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Other Are My Math Skills Proficient Enough?

  1. May 14, 2016 #1
    Hi, everyone:

    I'll be transferring from community college to a four-year university next Fall and am wondering if my math background is sufficient and proficient enough to do well.

    I haven't decided on a major(s) yet, although I listed philosophy (very provisional - I had to list something - and highly likely to change) on my application for admission, but am aware of how central the subject of math is to so many fields.

    I enjoy math and have done well (straight A's) at it in my community college (I took College Algebra, Pre-Calculus, and Applied Calculus there). I have yet to take "real" Calculus (with analytic geometry) or any type of "higher" maths. But from what I've taken, I have done well grade-wise and had fun in the math classes.

    For my first semester at university, I'll be taking (working schedule - subject to change) Statistics 1a and Calculus 1 for my maths, Principles in Microeconomics (econ.), Race and Inequality (sociology), and Social & Political Philosophy (philosophy).

    Some questions & concerns for university math:

    (I'd particularly appreciate insights from anyone who has gone from a community college to four-year university!)

    1.) What degree of help is typically available at a traditional college/university when it comes to math? At my CC, there was something called a "math lab," where students could go and ask questions related to any math course offered and be tutored by math proficient students and/or faculty. Our class sizes for CC were also roughly around 15-27 students on average.

    I'm worried that in a large lecture (the Statistics 1a class I've looked at already has 80 people signed up and it's not full yet with months to go before Fall!) that it would be impossible to ask questions or get to know the instructor personally for help.

    2.) How much mastery of pre-requisite math is expected? I know that each math class has a pre-req. listed and one should just assume that you'll need to know everything from day 1 that's a pre-req.

    In concrete terms, would that mean looking up formulas or rules, etc. would mean that a person was under-prepared for that college math class?

    I ask, because I've found that I've had to look up past math rules and formulas for all of the community college math courses that I've taken. For example, when I took Applied Calculus, I had forgotten the rules for doing logarithmic functions from Pre-Calculus and had to spend a day reviewing that before I could even do the math for my AC class. I had gotten an A in the Pre-Calc. I class where we first learned that topic, but it wasn't something that was committed to my memory. Or, similarly, I remember having to spend some extra time relearning/memorizing the quadratic formula, rules for exponents, rules for complex numbers, etc. for various classes I've taken, where it was assumed knowledge.

    I've been told by some people that math classes tend to move faster at a four-year university and that having to constantly look stuff up could be a drawback, but not necessarily such a strong impediment as to sink you in a class or make you unable to get an A.

    I'm curious from those with experience, how much "looking stuff up/review" would you say is reasonable for any given math class? Obviously, I would assume that if you forgot so much math as to have to look up 50% or more of things, then you're probably not prepared for that class. But in roughly estimated terms, how deep should a person's mastery be of pre-requisite material and what percentage of forgotten stuff would you think is "acceptable" for taking a university math class (i.e., you'd have to spend time looking it up)?

    3.) To succeed in a STEM or social science major, what degree of mastery of math do you think is needed?

    For example, would a typical successful student in those fields have gotten straight A's or all A's and B's in all their math classes, have memorized all of the material (so as to not have to look anything up), and have good intuitive grasp of math (so as to not have to seek tutoring help and can learn on their own)?

    In real terms, how good does one have to be at math to succeed in STEM or the social sciences?

    Feel free to add any additional thoughts to the topic, in addition to the questions I've asked. Thank you all so much for your help! Physics Forums has definitely been an integral part of my academic success through community college!
     
    Last edited: May 14, 2016
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  3. May 14, 2016 #2

    symbolipoint

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    Maybe you would need to review Trigonometry on your own, or you might plan on enrolling and studying Trigonometry before going into Calculus 1. If you did well already in College Algebra and in Precalculus, you are probably ready for Calculus 1. Doing Statistics and Calculus 1 in the same semester term may be difficult.

    Your university should have a tutorial service for Mathematics students.

    Studying physical sciences will both require you to be at least average with the stated Mathematics prerequisites and also will give you ways to apply your Mathematics which you have studied, so you may improve in them.
     
  4. May 14, 2016 #3
    If you enjoy math you'll be fine. To be honest I constantly find myself having to check basic things and I'm doing a masters in Particle Theory. The main thing is to enjoy it - if you do you'll be motivated to practice.

    Math is a bit like playing a musical instrument - its not a collection of facts to be learned - it's a way of thinking and approaching problems. There are techniques to be learned, but with mathematical maturity these can always be relearned at ease. For instance - I always forget the form of many of the basic Taylor expansions, but because I remember the form of the theorem, I can work them out as I go along. Another example is trigonometry - I can never remember which way round sin and cos go on the triangle, or where their zero's are - however I know if I draw a circle with radius 1 and then construct right angled triangles for particular angle values that I can derive almost all of the answers I need pretty quickly.

