Calculus 3 or LA/DQ to help decide a major

[TheKracken]

Hello everyone, I've read advice on here about waiting to decide on a major until you have taken most of the math and physics courses. I am here to ask which math class I should take in order to help me decide which major would be best for me? I am debating still between math/physics/ee and maybe statistics. Currently I have calculus 1 and currently in calculus 2. Next semester I will be taking physics 1 (mechanics and some wave stuff) and either linear analysis ( linear algebra and differential equations together class.) or calculus 3 ( vectors and multivariable calculus.) I am even considering a major in bioinformatics and geophysics. That is how lost I am :P

 

[jz92wjaz]

You are split between basically the same majors I was (though I was looking at Computer Engineering instead of bioinformatics and geophysics). I think the biggest difference between EE and Physics is if you prefer to build things or study things. I picked EE initially, which was a questionable choice for me because I knew I already I knew I liked research better than design. By the time I finally decided to switch, I ended up getting two majors (EE and Physics). It's hard to say what I would have done if I could go back in time, but the idea of a Math/Physics dual major is certainly appealing. I might have thrown in a couple of CS courses to go with it.

 

[TheKracken]

I think I have more of a scientific mind then a building and designing products mind. I just would really like to make a informed decision about what I want to major in. Consistently I see advice of waiting till you finish all the math courses. I am in calculus 2 and I feel like I have learned nothing to make a decision on major. I love math, but the few applications we have had I seem to do worse with ( fluid pressure, optimization is all we have done). Any advice on how to use your math classes to decide on a major?

 

[symbolipoint]

TheKracken,
Nobody can pin-point the decision for you. The only reasonable advice now is that your best choice for major field may be in the physical sciences or mathematics. Most of the physical science & engineering students need three semesters of Calculus-Plus-Analytical-Geometry and some form of course work for linear algebra and differential equations. If you do not find enough exercises in your mathematics courses on applications, you will find the applications in Physics and in Engineering courses. Also some other physical science courses will apply the mathematics which you study.

 

[IGU]

Have you taken any math courses that require doing math? I mean figuring out proofs as opposed to applying math to science problems. Until you spend a fair amount of time proving things (and I don't mean reading other people's proofs) you have no idea whether math is the thing for you. Have you spent a week staring at a math problem with no idea how to make progress? Research mathematicians can spend months or years like that.

 

[TheKracken]

No I have not had much experience with actual proof writing. As for the classes, I will only have only taken physics 1, calc 1,2 linear algebra and differential equations by the time I have to decide. So I won't really be able to experience engineering courses until next spring when I already have to had put down a major.

 

[IGU]

No I have not had much experience with actual proof writing. As for the classes, I will only have only taken physics 1, calc 1,2 linear algebra and differential equations by the time I have to decide. So I won't really be able to experience engineering courses until next spring when I already have to had put down a major.

Well, then get some experience. Study ahead in one of your classes, except ask your prof for a source that includes proofs. Then try doing the proofs yourself. No peeking. If you haven't been even reading proofs then go back and try to prove things, starting with the simplest stuff. Rework calculus from Apostol or Spivak, reading some proofs and trying to work out others for yourself. Do the problems. You don't have to wait until somebody hands you the opportunity.

As for engineering, see if you can get an internship doing engineering. That's how you figure out if it's the right thing for you. Note that taking classes and even getting a degree won't be certain either. What it's like actually doing things for a living in the real world is surprisingly unlike what it's like in school.

So simply accept that you'll have to decide without having much of a clue what it all means. When that's what you do, it's up to you how many options you leave open and how many you close off. And remember, if you don't enjoy the work actually being hard, then math and science and engineering probably aren't for you.

 

[vela]

If you want to hedge your bets, go with physics. It's relatively easy to go from majoring in physics to math or engineering. It's harder to go the other way.

 

[jbrussell93]

Hi Kracken,

I was in a similar position as a freshman with many interests and trying to figure things out. I started out in bioengineering/EE thinking that I wanted to do something with bioinformatics similar to you. It was after doing computational neuroscience research for a year that I realized I wanted to get away from the biological sciences. I took a geophysics course and started doing seismology research and that's where I really found my niche. I would highly suggest trying to get involved in research as soon as possible if that is an option for you. That is where you will really figure out what you enjoy (or not). Especially if you are considering graduate school.

Now to answer your question: For me, it was calculus 3 (and physics 2) that really got me excited about mathematics/physics and in fact caused me to change my major to physics. That was my favorite course in the calculus sequence with DiffEQ coming in at a close second. With either of those two courses you will start to see math that will really show up in your upper division physics courses. At my university, calculus 3 was a prerequisite for DiffEQ so I didn't really have a choice but my suggestion would be calc 3 ASAP.

Vector calculus is an intuitive, beautiful subject and for the first time in your math classes, you will really have to THINK. In calculus 1 and 2 it is just memorizing algorithms/tricks to solve integrals. In Calc 3 you will have to set the integrals up in 3 dimensions and really understand what's going on geometrically. That is what is important for physics. You will learn how to integrate over surfaces, lines, and volumes and you will derive Stokes', Greene's, and divergence theorems which will be central in your upper level Electricity and Magnetism courses.

Differential equations is also important for upper division courses in physics, but to me it was more similar in nature to the earlier calc courses. You are told how to solve differential equations with little intuition for where the solutions actually come from. You are told to "assume" a solution type which I had some trouble with at first but eventually learned to accept without proof. My favorite part of the class was solving the harmonic oscillator in all of its details which you will see again in your upper level mechanics course. That is where the intuition started to click for me.

