I Need All the Help Ever: Calculus Edition
February 10, 2011 11:59 AM   Subscribe

Help me arm myself for a future-determining showdown with calculus.

Hi all. I'm not sure how it all happened, but I've suddenly gotten myself into a weird situation involving math. Someday I'll be telling this story to grumpy teenagers groaning over their quadratic formulas or whatever, as a parable in why you should be grateful for being forced to learn math long before you have any use for it.

I was recently admitted to an unambiguously top graduate program, which has been an amazing thrill that I've fantasized about for months. My admission comes with one small caveat: I have to take a Calculus I course during a 5-week-long summer session and make a B- or better. I'm ready to accept their offer, which I imagine will then make me (morally? legally? both?) obligated to decline any other offers I may receive. Then, the only thing standing between me and attending this completely awesome program will be learning intro calculus in an outrageous 5-week doom-gauntlet of madness ... if I fail, or, I dunno, my car breaks down on the way to an exam, my admission will be rescinded and I'll be left with nothing. TRYING NOT TO THINK ABOUT THAT.

Here's the thing though. As you can see, the stakes are comically high, and I haven't studied math since high school, which was almost 10 years ago (?!). At that time, I took AP Calculus and worked myself to the bone for barely a B, electing not to take the AP exam because I didn't need the credit for my intended major of neo-Marxist cat husbandry and figured I'd bomb it anyway.

It's the same story of math trauma many of us are familiar with. Even though a B is all right, I still occasionally have actual nightmares about my high-school Calc class, like, at night, while sleeping, 10 years later. And back then, the foundational knowledge of algebra was fresh in my mind. On the potential pep-talk side, I did recently take a graduate-level statistics class, in which I got a 99 through sheer Cossack juggernaut pure nitro heck force. But, my mental repository of unexamined folktales about math tells me calculus involves some actual critical thinking, whereas my stats course fell heavily on the side of being told to plug stuff into one of several mostly opaque formulas.

So tell me ... how can I prepare myself to take on this 5-week calculus beast? There'll probably be an exam every week. I've forgotten all my algebra and trig. I have over 3 months until the madness begins. I know about Khan Academy, I know about Purplemath, but between algebra, trigonometry, "precalculus", and calculus proper, I hardly know what to study. And, I feel like a book or two made of actual paper might be superior to watching videos online. I dunno, there must be million resources for this, and I need some recommendations on the best ones and what the top priorities are for review. Right now, all I got is an algebra book from Bob Jones University that says, "Inequality is a quality of the devil" (seriously).

Also, there's a small possibility I may be allowed to take this class the first semester of my graduate studies. Is this a better or worse idea than doing it in a 5-week blitz? I could definitely see it going either way.

Thanks for your help and tell your children to F.O.I.L. those trinomials before the trinomials foil them.
posted by geneva uswazi to Education (28 answers total) 28 users marked this as a favorite
A couple of years ago I took a semester long calculus class 10 years after I'd last done any math, and that last math was pre-calculus and not calculus.

Here's how I prepared: I got a generic, random pre-calculus book off of half.com. Then I started working through it, a section at a time. That really ought to do it.
posted by hought20 at 12:07 PM on February 10, 2011 [1 favorite]

To be clear, I meant a pre-calculus textbook, so maybe not as random as all that. They don't change much year to year, so you can get one that's five years old for pretty cheap and get a good review.
posted by hought20 at 12:08 PM on February 10, 2011

Do you know about MIT's Open Courseware? You probably want their "single variable calculus" courses.

Five weeks to learn calculus would be a challenge, I think, but if you're essentially taking this one class as a full-time job during that time then you don't have to worry about focusing on other things.
posted by backseatpilot at 12:10 PM on February 10, 2011 [1 favorite]

This may or may not help you, but reading a narrative of the history of calculus -- its development, its uses, Isaac Newton, blah blah blah -- REALLY helped me. Once I understood what it was FOR and how it was developed (at a very high level), the whole thing seemed much less intimidating and I understood better how to do what I was trying to do. I mean, it's a really important piece of intellectual history, that even liberal arts nerds like me should try hard to understand ... and once I could place it in a historical and intellectual context, the MATH got a lot easier for me.

A quick google shows me there are several books on the history of calculus, some of which appear entertaining. You could maybe get one at the library to read, in no particular hurry, while doing your pre-prep work with a pre-calc textbook or whatever. Just to get your mind in the right place.
posted by Eyebrows McGee at 12:18 PM on February 10, 2011 [6 favorites]

I AP'd out of first-semester college calculus, which somehow led to me taking second-semester calculus second semester of my sophomore year (i.e. a good 1.5-2 years after my last math class). So, not as long of a break as you're talking here, but still a decent break.

