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kiana

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kiana last won the day on February 19 2015

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About kiana

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  • Birthday 10/08/1980

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    Aikido, fitness, math, generalized nerdiness

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  1. I haven't seen these recommended before, and I only stumbled on to them. I'm using MyOpenMath in a class this semester -- it's a free online learning system. They also have self-study courses available for pre-algebra up through pre-calculus, linked here: https://www.myopenmath.com/info/selfstudy.php There are two options for trigonometry -- the CK-12 text teaches with right triangles first, the other with unit circle first.
  2. She won't need the trigonometry but she will need solid algebra skills. In general, people don't fail calculus -- they fail algebra when they get to calculus. In other words, it's not the difficulty of the calc concepts, but the algebra weaknesses, that threaten students. If you go with stats + finance, I would include algebra review through the year to make sure she's prepared.
  3. I think if they compare the transcripts and notice that you left it off to raise the GPA, it may raise the question of the legitimacy of other grades.
  4. I think part of it is that tests in quantitative subjects, or subjects where there is a clear "wrong", are intrinsically more easy and rapid to grade. I still remember one of my undergrad profs saying "Well, I was a double major in English and Math, and I was thinking about graduate school ... and I thought "Do I want to grade papers, or problem sets?" and after that the choice was clear." Personally, I usually get test grades posted the same day, unless I have multiple students who are taking a delayed test -- I grade each problem together for consistency and fairness. Quiz grades are usually posted within an hour or so. But I'm in math. That being said, I completely agree that not getting some kind of feedback on paper 1 before being required to submit paper 2 is utterly ridiculous.
  5. This reminds me of a student that my undergrad adviser told me about. They were using a classic book on mathematical probability/statistics -- the issue was that sometimes for 2 SD they'd use 95% and sometimes they'd use 95.45%, and so he wouldn't get exactly what the back of the book said. It drove the student nuts.
  6. So I've just gone and checked the TOC. (went with this one -- https://www.sjaweb.org/ourpages/auto/2014/5/27/63078308/Precalculus with Limits _ 2E 2010 ISBN 9781439049099 _ Ron Larson_ Robert P_ Hostetler.pdf -- in case your numbering is different). First of all, he won't be crippled in calc if you just stop where you are. Other people may vary, but I'm going to give my opinion just as someone who sees what my calculus students struggle with. I assume (based on what you say about him) that he is solidly competent in basic algebra skills such as negative/fractional exponents, factoring, rational expressions/complex fractions, and graphical representation of functions. If he weren't, my advice would be more to review those. I've listed each chapter individually below, but I've summarized all the sections here. The ones I'd really hate to miss are 9.5 - 9.7, 10.1 - 10.4, 10.6, 11.1. The last two, just so that there is some basic exposure to coordinate systems beyond the standard cartesian plane. When I say "skim", I mean read the section, work through the examples and try to understand the big picture, and do at least the beginning computational problems. Chapter 9: I'd look at arithmetic + geometric sequences and series -- they'll be re-done in calc 2 as part of a much broader overview but calc 2 students find sequences + series horribly difficult in general. Some base knowledge is a good idea, especially becoming familiar with the sigma notation for series. Very few precalc students are going to get anything out of the mathematical induction section -- I'd look through it (it's an early exposure to proof), but not worry about doing a lot of the homework. You can return to this one later if there's time. Binomial theorem I *would* do, and counting + probability -- it's not so necessary in calculus, but imho every functional adult should have some basic understanding of counting and probability. The binomial theorem is actually a huge help if you need to expand something like (x + y)^4. I also think I'd skim the "proofs in mathematics" at the end of the chapter. Chapter 10: For analytic geometry, I would definitely cover lines, parabolas, ellipses (I assume circles fit in there as a special case?), and hyperbolas. Lack of understanding of these really hurts a lot of calculus students. Parametric equations and polar coordinates are also something that I'd like to include although the calculus textbook should also teach it. I'd at least skim the graphs of polar equations. I wouldn't worry about the rotation of conics and the polar equations of conics -- again, you can return to these. I don't even know if I'd skim them. We don't do a lot with them in calculus class, other than 90 degree rotations and polar equations of circles, and those usually aren't terribly difficult for people who understand the basic levels. Chapter 11: It's good to have some exposure to 3d geometry but it is customarily taught from scratch in calc 3 and/or linear (whichever comes first at the school) because many high schools don't teach it or don't teach it well. I would make sure to do the first section just so he has an idea that the cartesian coordinate system goes beyond two dimensions, and after that I would skim. Chapter 12: The limits + intro to calculus will be completely retaught in calculus. This is the last chapter in the book. I think at least skimming it would be a good idea just to ease the transition to calculus, but if by then you are just ready to be Done it won't hurt him to stop. It'll just make the beginning of calculus a little bit easier if he's seen it once before. HTH.
