Math classes....in what order?

Discussion in 'Math' started by subtech, Dec 1, 2006.

  1. subtech

    Thread Starter Senior Member

    Nov 21, 2006
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    I've had this question asked of me several times recently, and I would be very interested to see how some of you would respond if asked this question.

    Q. "I graduated high school having taken only the basic minimum math classes. Now that I'm out in the working world, I find myself more and more involved in things electrical/electronic and it's terribly obvious that my math is nowhere near what it needs to be. I have the desire and the funds necessary to take some math classes. In high school I had basic math and Algebra 1. I don't want to be an engineer at NASA, but I do want to be able to analyze electrical problems effectively and speak intellingently to the EE where I work. What classes should I take, and in what order?"

    Thanks to all who care to respond.
     
  2. Dave

    Retired Moderator

    Nov 17, 2003
    6,960
    144
    I take by some of your spelling that you are from the US? Therefore I personally cannot give you specific advice dependant on where you come from, but I am right in thinking you are looking at something like Night-School?

    As for the Mathematics you wish to learn, well for Engineering you are best looking at a combination of Pure/Core Mathematics and Applied Mathematics (preferably with an electronics focus). Some Statistics may be of use depending on which stream of electronics and engineering you wish to go down.

    The courses available to you are highly dependant on what is available at your local academic institutions; should you be in the UK you could look at doing a stand alone Pure and Applied Maths A-level which would give you the necessary grounding in the more advanced subjects that you are currently missing with your high-school education. Another course which has gain popular interest in the UK (although I don't speak from experience here) is the Access course which would give you the conceptual grounding, without too much focus on understanding Maths from a "first-principles" approach, which is more the case for the A-level. You could do with finding the equivalent of these two courses where you live and look at the suitablity of them dependant on your needs.

    As a final point I would suggest that whatever Mathematics you choose to do, make sure you can understand and apply the concepts to the real-world situations that the EE's at your place of work are engaged with - whereas the concepts of, say for example Calculus, bridge the grand divide of many engineering disciplines, translating that to an understanding of the dynamics and interactions of the world of electronic engineering is another ball game altogether.

    Good luck in whatever option you decide to take. And remember that being good at Maths is not just about learning the material - you have to practice the material on a wide range of real examples.

    Dave
     
  3. Papabravo

    Expert

    Feb 24, 2006
    10,137
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    From where you are now I would suggest:

    Geometry
    Algebra II (including Complex numbers)
    Trigonometry
    Calculus I (including analytic geometry)

    If you make it that far then we can have another conversation on where to go from there.
     
  4. Dave

    Retired Moderator

    Nov 17, 2003
    6,960
    144
    To give you a cronological sequence of early Mathematical education for Engineering in the UK (A-level to first/second (partially) year degree):

    1. Introduction to Algebra
    2. Expressions and Equations
    3. Linear Equations and Simultaneous Linear Equations
    4. Polynomial Equations
    5. Partial Fractions
    6. Trigonometry
    7. Binomial Series
    8. Differentiation
    9. Integration
    10. Functions
    11. Complex Numbers
    12. Hyperbolic Functions
    13. Determinants
    14. Matrices
    15. Vectors
    16. Differential Applications
    17. Partial Differentiation
    18. Curves and Curve Fitting
    19. Series
    20. Integral Applications
    21. Approximate Integration
    22. Multiple Integration
    23. First Order Differential Equations
    24. Second Order Differential Equations
    25. Laplace Transforms

    Many of these areas are largely developed in later years of a degree and you would look at subjects such as Vector Calculus and Fourier Analysis (although this is primarily approached as part of Signals and Systems courses). But then we are getting a little deep here, it is just to demonstrate the scope for Mathematics in engineering as part of A-level to degree-level education in the UK. I would imagine this is similar in other parts of the world.

    Dave
     
  5. serg_zone

    New Member

    Dec 2, 2006
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    0
    I'm not sure about electronic engineers, but if you're interested in network circuitry of network engineering, you'd have to go up to at least calc 3. Then you could take a class in numerical analysis and that's where calc 3 is a crucial prereq. You're essentially dealing with data flow and a lot of that has to do with sequential analysis covered in Calc 3. But i'd say for general stuff. Try to cover at least calculus 1 and 2. You'll hit a lot of subjects on your way up to calc2 such as matrices, vectors, curves, function, binomial equations, series, differentiation, integration and etc.
     
  6. subtech

    Thread Starter Senior Member

    Nov 21, 2006
    123
    4
    Thanks very much for the responses.
     
  7. jay4321

    New Member

    Jun 16, 2008
    4
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    BUMP - Hi, I'm Jay and come from the future (2008).

    I found this old thread an found it very helpful, and was hoping that I could get a little follow up information.

    Long story short: I was a high school dropout who returned to community college. I've done very well, have virtually finished my 2-year degree and will transfer to a four-year school in the spring. I completed "Introduction to Algebra 2" and "Intro to Statistics" as my first math classes in 20 years, and did very well. I only have one more course to take in the fall (a math).

