I dislike calculus/analysis. What can I do then with the math I love?

[isqrith]

Hello,

Just finished high school and will enroll in a college with a top math program this year, and I'm from a pretty mathy country. A few words about my mathematical tastes: my favorite branch is number theory, but I also like enumerative combinatorics, all kinds of algebra that I've studied(linear and abstract included), and some Euclidean geometry. I did mostly elementary, HS olympiad NT, but I'm pretty advanced in it(I use things like Dirichlet's theorem, Zsigmondy's theorem, Mobius inversion etc.) More often than not, I can solve number theory IMO problems pretty fast(though I never went to the IMO), and I also occasionally solve IMO-level combinatorics problems.

I had a quite precocious aptitude for arithmetic, and I had some excellent results in national math contests, but my passion for math was pretty on-and-off before high school. During math contests in my recent years, I also happened to rediscover some formulas(in discrete math) that more advanced math people failed to find.

However, despite studying it for almost 2 years, I find little pleasure in doing calculus. The issue I have with calculus is that it doesn't arouse my curiosity. Questions like: is that function continuous? what is the limit? does such a function exist? simply don't inspire me. I also never cared much for graphic representations of functions. Also, I find point-set topology as tiresome. Sometimes, the more difficult proofs seem very artificial to me, and I occasionally do not understand how some people can solve serious problems(not talking about homework here) in real analysis. There were some things that I enjoyed learning(like Taylor series), but I hardly remember an analysis problem that really made me want to solve it for pure fun.

So, I ideally want to become a researcher in math, but want to use very little calculus. Is this even possible? Of course, I know that I will need to take MV Calculus, Real&Complex Analysis in order to major in math, and then take analysis and topology if I do enroll into a math PhD program(or possibly earlier). Without being passionate about analysis, is there a chance I could grasp the analysis material and then concentrate on non-continuous mathematics?

I also have to mention that I had to learn almost all the math I know entirely on my own, and maybe that explains some of my difficulties with calculus/analysis/topology(calculus is certainly tougher than algebra and NT, and apparently, my Calculus teacher liked Calculus as much as I did). From your experience, is there a chance that an excellent teacher will be able to make me enjoy analysis?

However, if you think that not finding calculus interesting after 2 years of study is a sign that I should not do math, I'd like to hear your suggestions about what else I could study. I pretty much can't see myself doing anything but science, but I'm open to other suggestions too.

 

[Simon Bridge]

It is, in principle, possible to advance in maths to end up doing your work in a narrow field, however it is unlilely that you will be able to complete a maths degree without doing some calculus.

You should review the prospectus for your college to see what is possible.
You may be able to plan out a degree course that avoids subjects you dislike.

However, your dislike of calculus is not a sign you should not do maths.
Everything has a price and having to at least understand calc will probably be yours.
It is more likely that it means you need to approach calculus in a different way.

Certainly an excellent teacher, one who enjoys the subject, is grounded in it, can make all the difference.
A good teacher will try several different ways to approach a subject - it sounds like your calc teacher hated calc and so passed that on to the students.

 

[micromass]

It is certainly possible to do math research without ever doing calculus or analysis things. So don't worry there. I know many professors doing research in abstract algebra who haven't used a derivative or integral in years (except in teaching).

A lot of people have different tastes in math. I personally find number theory to be very boring and it doesn't get me excited at all. OK, I don't do anything related to number theory then. The solution for you is analogous, don't do anything related to analysis and calculus.

That said, you obviously know you will need to take analysis classes in undergrad. Study well for these classes, even if you don't like them. Sometimes intuition from analysis, topology or calculus can be very useful in things which appear totally unrelated. The more different kinds of math you know well, the more connections you have with things you know.

 

[TheAustrian]

Perhaps you have just had an uninspirational teacher, or read a bad book on calculus. It's entirely possible that your interests will turn around, and you'll end up tolerating, or who knows, even liking calculus.

Like the post above says, there are plenty of things you can do that avoids the use of calculus in the end, but you'll have to be relatively lucky to avoid a subject that touches upon so many things, but it's entirely possible to not have to use calculus in your future field.

 

[johnqwertyful]

For me the most interesting thing about analysis and why I like it was making precise notions of infinity. Abandoning ideas of "infinitely small" or "infinitely big" or things like that. That really speaks to me. I also like physics, which we need analysis for.

