Trip to California

Yesterday I finally booked my Amtrak Ticket to goto California. I will be starting my train journey on 18th December at 3 O clock and will be reaching San Jose on 20th around 21 hrs. Hopefully I will have tons of photograph to show you all of the scenery. This trip has been in my mind ever since I saw the "transcontinental railroad" documentary. Here are some wonderful links you can read more about the genesis of Transcontinental railway. http://www.bbc.co.uk/history/programmes/seven_wonders/launch_ani_fall_transcontinental.shtml
http://www.pbs.org/wgbh/amex/iron/

In between we have covered Riemann Integration. I learned some new terms like Partition and Refinements. A Partition is just an ordered set, whereas a refinement of a set is a superset of that set. For example if P is an ordered set then the refinement of P is a set Q and it is a superset of P. There are several lemmas the gist of those is as you add more points to your partition your ares gets sandwiched into the lower and upper areas with less number of points. The main consideration for Riemann integrability is when the lower sum becomes equal to the upper sum. So we have two main theorems.

1. A bounded function f is integrable on [a,b] if and only if for every epsilon, there exists a partition Peps of [a,b] such that

U(f,Peps) - L(f,Peps) <>

The second main theorem is

2. If f is continuous on [a,b] then it is integrable

*****The work on my white board shows about some of the terms and their definition in context of Riemann Integration*****