    I enjoyed those courses very much, and I'm even getting some hope of getting into a graduate school to study economics. That said, I realize that I will have a tremendous amount mathematics to learn and have no illusions about it. However I am willing to take math courses back-to-back for as long as I can stand it in order to give it my best effort.

    With the above in mind, which course should I take next? And, what would be a decent order for these (and which can typically be taken concurrently)?

    College Algebra
    Trigonometry
    Pre-Calculus
    Calculus 1
    Calculus 2
    Calculus 3
    Linear Algebra
    Discrete Mathematics
    Differential Equations

    I have other opinions, including those from school, but I was hoping for your perspectives. Thanks.
     
  8. Dave

    Retired Moderator

    Nov 17, 2003
    6,960
    144
    A couple of points:

    1) If you are planning to do economics then what maths courses do you need to do? Are differential equations a requirement for economics?

    2) Modern economics often places a large emphasis on economic (computer) programming. Does your course factor this in to the above course options? May be something worth thinking about.

    3) If you are just looking for a rounded theoretical mathematical background, then the options and order you suggested are more than suitable. It encompasses most of the syllabus I detailed some years back.

    Dave
     
  9. jay4321

    New Member

    Jun 16, 2008
    4
    0
    Hi Dave:

    I've collected a rough "wish list" that graduate economics programs seem to be looking for:
    multivariable calculus, linear algebra, real analysis, advanced probability/statistics, and differential equations. Matrix algebra is sometimes mentioned as well. It's so math-heavy that a lot of people are of the opinion that an undergrad major in mathematics is actually better suited to the task of getting into an econ program.

    But, obviously I have to walk before I can run. I'm still trying to figure out why geometry isn't offered, whether I need precalculus at all, and where things like linear algebra and trigonometry fit in. I was told that I could skip to straight to Pre-Calc with no problem just today - so what about Trig, College Algebra, etc.?

    I'm concerned because I'm afraid of taking courses I'm not prepared for. I'd like to do it the right way and make sure I can keep up.

     
    Last edited: Jun 16, 2008
  10. jay4321

    New Member

    Jun 16, 2008
    4
    0
    To answer your other questions"

    2) I have a reasonable IT job and don't expect a problem with learning or adapting to economic modeling software and so on. It does require some attention but my undergrad econ coursework will hopefully address this somewhat.

    3) I can't honestly answer this. While I am interested in a good overall grasp, I'm also trying to avoid taking the "business math" route. A lot of people seem to be taking the minimum math (kind of the way some people take 'Earth Science' to avoid Physics).
     
  11. Mark44

    Well-Known Member

    Nov 26, 2007
    626
    1
    Hi Jay,
    I taught all levels of community college math for 18 years, so I'm familiar with the math is offered at that level. Or at least I was up until 10 years ago, when I left teaching. I'm not sure what was covered in the Intro to Algebra 2 class, but I'm guessing that the classes you listed are the ones offered in you school.

    Because the concepts in mathematics build on previous knowledge, if you take more than one class at a time, your instructor in one class might assume you have mastered material you haven't yet covered in the other class. For this reason, I'd recommend against taking more than one at a time, although you might be able to get away with it in the earlier classes. I definitely recommend against doubling up on the calculus classes. The order that you show for the classes looks about right.

    WRT Geometry, very few colleges in the US offer Geometry, but some of the concepts are taught in courses with names like Analytic Geometry or Precalculus.

    WRT math prerequisites for Econ, I suspect that at least part of the reason for them is to act as a filter. That's not to say that Economics doesn't use a fair amount of higher mathematics.

    WRT some of your other questions, where I taught, the sequence was Precalculus I (which was college-level algebra), Precalculus II (which was trig + vector basics), then Calculus I, II, and III (engineering-level calculus), then Linear Algebra and Differential Equations.

    Linear Algebra is concerned with systems of linear equations (i.e., first-degree in the variables), and matrices (which can be used to represent linear systems), and linear transformations. There's more, but I'm not writing a book. Linear Algebra and Differential Equations are actually more related than a lot of people realize, and either one could be the prerequisite for the other.

    Hope that helps.
    Mark
     
  12. jay4321

    New Member

    Jun 16, 2008
    4
    0
    Mark:

    The Intro to Algebra 2 was basically factoring trinomials, rational expressions, dealing with roots and radicals, and left off with quadratic equations.

    Second, I have no intention of trying to double up with Calc classes, but are there any that could be taken concurrently? I would only be enrolled in two classes per semester so I'd have the study time. Something like Trig and Pre-Calc?

    And thank you both for your help.
     
  13. Mark44

    Well-Known Member

    Nov 26, 2007
    626
    1
    You might be able to double up on the Trig and Precalc classes. Keep in mind, though, what I said about concepts in follow-on classes being dependent on concepts in an earlier class.
     
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