But I get it if you don't like it. You don't have to use analysis, but if you want a PhD, you DO need to take it and pass quals and stuff. Just suck it up and push through those. Your research can have nothing to do with analysis, which is really the important thing.

To make it through the class try to like it, but I get you probably won't.

 

[finnk]

Have you looked at computer science ?

Did you use Rudin ?

Do you like geometry ?

Do you know why and how calculus and analysis exist ?

Btw, just curious. Feel free not to answer my questions.

 

[homeomorphic]

For someone who doesn't like calculus, I think computer science might be something to think about (there are definitely calculus applications, but they can be avoided by most computer scientists or programmers).

I do think being a math research is an option for you, but even with your great head-start, it's always very difficult to know how well that will work out, so it is always good to have a back-up plan. It turned out that for me, it was precisely when I got to research-level math that I found it was completely incompatible with my approach to...life, I guess, for lack of a better word. There wasn't too much warning before I started reading papers and trying to write my thesis that it would be such a bad place for me, even with the dozens of subjects I had previously studied from books.

My other question would be if you have taken physics. Physics, more than anything, is what makes calculus interesting to me, although I do like basic real analysis, too, just because it gave me a deeper understanding of it, and I like to have a deep understanding. One thing I really enjoy in calculus is doing discrete approximations and then taking the limit, particularly when there is physical intuition involved--you would see a lot of this sort of thing if you studied physics or engineering. I suppose I like that because that sort of turns it into discrete math with a limit thrown in, and I kind of like discrete stuff.

Probably, most people learn a lot of these subjects sort of out of context, so that they don't really see the point. I'm not saying it's the end of the world if you sometimes have to learn something that's a bit unmotivated at first and then sort of put the puzzle-pieces together when you have studied more, but I think people should be doing a lot less of it. To my mind, there's no point in learning something out of context because the context is what makes it really learn-able and memorable. To get more context, often you can turn to the history of math or maybe just browse around for other modern books that supply more motivation.

You might find complex analysis interesting, since it is surprisingly different from real analysis.

 

[isqrith]

Thanks everyone who replied.

It is indeed possible that I didn't find yet a good book, or a good teacher. I tried four or five calculus books, and found two of them occasionally interesting(the other three were horrible), but simply the questions in analysis don't really appeal to me.

However, complex numbers are one of my favorite topics in math. Would it make any sense to look at a good complex analysis book, and then return to real analysis if I like it?

I regarded CS as a serious option for some time, but I discovered that I simply don't like programming enough. And theoretical CS research, like improving one alg's complexity from O(N^2) to O(NlogN) is not my thing.

I have taken six years of physics. I originally hated it with a passion(stupid teacher), but after studying it for the SAT, I learned it pretty quickly and like most of it, but not enough to major in it. But I still dislike all the specific approximations(like alpha = sin alpha for some lenses) and I generally prefer to study problems with perfectly accurate answers(like diophantic equations, enumerative combinatorics).

Never really thought about engineering, I was never good at very practical things, never watched "How It's Made" etc. Still, I might like newer areas of engineering(e.g. biomedical), I don't really know.

I'm somewhat attracted to some other things, like neuroscience(at least, to have a backup), but I don't really know how I could use my math skills in it. Anyone has some insights about this?

To finnk's questions:

"Have you looked at computer science ?"

Answered above. :)

"Did you use Rudin ?"

First opened Rudin a few days ago. Started from the beginning to fill the gaps. For now I'm struggling to find anything interesting about compactness & connectedness, and then I'll force myself to advance to real analysis. But I can say Rudin's "Basic Topology" chapter is one of the most uninteresting and arid pieces of math I've read in a long time.

"Do you like geometry ?"

Euclidean geometry, yes, but I always felt like it was ultimately useless. Vector geometry/coordinate geometry/transformation geometry, I like them too, but less than synthetic geometry.

"Do you know why and how calculus and analysis exist ?"

Not sure, probably not/not enough. I know only the oft-repeated stories about Newton, Leibniz, the birth of the integral concept ect, but they don't fascinate me.

 

[micromass]

"Did you use Rudin ?"

First opened Rudin a few days ago. Started from the beginning to fill the gaps. For now I'm struggling to find anything interesting about compactness & connectedness, and then I'll force myself to advance to real analysis. But I can say Rudin's "Basic Topology" chapter is one of the most uninteresting and arid pieces of math I've read in a long time.

That seems an accurate description of Rudin. I like Carother's real analysis book, but that might be too advanced.

"Do you like geometry ?"

