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Failing Calculus and looking at other options.

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14 comments, last by slayemin 5 years, 4 months ago
59 minutes ago, LifeIsGood said:

Math is hard, and Calculus is especially hard for most people, you're far from alone with that.

This is surely a very good advice. Yet, I'm only talking about observed facts. In my math lectures, it was common that only around 50% of the students passed the exams. And these were all math/physics/cs students, so, very smart people who dedicated their whole life at that time to learn these things. The vast majority of the population doesn't even have a remote idea of what it is about.

1 hour ago, LifeIsGood said:

Calculus is a pretty easy subject once you stop telling yourself that you can't do it (I'm not saying you're telling it yourself, I'm just saying that's what I told myself) and especially once you start looking into visualizations / geometric interpretations.

We might have a little misunderstanding here. I looked into your YouTube recommendation. This is not the stuff I'm talking about. I'm not talking about high school level basic concepts and simple calculations. I'm talking about multidimensional integration/differentiation, Lebesgue and Riemann integrals, topology (open vs. closed sets etc.), and theorems, theorems, theorems about that kind of stuff. And, most importantly, not about just using these things to calculate some simple areas and volumes. I mean, even I know multidimensional differentiation in the sense that I can compute a gradient vector on a height map or something like this. I'm talking about writing crazily complicated proofs of totally abstract mathematical claims involving these things. You could not understand or solve these things by simply drawing a picture. The solutions to those exercises weren't numbers, the solutions were mathematical texts that explained your reasoning.

That said, I still believe that you might be better at this stuff than me. Like I said, I was exceptionally bad, even among hundreds of students who all had a hard time with this. Those who had even more problems than me, or less willpower, dropped out early. And really nobody, not even the very smartest of my fellow students, found this "easy". Everybody spent the whole week over the exercises. The only difference between the geniuses and the average or bad students was that the geniuses managed to solve most or all of the homework exercises on their own by the end of the week, while the others could do only a few of them, or nothing, and had to copy the solutions from the few geniuses if they wanted to get an admission to the exam (you needed to hand in like 60% of correctly solved homework exercises in order to be allowed to participate in the exams).

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1 hour ago, wurstbrot said:

We might have a little misunderstanding here. I looked into your YouTube recommendation. This is not the stuff I'm talking about. I'm not talking about high school level basic concepts and simple calculations. I'm talking about multidimensional integration/differentiation, Lebesgue and Riemann integrals, topology (open vs. closed sets etc.), and theorems, theorems, theorems about that kind of stuff. And, most importantly, not about just using these things to calculate some simple areas and volumes. I mean, even I know multidimensional differentiation in the sense that I can compute a gradient vector on a height map or something like this. I'm talking about writing crazily complicated proofs of totally abstract mathematical claims involving these things. You could not understand or solve these things by simply drawing a picture. The solutions to those exercises weren't numbers, the solutions were mathematical texts that explained your reasoning.

Yeah, that was basically my question. Wether you're struggling with the core concepts or the formal part (it's usually the formal part but I wasn't sure because of your mentioned disability)

Writing proofs etc. definitely requires effort, but I wouldn't consider it a hard "problem" to solve. My subject is probably a lot more math heavier than computer science though.
You usually have to remember & detect alot of stuff to solve those kinda tasks. For example, when determining the derivatives of the inverses of the trigonometric functions you need to know the identity sin^2(x) + cos^2(x) = 1^. It's a whole lot of memorization in my opinion...

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(you needed to hand in like 60% of correctly solved homework exercises in order to be allowed to participate in the exams).

Same here. The homework usually goes deeper into the topic & is harder then the exams though.

6 hours ago, LifeIsGood said:

it's usually the formal part but I wasn't sure because of your mentioned disability

The OP (RidiculousName) is the one who claims to suffer from a math disability. I say that I don't think he has one, and that his problems are just totally normal. I have never heard of a mental disability involving math (as opposed to calculating/arithmetic!), anyway. There is dyscalculia ( https://en.wikipedia.org/wiki/Dyscalculia ) , but this is about difficulties with basic understanding of numbers and simple calculations, not about higher mathematics (which, as you know, is a totally different thing).

