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Mathematics Problem

  1. Dec 11, 2009 #1
    Hello! Thanks clicking this thread. Please allow me to trouble you for a few minutes.

    I'm about to finish my first semester at CUNY's Bronx Community College. CUNY's math placement test landed me on Math 05, which is basically Algebra 1 remedial class. Even though I'm about to pass that course with an A, I feel I still have huge "gaping holes" in my Math knowledge and I want to correct them before I start taking Calculus. My interests are Physics and Chemistry and my goal is to become a Chemical Engineer.

    My Math professor believes I am doing great in Algebra and instead focus on sharpening my Arithmetic; I agree with him but that does not satisfy me. I do not know what order Mathematics starts but I'm assuming it goes Arithmetic → Algebra → Geometry/Trigonometry → Calculus. I want to start from the most basic Arithmetic, so I'm looking for books that assume the reader is mathematically illiterate. I'm looking for training wheels and as I advance then ride on my own.

    Now, I'm not a "gifted genius" or anything of the sort; I expect to have huge difficulties. I simply want to have all the Mathematical knowledge I can obtain. If others can learn Mathematics so can I; the only difference between myself and a Math genius is that the dude has been studying longer than me, nothing else; my dreams and goals depend on learning Math, so I have no choice but to learn it. Any assistance you may provide me will be appreciated. Thank you.

    edit: http://www.maa.org/devlin/LockhartsLament.pdf [Broken] just read it after checking out more threads related to my problem. I am now utterly confused! Hahah!
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Dec 11, 2009 #2


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    What kind of arithmetic do you feel you need work on, and what other gaping holes do you think you have in your math knowledge?

    The order you've written:
    "Arithmetic → Algebra → Geometry/Trigonometry → Calculus"

    is more or less the order elementary mathematics is usually taught. And it is true that a lot of mathematics builds on other stuff. But mathematics is not linearly ordered, and there is to some degree some arbitrariness in the order here. For instance, historically, geometry was studied long before most of what we would really consider algebra was developed.
  4. Dec 11, 2009 #3
    as an chemical engineer you dont need such an advance math so better focus in your chemistry
  5. Dec 11, 2009 #4


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    Science Advisor

    Calculus isn't an advanced math...it's required for Engineers.

  6. Dec 11, 2009 #5


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    Science Advisor

    You're on the right path...just build your mathematical background by taking the courses you have outlined above. They are designed to give you the necessary tools to prepare you for not only Calculus, but engineering concepts as well.

    Last edited by a moderator: May 4, 2017
  7. Dec 11, 2009 #6
    I'm not sure why. I've really found good arithmetic to be not that useful in geometry and calculus. My arithmetic is totally dreadful, probably since I've never had to use any of it in the last decade or so. If you've mastered algebra, I really don't see how being good at arithmetic is going to be that useful to you.

    You have to realize that the arithmetic->algebra->geometry->calculus routine is a tiny, tiny fraction of what mathematics there is. The reason it's taught this way is that calculus is the bare minimal requirement for any sort of science and engineering.

    Now if you want to go off the beaten path and look at something really different, there are lots of different areas that you can look at. Wikipedia is pretty good for doing that sort of thing.

    I'm not sure that's true. There are people that are really, really good at math, and they tend to pick things up a lot faster than me. One reason that I got my Ph.d. in physics is that I'm not particularly good at math.

    Also a lot depends on the quality of teaching. A good math teacher can make the difference between something that is totally obvious and something that is impossible to understand. One problem with thinking that effort will get you somewhere, is that especially with math, sometimes you are expending a huge amount of effort because its being badly taught.
  8. Dec 11, 2009 #7
    And if he plans to stay in the CUNY system, he's gotta take 5 classes worth of calculus (calc 1-3, diffEQ, vector calc/linera algebra).

    A lot of schools have pre-calc before calc, and it usually covers limits, interest, and some other random odd little things. (It's the first course in the math sequence at most CUNY schools if you don't place into calculus.)

    As for starter stuff, if you have no qualms about doing stuff for kids, I adore the BBC maths review sets. home page - look around for the topics you really want to beef up.
  9. Dec 11, 2009 #8
    Thanks for the replies. I think I need to explain what my intentions are more clearly so I will list what my goals are:

    1) I want and need a solid, robust Mathematics foundation that will allow me to study Physics, Chemistry, and Chemical Engineering properly and efficiently. Mathematics is a tool and I desire to use this tool to express the thoughts and ideas flowing through my head. I want and need to understand what the tool is and how to use it. I want my mathematical knowledge to be "stainless steel-solid" and water-proof. I think Stewartcs addressed this.

    2) Building on #1, I desire to understand the mathematical concepts behind this knowledge to satisfy my curiosity. I'd like to understand where concepts come from, what led to them, etc. For example, while (re)learning the quadratic formula, my Math 05 demonstrated how it was derived starting from the general form ax² + bx + c = 0 and ending at -b ± square root b² - 4ac divided by 2a. I was amazed and from that moment I can't stop thinking where other concepts come from and spend considerable amounts of time trying to figure them out. I want to understand why I am doing something and the concept behind that something, not just memorize a series of steps like an automaton.

    3) Building from #2 and #3, I am searching for books that assume the reader has little to no previous knowledge of the Mathematics subfield covered but progressively increases the depth of the subject. In other words, I want to start crawling, then have someone hold my hands while I take those first steps, and finally be able to walk on my own to explore the world.

    I do not know how Mathematics should be taught. I believed (incorrectly?) that Mathematics began at Arithmetic and progressed from there. I just want to start from 0, 1, 2, 3... basically, I want to build a solid base for my house before I build the walls, roof, piping, etc. Thanks for your patience.
  10. Dec 11, 2009 #9


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    Mathnomalous -

    Arithmetic is some of the first mathematics taught to students because it is simple and useful and necessary for other things they need to be taught, but not because it is in any real sense a foundation or starting point for mathematics.

    And, in fact, topics in the foundations of mathematics are out of your reach right now.

    You certainly have the right attitude (about wanting to actually understand how things work). Maybe you could be more specific about what it is you want to know?
  11. Dec 12, 2009 #10
    Most of the foundational stuff is taught in the upper-level math courses because it's very dependent on proofs and all sorts of theorems and advanced concepts that you have to learn first.

    Try your textbooks. For example, the Stewart calculus book has digressions into history and sometimes touches on the conceptual stuff.

    Math/history/philosophy books? Maybe "The Nothing that Is: A Natural History of Zero" and working up from there to others in a similar vein?
  12. Dec 13, 2009 #11
    Concerning the underlined, I will start from arithmetic because it will likely provide me with what I need to understand more advanced mathematic topics. These 3 books were recommended to me so I will begin with them:


    Concerning the bolded, I want to be an efficient and reliable chemical engineer; this means mastering algebra and calculus (and other necessary mathematics) to perform my job to the best of my abilities. I'd like to be able to work on issues like this: http://newsroom.ucla.edu/portal/ucla/ucla-researchers-engineer-bacteria-149726.aspx

    Basically, use my knowledge of mathematics, physics, and chemistry to design useful things. For example, I'd like to design a water treatment/power plant hybrid, obtain methane supplies from termites, and/or invent a new and advanced type of electrochemical battery.

    Nonetheless, thank you and the rest of you for taking the time to address my concerns.
    Last edited by a moderator: Apr 24, 2017
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