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| ubuntourist | Professor. | 10:00 |
|---|---|---|
| ubuntourist | G'day Professor jelkner, young Jedi, mjsir911 | 10:01 |
| ubuntourist | Can you translate to English, the question: | 10:02 |
| ubuntourist | "Find the value of the constant a for which the polynomial x**3 + ax**2 − 1 will have -1 as a zero" | 10:03 |
| ubuntourist | Do they mean "When x is -1, what values for a will result in zero?" | 10:03 |
| jelkner | Good morning, ubuntourist! | 10:04 |
| ubuntourist | Hold on. After the sixth reading, I think I understand the question. Never mind. | 10:04 |
| ubuntourist | (And it does appear to mean what I had postulated.) | 10:06 |
| jelkner | Great! I'm trying to review logorithms on Khan Academy before taking that section | 10:08 |
| jelkner | I bombed the trig section | 10:08 |
| ubuntourist | So they separate trig and logs? (Seems I had them in the same course in high school...) | 10:12 |
| ubuntourist | I'm as usual, relying on my logic skills rather than my memorization skills. This makes me VERY slow, as I am essentially reinventing the math | 10:14 |
| ubuntourist | and not necessarily coming up with formulas for solving the equations, but rather, constructing one-off solutions. | 10:14 |
| ubuntourist | That, plus the few mnemonic devices I remember (e.g. FOIL for polynomials) | 10:17 |
| jelkner | Wow, mjsir911, what a lot of pre-course work! | 11:15 |
| mjsir911 | yea | 11:16 |
| mjsir911 | I stopped after the trig | 11:16 |
| jelkner | Since I did well enough on the logorithm and exponent section, it wanted me to take the calculus pretest, but I skipped that, since I'm going to take the course along with you in any case. | 11:16 |
| jelkner | You're bad, mjsir911! | 11:16 |
| mjsir911 | The geometry questions were a bit confusing, what did it mean with that sphere one? | 11:16 |
| jelkner | You can't skip anything else now that the course has started! | 11:17 |
| jelkner | Ahh, the surface area | 11:17 |
| mjsir911 | of the entire sphere on 1/8 of it? | 11:17 |
| jelkner | you basically has 3/4 the area of the circle | 11:17 |
| jelkner | since 3 of the sides were 1/4 sections of a circle | 11:17 |
| jelkner | and then a 1/8 surface area of a sphere for the 4th side | 11:18 |
| mjsir911 | ik the equation of a circle is 4*pi*r**2 | 11:18 |
| jelkner | the area of a circle is pi r **2 | 11:18 |
| jelkner | so 3/4 pi r ** 2 | 11:18 |
| jelkner | + 1/8 4 pi r ** 2 | 11:19 |
| mjsir911 | im confused, am i trying to find the entire surface area or a part of it? | 11:20 |
| jelkner | remember we are on our honor not to post solutions to these problems | 11:20 |
| mjsir911 | I'm asking what the question is asking | 11:20 |
| jelkner | i wonder if there is a good online free software whiteboard tool we could use to meet online while i'm in vermont? | 11:20 |
| jelkner | the question was asking you for the surface area of that four sided figure | 11:21 |
| jelkner | three of the sides were quarter circles | 11:21 |
| mjsir911 | Oh I see | 11:22 |
| mjsir911 | Thats where I was confused | 11:22 |
| jelkner | and the fourth side was an eighth of a sphere | 11:22 |
| mjsir911 | Yea I figured it out | 11:22 |
| mjsir911 | ty | 11:22 |
| jelkner | but you're in the course now, yes? | 11:22 |
| jelkner | btw, are your folks around? | 11:23 |
| jelkner | would this be a good time to call them? | 11:23 |
| jelkner | mjsir911? | 11:23 |
| mjsir911 | Yea you could call my dad | 11:23 |
| mjsir911 | my mom is in chicago | 11:23 |
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| jelkner | mjsir911, are you here? | 12:07 |
| mjsir911 | I am here | 12:07 |
| jelkner | We are a week behind in our course (since it started on June 7), so we should try to catch up. | 12:07 |
| mjsir911 | Yep, im doing just that | 12:08 |