The german Wikipedia article (I didn't read the english one yet) even says that higher level mathematical skills are not necessarily impaired by dyscalculia. I mean, of course you need arithmetic as a tool to do math, and I can imagine doing math to be even harder and even more frustrating for somebody with dyscalculia, but in the end, arithmetic are not the "core" cognitive skills that is required for math, after all. I can very well imagine somebody who is bad at arithmetic and still a math god, while being a calculating machine on two legs does not automatically get you anywhere in "real" math.

6 hours ago, LifeIsGood said:

My subject is probably a lot more math heavier than computer science though.

The difficulty of the university courses required for a CS degree is different everywhere, of course. It depends on the exact type of degree, on the university, on the professors, on the tutor you're assigned to, and perhaps on more things.

On 2/23/2019 at 5:14 PM, RidiculousName said:

I am currently taking Calculus 1, which I must pass with a C-grade to take Calculus 2. Both of these classes are required, and the Computer Science department doesn't allow students to design their own degrees. ... I have previously passed my precalculus class with a C. It was probably the most difficult class I've completed so far. I had to prioritize studying it, and my grades in other classes suffered. 

I admit I don't like Calculus. Math has always been my least-favorite subject, and the one I am forced to spend the most time on. Currently I often work from 9:00 am to 8:00 pm, and most of this time is spent with Calculus. Even so, most of my work is graded F.

You should TALK WITH YOUR INSTRUCTORS.  Let them know all of this.  Talking with them is incredibly important, it should be the first thing you do. Talk to them about your struggles, tell them it is required for your major, talk to them about it being your third school, talk to them about the difficulty you are having in the required course.

If you do not tell them they will not know.  If they do not see an effort they don't know it exists. You must talk with them.  It is especially important to do NOW if most of your work is already graded as failing. The longer you wait, the more difficult it will become.

 

Many people struggle in calculus because they don't really understand the prerequisites. Too many students take college calculus without a firm mastery of the earlier topics.  They assume that since they struggled through algebra and could basically pass trigonometry by plugging numbers into a calculator that they could jump into calculus.  This does not work.

You've got to know the topics. Not superficially understand them, not just enough that you can do assignments, but truly understand them.  Pulling a list from other sources including Khan Academy and from the school I teach at, here is a list of things you should have mastered before calculus:

  • Manipulate polynomial expressions (like x2+3x+5), including adding and subtracting them, multiplying them, and factoring them.
  • Understand how to interpret, graph, and solve linear equations
  • Understand how to compute and use distance formulas, how to compute and use slopes, and the various forms of line equations.
  • Know how to solve quadratic equations (like 2x2+3x+5=0), including using the quadratic formula to find roots, and how to complete the square.
  • Know about logarithms, their properties, their graphs, their relationships to exponents, and how to manipulate them.
  • Understand how to graph linear functions, quadratic functions, exponentials, logarithms, and the shape of any polynomial graph for any N'th degree polynomial (xN).
  • Now how to manipulate functions, including adding and multiplying functions.
  • Know how to compute the area of 2D shapes, especially rectangles, triangles, circles, and trapezoids.
  • Know how to compute the volume of basic 3D shapes, cubes, prisms, and spheres.
  • Be comfortable with the basic trig functions sine, cosine, and tangent.
  • Understand what each trig function actually means, know what their graphs look like.
  • Understand the angles 0, pi/6, pi/4, pi/3, pi/2, and learn (memorize) their results in the basic trig functions.
  • Have a basic understanding of complex numbers.
  • Have a basic understanding of conics, and how 3D objects can be sliced.
  • Have a basic understanding of sequences, series, and probability.

You have probably already discovered your calculus instructors will expect that you know ALL of these.  If you don't have those completely mastered, go talk to your instructors NOW and figure out options. Don't wait until you fail the course.  Options include withdrawing from the course and taking remedial courses, or getting 

 

On 2/23/2019 at 5:14 PM, RidiculousName said:

Even so, while my precalculus class was four-credits, my calculus 1 class is five-credits, and seems to take more than twice as much time as my precalculus class did.

Yes, university courses take a lot of time.  That is something many incoming freshmen discover after a series of failing grades.

At the university level many students find they need to spend 3x number of credits in hours per week in studies. This means spending at least 15 hours per week studying on the 5 credit hour course. I've worked with students and watched some struggle spending 5x the hours in order to fully understand the topic, this would mean 25 hours per week, every week. When finals come around, it may require even more time.