    Just make sure to attend all the classes and do all the homework - sounds obvious right? I did not heed this advice as an undergraduate and made life unnecessarily difficult for myself. In the end I had to teach myself most of the math for my physics degree - I feel that that process actually helped me become a much stronger mathematician than most of my contemporaries - however I had to work bloody hard at it. Lucky that it turned out that I quite enjoyed it eh!
     
  5. May 14, 2016 #4
    I concur. I highly recommend taking a trigonometry course before taking calculus. I also do not recommend taking two math courses during the same semester. For a degree in the social sciences, trigonometry and calculus 1 is all you will really need to know. Physical sciences are heavily mathematics dependent, and usually require at least 4 years of progressively more difficult mathematics.
     
  6. May 14, 2016 #5

    symbolipoint

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    Some or many social science degrees have a Statistics requirement. Trigonometry might be either a requirement or (more likely) something useful to include, simply because some sequences of events or conditions could be cyclic and some Trigonometry might give social scientist a handle on making descriptions.
     
  7. May 15, 2016 #6
    Forgive me, I don't know how the american system works, but a whole lecture course on Trigonometry seems somewhat excessive?
    We just kind of picked it up as we went along...
    I mean what is there really to know beyond the definitions of sin cos tan & reciprocals, some identities?
     
  8. May 15, 2016 #7
    Well, one of the hardest things I encountered in math was solving a problem that could only be solved by using several trig identities to rewrite an equation. You would have to see first that you had to use a trig id, then which one to use so terms would cancel out. Then use another one to get something simple.

    Can't imagine how hard it gets when you need to memorize all known trig identities for all known advanced trig functions.


    Then again, I doubt they learn this in the American system. Mixing advanced trig in with calculus is also how I learned math.


    If you don't even want to go into physical sciences and you like math and had good grades, I wouldn't even worry about it.
     
  9. May 15, 2016 #8
    I think memorising all such identities is a waste of time to be honest. No professional mathematician would do such a thing when they could simply look them up and check the proofs when they needed to employ them (which would be rarely).

    When I first saw trigonometric substitution for solving integrals, I was like "whoa man - how did anyone ever think of that?" but truth be told I do it in my sleep now - there are always giveaways and tell tale signs.

    The students in the string theory group who came from a pure math background actually know LESS practical math then I do (I am in Cosmology). However I wouldn't dare call myself a better mathematician than them - its a different way of thinking involving a level of abstraction I cannot personally attain. For example, I might be shown a technique in contour integration - however I would soon forget it unless I was applying it regularly. A mathematician proper would invent such a technique for himself. Thats the difference...

    TLDR - don't worry, just enjoy. There are unlikely to be math courses available to you that you can't handle. If you encounter stuff you don't understand - go to the library, get a book and work through the chapter making your own notes and solving the exercises. To be honest, most of this years grad level courses (especially Lie Algebra) I had no clue what was going on in class - understanding came with my own work and time to let to material sink in after mulling it over a lot.
     
  10. May 15, 2016 #9
    Both universities I attended and the few others whose math and science departments I visited had paid tutors whose job it was to help students who arrived to study during their posted tutoring hours. Tutoring was typically in a room at the library or a room chosen by the department whose subject was being tutored. In addition, my alma mater had a math lounge and a physics lounge next to their respective department offices which served the same purpose as the math lab you described.

    It sounds like you'll be fine as long as you maintain enthusiasm. The key is to come up with your own applications and "exercises." If you are capable of having fun playing with applications of what you're learning, you'll likely be in the top 5%-10% of your math classes.

    The real test will come in calculus II and/or differential equations, for which some professors require the memorization/internalization of several "arcane" techniques for integration and solution of differential equations. If you can maintain your momentum through those two classes, or you get good professors who teach understanding and the ability to recover mastery rather than memorization for tests, you'll likely be fine with all the rest of the math you learn.

    Oh, and I highly, highly, highly recommend that you take a matrix algebra/linear algebra class as soon as you can. You're already qualified for it, and it will help you understand and tie together nearly every math class after that, especially differential equations. I took my first diff eq. class without having taken linear algebra, and now I wish linear algebra I had been a prerequisite for diff eq.
     
  11. May 15, 2016 #10
    I second the notion of taking linear algebra as soon as possible. Its basically the most important thing ever.
     
