There are many different sub-catagories in the field of architecture. An architect can do anything along the line of city planning (an example in the city of Hong Kong, as seen in the picture down), community planning (i

Math plays a major role in the field of architecture. Greater knowledge in math help the architect to understand the structures and concepts, with calculations, at a more indepth level. Geometry contains a large portion of the mathematics used in everyday architecture. An example of this can be taken from Renaissance architecture, were the concept of symmetry plays a huge role. Symmetry can be seen easily in Egyptian Pyramids. An impressive example of a more modern architectual building that uses many complicated symmetries can be seen in the Sydney Opera House, located in Australia. One interesting building that can be seen is the Leaning Tower of Pisa, which uses broken symmetry for a very dramatic effect. Geometry can also be seen in the planning of cities using a grid plan (cartesian coordinate system). In Greek architecture, the golden mean (a.k.a. golden ratio) served a huge role in the planning of buildings. It is the proportion 1:1:618, which in Western architect was found very pleasing. This has been used in many Greek buildings, such as the Parthenon, as well as many sculptures, paintings, and vases.
Links to some other interesting images of architecture that I have found in buildings:
http://upload.wikimedia.org/wikipedia/commons/f/f6/FallingwaterWright.jpg
http://www.trendir.com/ultra-modern/architecture-insitute-amsterdam-3.jpg
http://condo-user.pamjundy.com/wp-content/plugins/wp-o-matic/cache/42c10_revolve.gif
http://www.flickr.com/photos/25830962@N06/3198161084/
http://www.flickr.com/photos/22784225@N07/2674003861/