| jelkner | i'm doing the section on limits now, which will be easy for me, but will be new to you. | 12:08 |
| jelkner | i would encourage you to think about how you can leverage jupyter while you are learning this | 12:08 |
| mjsir911 | I'm doing just that! | 12:09 |
| jelkner | and the testing tool you showed me that generates lots of data points | 12:09 |
| mjsir911 | ? you mean for a graph? | 12:09 |
| jelkner | i figured you were, but just saying ;-) | 12:09 |
| mjsir911 | or hypothesis? | 12:09 |
| jelkner | hypothesis | 12:09 |
| jelkner | yes | 12:09 |
| mjsir911 | oh yea how could I use that? | 12:09 |
| jelkner | i'm not sure, since you know it and i don't | 12:10 |
| jelkner | but if you could tune it to generate a lot of points near (but not equal to) the value you are looking for | 12:10 |
| jelkner | and to come in from the left and right respectively | 12:10 |
| jelkner | it could be a big help in visualizing these ideas | 12:10 |
| mjsir911 | ill try to look into it | 12:11 |
| jelkner | anyway, the most important thing is to do the math | 12:11 |
| jelkner | so don't get too distracted | 12:11 |
| mjsir911 | of course :P | 12:11 |
| jelkner | but if you think of any low hanging fruit, go for it! | 12:11 |
| jelkner | ok, back to my lessons... | 12:11 |
| jelkner | mjsir911, just added you as a collaborator on https://github.com/jelkner/Calculus1A | 12:20 |
| jelkner | I wanted to add ubuntourist as well, but I can't find his github name | 12:21 |
| mjsir911 | thx | 12:21 |
| jelkner | found it | 12:23 |
| jelkner | invited him too | 12:24 |
| jelkner | anytime they say "bring out a calculator", we should use python | 12:24 |
| mjsir911 | Ok so I found an extension to link github and jupyterhub | 12:26 |
| jelkner | mjsir911, did you study the formal definition of limit in precalc this year? | 12:31 |
| mjsir911 | its just placing a limit on the domain of a function isnt it? | 12:32 |
| mjsir911 | i think we did | 12:32 |
| jelkner | so that means you didn't learn it :-( | 12:32 |
| jelkner | since you wouldn't "think you did" if you did ;-) | 12:32 |
| jelkner | limit has a precise mathematical definition | 12:33 |
| jelkner | it is a very interesting idea | 12:33 |
| jelkner | it says basically that a function has a limit of some value when given any delta (they love to use greek letters for variables in calc ;-) close to x, there is an epsilon within which f(x) will fall | 12:36 |
| jelkner | since we say *any* epsilon, it means you can find a range of values close to x that will guarantee that f(x) is as close to the value as you want. | 12:38 |
| jelkner | if you can do that, you have a limit | 12:38 |
| jelkner | you will need to grok that idea to be ready for calculus | 12:38 |
| ubuntourist | Do you have time for the slower child? | 12:38 |
| jelkner | certainly | 12:38 |
| jelkner | i think talking about it together will help all of us really "get it" | 12:39 |
| jelkner | but we need to work hard, since we need to try to keep up with the course | 12:39 |
| jelkner | i'm going to pitch this to Mr. Zawolo tomorrow | 12:39 |
| ubuntourist | I'm only missing one of the algebra questions: I get 0, 2, -2 for all solutions to x**3 - x**2 - 2x = 0. Apparently, I'm wrong. Is there one that I'm missing? | 12:40 |
| jelkner | and argue that doing this is why he should setup an special section for our young Padawan here | 12:40 |
| mjsir911 | ubuntourist plug all your answers in to confirm they are correct | 12:41 |
| jelkner | so you factor out x, and get x * (x**2 - x - 2) | 12:41 |
| jelkner | then factor (x**2 - x - 2) into (x - 2)(x + 1) | 12:41 |
| jelkner | so the solution set is... | 12:42 |
| jelkner | x is an element of {0, 2, -1} | 12:42 |
| ubuntourist | (I've correctly answered all of the others.) I did. (2**3 - 2**2 - 2*2 = 8 - 4 - 4 = 0). (-2**3 - -2**2 - -2*2 = -8 + 4 + 4 = 0). (0**3 - 0**2 - 2*0) = 0 - 0 - 0 = 0). | 12:44 |
