Catherine Kellar MTH 320

difficult: In the proof of proposition 3.2.4, there was a double contradiction that was difficult to follow. It makes sense intuitively, though. application: This whole section was generally things that I already know, from having taken CS classes. It was cool seeing the mathematical representations of each of these things.

Difficult: I don't quite understand how to make the jump from def 3.1.15 to the actual transition matrices shown in examples 3.1.16 and 18. Setting up those matrices I'd like to see. Application: Establishing the existence of data structures as mathematical graphs, much like having a formula for the master theorem to evaluate recursion, will allow us to prove things and show things about the theory of computer science. It's so odd (but good) that a math class is teaching me more about CS theory than several semesters of CS classes themselves.

For Wednesday September 27 lecture: Read and blog about Section 2.8. Additionally, answer some or all of the following questions. Difficult:  The hardest part of this section is following the formulas. Once I figure out what they're saying, it makes a lot of sense, but there are a lot of variables being thrown around, and it gets hard to follow at some point. I also had to go back and remember exactly what the Master Thm says. Application: Well, clearly, the obvious application here is that the Master Thm is proven, so we can use it now. Good to know. I guess, since this whole section is a proof, there isn't a lot of room for examples, but somehow if those could have been worked in, it would have been nice. How long have you spent on the homework assignments? 4-5 hours per assignment, in each class.  Did lecture and the reading prepare you for them? Yes, a lot. What has contributed most to your learning in this class thus far? The examples that we go over ...

Difficult: The most difficult part of this section was understanding Sterling's approximation. I get that it's approximating the Gamma function, but formula 2.24 and 2.27, which they call the zeroth-order Stirling's formula and Sterling's approximation respectively, don't seem at all related to me. I am also really confused at the big Pi non-summation things (I don't see where that symbol has been defined in this book). Application: Because logarithms are so much smaller than actual factorials, etc, logs would be very useful in many calculations, whether in conjunction with factorials or another context. However, calculating the gamma function would be resource intensive. Honestly, it's really impressive how much we've managed to find acceptable approximations that are usable and useful.

Hardest part: The most confusing part of the reading was remembering Pascal's triangle, which I completely forgot about. I also had to remember how combinations work. It's interesting, though, that I actually understand, now, how we get them rather than only that they work. Application: Permutations and combinations are useful in many, many scenarios. But I really like Fermat's little theorem. I'm not entirely sure how to use it yet, though. Also, the whole combinations to figure out lottery probabilities is interesting.

Hardest thing: The hardest thing in this section was understanding the delta function. Once I followed the examples through, it became clear that we were talking about the summation version of a derivative, but it was a bit hard to wrap my mind around. Application: The application seems relatively obvious- applying this to the calculation of for-loop complexities. However, I'm not entirely sure how, unless we compute each for loop as a sum, find the complexity of the sum, and then add all of the complexities together, which brings us back to the idea of whether big-O complexities can be added or not. We'll see.

I attended the Google presentation for Careers in Math. It was a fun presentation in which the woman presenting talked a bout the different tools, apps, and programs that Google participates in. She discussed the different career paths available, and the degree(s) necessary to get there. It was interesting that she plugged for the ACME program so much, and also that she described certain higher-level jobs as requiring either grad school or industry experience, and that she had decided to go for industry experience. I don't know where I want to end up, but I'm leaning towards academia. This was a good thing to go to to explore options, though.

Did I read/what was the hardest part? I don’t fully understand why the integers are not well-ordered, when any Z^>=n is. I also don’t really get Theorem 2.1.8 about how d can be both the least and the greatest positive integer that divides both a and b. How does it apply to life? I think it’s really cool that we can teach computers to do division in the same way that we were taught to do in elementary school. By defining the relation as a linear combination instead of using division in the definition, we are able to verify that the algorithm holds without needing the computer to try and divide by 0. Also, I think it’s really nice that we have application examples at the end of each section.

1.   (Difficult)   Answer the question "Did you carefully read the entire assignment, and what was the most difficult part of the material for you?"   Note that "nothing" is not an acceptable answer. If nothing challenges you, then you should think about the material at a deeper level and generate some honest questions. Yes, I did the reading. The most difficult part of this reading  was trying to understand the master theorem, or rather how it works. Plugging in values, I could understand what it was saying, but I didn't understand where the values for those variables were coming from. 2.   (Reflective)   Write something reflective about the reading. This could be the answer to the question "What was the most interesting part of the material?" or "How does this material connect to something else you have learned in mathematics?" or "How is this material useful/relevant to your intellectual or career ...

1.   (Difficult)   Answer the question "Did you carefully read the entire assignment, and what was the most difficult part of the material for you?"   Note that "nothing" is not an acceptable answer. If nothing challenges you, then you should think about the material at a deeper level and generate some honest questions. One of the more difficult parts of this section was trying to follow the spatial requirements for matrix-matrix operations. They were using the '~' sign/operator, which I remembered being an equivalence relation for O(f(n)), but with only one function. Also, just following the matrix operations in general was a bit difficult. 2.   (Reflective)   Write something reflective about the reading. This could be the answer to the question "What was the most interesting part of the material?" or "How does this material connect to something else you have learned in mathematics?" or "How is this ...

1.  (Difficult)  Answer the question "Did you carefully read the entire assignment, and what was the most difficult part of the material for you?"  Note that "nothing" is not an acceptable answer. If nothing challenges you, then you should think about the material at a deeper level and generate some honest questions. I did read the assignment. The most difficult part to understand was following where all of the bits were going while describing bit notation. Most specifically, trying to follow the representations of exponents as negatives or positives for position shifting had me lost. 2.  (Reflective)  Write something reflective about the reading. This could be the answer to the question "What was the most interesting part of the material?" or "How does this material connect to something else you have learned in mathematics?" or "How is this material useful/relevant to your intellectual or career interests?" I hadn't ever consi...

1.   (Difficult)   Answer the question "Did you carefully read the entire assignment, and what was the most difficult part of the material for you?"   Note that "nothing" is not an acceptable answer. If nothing challenges you, then you should think about the material at a deeper level and generate some honest questions.  I read the assignment carefully. The most difficult part was trying to work through some of the examples. Example 1.2.3 was particularly hard- because of the sub- and superscripts, epsilons, etc, I'm still not completely sure I follow how it got where it did. I tend to understand the gist of what they're saying, but unless I try to dissect the examples, they can be difficult to follow.  2.   (Reflective)   Write something reflective about the reading. This could be the answer to the question "What was the most interesting part of the material?" or "How does this material connect to something else...

What is your year in school and major? Junior (though this is only my second year actually at BYU) and ACME Which post-calculus math courses have you taken?  (Use names or BYU course numbers.) (assuming post-calculus = post calc 3) MTH 290, 313, 341 Why did you choose ACME?  (Be specific.) I chose ACME because Jeff (Dr Humpherys) talked with me for 3+ hours about the benefits of it. I want to go to graduate school, but I feel that ACME will provide me with a cross-disciplinary basis for my knowledge, and not leave me with only one possible direction to go in after my baccalaureate. Tell me about the math professor or teacher you have had who was the most and/or least effective.  What did s/he do that worked so well/poorly? I hated it but loved it, but the most effective professor I ever had was Dr Humpherys. He pushed us hard and fast, and made it almost impossible to keep afloat. I didn't get an A in that class, but I learned more than in any other clas...