Stolen from the Course Description: we covered "the basic properties of natural numbers, countable and uncountable sets, the construction of the real numbers, some basic facts about the topology of the real line, cardinal numbers and cardinal arithmetic, the continuum hypothesis, well ordered sets, ordinal numbers and transfinite induction, the axiom of choice, Zorn's lemma. Optional topics if time permits: infinitary combinatorics, filters and large cardinals, Borel and analytic sets of reals."
Part of the lectures notes are as follows, will keep working on it according to time availability
In 2014, building accounts for 41% of the total U.S. Energy consumption (U.S. Energy Information Administration, 2015). Within this, 43% goes to the HVAC. The design of thermal comfort directly relates to the energy performance of the HVAC system. Moreover, thermal comfort has great variation between occupants, as is shown in the study of Takashi et al (Takashi, Shin-ichi, Takashi, & Masato, 2010). PMV is the most commonly adopted model for thermal comfort, but it does not take personal and seasonal variation into consideration. On the contrary, fuzzy logic expert system imbedded the complexity and uncertainty (fuzziness) definition (Dounis & Manolakis, 2001) of thermal comfort and integrates personalized preferences into the HVAC control system (Farrokh, Ali, Burcin, Tatiana, & Michael, 2014) and is promising in providing a higher level of thermal comfort a lower energy consumption. In the following section, we will have a brief review of the approaches of fuzzy control logic in building thermal environment control.
Fuzzy control is based on fuzzy logic, which maps continuous analogue input to propositions regarding membership of “fuzzy sets” (Wikipedia). Fuzzy set is an ordered pair of a set U and the membership function m: U -> [0, 1]. The term “fuzzy” expresses the “partial truth” or the degree of membership of fuzzy sets.
According to U.S. Energy Information Administration (EIA), in 2012, 12% of the electricity is consumed in lighting of residential and commercial buildings (U.S. Energy Information Administration, 2014). Automatic lighting control is widely applied in reducing lighting energy consumptions in commercial and residential buildings. It is also important in ensuring the visual comfort of Indoor Environment Quality and reduce the carbon footprint of building operation. In addition, the system enables a convenient control of multiple lighting devices through a single user device.
Typical input of lighting control systems are driven by the following one or more aspects: time (chronological or astronomical time), occupancy (occupancy sensors), daylight availability (photocells) and program logic etc. (Wikipedia, 2014). This summary will present a brief review of the energy performance of the daylight-availability and occupancy based systems.
The present urban environment, especially in the U.S. tends to be designed for cars rather than human. The low density and high level of separation of different age group, different income group and different use also the separation from natural environment actually make the city a big prison where residents are trapped inside and have nowhere to escape to. When you live in a city where without a car you cannot anywhere (which is the case for lots of U.S. cities), when you are not old enough or too old to drive a car, then you are totally trapped. You can connect your friends through phones, facebook and other electric based methods, but you can never see them in person. The only thing you can do is to wait until your parents come back and willing to take you somewhere. This may be one of the reasons why people get bad impression on teenage drivers. After years of “jail" they are so desperate to rush their way somewhere else. If you are too old, you are thrown into special elder citizen residential facilities far away from normal social life. From then on you are never going to see the younger. People of high income live in their “Garden of Eden", completely separated from their low-income neighbors, thinking that they were all evil persons. There are always a certain percentage of good people and bad people in an each social group. Bias, scare and conflicts grow as a result of high level of separation and resulted lacking of contact.
These problems are believed to be associated with a poorly designed built environment and an un healthy (or “dysfunctional”) mode of development, commonly addressed as Urban Sprawl which has properties as: low density, rigidly separated land use, inaccessible huge blocks and an absence of vibrant city center (Reid et al., 2003) . A serious of multi-dimensional social, economic, environment and health problems are believed to be a result of Urban Sprawl as follows: higher driving distance, high car ownership, more polluted air, higher car accident death rate , less physical activity, high obesity rate, and high hypertension (Reid et al., 2003).
For the future and sustainability oriented CMU ecological footprint analysis, my focus is on the neighborhood scale with focuses on: 1) the improvement of quality of life of the neighborhood as a whole, especially on the improvement of living quality of senior citizens; 2) providing access to safer, more affordable and more environmentally friendly housing choices for students and faculty members; 3) reducing the travelling distance of faculty members to provide both more sustainable and more affordable housing choices. The study is done with the platform of GIS using the software of Arcgis 10.1 (Arcgis for Desktop, 2013)