Euclidean geometry, yes, but I always felt like it was ultimately useless.

And you don't feel that way about number theory?

 

[homeomorphic]

I regarded CS as a serious option for some time, but I discovered that I simply don't like programming enough. And theoretical CS research, like improving one alg's complexity from O(N^2) to O(NlogN) is not my thing.

There's a lot more to CS than just improving algorithms. How about artificial intelligence or computer graphics or computational geometry?

One thing to keep in mind is that you might not want to take your likes and dislikes that seriously. I used to be a little bit finicky about little particular things in a subject that I didn't like, but after studying math in graduate school, I disliked it so much that I really am not bothered anymore by little irritating details of other subjects. For example, although I pretty much always liked programming, when I first started doing it, there were aspects of it, like getting all the syntax exactly right (these days, the IDEs make that quite a bit easier), that I found annoying enough to make me question whether I would want to do it for a living. But after studying math in grad school, I look back at it, and those things seem like hilariously small things to be bothered by. I couldn't really handle the information overload in grad school, and I tend to like digging a different hole, rather than digging the same whole deeper, which is why I liked undergraduate and graduate level math, but not research, which is, unfortunately, mostly concerned with digging what seems to me like excessively deep and narrow holes. Digging shallow holes gives me more coverage. A broader understanding of the world around me.

First opened Rudin a few days ago. Started from the beginning to fill the gaps. For now I'm struggling to find anything interesting about compactness & connectedness, and then I'll force myself to advance to real analysis. But I can say Rudin's "Basic Topology" chapter is one of the most uninteresting and arid pieces of math I've read in a long time.

Don't use Rudin, then. I've never read it myself, but my impression is, it seems a bit too abstract.

 

[verty]

There's a lot more to CS than just improving algorithms. How about artificial intelligence or computer graphics or computational geometry?

Artificial intelligence, is that still a big deal? It was some years ago but we've seen robots that can walk, swim, and for example the robot that can always win at rock/paper/scissors (look it up if you haven't seen it). And just the other day it was reported that Turing's test of computer intelligence was just passed. AI is looking like yesterday's problem to me, the future is going to be more hardware, more throughput and probably not a lot of change to the software.

 

[homeomorphic]

Artificial intelligence, is that still a big deal? It was some years ago but we've seen robots that can walk, swim, and for example the robot that can always win at rock/paper/scissors (look it up if you haven't seen it). And just the other day it was reported that Turing's test of computer intelligence was just passed. AI is looking like yesterday's problem to me, the future is going to be more hardware, more throughput and probably not a lot of change to the software.

I don't think so. There are still quite a few problems in AI. I'm no expert. One example problem would be to design a computer program that can beat professionals at the game of go. Also, even though a lot of problems have been solved, that doesn't mean there isn't room for improvement. Sure, Asimo might be able to walk, but they are still working on making those sort of robots really practical for applications like nuclear clean-up or other hazardous environments. Getting things to work in the lab, under ideal conditions is one thing, but developing an approach that deals with all the curve-balls thrown at you in a more practical setting is a bigger challenge.

We're a long way from really getting a computer to think more like humans do in many ways.

 

[AlephZero]

AI is looking like yesterday's problem to me, the future is going to be more hardware, more throughput and probably not a lot of change to the software.

Hm... I don't know much about AI, but I have been working on computational (solid) mechanics for a few decades, and I know a bit about computational fluid dynamics. Some of the the "standard" algorithms that are used today hadn't even been discovered 20 or 30 years ago. Others were known as nice-looking theoretical mathematics, but nobody had figured out how to make them work on real computer hardware using finite precision (i.e. inaccurate) arithmetic.

I wouldn't write off the invention of "something completely different" in AI software (or any other software topic) too quickly - but of course you can't predict what new stuff will be invented, and when, before somebody actually invents it.

 

[TheAustrian]

Artificial intelligence, is that still a big deal? It was some years ago but we've seen robots that can walk, swim, and for example the robot that can always win at rock/paper/scissors (look it up if you haven't seen it). And just the other day it was reported that Turing's test of computer intelligence was just passed. AI is looking like yesterday's problem to me, the future is going to be more hardware, more throughput and probably not a lot of change to the software.

It's a very big deal in military research. Developed countries are going to employ more and more AI in their armies, although this seems distant from now, it is going to happen. There are already some informations released to the public:

http://www.newscientist.com/article...ops-to-defend-missile-bases.html#.U3Y7oa1dU00