Is there a connection between aptitude for high school math and university math?

[cjwalle]

Hello PhysicsForums,

My previous posts here do a rather good job at illustrating my indecisiveness. Here's some background:

I started uni in the fall of 2010. After applying to maths programs at many Canadian universities, and Economics at Norwegian ones, my choice fell on Economics at the University of Oslo. I realized rather quickly that Economics wasn't quite my cup of tea. Limited in transfer options mid-year, I decided to give Law a try (Law is a 5 year combined undergrad/grad degree in Norway). I mainly chose law because it was the only program I could easily transfer to in the middle of an academic year, but ended up quite liking it.

Now, here's my problem. I miss math. Mathematics was always my favorite subject in high school (IB). I was always fascinated by how.. well, true, it was. And applicable to pretty much all areas of life. However, I am unable to determine whether I'm just suffering from "the grass is always greener on the other side of the fence"-syndrome.

So I turn to this forum, a forum which has always been incredibly helpful for the education-related questions in my life. Granted, I'm not asking anything related to Physics, but judging by other posts here, Mathematics should be close enough.

Mathematics appeals to my ambitions. Mathematics is an international subject, and the possibility of going to grad school at an Ivy League school is there. That is not the case for law.

I'm not quite sure what I'm asking. I realize only I can determine whether law or mathematics is best for me. Any insight would be helpful, though. My main concern is that my love of High School math does not necessarily mean I'll like, and succeed at, university math. In your experience, is there a connection between aptitude for HS math and aptitude for uni math? If it's of any relevance, I would be aiming for a concentration in financial mathematics.

Thank you for any input you're able to give, I greatly appreciate it :)

 

[chiro]

I am not sure quite what you are asking, but I'll make an inference by answering in my opinion what the difference between math in high school and math in university is.

In high school, (even in higher level classes), a lot of math was pretty procedural. The understanding behind it like the motivation behind its creation, the background that led to the invention of something like say calculus was far from complete. I wouldn't say it was entirely missing, because you do get an idea of how things started, but it wasn't deep.

This kind of procedural introduction to some areas of math put me behind in some areas since I wasn't introduced to a "first principles" or a "philosophical or motivational approach" to the problem.

With university its different. It is true that ability to compute is still important and I think there should be some importance for doing this since making errors in the real world has the potential to do damage in many ways, but thankfully a different perspective is brought to the table by people who offer not only a computational perspective but also a motivational and philosophical perspective to give students the background to understand and appreciate the math they are being taught.

In lower level math (and especially in high school math), you are concerned more with specificity. You are applying algorithms, procedures to problems that are very specific. You probably don't get completely why you're doing it, but none the less you are taught how to do it, and you are taught what its used for, but the motivation and philosophy isn't there.

In higher level math, you are looking at from a different point of view. You see frameworks of thought that have been evolving for many hundreds of years to help answer more than one specific problem. As a natural consequence, you would expect that the thinking diverges from lower level math and indeed it does.

Most math finds a balance between these two extremes depending on the domain. Most engineers will understand calculus and will know how to compute complicated integrals and ODEs or PDEs (even by a computer), but most will probably not know why Riemann Integration actually works in the first place.

Statistics (which is one of my majors) have kind of the same approach. We have to understand a lot of math including linear algebra, all of calculus, optimization and so on, and for a lot of problems we apply this knowledge to specific situations. But for the most part we are more interested in how specific knowledge helps us answer problems in statistics than problems in math per se.

I guess the answer that it is domain dependent is probably the best answer I can give you. Plenty of fields mix math that is both very abstract and both very specific, but that will ultimately depend on what goal you have in mind. University tends to have a healthy mix of both, especially for applied science domains like engineering, natural sciences, computer science, statistics and so on.

 

[DivisionByZro]

It really boils down to: How passionate are you about math?

I speculate that, if a lengthy study were conducted, you'd find that there isn't much of a correlation between aptitude for HS math as compared with University math. In other words, I speculate that being good at HS math does not make you good at University math. The two are very different.

As Chiro puts it, in HS you apply algorithms; educators tell you, "Use the quadratic formula blah blah...". Why does it work? Why can you use it? If these types of questions are questions you asked yourself regularly, then perhaps look into it. University math is about creativity, abstract thinking, and logical thinking, not just applying algorithms.

My suggestion to you is, pick up a decent math book from where you left off (A lot of people can help you find a challenging one), and also watch some university mathematics lectures online; it will give you a taste of the classroom at the university level.

 

[thegreenlaser]

I would be very wary about switching into math. Like others have said, university math is very different from high school. Financial math might be less abstract than other streams, but I definitely wouldn't jump into it without knowing for sure. Before you switch over completely, I would maybe start working towards it as a math minor. One thing you still have to be careful of there is that a lot of schools will 'hold back' on the math in first semester, so as not to kill the incoming high school students who are used to plug-and-chug math. I thought I had seen 'pure math' at it's worst when I took linear algebra 1 in first year, and I actually really enjoyed it. Now, however, I'm taking linear algebra 2, and I'm shocked all over again by the level of abstraction. It's a very different world, and I've heard that it only gets more abstract. Just make sure you really do get a taste of it by taking some 2nd year courses before you jump in. If you can, talk to an adviser in the math department as well and ask them which courses would give you a real flavour of what university math is. Unfortunately, your aptitude for high school math gives very little information about how much you'll like university math. A minor might be a very viable option though, if you're able to.

 

[General_Sax]

Can't you just take a couple math classes as an option?

 

[Maxter]

I agree with the others, trting to find a way to incorporate more math into what you are doing now (a minor, or a more mathematical emphasis), as a way of testing the waters. Many economists end up taking analysis and theoreitcal probability at advanced levels, so that might interest you.

If, in high school, you enjoyed the "lightbulb" moments of math, you might enjoy continuing on.

The distinction isn't so much high school vs university math, but lower division versus upper division math, in most cases. Upper division math tends to be more theoretical, and has a completely different flavor than most lower division courses. Would hate for you to get into upper division math, and then realize that that's not what you want. However, once that math bug bites, sometimes you can't shake it...