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Thread: The road ahead

  1. #1 The road ahead 
    Member epidecus's Avatar
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    So I've been trying to independently learn some math recently... I'm almost done with single-variable calculus, and I'm not exactly sure what's in store for me in the long run. I am taking formal classes below this level however, but since I'm proficient I thought I might do some learning ahead.

    So after single-variable calculus, I assume the subject moves to multivariate. I know several subjects that would come after that, but I'm not sure at all in what order: differential equations, linear algebra, vector calculus, some analysis, etc.

    Can someone enlighten me as to the order of prescribed courses typical of math in college? I'm much curious so thanks in advanced.
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    Quote Originally Posted by epidecus View Post
    So I've been trying to independently learn some math recently... I'm almost done with single-variable calculus, and I'm not exactly sure what's in store for me in the long run. I am taking formal classes below this level however, but since I'm proficient I thought I might do some learning ahead.

    So after single-variable calculus, I assume the subject moves to multivariate. I know several subjects that would come after that, but I'm not sure at all in what order: differential equations, linear algebra, vector calculus, some analysis, etc.

    Can someone enlighten me as to the order of prescribed courses typical of math in college? I'm much curious so thanks in advanced.
    After elementary calculus, there is no fixed order to the courses. If your interest is in pure math, advanced calculus should be next. However for applied math areas, vector calculus, linear algebra, probability, etc. are all relatively independent.
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    Quote Originally Posted by epidecus View Post
    So I've been trying to independently learn some math recently... I'm almost done with single-variable calculus, and I'm not exactly sure what's in store for me in the long run. I am taking formal classes below this level however, but since I'm proficient I thought I might do some learning ahead.

    So after single-variable calculus, I assume the subject moves to multivariate. I know several subjects that would come after that, but I'm not sure at all in what order: differential equations, linear algebra, vector calculus, some analysis, etc.

    Can someone enlighten me as to the order of prescribed courses typical of math in college? I'm much curious so thanks in advanced.
    Typically after one sees elementary calculus of one variable the next class is calculus of several variables combined with analytic geometry in 3-space. This is usually the third semester of calculs and is quite often done using the same text that was used for single variable calculus.

    After that one might take a course in linear algebra, differential equations or a combination of linear algebra and differential equations. This would typically be completed in the second year at a U.S. univresity.

    After that one is ready to take slightly more advanced mathematics classes, and those are dependent on one's interests and major field of study. Fairly typically one would take a class in introductory real analysis, abstract algebra, intermediate linear algebra, introductory topology and geometry, probability and statistics, etc. In such classes one might reasonably be expected to not only understand proofs but to construct one's ow proofs.
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    Thanks a lot for the responses, guys.

    As of now, I'm pretty confident that mathematics will be my (primary) major. I think I understand the gist of proofs decently (more so than my peers to say the least).

    I'm actually not sure which route I want to take: pure or applied math? Both sides seem to have interesting prospects I'd like to dive into. Even after narrowing my major down to one subject, there's still a broad range of included or related fields... set theory, analysis, abstract geometry, physics, etc. Suggestions?
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    Quote Originally Posted by epidecus View Post
    Thanks a lot for the responses, guys.

    As of now, I'm pretty confident that mathematics will be my (primary) major. I think I understand the gist of proofs decently (more so than my peers to say the least).

    I'm actually not sure which route I want to take: pure or applied math? Both sides seem to have interesting prospects I'd like to dive into. Even after narrowing my major down to one subject, there's still a broad range of included or related fields... set theory, analysis, abstract geometry, physics, etc. Suggestions?
    As you learn more you will be able to determine what you like and find those areas that fit your aptitude. It is too early for you make a decision, since you have not yet seen enough to be able to appreciate the menu.
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    Quote Originally Posted by DrRocket View Post
    As you learn more you will be able to determine what you like and find those areas that fit your aptitude. It is too early for you make a decision, since you have not yet seen enough to be able to appreciate the menu.
    You're right I guess. I've got some time, so I'll see what comes of my learning.
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    Quote Originally Posted by epidecus View Post
    You're right I guess. I've got some time, so I'll see what comes of my learning.
    You actually have a lot of time. There is no need to make that sort of decision regarding the degree of specialization that you suggest until graduate school. In fact you can make that decision rather late in graduate school. Some people even switch areas of concentration long after they have completed graduate school. Raoul Bott made major contributions to topology and geometry, but his education was in electrical networks. Pontryagin is best known as a topologist, but he made major contributions to dynamics optimization and abstract harmonic analysis. Pierre Conner wrote his dissertatioin on an aspect of differential equations, but is best known for work on cobordism (a topic in algebraic topology).

    Take the time to enjoy the landscape. There is a lot out there, far more than you can master in a lifetime. In that regard there is no "correct" choice either. You will probably find several things that interest you. Pick one and if you find later that something interests you more, then make the switch.
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    Yeah, I guess you're right (well, you are right). Thanks for the suggestions.
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