It took me a while to get back into it - I tanked on the first test, but I did fine in the end (A-/B+ range, I forget).

So, I would say if you're going to take the five-week course, definitely work through something beforehand. A review text for the Calculus AP course might be a good choice, if it doesn't send you into frightening high school flashbacks!
posted by mskyle at 12:19 PM on February 10, 2011

Best answer: I took AP Calculus (the easier AB, not the more difficult BC version) in high school, Calculus II over the summer at a community college, and Calculus III about seven years later, with no math of any kind in between. And I got an A. So a long gap is not impossible to overcome.

Please know:
  • what a function is (naively)
  • values of sin, cos, and tan for angles of 0, π/6, π/4, and π/3 radians
  • how to find the zeros of linear and quadratic functions
  • This will almost certainly suffice.
Things to remember: the instructor will reteach almost everything you need to know as far as background. There will, in all likelihood, never be a moment when the instructor says, "Now, class, think back to that vital preparation all of you received a little while ago — except Geneva, who will now fail."

Also, Calculus I is not thinking math. It's still "plug numbers in" math. You may very occasionally need to be creative in the application of the rules of differentiation and integration to a confusing function, but there is almost almost the one right way and the one right answer.
posted by Nomyte at 12:19 PM on February 10, 2011 [4 favorites]

Before you accept this offer:
In the US many PhD programs agree to a common deadline of April 15 for acceptances. If your field is a field that follows this guideline (ask your undergrad advisors) then you should not feel under any pressure to commit to this program before April 15.
posted by LobsterMitten at 12:22 PM on February 10, 2011

Schaum's Outlines are kind of like the Cliff's Notes of math, except solid and respectable enough that I've used them as required textbooks in college calculus classes before. If you'd like to work through a book instead of watching videos (which I think is the right call!) you'd do very well to pick up the basic calculus outline (or pre-calc subjects if you need them) and start working through it. It's very straightforward and you'd give yourself a HUGE jump if you've already started doing some problems that way.

Personally, I think the five-week blitz is far preferable to doing it during your [already quite stressful] first semester of grad school! I have taught a five-week calculus course and I think it's pretty brutal on the students, but you might as well get it over with in concentrated form. I guess one thing to think about is how well you need to know calculus in the future, though... The five-week-course students definitely did not reach the same level of calculus knowledge as the semester-course students. If you just need to check it off the list, that might be a vote in favor of the short course, though!
posted by adiabat at 12:26 PM on February 10, 2011

I failed calculus my first time through in college. Had to take it again the next semester and ended up passing with a B-. I hate calculus and motivation was a major factor for me. Having to slog through an entire semester really hurt and I believe was a large factor in me getting a low grade. I wish I had taken it in the summer, just so it wasn't as long and painful. Anecdotally, I know a lot o people who took calc in the summer and said it was a lot easier. Less time to cover can mean that they go less in depth into each topic. So basically, the problems may be easier and more formulaic because there's less time to teach how to solve more complex problems. Also, the class is likely to be smaller which means you'll get more one on one time with the teacher. This will also depend a lot on if your prof is an ass. But it will be sunny out and they will probably be less of an ass then they were in the winter. Good luck!
posted by smokingmonkey at 12:36 PM on February 10, 2011

I took a calc class long after my last math class and did horribly cause I could never remember the trig identities and stuff. If I were you, I would get some sort of precalc source and work through that. As someone said, old texts should be fine as mathematical principles don't change very often.
posted by d4nj450n at 12:41 PM on February 10, 2011

First off, burn that Algebra book. Pour lots of lighter fluid on it and put it in the Weber and burn it to ashes.

I used the Schaum guide to prepare me for Calc and it helped. You could just as easily pick up a used copy of the Complete Idiot's Guide and it will serve you just as well.
posted by JJ86 at 12:55 PM on February 10, 2011

Sparknotes helped me quite a bit (any kind of laminated "all of Calculus I on three pages" study guide will do.) If the book's explanation didn't make sense, I checked the guide. I also made flash cards for any sections I had trouble with. These weren't the Q front/A back flash cards, but more a recipe book with one formula per card.

In my last stats class I used many other sources aside from the book like Schaum's outlines, Wikipedia, You Tube and even just Googling things until an explanation made sense. You do need good algebra and trig foundations, so I don't understand the suggestion to burn the algebra book.
posted by soelo at 1:07 PM on February 10, 2011

Try Professor E. McSquared's Calculus Primer: Expanded Intergalactic Edition.