These are not high school courses. The expected work load is serious.  At many schools 12 credit hours is considered full time, because it equates to about the same as a full time job.  Most schools discourage students from taking more than 18 credit hours because it would require over 50 hours of effort at those rates.

Some students who have a natural affinity for the topic, or who already mastered the prerequisites, or who have prior experience relating to a course can complete the work in less time, but they are the minority.  Based on my own observations, they're less than 10% of the students. About half need to invest serious time in thoughtful study.

 

On 2/23/2019 at 5:14 PM, RidiculousName said:

However, I love programming, and I don't want to transfer to another major. So, I want know what you guys think. I have already transferred colleges twice, so this is my third college. Assuming the dean of Computer Science (who has a PHD in Mathematics) doesn't let me replace my Calculus classes with other coursework, what should I do?

I don't mind working outside the game industry, but would I be unemployable without Calculus? How cheap and reputable are degrees from online colleges? Could I ascertain whether they'd waive any otherwise-required calculus course beforehand? What could I do that would improve the chances of the Dean of Computer Science allowing me to switch the courses for other ones?

First you should make sure you are doing EVERYTHING you can to set yourself up for success.  Make sure you have the ability to devote the time necessary for the course.  If you are unable to spend 15+ hours every week on the subject then you may have issues. If you have not mastered the prerequisites then you may have issues.  Those will not be because math is hard, or because you have a disability, those issues are because you did not properly prepare for the course.

First and a half:  Be serious about those 15+ hours.  That doesn't mean 3 hours daily "studying" with Fortnite up in a second monitor, or studying between League of Legend matches, or chatting while studying. That means time spent at a desk entirely focused on the course for that time, engaged in serious study at the exclusion of everything else.  For many students, that also means turning your phone all the way off. Use the power button. You can turn it back on again when your study session is over.

Second, talk with the teachers every day, or if the course is run by a teaching assistant, talk with them.  If the course meets five times each week, that means a quick one-on-one chat five times each week.  It may be only a few seconds on some days, it may be a half hour long on other days, but it should be daily time speaking with them. 

There are options for other schools. People mentioned trade degrees at schools that do not require calculus. You can also find jobs that do not require degrees, but be aware you will always have more difficulty finding a job since you'll be interviewed after your degree-earning peers, and you'll probably negotiate lower salary than your degree-earning peers.  It is still possible, but you don't exist in a vacuum.

The best option is not to seek out a fourth school, but to make sure you do the work and complete the degree you've already started.

I have not been brilliant at mathematics. I've been close to where you were, so our stories aren't too different. At the end of my story, I got my CS degree. If I can do it, you can too.

My math story starts off a bit depressing. I went all the way to pre-calc in high school, but did miserably and didn't pay attention and put in the diligent effort. I retained very little. I took a placement test and got placed quite far behind, but I felt the placement test was in error. No big deal, if the class material is easy, I can breeze right through it and fill in any gaps. I didn't have to work very hard to pass with A's. That became a bad habit. I got to pre-calculus and in order to do well, I actually had to start studying. I didn't. I passed with a C, but it's still passing. I moved onto Precalc 2. This would turn out to be a stumbling block for me. I had learned that math builds upon the previous material, sort of like a pyramid, so if your foundation is weak and you build on top of that, you are going to be miserable. With Precalc 2, I got another C. Not a great start for my adventures in calculus, so I decided I would retake it. I did, and I got another C.

Then, life kind of got in the way. I had joined the US military during the summer and 9/11 happened, and I ended up bouncing between war zones and class rooms, and being away from school for 10-12 months makes you forget things. I ended up taking Pre-calc 2 a third time as a refresher course, got around a B. I think, all in all, I ended up taking Precalc2 about 4 times. What's interesting is that, that experience made me really familiar with the material. I still can't for the life of me memorize the half angle formula or double angle formula, but I am very comfortable with sine, cosine, tangent, cosecant, unit circles, etc. This is where I learned to stop breezing by in my classes and how to actually study and learn, and how to teach myself. It was the most critical thing I learned.

