. I’m not at all sure that current math curricula are really good enough to prepare you for Calculus, unless that’s dumbed down too (which it may be… see below).

Here’s my point in all this: If you’re really serious about it, hit up the used-book stores and find some really old math textbooks – say, 1940’s and 1950’s era. And study those thoroughly too, along (or even instead of) your class text. If you are able to do that, you will definitely be ahead of the curve. (I once had a trig book from 1914!) And I still have a college algebra book from 1942, which is vastly better than the butt-wipe textbooks you can find now. Those old books always went into much greater depth.

Here’s one more specific topic you should study on your own, because it’s only covered superficially any more, but is great help to get your head around calculus: INEQUALITIES. If you can learn about that in detail, it will greatly help you learn to think about “epsilon-delta” definitions and proofs.

As for Calculus getting dumbed down too: I’ve been told that they don’t even teach epsilon-delta any more in lower division – it’s now deferred to upper-division advanced classes. Still, if you know inequalities, that’s a good conceptual thing to understand. My old 1942 college algebra book has a whole chapter on it, including proving unconditional inequalities (that is, given an inequality that is allegedly true for all values of all the variables, prove it). If you can find a textbook with that, it’s a great help for wrapping your mind around epsilon-delta.

Since, as you say, you’re teaching yourself, and if you are really wanting to get all into it, you should try to do all these things.

11

Does the college you intend to attend require a placement test prior to taking any Mathematics courses there? If so, you’ll placed in the appropriate class to prepare for higher math.

12

Side question: you guys seem to have a very clear notion of what’s the division between Algebra I and II, but we used descriptions. Basic Algebra, Linear Algebra, Multivariant Algebra, Matrix Algebra…

Is the division between I and II sort of homogeneous throughout the US/the Anglosphere, and if so, what is it? Or is each of you assuming it’s going to be whatever it happened to be at his own Alma Mater?

I don’t think it’s important to know the formula for the volume of a sphere in order to be able to integrate it, but understanding the notions underlaying geometry is very useful in order to comprehend trig (as opposed to parroting it). Knowing what a tangent line is helps understand what the trigonometric tangent is.

13

For calculus, you just need to know algebra and some trig. Plane geometry? Not that much. Of course you need to know basic mensuration formulas, but you can just look those up when necessary. As I recall, knowing right triangles and similar triangles will help you solve some problems during the course. You’ll be introduced to analytic geometry in calculus, and your algebra skills will come in handy. One thing for sure … if you’re shaky in algebra you’re going to have a hard time in calculus. You’ll be expected to have a facility in dealing with equations and inequalities, and in manipulating and simplifying expressions. The last thing you want is to be caught in an algebraic fog when you’re trying to absorb calculus concepts. Take this from someone who has taught calculus for a long time and have seen which students do well and which fall by the wayside.

14

I intend to work on this for one hour every night and a few more hours every weekend for as long as it takes. I’m starting from scratch, working the playlists at Kahn Academy including the very basic ones, if only for review. Hopefully I’ll be able to get through it all by next fall. Thanks for the rest, good information.

Not that I know of. A student not ready for Calculus would be unlikely to get in here, and I’ve kind of side-stepped the requirements by being an employee. I have been given a second chance to get an excellent education after having squandered the first one, and a chance to overcome my past poor performance. I’ve earned this second chance with dedication to my craft and hard work and do not intend to let the opportunity pass me by. But it’s going to require catching up on my own where necessary.

I’m holding a 3.8 GPA so far, having taken Multimedia, Philosophy, Literature and History classes, and I would like to keep it thereabouts. I’m convinced that I am capable of learning all of this, and unlike the first time, dedicated to doing so.

15

In the US at least, the word “algebra” is used both for the basic mathematics courses, often taken in high school, as a prerequisite for things like trig and calculus, and for the branch of advanced mathematics that often called “abstract algebra” or “modern algebra” which includes things like linear algebra.

I don’t know that there’s a universal description of what “Algebra I” vs “Algebra II” would cover.

16

I used to teach Calculus.

The below is what you need:

  • As much Algebra as you can have…at least Algebra II from high school.
  • Preferably a Senior prep course that conains even more Algebra and Trigonometry.

That’s it…Algebra and Trig.

Trig is not a huge subject area. I used to teach a 2-week/10 day all day trig course during the summer and I didn’t feel all that rushed. Trig is tiny compared to Algebra.

MOST IMPORTANT! - Have had no high school calculus.

The last one is snark, but students that came into Calc I that had high school calculus perfromed measurably worse than ones that didn’t have any Calculus. I think this is because ones that had Calculus were more cocky/lax and, more importantly, had sacrificed that year of college prep math for Calculus (Calculus WAS their college prep math course) and so they didn’t have as much background as students who didn’t have any calc but still took college prep math.

If you are out of high school and asking as an ‘adult’…then get as much algebra and Trig as possible and you’ll be set.

17

Plato valued geometry (in a form such as that presented by Euclid, in which everything is logically built up from “self-evident” axioms) as a prerequisite to philosophy, not calculus, because he thought it provided training in logical thinking and deductive reasoning.

18

This!

Perfect answer :slight_smile:

19

With your background, I’d say your best bet is to get a precalculus text like this one and work your way through it, using online resources like this to help you when you get stuck.

Almost all of the authors of the popular calculus texts, like Stewart, Anton, and Larson, also have precalculus texts. Those books pretty much start from scratch and cover algebra, trig, series, etc. And analytic geometry (think graphing), which is EXTREMELY important for calculus.

And DON’T pay $150 each for math books. Algebra, trig, and calculus haven’t changed much in the last few decades, so get an older, used edition for no more than ten bucks. There are also a lot of free editions online.

Best of luck to you.

20

Do not worry about Geometry.

While something called ‘Analytic Geometry’ will appear in Calculus, don’t let the Geometry fool you. You will not being doing Geometry proofs and SAS, ASA and stuff like that :stuck_out_tongue:

You will just be using the formulas of Geometry to do Calculus which is much more Algebra-like than Geometry-like.