Amazon reviews here, but the book can be bought at the first link for much less than Amazon's charging.

It's a great, low-stress intro to Calculus, somewhat reminiscent of _why's Poignant Guide to Ruby, if you've ever seen that. If not, it uses cartoons to illustrate basic and more advanced concepts in a non-condescending, fun way.
posted by Bourbonesque at 1:09 PM on February 10, 2011

Best answer: I would prefer to take the course during the semester, but that's just me. It may also be more stressful since you will have other things to focus on. You sound like a dedicated student, so here is some advice should you choose to take the 5 week intensive:

For the next three months, you will absolutely need to brush up on your algebra and pre-calc. This is the number one thing that hinders success in calc. Please have a very good handle on EVERYTHING in Algebra 1 & 2 and trig. The most important things to be comfy with are fractions, exponents, functions, and sin/cos/tan. Others have had good advice on books (I also vote for Schaums, although you may require a more in-depth text). I found Paul's Online Notes to be of IMMENSE help in my earlier undergraduate studies and I would highly recommend them to anybody. Use them! Algebra, the full site.

When you begin taking the course, utilize the college's tutoring center. Make it your life. If your school doesn't have one, pay a tutor to give you a few hours of their time every day for the five weeks you are in the class. It will be a worthwhile investment. You may need someone to do all of your homework with and make sure that your algebra is up to par. Do homework every single day with only Saturdays or Sundays off. Additionally, it always helps to have a friend in the class to study with.

Calculus courses are mostly memorization and repetition. I have tutored countless students in calculus courses and the ones who succeed are the ones who drill it into their brains and don't make excuses. Math courses can be a lot more initial work than other courses, and you should be doing many practice problems. Doing all of the extra work will prepare you and boost your confidence levels during the exams. For every problem the instructor assigns you, do at least 5 similar ones.

Congratulations on your graduate school acceptance! I'm sure you'll pass this required course with flying colors and go on to love calculus with all of your heart. It is a beautiful subject.
posted by 200burritos at 1:19 PM on February 10, 2011 [3 favorites]

Definitely brush up on your algebra - they'll take that for granted.

For me (post-grad economics course with only high school maths many years ago), what made calculus easier was understanding WHY I was doing what I was doing - what, in plain english, was the problem that I was trying to solve? That in turn made it easier to figure out what formula to apply.

eg: So you have distance - speed - acceleration - rate of acceleration, for instance, and calculus just enables you to get from one measure to another up and down the scale. Rate of change of x as y changes (what is x? what is y?).

So I'd advise you to ask lots of questions during the course to make sure that you understand the how and why calculus is applied to various situations, rather than just focussing on applying a formula to get an answer. Ask for real life examples of when you would be performing that function.

Good luck.
posted by finding.perdita at 1:42 PM on February 10, 2011

First and last, drill the algebra. A calculus teacher of mine said that no one had ever failed calculus, but lots of people had failed algebra while taking calculus. Can you factor this?


Can you multiply this out?


IMHO, you need to be able to do this sort of thing in your sleep. The good news is that if you can do this sort of thing in your sleep then you can pass a basic calculus class. Computing a derivative is just applying basic algebraic rules.

BTW - That algebra text from Bob Jones University sounds like the most awesome thing ever! It should not, however, be used as a study guide. Perhaps as entertainment?
posted by It's Never Lurgi at 1:49 PM on February 10, 2011

I'm in pretty much this same situation!

I started working with a tutor and found that *extremely* helpful. Being able to ask, "But why...?" over and over and get an immediate answer is a lot less frustrating than googling and sifting through lesson after lesson to find a half-answer to a specific question. Yeah, tutors are expensive but in terms of stress reduction, time saved, and not having to repeat the class, I think it's worth it.

Other random advice from my recent math adventures:

When I was reviewing algebra and trigonometry I thought the Dummies books were pretty useful. They're also cheaper and more readable than text books.

Maybe this is obvious, but what you need to look for is a textbook that gives step-by-step instructions for every problem-- not a bunch of stuff about real-world applications or theory or proofs or whatever. I found such a book for algebra but am actually still looking for a good calculus one. A good, easy-to-use index is also important when you're using the books for reference/ review.

FWIW (this might just be personal experience) I've concluded that it's worth starting at square one (the last math concepts you feel fluent in) and working from there. I tried to jump in to calculus, thinking that I'd review the algebra/ trigonometry/ etc. as it came up. That proved to be really frustrating and a waste of time. Going back to intermediate algebra was kind of humbling but it's turned out to be time well invested. It's not as impossible as it sounds-- the review will go very quickly.