  7. The only way that I get 1239 is if I round r^2 and h two decimal places prior to substituting into the final formula. Which is WRONG. ARGH.
  8. I guess that I'd think of it as ... does she buckle down and do her math? Is she a "just get it done" type of person? Saxon may work. But otherwise, I'd be far more inclined to go with something a little less tedious. Saxon is kinda like digging into a plate of boiled broccoli because you're eating your veggies. It gets the job done, but ...
  9. I agree. I'd skim through it and if it piqued interest, go for the intermediate -- if not, choose another topic.
  10. There are different kinds of applied math. Someone who's looking at engineering would be looking more at the calculus side. Someone who's looking at actuarial science would need the probability side (and the calculus side, but). University-major applied math is still pretty theoretical. I went back and looked at the requirements for one school I attended. They required calc 1-3, linear, diffeq, modeling, advanced calculus 1-2 (this is a theory class, calculus with proofs), a survey of probability and statistics, and three electives. Their electives all included significant quantities of theory. Examples were differential equations with proofs, complex analysis (calculus with proofs and complex numbers), numerical analysis (again, proofs). They also needed to pursue an approved minor. Someone who was looking at actuarial science, for example, might choose something like economics or finance. Someone else might choose physics because it's more in line with their interest.
  11. re: calc 3 and linear algebra. It is quite uncommon to require linear algebra as a prereq for multivariable calculus; it is generally taught on an as-needed basis. Calculus is usually required as a prerequisite for linear, not because the linear algebra content itself requires calculus, but because a certain level of mathematical maturity is required. Calculus examples are used in some of the popular linear algebra textbooks (Anton, for one) but they are asterisked and could be omitted. There are other courses (modern algebra, for example) where technically they could be done after precalculus (there are modern algebra texts that are structured for intro to proofs) but it would be rare indeed for a student to have that level of maturity and not had calculus. re: op, if she thinks calculus is easy and boring I would not do diffeq or mvc, I think it would be more of the same. I think that a discrete math course would be a wonderful idea. I had taken calc 1-3, linear (computationally oriented), diffeq, and stats, all of which were easy and boring. I took discrete, which at my college was intro to proofs, but it was also the last class required for my math minor, and halfway through the semester I changed my major to math. I think I'd consider the following: The aops discrete math classes -- the intro level might not be very challenging to someone who has already had calculus, but the topics are fun and it certainly will fill the bill of a senior math class. If nt/combinatorics are completed I'd say 1cr discrete math. For each one I'd say a semester's credit would be totally reasonable. The stats II -- AP stats often doesn't transfer in very well, and especially if she took stats at the CC. Stats II should transfer as something. A CC liberal arts math class -- again, it will be a bunch of fun topics that won't be especially challenging, but will be generally chosen to be of either high interest or high applicability. It'd probably end up transferring and counting for a general elective. Doing math for liberal arts on your own with Lippman's math and society (free) and/or jacobs MHE, choose your own units based on interest. Many of these would be great one semester courses, so you could mix and match. I've headed towards the easier and of more interest to the humanities side because you mentioned her desire to git'r'done and study languages.
  12. See, I do think there's a place for a graphing calculator. But it should come after some idea of what you're up to in the first place. I also teach them to use it as an error checker for "did I simplify this horrible thing correctly" -- if you graph f(x) = "horrible thing" and g(x) = "simplified horrible thing", the graphs should line up, and if they don't, you goofed. I've spent a lot of time coming up with problems where the calculator won't help them if they don't understand the concept, and isn't necessary if they do.
  13. So I don't think the limit definition for chain rule is really illuminating for calc 1 students. I skip it unless I have someone who really wants to see it. It's in the appendix. Product rule, yes, and quotient either from the limit definition or from product + chain, yes. For the chain rule, at that level it's pretty common to also verify by computing d/dx (9x^2 + 30x + 25)
  14. I also could not remember which term went first in the quotient rule until I was teaching calculus for the second time. But if I used the chain + product, I would get it correct every time. I also agree about the product rule. It's interesting. It's a nifty little proof. But it's one of those that CAN be a formula. I'd do it if the kid is interested and not if they aren't.
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