<p>How essential are proof-based math classes for engineers? If any, which proof-based math courses should engineers (any branch) take? </p>
<p>Thanks!</p>
<p>Interesting thread.</p>
<p>Proof based maths is not really that useful for engineers - unless they want to see how the mathematics they use is derived rigorously. I took a two-quarter introduction to real analysis and I haven’t found any real engineering applications. But proof based maths trains the mind to think differently and this different thinking may be useful.</p>
<p>But most engineers who I know do not know proof maths and they are doing perfectly fine.</p>
<p>That’s a relief. I recently found out I’m not too fond of proofs. A friend majoring in math was trying to teach me some basic calc proofs, and even though I could follow him here and there, I really did not see the point…</p>
<p>But I can see the benefits of a course like real analysis; I might take it just for the hell of it.</p>
<p>I’m a computer science major. There are about 3 classes I need to take that involves proving things. I’m in the major to develop software, not because I think proving math is interesting. I just need to get through these classes, which aren’t that terrible when I study.</p>
<p>Any comp. sci students out there who agree with me?</p>
<p>Proof-based Math is exactly why yours truly chose applied (computational) math as a major. I was never fond of proof-based Math. Once I knew I passed Advanced Calculus (which at my school was a less-rigid version of the Real Analysis course), I was done with my proof-based Math courses and never to be seen again NEAR a proof.</p>
<p>I think a lot of people seem to get overwhelmed when they see proofs in calculus. You’ll have a pretty hard time if you try to start out with proofs like that (unless it just comes naturally to you, but this isn’t the case for most people). If you start from the basics, I mean the really fundamental stuff, I think it becomes easier. Those sorts of things are usually taught in an introduction to proofs class, discrete math, propositional calculus/logic, etc.</p>
<p>Foundations are key in math, that’s why so many people suck at it.</p>
<p>Oh, didn’t reply to the actual question. I agree with whoever said it gives you a different way of thinking, but beyond that I’m not sure… even research doesn’t require actual application of rigorously proving things. Even in most areas of physics research it isn’t required, and that’s regarded as more ‘fundamental’ than engineering.</p>
<p>Yes, being able to prove things is definitely a plus. But, I derive more pleasure from applied math; math for the sake of more math is not my thing. Also, I prefer to rely mostly on intuition (yes, I know it has its limits).</p>
<p>Btw, my friend was showing me a proof of why a number multiplied by 2 is always an even number. Why I need to prove something my intuition tells me make sense is beyond me, but this is why I say mathematicians are useless.</p>
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<p>LOL…oh wait until you have to use axioms to prove that a number N times Zero = Zero. That’s right, prove that n x 0 = 0.</p>
<p>That is a 9 or 10 step process.</p>
<p>I wanted to throw my textbook at my professor’s head and say “If you don’t put something on that board that I can use…”</p>
<p>Oh wow… </p>
<p>I’m sure a higher-intelligence being will eventually explain that to me and make me the happiest person in the universe… but for the moment I’m quite happy with my plug-n-chug math.</p>
<p>How do you know a number multiplied by 2 is even? Someone had to prove that it was so, someone else had to teach it to your 2nd grade teacher who taught you that it so that it should be your ‘intuition’.</p>
<p>Plus, that’s just elementary. A lot of these things have a ridiculous amount of usefulness. Knowing how prime numbers work keep people from swiping your bank account IDs and passwords (talking about RSA encryption of course). There’s tons more. Saying mathematicians are useless is just ignorant.</p>
<p>Found on the internet, just for you, my esteemed Hadsed:</p>
<p>There was a mad scientist (a mad SOCIAL scientist) who kidnapped three colleagues, an engineer, a physicist, and a mathematician, and locked each of them in separate cells with plenty of canned food and water but no can opener. </p>
<p>A month later, returning, the mad scientist went to the engineer’s cell and found it long empty. The engineer had constructed a can opener from pocket trash, used aluminum shavings and dried sugar to make an explosive, and escaped. </p>
<p>The physicist had worked out the angle necessary to knock the lids off the tin cans by throwing them against the wall. She was developing a good pitching arm and a new quantum theory.</p>
<p>The mathematician had stacked the unopened cans into a surprising solution to the kissing problem; his desicated corpse was propped calmly against a wall, and this was inscribed on the floor in blood:</p>
<pre><code>THEOREM: If I can’t open these cans, I’ll die.
PROOF: Assume the opposite …
</code></pre>