  12. May 15, 2016 #11
    The reason why I highly recommended taking trigonometry before taking calculus is because it will make calculus much easier. Trigonometry should be a prerequisite to calculus, in my opinion. Some schools will offer a combined algebra and trigonometry course, or include trigonometry in a pre-calculus course. Either way, if your goal is to achieve better than a 2.0 ("C") grade from calculus 1, then taking a trigonometry course first would be a very good idea.
     
  13. May 15, 2016 #12
    In the UK a whole lecture course is usually 24 lectures. This seems excessive for solely trigonometry. Is the US streaming system different?
    I am always terribly confused when everyone goes about "Calculus 1" or "Calculus 3" - is there some sort of national standard, such that one's third calculus course always the same material?
    I wholeheartedly agree that one should ones sin cos and tan identities before embarking on calculus, but do you not learn this at high school?
     
  14. May 15, 2016 #13
    The US system is not uniform due to the lack of national curriculum. That being said many states have reciprocal agreements on courses (especially mathematics) between universities for intrastate transfers (interstate you are at the mercy of the admissions committee).

    Calculus 1 typically denotes single variable differential calculus, Calculus II single variable integral calculus, Calculus III multivariable calculus culminating in vector calculus. These are typically spread over three long semesters or 3 to 4 quarters. There are variations: I have seen a year long course covering all of this material.

    Calculus 4 and 5 may denote vector analysis or complex variables or a first course in real analysis depending on the university.

    That being said trigonometry at the college level is 45 lecture hours (high school is roughly 80 lecture hours). Each Calculus class varies from 45 to 90 lecture hours.
     
  15. May 15, 2016 #14
    Does one not cover single variable single differential calculus at high school?
    45 hours of lectures on just trig at college level? I'd probably shoot myself!
     
  16. May 15, 2016 #15
    Some do take differential calculus in high school (like myself) and then take it again depending upon whether they earned AP credit or don't score high enough on the placement exam (again like myself). Actually, I took it a third time several years later as a TA... guess it took that many time for the material to sink in :biggrin:.

    I would estimate that one third to one half of undergraduate university education in the US is to correct for deficiencies from high school (mathematical or otherwise) unless you are attending a very prestigious institution that can set higher entrance standards

    Never know when you might need to prove an esoteric trig identity! Seriously though the requirement for students to take and pass trigonometry for non-science/math majors is historic standard (as was calculus for a short time before it) and will probably be removed eventually. I believe it was imposed by the same people that thought rigorous mathematics is the only way to teach people to think critically.
     
  17. May 16, 2016 #16
    I'm currently signed up to take Trig over the summer (starts May 23rd), so I am set! Thanks!!
     
  18. May 16, 2016 #17
    Thank you very much for the longer answer above, DrS.

    It was encouraging and helpful! I do find that memory of certain math formulas or rules is a weakness of mine and something I actually plan to work on this summer. The other subject area I'll be working on is English (yes, I was born in the U.S.!). I want to have faster reading skills without losing comprehension.

    I know the SATs (taken in high school) test math and English primarily (the general test - not the subject specific ones), because you need both to do well in college. Almost all the sciences require math from what I can tell and all the humanities and social sciences require heavy reading.

    I did want to follow-up on your post above and ask why you felt linear algebra was important (e.g., what is it used for/in?)? I've heard of it before, but don't know anything about it.

    Is it really true that simply having gone through Applied Calculus is enough to take such a course? I'll take a look at my university's offerings if all I would need is Applied Calc. It does sound intriguing. Thanks so much again!
     
  19. May 16, 2016 #18

    symbolipoint

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    bballwaterboy said:
    Reading for Humanities and reading for Sciences & Mathematics are different kinds of reading. The thinking going along with each is very different. With sciences, you need to read fewer pages, thinking deeply/intensely and must try to achieve full understanding, as near to 100% understanding as you possibly can. You cannot read this stuff fast, most of the time. You are often not using social feel and maturity in reading for Sciences and Math - but often you DO when you read on topics in the Humanities.
     
  20. May 16, 2016 #19
    Hi, SP

    I definitely agree that reading for those two knowledge areas is very different.

    I do want to practice both and improve in both. I find the humanities to have a more intuitive feel to them when reading in those subject areas. With math and science, there's a lot more time I have to spend conceptualizing what is even being talked about to begin with!

    My goal is to get better at both over the summer and one area of targeted improvement for me is speed - yet, without loss of understanding. It's good that you reminded me of how both types of knowledge are different, though. That's something I'll have to keep in mind when learning to improve my reading comprehension and speed in both areas!
     
  21. May 16, 2016 #20

    symbolipoint

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    Good. You understand the differences. You CAN improve at both. Humanities requires more human maturity, and this comes with further life for some people. Some humanities & social science people are very intelligent, and since some people mature in their human understanding sense much earlier, they find reading about these things to be areas that they are good at doing.
     
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