Difficult
In section 1.4, I still don't understand how property #8 works. I'm assuming this property applies when the events are not disjoint, or else property #3 would apply. When comparing this with Example (13), I come up with more questions. Why do we add some probabilities and subtract others? How can we be sure that this outcome will be less than or equal to 1? What happens when there are more than three events?
Reflective
I'm having a little trouble grasping the concept of F, a collection of subsets of omega, but I think it's analogous to the concept of a field F in linear algebra. When deciding whether or not A is an event, you must make sure A and its complement are in F. Although, if F is a collection of subsets of omega, how can omega be in F?
Sunday, September 30, 2007
Week 0 - Friday
Difficult
It's always difficult to get used to a new textbook and the type of terminology and notation it uses. I'm still a little unsure about what the author means by "symmetry." Based on the context, I'm assuming that it means all possible outcomes have an equal chance of occurring, since "symmetry" is not used to describe the case with the weighted die. I'm also confused about when "capital omega" denotes the universal set or a sample space.
Reflective
It was nice to get some review on series and limits, since it's been a while since I've seen the formal notation. I found the Venn diagrams very useful in trying to visualize unions, intersections, and differences. I thought Example (13) on page 29 was a very good problem to show how we can use sets to draw more conclusions.
It's always difficult to get used to a new textbook and the type of terminology and notation it uses. I'm still a little unsure about what the author means by "symmetry." Based on the context, I'm assuming that it means all possible outcomes have an equal chance of occurring, since "symmetry" is not used to describe the case with the weighted die. I'm also confused about when "capital omega" denotes the universal set or a sample space.
Reflective
It was nice to get some review on series and limits, since it's been a while since I've seen the formal notation. I found the Venn diagrams very useful in trying to visualize unions, intersections, and differences. I thought Example (13) on page 29 was a very good problem to show how we can use sets to draw more conclusions.
Thursday, September 27, 2007
HW 0
My name is Sara Chan and I am a third-year math major at UCLA. So far, I've taken Math 31B, 32A, 32B, 33A, 33B, 61, and 115A.
What I like about math is that once you figure out the pattern or process behind a problem, you can solve any similar problem. I'm a very detail-oriented and systematic person; if you show me something step-by-step, I will always follow each step in that same order. I really like finding patterns and I think that's what makes me "strong" in math.
Of course, everyone has their weaknesses. As much as I love patterns, I do find it difficult at times to actually *find* them. Often times, a TA or professor may ask "what pattern do you see?" and my mind draws a blank. It's only after I stare at the problem for a long time that I can see a pattern. New math concepts no longer come to me as quickly as they did in high school, which frustrates me. Now in college, I find that I have to work harder in my math classes. This doesn't make me dislike math, but it's definitely a challenge to change my mindset and realize that I have to put more effort into my math work in order to succeed.
I believe a good math teacher not only needs to explain the material well, but also needs to be enthusiastic about math. My favorite math teachers are the ones who make me want to go to class and learn. When I see their enthusiasm in their teaching, it makes me want to continue my line of study. I also believe a good math teacher should be flexible and approachable. In my experience, when a teacher seems reserved or intimidating, it's more difficult for students to build up the courage to go to office hours. It's difficult to get excited about math when your professor is always facing the blackboard and lecturing in a monotone voice.
For this course, I've read the syllabus and understand the following. After final exams are graded, they are kept for one quarter and then available for pickup the following quarter. After two quarters have passed, they are recycled. An assignment is considered semi-late if it is turned in during class (between 11:00 and 11:50 am). The five minutes rule states if I run into
Professor Brose, she'll (almost) always have five minutes to talk with me.
What I like about math is that once you figure out the pattern or process behind a problem, you can solve any similar problem. I'm a very detail-oriented and systematic person; if you show me something step-by-step, I will always follow each step in that same order. I really like finding patterns and I think that's what makes me "strong" in math.
Of course, everyone has their weaknesses. As much as I love patterns, I do find it difficult at times to actually *find* them. Often times, a TA or professor may ask "what pattern do you see?" and my mind draws a blank. It's only after I stare at the problem for a long time that I can see a pattern. New math concepts no longer come to me as quickly as they did in high school, which frustrates me. Now in college, I find that I have to work harder in my math classes. This doesn't make me dislike math, but it's definitely a challenge to change my mindset and realize that I have to put more effort into my math work in order to succeed.
I believe a good math teacher not only needs to explain the material well, but also needs to be enthusiastic about math. My favorite math teachers are the ones who make me want to go to class and learn. When I see their enthusiasm in their teaching, it makes me want to continue my line of study. I also believe a good math teacher should be flexible and approachable. In my experience, when a teacher seems reserved or intimidating, it's more difficult for students to build up the courage to go to office hours. It's difficult to get excited about math when your professor is always facing the blackboard and lecturing in a monotone voice.
For this course, I've read the syllabus and understand the following. After final exams are graded, they are kept for one quarter and then available for pickup the following quarter. After two quarters have passed, they are recycled. An assignment is considered semi-late if it is turned in during class (between 11:00 and 11:50 am). The five minutes rule states if I run into
Professor Brose, she'll (almost) always have five minutes to talk with me.
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