As far as choosing a major, I've found physics to be a safe bet especially if you are planning to attend graduate school. I will be going for geophysics but I could just as easily have gone the biophysics or pure physics route... You really do have more room to explore (or specialize) as a physics or math major than engineering. I think it is good that you have identified that you have more of a "scientific mind". I think you might be disappointed with the engineering curriculum and the way engineers do things - I know I did.

Good luck!

 

[TheKracken]

I appreciate everyone's responses. They are very helpful! To jbrussells93, what made you decide against the bio type area's? You said you had some research in comp. neuroscience, which is another area I find fascinating, what made you go away from that route? I am interested in most area's of natural science except maybe chemistry. My main area's being physics, biology and geology. With Biology, many things interest me from population ecology modeling, to neuroscience and bioinformatics. One career I thought would be cool would be some sort of statistician for fish and game type agency's. I am a big fan of being out in the wild and exploring nature but would realize I will be mostly on a comp no matter what I do. With Geology, I tried out a course in physical geology but it didn't seem to be what I was into. At least the first part of the course, it was all about "rocks" and mapping. I would find think seismic waves, and other physics/math heavy area's of geology might be cool. But I feel like in this case I wouldn't actually be doing anything outside, but maybe I am wrong?

Sorry for all the questions, it just seems like you have been through my dilemma before and advice would be helpful!

 

[jbrussell93]

Happy to help when I can.
I decided against bio and particularly comp neuro for several reasons. First, I realized that I enjoy thinking about large scale phenomena as opposed to the small scale. For example, the collision of two continents forming a mountain belt or understanding the rotation of the Earth's inner core are fascinating to me. This is why I love geology/geophysics, especially at the tectonic scale. You should definitely try to to take a course on Plate Tectonics if you can... I also did not care for my intro physical geology course because I found the rocks to be boring. On the other hand, I took a cell biology course and grad level neurophysiology course, both of which I really disliked. They would show us little cartoons about what is going on in the cell and the "machinery" but I just couldn't convince myself of the physics behind it. I feel that we really don't fully understand the physics behind what's going on in a cell for example... it's all chemistry. With geophysics, most things are very intuitive and as a physics major, I like thinking about things that are physically intuitive to me.

Another reason for leaving comp neuro is that I really wanted the opportunity to do fieldwork and be outdoors some. With geophysics (and seismology in particular) you have this opportunity. I spent 2 weeks in Kentucky deploying seismic stations in order to learn about the formation of the continental craton and its structure. Also, I'll be going to Turkey for two weeks next semester to help with fieldwork. My research mentor has literally been all over the world doing seismology fieldwork.

I also considered just changing fields of biology to something more ecology or behavioral biology related because that's where you'll find most of the fieldwork. I am an avid birder so I was interested in doing something quantitative related to studying avian migration patterns or something. Although there is some very mathematically intensive work in those fields, you really won't find much physics. It is primarily applied mathematics and statistics which personally, I was not comfortable with.

Seismology has turned out to be a good fit for me. I feel that I have a natural interest in wave phenomena and an intuitive grasp on the subject. It is essentially wave mechanics with a lot of theoretical overlap with optics. Definitely enough math/physics to keep any physicist happy. It turned out that my favorite physics courses were classical mechanics and optics so it was perfect, really. I think when you find the field that is "right" for you, you will know.

I think you should try to figure out where your deepest interests are and follow a field that contains as many of those things. It sounds like an obvious first step, but I mean REALLY think fundamentally about your interests. Do you like thinking in large or small scale? Do you care about scale or are you only in it for the interesting mathematics? If you are interested in physics, what kinds of physical phenomena do you find most interesting? How important is fieldwork for you? Can you handle being behind a computer all day every day in your research?

Once you've thought about some of these questions, then ask yourself which field (biology, geology, engineering, physics, applied mathematics, statistics) might fit your temperament best.

 

[homeomorphic]

I think you might be disappointed with the engineering curriculum and the way engineers do things - I know I did.

Ah, but it's not that simple. Grad school in engineering can be quite different. And really, it is possible to learn engineering in a better way than they tend to teach it. You're just going to be on your own to some degree, figuring it out, but I think that applies to a lot of subjects. I switched from engineering to math and now I sort of regret it. My problems with engineering turned out to be trivial ones. I didn't like the way they did things, but I was able to figure out my own explanations, most of the time, which converted it into something that I liked (and some of it was pretty cool as presented, too. So, then, in my senior year, I finally wasn't able to come up with my own explanations. Out of frustration, rather than just gritting my teeth through one more extremely annoying semester that is not necessarily representative of all of EE, I hastily changed my major to math, unaware that I was walking into a trap in the long run. I think it can be misleading to judge a major based on 2-3 classes that you really hate, and to blame it on the subject, when it's really the presentation that's at fault. You have to keep an open mind.

So, you have to think of a plan that's actually going to work out, and if it's a risky one, have another plan to back up the first one. This is somewhat tongue in cheek, but studying physics is like a lottery where the prize is that you get to work really, really hard. Well, if you're not careful, anyway, that's what it can be.

No matter what you choose, it's going to be a little bit of a gamble, and the more education required, the more of a gamble it will be. It's hard to reach a point where you're really sure that you have made the right decision. At least, I never got to that point, and I have a PhD. Actually, I repeatedly was sure that I made the wrong decision, but then, looking back, I don't know if I did every time. Some people might just think I'm too fussy and won't be satisfied by anything, but the opposite is true because I learned not to sweat the small stuff. My problems with EE were small stuff. My problems with math are BIG, BIG stuff. I learned what it is like to have fundamental, irreconcilable problems with a certain profession. I suppose I'm a bit of a misfit/maverick, though. Anyway, I think part of it is going to be just accepting that there's going to be some risk involved in the choice.