Electronics > Beginners
Maths in Engineering
coppice:
--- Quote from: james_s on January 01, 2020, 09:27:15 pm ---
--- Quote from: coppice on January 01, 2020, 08:43:35 pm ---In most English speaking countries the first party is the driver, the second parties are the passengers accompanying the driver, and the third parties are anyone outside the car. That's why drivers are typically required to have third party insurance, to protect anyone not directly involved with the driver.
--- End quote ---
Hmm here it's just called liability insurance, it covers damage and injury to others and their property but not the driver themselves, sounds like it's pretty much the same thing.
--- End quote ---
Does that mean your US liability insurance includes injuries to passengers in your car? That's more than just covering third parties, so its not directly equivalent.
Nominal Animal:
--- Quote from: Rick Law on January 01, 2020, 08:55:57 pm ---
--- Quote from: Nominal Animal on December 31, 2019, 11:10:28 pm ---
--- Quote from: NANDBlog on December 30, 2019, 11:29:30 pm ---University math is different than high school math. Profs have a lot of possibility to be crazy, both ways.
--- End quote ---
Very true. There is also a huge difference in "math" math and "applied" math; i.e. between math as a research subject and math as a tool.
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Math is science in its pure abstracted form.
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Well, I'd say that math is the language in which we express science; science itself being the systematic application of the scientific method to find answers and solutions to all sorts of questions and problems. (This is why I also prefer to call it a tool instead of a language.)
You see, math itself goes much, much deeper. Most of what you described is still all "applied" math (i.e., using math to describe stuff) in my opinion, as there exists math about math, metamathematics; and mathematical logic and so on.
Even in physics, the exact same physical phenomena can be described using very different mathematical expressions. My favourite example is optics: you can use either Fermat's principle or Snell's law to describe the path light rays take. (It is not the best example, though, because a mathematician can derive the latter from the former by applying the wavelike properties of light.)
Circling back to the original topic, if we treat math as a tool or language to precisely describe physical phenomena, there are many different ways to learn that language, was my point. Some believe in theoretical investigation, learning the syntax and grammar first, with the application left as an exercise. Others believe in full immersion: dropping one in the deep end, and forcing them to learn to survive. Yet others believe in memorizing most common phrases, minimizing the effort needed to work with a specific limited set of problems. All work, none is obviously superior. I have my own preferred methods I outlined already, but the optimum approach differs for each individual. That is, although it is much more work initially, one should try to find out the study approach that works best for themselves; there is certainly enough material online and in books to suit just about anyone. Even if a book or author is considered "the best" or "recommended", there may be other material better suited for your needs -- or you might have to do your own study notes from scratch, using several different sources, like I had to --, because us humans vary.
james_s:
--- Quote from: coppice on January 01, 2020, 09:31:59 pm ---Does that mean your US liability insurance includes injuries to passengers in your car? That's more than just covering third parties, so its not directly equivalent.
--- End quote ---
No, bodily injury is a separate thing and that's where it starts to get complicated and requirements vary from state to state. Thankfully I've never been in an accident where I was at fault so this is not something I've ever had to deal with.
Rick Law:
--- Quote from: Nominal Animal on January 01, 2020, 11:10:39 pm ---
--- Quote from: Rick Law on January 01, 2020, 08:55:57 pm ---
--- Quote from: Nominal Animal on December 31, 2019, 11:10:28 pm ---
--- Quote from: NANDBlog on December 30, 2019, 11:29:30 pm ---University math is different than high school math. Profs have a lot of possibility to be crazy, both ways.
--- End quote ---
Very true. There is also a huge difference in "math" math and "applied" math; i.e. between math as a research subject and math as a tool.
...
...
--- End quote ---
Math is science in its pure abstracted form.
--- End quote ---
Well, I'd say that math is the language in which we express science; science itself being the systematic application of the scientific method to find answers and solutions to all sorts of questions and problems. (This is why I also prefer to call it a tool instead of a language.)
...
...
--- End quote ---
We are in agreement. I would "refine" it one step further (but by doing so, it also expose where I am fuzzy myself). Math is a language for science when it comes to quantification. Where quantification is not required, math does not seem necessary.
Electron flow in LED creates photon. No one needs math to clarify that. But one cannot describe the relationship between electron flow vs number of photons created without mathematics.
This is where I am fuzzy myself. Say "dark matter", you do not need math to conceptually understand it exist. Existence itself is a binary - a quantification between 0 and non-zero. To prove that "there is something required to making the forces balance" requires math. So if one can accept it exists without proof, one can forgo math. But is that really "understand"?
We "accept" a lot of things. V=IR is something we accept. Most of us don't really dig deeper: Why V=IR? When will this relationship fail? How will it fail? And we all know it WILL fail! When electron flow goes down to electrons you can count, V=IR doesn't apply anymore when you are talking a mere dozen electrons per minute. Now you are talking statistics and probability.