I took Calc 1, got a C, didn't like it, went to war, retook the class, still got a C, and went onto pre-calc 2. Precalc 2 was actually a little easier than Calc 1, but I still got a C the first time around. I decided to take it a second time to try to improve my grade for my transcripts. I #*@!ed up. I started to get lazy. Our teacher required ALL homework to be turned in before mid terms and finals. If you didn't do your homework, you automatically failed the test. I started procrastinating on the homework. The day before the final, I started doing all of my Calc 2 homework since the mid term (around 2pm). I was "getting it" and blazing through the math as fast as I could write. Pages, upon pages, of calculus. I was writing homework until about 4am. Math class started at 8am and I had to be there in time for the final, or I would fail. I was exhausted. I decided to take a short nap, I set my alarm, and went to bed. Then, I woke up. I felt *too* rested. I didn't wake up to an alarm. Something was *very* wrong. I look at the clock. It's exactly 8:30am. If I rushed out the door, I'd get into the classroom by 9am and be an hour late. So, that's exactly what I did. I show up an hour late to take a two hour test. I felt like if I could do math as fast as I was doing it the previous night, I could still blaze through it, and maybe, if I'm lucky, get a 70%. About 30 minutes in, I realized I wasn't going to finish the test in time. My strategy changed: Rather than doing all the problems, I would only do the problems I could do the fastest. I might know how to do a problem, but if it took too long to write out the solution, I would skip it in favor of low hanging fruits. If I grab all the low hanging fruits and still have time left over, I can revisit the harder and longer problems. I turned in my test, with my homework, and... got a 55%. Ouch. I barely got a C in that class.

The thing is, I learned how to learn. I learned how to crunch. I felt, that with enough perseverance and effort, I could figure anything out. I would go onto university, and while the CS courses were quite hard and challenging, I could pass them. My secret weapon was my study habits. While others might be smarter, I even the playing field by studying harder. There were other late nights in university where I was working until 4am, but I was used to that now.

I did find a class that was harder than Calculus 2. It was "Elementary Logic", which was a 400 level course offered by my philosophy program. I loved it. The class was taught by a really old man, an obviously tenured professor, and he chose to start the class at 8am and teach in a room with the heat turned all the way up. It would be really easy to fall asleep. On the first day of class, I arrived about 10 minutes late. I walk in, and the class room is PACKED. The 30 desks were filled and about 10 more students were standing in the back taking notes. There wasn't even standing room! I ended up sitting in the window sill (they were recessed). The course material was... really hard. The textbook was really terse. You'd have to re-read the same page about 5 times just to grasp what it was saying, and another 5 times to understand it. Most logic classes are just an introduction to formal logic, this was using logic to prove that the logical proofs in formal logic were sound. We explored set theory, uncountable sets, small infinities and large infinities, russels paradox, godel, peano arithmetic, and meta logic. I remember getting stumped on the proof for the "existential specification". It was so convoluted and circular, that no matter how many times I tried to make sense of it, no matter how much I studied it, it would not click. This... was my intellectual limit it seemed. No amount of perseverance would make sense of it, and I hate rote memorization. By the middle portion of class, about 80% of the students had dropped. We were down to a small group of 12 students! Quite a contrast to the beginning of the course.

My point is, Calculus 1 & 2 may not be the hardest classes you end up taking. But, what it takes you to pass Calc 1 & 2 is going to be the same thing that carries you through the other, hard classes.

I would also say, schooling in general is actually the easy part of ones career. All of the knowledge is given to you, someone else has gone before you and found all the answers, and you are being given them by an expert. If you feel bad about the difficulty of Calculus, don't. It took mankind thousands of years to get to it, and then it was developed and refined over centuries. You are getting centuries worth of mathematical knowledge crammed into your head in a matter of months. Cut yourself some slack, but don't give up.

After you graduate and enter into the professional world, it's quite different. Technology moves fast. It's constantly changing. You may venture into areas where nobody has ever been before, doing things that have never been done. There may be no existing body of knowledge to fall back on, no experts to guide you, not even google search results to give you the answers you seek -- you may be the google results others find later. The murkiness and uncertainty may end up making you wish to go back to the black and white days of calculus classes... but really, if we're going to be honest, the same underlying universal principle is at work here: learn how to teach yourself and how to work hard. If you can master that, nothing set before you is insurmountable -- except maybe a proof of the existential specification using meta logic.

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