Mathochism: Hitting the test wall

One woman’s attempt to revisit the math that plagued her in school. But can determination make up for 25 years of math neglect?

On Thursday, my spouse and I went away for a long weekend. We drove to a lovely inn in a small town by the ocean.

All my calculus books went with me, and while my husband was reading a book by the fire, or at the beach, I was sitting near him boning up on limits and derivatives.

I spent about 16 hours total studying. I now know how to spot an indeterminate form, and why a limit at negative infinity makes a huge difference over a positive one when dealing with, say 5 + √x+1. I know how to prove the power rule, product rules and quotient rules.

Mathochism: Becoming independent

One woman’s attempt to revisit the math that plagued her in school. But can determination make up for 25 years of math neglect?

I went to office hours today before class, because I had a few questions. I’ve been going over limits again, helped by a take-home review supplied by the professor.

The problems on this review are far more challenging, and far more rigorous, than what I encountered in the book. And boy, I wish I had had it before the test! Mastering these problems would have prepared me so much better, really reinforcing my understanding of limits.

Oh well. I feel somewhat vindicated by the fact that the Calc Professor told me she wished she had given us that review during my office visit. I also felt vindicated when she agreed that the homework problems in the book are at times too simple.

Mathochism: Shame shame shame

One woman’s attempt to revisit the math that plagued her in school. But can determination make up for 25 years of math neglect?

We got our tests back today. I had been crossing my fingers for a high C, since I knew I had messed up on at least two problems, and hoped to get partial credit on a third. When you only have 10 problems total, the margin for error is slim.

But I got an F.

Well, that was unexpected! In fact, it’s quite a shock. I’m still processing this failure, but at least we went over the exam in class.

In one of the problems I unexpectedly got wrong, I ironically had the right answer.

The problem was to find the limit of √(x-3)²/x-3 as x goes to 3. I immediately recognized that as a limit that can’t exist, because there are two pieces that each have different limit. I tried to
explain, but still got it wrong, and the reason my explanation didn’t pass muster is because I should have recognized √(x-3)² is absolute value of x-3 in disguise.

Mathochism: Smooth derivatives

One woman’s attempt to revisit the math that plagued her in school. But can determination make up for 25 years of math neglect?

We’ve moved on to derivatives. I’ve been kind of looking forward to them, even if I much prefer the quickie technique over the groan-inducing f(a + h) – f(a)/h one.

Still, the latter choice feels much more comfortable this time. I remember how I agonized over how to apply the formula to functions like √x and x³. I tried getting help from the Calc Dementor, which he gave, albeit begrudgingly and condescendingly.

The Calc Professor’s approach to the painful formula was much better. First of all, she broke everything down very clearly. Then, one of her examples for how to apply it involved √x. It’s like she knew that one would stump students, so she did her best to demystify it.

Mathochism: Testing my limits

One woman’s attempt to revisit the math that plagued her in school. But can determination make up for 25 years of math neglect?

The test was today. I’m keeping my fingers crossed for a C.

It had 10 questions, and was not horribly difficult. I felt confident working with infinite limits and a delta and epsilon proof. I was okay with an intermediate value problem and a piecewise continuity problem (hoping for partial credit on the last one). I believe I identified the sandwich theorem problem correctly.

I really only had issues with two problems. One was identifying continuity of a c value (am hoping for partial credit), and the other graphing from various limit parameters (complete loss). I’m annoyed with myself on that last question, because I have been practicing that kind of problem. But in most of those, I had at least one point, one anchor to go on, and this problem had no anchors. It was way more nebulous than I was used to and I likely tanked it.

Oh well. We do get to drop this test, in case I messed up completely. But the good news is that I didn’t feel mind-numbingly anxious this time. I felt in the zone on several problems, and managed to reason my way through the others in a way I hope is acceptable.

I feel I really do understand limits. But even when you understand something doesn’t mean you will solve all problems correctly right away. Sometimes you need a little extra time to work through the various permutations. And that’s okay.

