The course is structured around writing assignments which will be peer reviewed and/or graded by the instructor and the course TA. We will also explore (in the above context) how mathematics and physics interact, why (whether) mathematics describes the 'physical' universe so accurately, how (whether) aesthetics, art, philosophy has an impact on mathematics, and how mathematical ideas could be conveyed to a non-expert audience. The various ideas and view points humanity had over the past 2000 or so years about those topics will be part of our exploration.There will be lectures on this topic by the instructor and video taped lectures/demonstrations by eminent mathematicians who worked on these problems. We will study the concept of dimension in geometry and physics beginning from dimension 0 to dimension 3 (and perhaps 4) leading to the Poincare Conjecture, which provides the possible shapes of the spacial 3-dimensional universe.
