DIFFICULT
I never liked Delta/Epsilon proofs in calculus because I didn't know their purpose, I also found them to be quite hard. Being a lower division math tutor I still found them hard to explain to students just because I never knew their purpose, so this chapter will help me in the future.
REFLECTIVE
I always wanted to know how Delta/Epsilon proofs proved limits in calculus. I work in the Math Lab as a lower division tutor, Math 112 and 113 students are finishing up their individual sequences and series sections, so I should be well versed in at least this section.
Sunday, November 30, 2014
Monday, November 24, 2014
Reflective Questions, due on November 25
WHAT HAVE YOU LEARNED IN THIS COURSE?
I have learned a great deal of things in this class, although when a test comes around I tend to forget all the things I have learned. I love taking notes in class and understanding 80% of it. Some of the cool things I have learned were logic and logic tables, cardinalities and denumerability, mathematical induction was fun, and this prime stuff in Chapter 11 is great too.
HOW MIGHT THESE THINGS BE USEFUL TO YOU IN THE FUTURE?
I really don't know how this class would be useful in my future. I guess the use of logical thinking in problem solving in civil engineering would be useful, it might also be annoying. I'm sure this class will be very useful in the future, I have just yet to see that yet.
Sunday, November 23, 2014
11.5-11.6, due on November 24
DIFFICULT
The only thing that will be rough will be the material found in section 5. This whole prime number thing is kind of hard to grasp, where at the same time it isn't that bad. We'll see how the final does though.
REFLECTIVE
These sections are highly reminiscent of elementary school days. I remember doing all sorts of math things pertaining to finding multiples of 2, 3, 4, 5, etc... Like the rules found on page 258.
The only thing that will be rough will be the material found in section 5. This whole prime number thing is kind of hard to grasp, where at the same time it isn't that bad. We'll see how the final does though.
REFLECTIVE
These sections are highly reminiscent of elementary school days. I remember doing all sorts of math things pertaining to finding multiples of 2, 3, 4, 5, etc... Like the rules found on page 258.
Thursday, November 20, 2014
Exam III, due on November 21
DIFFICULT
Theorem 10.1, Theorem 10.3, Result 10.5, Result 10.7, Theorem 10.13, Theorem 10.14, Theorem 10.19, Corollary 10.20, Lemma 11.1, Theorem 11.2, Theorem 11.3, Theorem 11.4, Theorem 11.7, Theorem 11.8.
What does countable mean?
REFLECTIVE
Result 10.2, Theorem 10.8, Corollary 10.10, Theorem 10.11, Theorem 10.12, Theorem 10.15, Theorem 10.18, Theorem 11.4.
I feel like I understand what is happening in class, but when I sit down to write my exam, my mind goes blank. So any strategies specifically for this exam would be helpful, I really want to do about average on this test if anything.
How do your final grades work? Like if a student attends every class, and takes notes on all those lectures, does all the homework, and all the pre-class readings, but scores below average on all the exams, what can that student expect his final grade to be? I just want to know if our final grade is dependent on our best effort.
Theorem 10.1, Theorem 10.3, Result 10.5, Result 10.7, Theorem 10.13, Theorem 10.14, Theorem 10.19, Corollary 10.20, Lemma 11.1, Theorem 11.2, Theorem 11.3, Theorem 11.4, Theorem 11.7, Theorem 11.8.
What does countable mean?
REFLECTIVE
Result 10.2, Theorem 10.8, Corollary 10.10, Theorem 10.11, Theorem 10.12, Theorem 10.15, Theorem 10.18, Theorem 11.4.
I feel like I understand what is happening in class, but when I sit down to write my exam, my mind goes blank. So any strategies specifically for this exam would be helpful, I really want to do about average on this test if anything.
How do your final grades work? Like if a student attends every class, and takes notes on all those lectures, does all the homework, and all the pre-class readings, but scores below average on all the exams, what can that student expect his final grade to be? I just want to know if our final grade is dependent on our best effort.
Tuesday, November 18, 2014
11.3-11.4, due on November 19
DIFFICULT
The Euclidean Algorithm is a little hard for me to comprehend, but I am sure it will be covered in lecture. Is this an iterative process?
REFLECTIVE
Greatest Common Divisor is something I haven't cared about since primary school, back then it was easy to understand so I an hopeful it still will be. Theorem 11.8 is also intuitive enough to understand. Lemma 11.9 is fairly straight forward too.
The Euclidean Algorithm is a little hard for me to comprehend, but I am sure it will be covered in lecture. Is this an iterative process?
REFLECTIVE
Greatest Common Divisor is something I haven't cared about since primary school, back then it was easy to understand so I an hopeful it still will be. Theorem 11.8 is also intuitive enough to understand. Lemma 11.9 is fairly straight forward too.
Sunday, November 16, 2014
11.1-11.2, due on November 17
DIFFICULT
These sections seem to be a piece of cake compared the last section of chapter 10. Although since this is chapter 11 and since up till now sections have depended on prior sections, I can only assume chapter 11 will get harder
REFLECTIVE
The theorems in section 1 & 2 are pretty understandable and intuitive. I remember doing this prime number stuff back in primary school. I really liked the equivalence classes before, although that didn't reflect in my exam score.