All text copyrighted by A.K. Whitney, and cannot be used without permission.

Mathochism: Unnatural women

One woman’s attempt to revisit the math that plagued her in school. But can determination make up for 25 years of math neglect?

Unlike my undergraduate and graduate alma maters, my current college is extremely diverse. White people are in no way a majority; in fact, I’m not sure there even is a majority. I mean, I’m sure there must be more students of one ethnicity over another overall, but if you take a random sample, say a line for IDs or parking passes, you’ll see as many white people as black, as many asian as latino.

We also have a huge international contingent, and you’re as likely to hear Chinese, Arabic or Spanish as English while walking the halls. There’s also Farsi. Southern California has a sizable Iranian population, and in Los Angeles, there is a whole stretch of Persian restaurants and markets near UCLA.

Mathochism: Removing the discontinuity

One woman’s attempt to revisit the math that plagued her in school. But can determination make up for 25 years of math neglect?

I got to the college early today, because I wanted to ask the calculus professor about a few homework examples. One example was that trig verification that was befuddling me last week. The others were of the graph and sandwich varieties.

A student was already there when I arrived, but he was asking about one of the problems I wanted to ask about, so the professor suggested I sit in (this is in complete contrast to Calc Dementor, who disliked such collaborations).

We wound up going over a number of problems, since it turns out the other student was befuddled by the exact things I was. Like me, he found it difficult to connect with the book, which surprised the professor. In fact, a number of mathematicians I have spoken to seem to love this book. I have to wonder if it’s because they are viewing it from a solid base of knowledge, not a blank slate. Or maybe it’s because I and my fellow student just don’t think like mathematicians?

Mathochism: The need to do better

One woman’s attempt to revisit the math that plagued her in school. But can determination make up for 25 years of math neglect?

We officially got our quizzes back today, and I did as poorly as I had feared. Again, it was not a tough quiz. I was felled by nervousness and carelessness and exhaustion. But it’s okay. It’s not a crucial part of the experience, or of the final grade. I plan to treat this like the awful dress rehearsal before a much better opening night.

On the positive side, the Calc Professor was a fair grader on this quiz, giving me partial credit on several problems. And in today’s class, she addressed several sandwich problems, including the one the Calc Dementor was so unhelpful on last semester. In her hands, it felt clear and simple, and I feel more courageous about biting into those sandwiches again.

Mathochism: Fighting indigestion

One woman’s attempt to revisit the math that plagued her in school. But can determination make up for 25 years of math neglect?

We’ve run across the sandwich theorem again. While I enjoyed it a lot the first time, and it felt quite intuitive, I am now as wary of it as I am of tuna salad on a 110-degree day.

That is because the very simple explanation feels a lot trickier in actual practice. And the book’s problems are no less befuddling this time around. I was able to find a kickass online function grapher (thanks, kind commenter who supplied it!), and by putting in the f(x) function, and the g(x) and h(x) functions that serve as the sandwich bread, I can see the magic.

But when it’s just an equation? Well, not so much.

Mathochism: In the neighborhood?

One woman’s attempt to revisit the math that plagued her in school. But can determination make up for 25 years of math neglect?

We continued our discussion on limits today, and applied them to intervals defined by epsilons in the y axis and their relationships to deltas in the x axis.

I remember covering this during the spring, and not being particularly befuddled by it. But after going over the material this time, the professor told us this was one of the hardest concepts in calculus. Is it? Maybe I’m really not getting it, then.

Here is my very non-mathematical take on limits: I’m driving my car down a freeway, heading for a specific destination. Suddenly, traffic comes to a screeching halt. Now, whether my journey continues depends on what made traffic stop. In the best case, it’s just an obstacle in the road, like, say, a couch. After the CHP removes it, we can get moving again! (Can you tell this may have actually happened to me at one point, say on the 405?)