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Thread: Mathematics Paper

  1. #1
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    Mathematics Paper

    This is really off-topic.

    Many years ago, the son of some friends of ours was graduating from high school and heading to Georgia Tech to study engineering. I wrote a paper on some basic mathematics that he would encounter in his engineering studies.

    If you have, or know, a child who is heading to college for engineering, mathematics, physics or related subjects, this paper may be of use to him or her. If you find errors in the paper, please let me know.

    Mike

    [Oops, the paper is larger than the the forum allows for .pdf. You can see it here.]
    Go into the world and do well. But more importantly, go into the world and do good.

  2. #2
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    Id prefer not to pass on the joy of diff EQ. Lol

  3. #3
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    The high school and I think college miliatary recruiters used to give out nice printed outlines of important formulas and rules etc for chemistry, physics, math and other sciences. Printed on heavy cardstock making nice binder dividers.
    Bil lD

  4. #4
    If I knew how to use it ...I would certainly want one! My engineer son gets tired of me needing help with higher math.
    Mike, that is most kind to offer that and I'm pretty sure they will become dog-eared treasures.

  5. #5
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    Nice paper Mike. That's a good intro to what's ahead for an engineering student. My favorite: "Get used to radians. Youre going to be using them a lot."
    Beranek's Law:

    It has been remarked that if one selects his own components, builds his own enclosure, and is convinced he has made a wise choice of design, then his own loudspeaker sounds better to him than does anyone else's loudspeaker. In this case, the frequency response of the loudspeaker seems to play only a minor part in forming a person's opinion.
    L.L. Beranek, Acoustics (McGraw-Hill, New York, 1954), p.208.

  6. #6
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    When my Son in Law finished his Masters in Mathematics from the Colorado School of Mines, he showed me his thesis. It was like a small phone book filled with equations. I've been an Engineer for almost 40 years and have done all kinds of math. None of this made the least bit of sense to me. Smart kid. Works on cool stuff now.
    Sharp solves all manner of problems.

  7. #7
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    Mike - thanks for sharing, you obviously put a lot of effort and energy into the paper! Your introductory section, with some life lessons learned, might be the most important part, especially in todays social media driven world.

    In the preface, you ask if readers would respond. What feedback have you gotten over the years?

    Jim

  8. #8
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    When a high school student, I struggled with math. In one of my numerous meetings with the math instructor, he explained how I would need math in the future.
    I explained, with all the assurance a 17 yr old can gather, that I would never be so foolish to pursue a career that required any math ability.

    So now I use math everyday, and I enjoy my ability, my facility with it. Granted, I am not working with quadratic functions.
    I want to stay as close to the edge as I can without going over. Out on the edge you see all kinds of things you can't see from the center.
    - Kurt Vonnegut

  9. #9
    Thats quite a paper Mike! Thanks for sharing it. My neighbor kid starts college this Fall (somehow) and I will give him a copy. I agree with your preface - it's always about hard work.

    I might have missed it, but have you copyrighted this in some fashion? It's your intellectual property.

    Best regards,
    Fred
    "All that is necessary for the triumph of evil is that good men do nothing."
    - Sir Edmund Burke

  10. #10
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    Extraordinarily well written paper, but in a nutshell, why I became a biologist. Even though I got through differential equations in college (and pchem, but that's a different story) that was about the end of my mathematical career; tried algebra (the real thing, not the high school stuff) and ran screaming. I managed a 40 year happy career as a productive working scientist without ever again finding a need to use calculus.

    What I wish someone had told me while I was still young enough to absorb it, was how important statistics were going to turn out to be in both my working and personal life. The personal side is obvious, one has only to read the paper these days to see that virtually no one, from the leader of the free world to the morons posting on Facebook has a clue about statistical reasoning, how to interpret the idea of a 30% chance of rain, or why a couple of anecdotes about how Aunt Mary didn't get Covid after standing on one foot while gargling Drano don't constitute data. Needless to say they wouldn't know a Bonferroni correction if it bit them on the big toe. (this lack of understanding, shared by too many scientists, explains a vey large fraction of the hyperbolic headlines that quickly turn out to be wrong).

    At work, analyzing genomes, gene expression data, and proteomics on the one hand, deciding where to set cutoff limits in drug screening (and how many replicate assays of what sort might cause you to believe you had a real result), and (pretty relevant these days) whether a drug you were looking at in the clinic was doing anything (good or bad) turned out to be all statistics all the time.

    All that said, my friend the mathematician (a leader in algebraic K-theory, whatever that is) would look at any of this and scoff 'that's not math, that's just arithmetic'.

  11. #11
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    Thanks Mike - well done and very generous to share it. My 12 year old grandson - the one who helps me with programing problems - is reading it. Says it's pretty cool.
    If it wasn't for the "last minute", nothing would ever get done.

  12. #12
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    Very nicely written paper.

    As someone who originally trained in physics and mathematics, I have always been intrigued by the different kinds of rigor and motivation mathematicians, physicists and engineers each put into the same basic mathematics. When my son became a professional statistician in bio-medicine, I added statistics as a fourth domain of intrigue. The explanatory power of differential and integral calculus in each of these domains is one of the great monuments to human ingenuity, and never fails to settle my mind into a better place ... except when I get to something I want to understand but which is simply too hard for me to penetrate.

  13. #13
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    Mike, If only you had been my high school mat teacher.

    This paper is such an important aspect of learning mathematics, and should be mandatory course of study in my opinion.

    Thankyou for writing it, and posting it here. I will be reading it over and over, as it really is what I needed a long time ago.

  14. #14
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    Did I miss something or are partial diffy Q's coming in the 2nd edition?

    Great stuff, Mike!
    "Don't worry. They couldn't possibly hit us from that dist...."

  15. #15
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    Very cool Mike. The thought and effort you put in to author an assistance paper for your friend's son is to be commended. Much of it is over my head but, the parts I could hang onto are well written and systematically presented. My barometer is generally if something I am unfamiliar with can be presented so that I can follow it, the author must be doing an exemplary job. Kudos to you for your thoughtful effort. It is just another example of you sharing your talents; something that I have benefited from myself.

    P.s. For others, I am referring to Mike's dovetailing class which I have the pleasure of attending one on one. This really helped me with my dovetail technique.
    "The Danish government believes that if we train 5,000 designers, and produce
    one Hans Wegner, the money is very well spent." - Ole Gjerlov-Knudsen

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