These sections seem to be a piece of cake compared the last section of chapter 10. Although since this is chapter 11 and since up till now sections have depended on prior sections, I can only assume chapter 11 will get harder
REFLECTIVE
The theorems in section 1 & 2 are pretty understandable and intuitive. I remember doing this prime number stuff back in primary school. I really liked the equivalence classes before, although that didn't reflect in my exam score.
Thursday, November 13, 2014
The rest of 10.5, due on November 14
DIFFICULT
I'm not grasping the Axiom of Choice, I need it in layman's terms. Theorem 10.19 is mind blowing, I don't usually find math interesting, but when I do my mind usually ends up being blown. Corollary 10.20 is also interesting.
REFLECTIVE
Theorem A and B are are easy to understand and pretty intuitive. I'm interested in seeing how Theorem 10.19 and the Corollary pans out in class, once they are verbally explained to me.
I'm not grasping the Axiom of Choice, I need it in layman's terms. Theorem 10.19 is mind blowing, I don't usually find math interesting, but when I do my mind usually ends up being blown. Corollary 10.20 is also interesting.
REFLECTIVE
Theorem A and B are are easy to understand and pretty intuitive. I'm interested in seeing how Theorem 10.19 and the Corollary pans out in class, once they are verbally explained to me.
Tuesday, November 11, 2014
10.5 up to Theorem 10.18, due on November 12
DIFFICULT
I'm not fully understanding this Restriction business, why we need it and what help is provides and how it correlates with Theorem 10.18. Trying to understand Theorem 10.18 is a little odd. I hope that this will be clarified in lecture tomorrow.
REFLECTIVE
Some things are familiar from earlier sections in the chapter. We have talked about Cantor earlier this book when we talked about denumerability. This section seams to be pretty difficult, good thing we are spending two lectures on it.
I'm not fully understanding this Restriction business, why we need it and what help is provides and how it correlates with Theorem 10.18. Trying to understand Theorem 10.18 is a little odd. I hope that this will be clarified in lecture tomorrow.
REFLECTIVE
Some things are familiar from earlier sections in the chapter. We have talked about Cantor earlier this book when we talked about denumerability. This section seams to be pretty difficult, good thing we are spending two lectures on it.
Sunday, November 9, 2014
10.4, due on November 10
DIFFICULT
Again this single section that was assigned to us is pretty intuitive. The Continuum Hypothesis is difficult and not so clear.
REFLECTIVE
Theorem 10.14 is pretty understandable. Theorem 10.15 is also pretty intuitive. The definition Smaller Cardinality is also easy to understand.
Again this single section that was assigned to us is pretty intuitive. The Continuum Hypothesis is difficult and not so clear.
REFLECTIVE
Theorem 10.14 is pretty understandable. Theorem 10.15 is also pretty intuitive. The definition Smaller Cardinality is also easy to understand.
Thursday, November 6, 2014
10.3, due on November 7
DIFFICULT
Theorem 10.3 is a little bizarre, but ever since that one lecture my idea of countable has been skew. All the rest of the theorems are pretty intuitive.
REFLECTIVE
I haven't been using many other proof tools. So it is neat to see a proof by contradiction in this chapter. My favorite technique is proof by contradiction. The theorems in this section seem pretty intuitive.
Theorem 10.3 is a little bizarre, but ever since that one lecture my idea of countable has been skew. All the rest of the theorems are pretty intuitive.
REFLECTIVE
I haven't been using many other proof tools. So it is neat to see a proof by contradiction in this chapter. My favorite technique is proof by contradiction. The theorems in this section seem pretty intuitive.
Tuesday, November 4, 2014
10.2, due on November 5
DIFFICULT
The idea behind Denumerability is a little intense. Maybe I am not thinking deep enough, but I think I understood most of section 2.
REFLECTIVE
We talked about section 2 on Monday. After reading through the section, I think we covered all of it.
The idea behind Denumerability is a little intense. Maybe I am not thinking deep enough, but I think I understood most of section 2.
REFLECTIVE
We talked about section 2 on Monday. After reading through the section, I think we covered all of it.
Sunday, November 2, 2014
10.1, due on November 3
DIFFICULT
As all of these tools are being put together, the thing that will remain hard will be knowing when to use one or the other, and remembering them all.
REFLECTIVE
Obvious there are concepts in this section from chapter 9. As I have come to accept, this book is organized in such a way that you learn things that help you solve things in later chapters. Showing that things were bijective in chapter 9 weren't too hard.
As all of these tools are being put together, the thing that will remain hard will be knowing when to use one or the other, and remembering them all.
REFLECTIVE
Obvious there are concepts in this section from chapter 9. As I have come to accept, this book is organized in such a way that you learn things that help you solve things in later chapters. Showing that things were bijective in chapter 9 weren't too hard.
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