May be that is why the Ph in the PhD stands for Philosophy... Eventually, it all gets down to Philosophy.
Nominal Animal:
--- Quote from: Rick Law on January 02, 2020, 05:25:42 am ---
--- Quote from: Nominal Animal on January 01, 2020, 11:10:39 pm ---
--- Quote from: Rick Law on January 01, 2020, 08:55:57 pm ---
--- Quote from: Nominal Animal on December 31, 2019, 11:10:28 pm ---
--- Quote from: NANDBlog on December 30, 2019, 11:29:30 pm ---University math is different than high school math. Profs have a lot of possibility to be crazy, both ways.
--- End quote ---
Very true. There is also a huge difference in "math" math and "applied" math; i.e. between math as a research subject and math as a tool.
--- End quote ---
Math is science in its pure abstracted form.
--- End quote ---
Well, I'd say that math is the language in which we express science; science itself being the systematic application of the scientific method to find answers and solutions to all sorts of questions and problems. (This is why I also prefer to call it a tool instead of a language.)
--- End quote ---
We are in agreement. I would "refine" it one step further (but by doing so, it also expose where I am fuzzy myself). Math is a language for science when it comes to quantification. Where quantification is not required, math does not seem necessary.
--- End quote ---
There is math and logic for qualification as well; it's just in the abstract math-about-math domain. Other tools, like dimensional analysis (which considers types or units instead of quantities), can be combined with math to handle non-quantification type problems. (Thus, I do agree.)
--- Quote from: Rick Law on January 02, 2020, 05:25:42 am ---Electron flow in LED creates photon. No one needs math to clarify that. But one cannot describe the relationship between electron flow vs number of photons created without mathematics.
--- End quote ---
Right; to describe the interactions of the subatomic particles (electrons and photons in this case), we can use for example Feynman diagrams.
I believe it is important to realize this in all subject matters where math is an important tool: it can be used in different ways (and one can approach it in so many different ways, it is important to find the way that works efficiently for oneself), but properly "applying" it with other, non-math methods, is crucial.
For electronics, network analysis and equivalent impedance transforms are excellent examples of such.
--- Quote from: Rick Law on January 02, 2020, 05:25:42 am ---To prove that "there is something required to making the forces balance" requires math. So if one can accept it exists without proof, one can forgo math. But is that really "understand"?
--- End quote ---
One of the reasons I love computational materials physics is that every time you run a simulation, the first question both before and after, is always "Does this make any sense?"
Because math is only a tool, it cannot tell you how and when to apply it. Science, on the other hand, gives us a method (the scientific method, obviously) to direct and guide a questioning mind to examine the phenomena. Models (usually in the form of a theory or law, often called "something analysis" by mathematicians) bridge the two.
Newtonian physics is one such model. We know the domain where it applies to an amazing accuracy, and where it fails.
We can even start with ab initio simulations of electrons (using density functional
theory), and derive the electrical properties of semiconductor materials; in fact, this is what a lot of computational physicists do in practice.
Although this stack, science + methods + math, has completely arbitrary definitions (I'm sure many of those reading this post will disagree with my definitions), it is useful in the same way a well-organized workshop is: it works in practice, because it gives a logical place to store everything one uses.
And just like workshop tools, there are different approaches to math that one can choose. Some woodworkers only use hand tools; this is roughly equivalent to those that say that you need to be able to derive the Bessel functions yourself, to truly understand and correctly use them (in say solutions to Laplace's equation in cylindrical coordinates). Some only use a hammer, because all problems can be described as nails of various sorts, and so on.
Just because an approach is popular, does not mean it is optimal/best; just that a lot of humans like it. It is important to get past that, and examine oneself, to find out which approaches work best for themselves. This is particularly important in "higher learning", be that in an university, or in just-for-my-own-amusement type of thing.
A particularly good example of that, in my opinion, is in geometry or linear algebra: how to rotate 3D coordinates. A lot of people learn how to do that by using Euler angles, but it is actually a horrible tool for that: it is vague (there being a couple of dozen different ways to define the angles, and practically nobody bothers to specify which one they mean!) and subject to gimbal lock. Very few are familiar with versors or unit quaternions, which can describe any rotation; allows adding, subtracting, or interpolating between rotations; is numerically stable when "stacking" any number of rotations; has unambiguous forms for converting to and from rotation matrix form; and while the mathematical operations (like multiplying two versors is done using Hamilton product) look complicated, is in practice very easy and simple to use.
I would go as far as claim that anyone doing 3D computer graphics and using Euler angles, is a fool: doing a lot of hard work for unimpressive results, when a simple, efficient, and problem-free (no gimbal lock) solution exists. (If someone is using Euler angles in a microcontroller dealing with 3D orientation or rotations, I'd say they are an idiot. Harsh, but in my opinion, one must acknowledge crap is crap, even if a billion flies love it.)
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