If you do take a summer class and it's at all possible for you to consider yourself a full-time student, do it. I took a six-week calculus course in college and it was brutal-- the lectures flew through several chapters every day and there was a massive amount of homework. If you didn't grasp one concept, you fell behind very fast.

Good luck and congratulations on getting into graduate school!
posted by Sifleandollie at 2:09 PM on February 10, 2011

Paul's Online Math Notes
posted by tomtheblackbear at 2:40 PM on February 10, 2011

If you prefer the visual approach to learning. I would use http://www.mathematicalradical.org. It has a lot of materials so if you dont' feel like purchasing a book or need more resources in addition to a textbook, you can use these online resources. It may feel like you're reviewing a lot of things you already know, but I found that many of the students in my Cal classes were having a hard time because they didn't have the basics down as well as they'd thought.

A former Pre-Cal teacher is a contributor to that website, and he gave me the best preparation for calculus I've received yet (took Pre-Cal and Calculus in HS, got good grades yet didn't understand nor retain the information).
posted by Shirley88 at 2:42 PM on February 10, 2011

Best answer: I've been teaching calculus classes at the university level for 7 years now. Here is my take on your situation, no sugar-coating.

I've forgotten all my algebra and trig.

You are absolutely screwed and stand no chance unless you can use this 3 months and really get back in the groove. People mentioned getting a Pre-Calculus textbook online (Stewart has some good ones) and working through it. You should also hire a tutor who will help you answer questions quickly instead of being forced to search things out (as I see mentioned on preview).

The fact that you got a B in AP calculus 10 years ago means you didn't really know anything about calculus back then. Now is much, much later. I have students in my calculus courses who tell me they got a B in their AP class and they can't do a damned thing. So no, a B in AP calculus is not "all right".

You really need to know what a function is. You need to know what polynomials and rational functions are. You need to understand the notation we (mathematicians) use for piecewise defined functions. You need to familiarize yourself with the trig functions of sine and cosine, including what their values are at the "special" angles (not n/6, n/4 and n/3 as Nomyte says, but rather n*pi/6, n*pi/4, n*pi/3, etc.). The other trig functions are just quotients or reciprocals of these two. You need to be able to look at the graph of a function and analyze it to the extent that you can tell me what the value of f(4) is, say. You need to be able to factor polynomials in your sleep (as mentioned above).

Nomyte mentioned above that Calculus isn't "thinking" math, that it's still "plugging things in" math. With that attitude, I guarantee you would fail my course. There's no telling what your instructor might be up to, but if you want to be in the business of memorizing formulas and plugging stuff in, you will fail spectacularly.

This is exactly what students want to do when computing limits; they just want to plug stuff in all the time. This is why they get things wrong again and again and again and again. They refuse to believe that it's not just "plugging stuff in" anymore.

That being said, this is only a 5-week course. Do you meet every day? For how long? It's hard to say what the goals of a 5-week course are; they certainly differ from those of a 16-week course.

If you could take the semester-long version, I'd opt for that. You will have more time to let ideas sink in.

Lastly, and perhaps most importantly, do not try to remember anything from when you took calculus eons ago. This may cloud your understanding, since you probably didn't understand them 10 years ago, and bringing back those incorrect thoughts will harm you now. Approach the calculus topics with a fresh mind. You can do it, you just have a hard road in front of you.
posted by King Bee at 2:42 PM on February 10, 2011 [5 favorites]

You shouldn't need to try to teach yourself calculus before you start the course---that's what the course will be doing (presumably).

But, you will need to be fluent with basic algebraic operations and functional notation, and with the general behavior and rules of functions like sine, cosine, tangent, ln(x), exp(x).

I'm not your calculus teacher, but MeMail me and I can send you the prerequisite quiz I had my students take the second day of Calc I this semester. If you look at the problems and you have *no idea* even how to approach them, then...you'll have some work ahead of you, but you'll have some idea of the sorts of problems you maybe should know how to do.

(Alternately, you can try to find a cheap copy of Stewart's Calculus (some old edition, say, although I don't know for sure when they introduced it; I know it's in the 6th edition) online or better, in a library. In the first chapter, there is a set of diagnostic tests. Do them. See where your holes are.)
posted by leahwrenn at 2:47 PM on February 10, 2011

Here's my take on the background of calculus I.

