Comments by "Beth Hentges" (@bethhentges) on "Numberphile" channel.

  1.  @EdwinWiles  Depends in if you are an early bird or a night owl.
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  2. Thanks for the explanation regarding using a “loop” to decide whether a train can continue or wait for the opposing traffic.
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  3. I have usually seen it in the other direction. Start with the Taylor Series of e^x, cos(x), and sin(x), and use them to prove cos(x)+isin(x)=e^(ix).
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  4.  @galacticminx  A college in the US may offer a two-year degree(AA) and/or a four-year degree (BA). A university also offers graduate degrees (MA and PhD).
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  5.  @galacticminx  Believe me I tell them to multiply (a+b)(a+b). And I remind them that mult. distributes over ADDITION. Exponents distribute over multiplication. Yet,…
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  6. Or just one of them is zero.
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  7. I have many college students who make this mistake—even when significant time in class is devoted to why it’s wrong.
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  8. Freshman in both hs and college.
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  9. Yes, at first.
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  10. Because students forget and fall into the “Everything is linear” trap.
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  11. Because the exponent is a cardinal number, not an remainder, by convention.
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  12. I have never heard anyone say “cuz” rather than “cosine” when reading cos(x). Also, from Day 1, I tell my students to always use parentheses around the argument. Clarity is paramount. Also, one should type (1/2)cos(x) rather than 1/2cos(x) because 1) it’s clear and 2) some machines are programmed so that implicit multiplication takes precedence over explicit multiplication and division. Never type 1/2cos(x). Type (1/2)cos(x) or 1/(2cos(x)) depending on which you mean. It’s always better to have more parentheses than might be required than to not have a set that is necessary. Avoid any potential ambiguity or miscommunication.
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