| mjsir911 | 2 ** 3 = -8 | 12:44 |
| mjsir911 | i mean -2 ** 3 | 12:44 |
| mjsir911 | oh duh sorry | 12:45 |
| mjsir911 | 1 second | 12:45 |
| mjsir911 | -2 ** 2 = 4 | 12:45 |
| mjsir911 | its a problem with the math on the -2 | 12:45 |
| ubuntourist | This is why my logic scores were always in the 98 percentile, while my clerical speed and accuracy were always in the 3 percentile. ;-) | 12:46 |
| jelkner | ubuntourist, did you accept my invitation to the github repo for this? | 12:46 |
| jelkner | we can leverage our python skills to make exploring these functions a lot more accurate | 12:47 |
| jelkner | so we can focus on the logic | 12:47 |
| jelkner | we'll learn some computer science along the way, too, since we will have to deal with the details of floating point numbers (yuck!) | 12:48 |
| jelkner | i'm planning on leaning on mjsir911 to learn jupyter notebooks while we go through this | 12:49 |
| jelkner | so we can easily generate graphs and visualizations that will help us | 12:49 |
| jelkner | grok the math | 12:49 |
| mjsir911 | jelkner, look into numpy.linspace for limits | 12:57 |
| mjsir911 | to calculate 1000 numbers, starting at 0 and approaching 1, you would generate an array: numpy.linspace(0, 1, 1000, endpoint=False) | 12:58 |
| jelkner | here is my plan, mjsir911: i am going to move as quick as i can to catch up with the course | 12:58 |
| jelkner | since i already know this math, it shouldn't take that long | 12:58 |
| jelkner | then, while you proceed through the math looking for understanding, i'll focus on the python tools to support learning | 12:59 |
| jelkner | i just pushed g, h, and j functions to the repo | 12:59 |
| jelkner | i just used the python shell to explore them | 12:59 |
| jelkner | there are better ways, i know, but for now, i want the simplest thing that works | 12:59 |
| jelkner | python as a calculator ;-) | 13:00 |
| ubuntourist | jelkner, I wasn't looking at e-mail. Just saw the invite. | 13:08 |
| jelkner | great | 13:09 |
| ubuntourist | jelkner, also in my inbox: "Re: [EDU-SIG] AP Calculus with Jupyter". I forwarded more so you'd know who's talking about it, rather than the conversation itself. | 13:11 |
| ubuntourist | And, with that, I'm off-line and getting lunch | 13:12 |
| jelkner | *very* important quote from Unit 0.9: "this idea of the limit is really the building block for all of calculus" | 13:13 |
| jelkner | mjsir911, still here? | 13:25 |
| mjsir911 | yep | 13:25 |
| jelkner | my brother is visiting me from puerto rico, so i need to leave soon, but i plan to finish Unit 0 first | 13:26 |
| jelkner | then do Unit 1 tomorrow | 13:26 |
| jelkner | it occurs to me that if mr. zawolo is game, you could be a real resource in the class | 13:26 |
| mjsir911 | I'm still on the introduction to limits | 13:27 |
| jelkner | np, i've done this before | 13:27 |
| jelkner | so i plan to move faster than you should | 13:27 |
| jelkner | this is just a quick review for me | 13:27 |
| mjsir911 | ok, i'm going to log everything im doing on jupyter so yea I could be helpful | 13:27 |
| jelkner | when i get ahead of you, i'll focus on the python tools you tell me to look into | 13:27 |
| jelkner | sweet | 13:27 |
| jelkner | that | 13:28 |
| jelkner | is what i was thinking | 13:28 |
| jelkner | by completing math 173 before september | 13:28 |
| jelkner | or largely completing it, in any case | 13:28 |
| mjsir911 | yea, I have to go too | 13:28 |
| jelkner | you can help mr. zawolo and i do integration for the other students | 13:28 |
| mjsir911 | Oh definitely | 13:29 |
| mjsir911 | see you later | 13:29 |
| jelkner | later gater | 13:29 |
| * jelkner logs off for the day | 13:29 | |
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