Calculus I is focused on understanding how a value changes over time that's all that mystical thing called a derivative is. Principally you'll be talking about a line, but you could be just as easily talking about how many eggs you can eat week.

I'm assuming you aren't taking calculus for math majors, but if you are - seriously they just do a heck of a lot more problems and don't cover the refresher stuff that well.

If I was retaking calculus, I would want to know what y= ax+b graphs like, what the difference between what x^2 and x^3 looks like. I would want to know what 1/x looks like, what log(x) looks like, what e^x looks like, what tangent, sine, and cosine each look like. I would want to feel comfortable with thinking about how varying your speed on your way to work changes the amount of time that it takes to get there, likewise. If you leave your house and drive for 10 minutes, but change your speed (and do this several times), you wind up at a different point - and at each discrete minute interval you were probably at a slightly different distance from your starting point. As I'll reiterate, all derivatives are is taking that information and coming up with a way to describe the rates of change, whether that be distance traveled over time, or time it took to travel a distance.

You are about to learn about how things change - that's it. There's nothing scary about it, or mystical. Just keep focused on what you start with, where you finish, and be ready to think about how you get there. (Also - try to enjoy it)
posted by Nanukthedog at 3:57 PM on February 10, 2011

hi. i taught calculus at a large state university for many many years.

why do pre-med students believe their grade in calculus will determine their future career?

answer: medical schools use calculus as a filter for applicants.

why do they use calculus as a filter?

answer: because not only do you have to memorize the answers but you have to memorize procedures, sometimes involving several steps.

most people don't learn much mathematics in calculus, pre-med students especially. what seperates those with good grades and those with bad grades is almost entirely 'study skills." a 5 week course in calculus will test your study/student skills even more. you will need to be totally focused on completing homework, studying for quizzes, making sure you understand which problems will be on the exam, etc. etc. if you can do this, you will be fine. don't obsess over whether you know any mathematics or not, most people don't.

on the other hand, if you can factor a quadratic equation and know what that means, and know sin cos tan and what they have to do with a right triangle you will be in good shape. and you might try some word problems in algebra just to remember what that is all about.
posted by ennui.bz at 4:04 PM on February 10, 2011

If you're already feeling math-phobic you need to avoid the MIT OpenCourseware version of 18.01 (calculus 1) like it's made out of poison. It covers approximately 2 semesters of theory- and proof-heavy calculus in 13 weeks and induces math-phobia in super-nerds who ALREADY KNOW CALCULUS.
posted by range at 6:02 PM on February 10, 2011

Calculus is actually super easy. Provided you have a pretty solid grasp on Trigonometry and a really solid understanding of most of algebra. It is just using those skills in a new way.

1- You got into the program, you likely have the ability to complete this course.
2- Get an algrbra textbook, read it, and work as many of the problems as you can manage.
3- Same for Trig.
4- You will have no problem.

Also, read the wikipedia article on calculus and why it was discovered/invented. Knowing the kinds of problems that calc can solve really helps in learning it.

(To refine, #2 and #3 a little, buy your textbook for the Calc class early and skim it, looking for the kinds of math you will be expected to be good at.)

(Also, don't use a calculator. Be able to do the Algebra and Trig on paper. It will make you 1000% faster.)
posted by gjc at 7:03 PM on February 10, 2011

King Bee: not n/6, n/4 and n/3 as Nomyte says, but rather n*pi/6, n*pi/4, n*pi/3, etc.

Sir, I submit to you that this — π — is a pi and this — n — is a lowercase N. Please to distinguish the two. I can hardly be blamed if they look similar.

By "not thinking math" I mean that in the section on (e.g.) the chain rule of differentiation the student will be often called upon to apply the chain rule of differentiation. The student will certainly not have to think about deltas and epsilons while doing this.
posted by Nomyte at 7:47 PM on February 10, 2011 [1 favorite]

Sorry, looked like an n.

Yes, there are the "hey you just compute a thousand derivatives" types of problems. No one has to think to do these, and I purport I could train an especially skilled chimpanzee to properly compute them.

That same chimp would have a hard time with questions involving the fundamental theorem of calculus, mean value theorem, intermediate value theorem, doing integration by substitution (which is a calculus I topic in many curricula), etc.
posted by King Bee at 8:59 PM on February 10, 2011

Make sure you you can work through the examples in Larson's Algebra and Trigonometry Refresher for Calculus Students without a calculator. What separates this book from other precalculus/ algebra texts is that every included topic will show up somewhere in calculus.

Another good resource is MEP Math.
posted by oceano at 10:46 PM on February 20, 2011

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