Waking up Early
Dear Sumant,
Today I woke up at around 4 am I lingered for a while before out of bed at 5:am. I loved it. I had time to read section of book by Richard Carlson. I went over 501 and 449 subjects. In 501 at present we are doing Lebesgue Measure Theory. Here are some tidbits of what I right now can recall. There is a concept of outer measure and for any interval its the length of the interval for ex for interval (a,b) where a < b its (b-a). One of the important theorem is any open set can be written as a countable union of disjoint open intervals. It has a 5 step proof in which the countability is shown by mapping with rational number and overlapping intervals are contained in a maximal open interval. The other is E1 and E2 are two measurable sets that so is their union ie E1 U E2. The outer measure is denoted by lambda* and it has 3 main properties including that its translation invariant. In 449 we are doing product of generating functions and all you have to do is find the coefficient of x^n. So far we discussed mostly product of ordinary generating functions.
SIUC was closed on last Thursday and Friday which is kind of unprecedented because of winter snow and ice. My car was all cocooned in sheet of ice. The weekend I went to two parties including one thrown foe Elmer, who is now going back to Columbia and the other at Charles House. So in a way it was a nice long weekend. I did go to Walmart to get my car battry replaced. I also went to Barnes and Noble and spent some time going over the "Walking in this world" and "The Artist's Way" both book seem pretty interesting and I am going to order these soon. Apparently her other book "The Right to Write" inspired me to get back to writing more and one of the very reason I am updating this block. In her all books she advocate the importance of writing, walking and thinking.
That's for now
Sumant
Today I woke up at around 4 am I lingered for a while before out of bed at 5:am. I loved it. I had time to read section of book by Richard Carlson. I went over 501 and 449 subjects. In 501 at present we are doing Lebesgue Measure Theory. Here are some tidbits of what I right now can recall. There is a concept of outer measure and for any interval its the length of the interval for ex for interval (a,b) where a < b its (b-a). One of the important theorem is any open set can be written as a countable union of disjoint open intervals. It has a 5 step proof in which the countability is shown by mapping with rational number and overlapping intervals are contained in a maximal open interval. The other is E1 and E2 are two measurable sets that so is their union ie E1 U E2. The outer measure is denoted by lambda* and it has 3 main properties including that its translation invariant. In 449 we are doing product of generating functions and all you have to do is find the coefficient of x^n. So far we discussed mostly product of ordinary generating functions.
SIUC was closed on last Thursday and Friday which is kind of unprecedented because of winter snow and ice. My car was all cocooned in sheet of ice. The weekend I went to two parties including one thrown foe Elmer, who is now going back to Columbia and the other at Charles House. So in a way it was a nice long weekend. I did go to Walmart to get my car battry replaced. I also went to Barnes and Noble and spent some time going over the "Walking in this world" and "The Artist's Way" both book seem pretty interesting and I am going to order these soon. Apparently her other book "The Right to Write" inspired me to get back to writing more and one of the very reason I am updating this block. In her all books she advocate the importance of writing, walking and thinking.
That's for now
Sumant
posted by Sumant at 9:06 AM
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