The principle of least action is an extremely powerful reformulation of Newton's laws of motion that is plays a vital role in a myriad of fields, ranging from the mathematics of symplectic geometry to the deep and fundamental laws of quantum field theory. In this course, I will motivate the need for Lagrangian mechanics, mostly on the basis of its independence of vectorial forces and instead, the emphasis on energy. I will give a general derivation, a couple of examples, and describe the implications in modern physics, such as quantum mechanics as general relativity.

This course will introduce the basic ideas of particle physics, both theoretical and experimental, ranging from accelerator physics and the Standard model to the statistical analyses applied to the data and even the vibrant scientific atmosphere at CERN (especially during exciting times like these). Emphasis will be placed on the Higgs boson and this summer's discovery, with a focus on the $H\rightarrow\gamma\gamma$ analysis channel. --- SUMMARY: The Standard Model of particle physics, developed during the latter half of the twentieth century, explains in its current formulation a truly wide variety of particle phenomena. However, the mechanism through which fundamental particles attain their mass - electroweak symmetry breaking - has only recently (and rather tentatively) been observed experimentally at the LHC. This mechanism is predicted by the Standard model to manifest itself through the presence of the electrically neutral, spin zero Higgs boson. Indeed, in July of 2012, CERN formally announced the discovery of a boson with properties that seem to be consistent with those expected of the Standard Model Higgs (SM Higgs). However, more data is needed to confirm that this is so; quantities such as production and decay channel cross-sections, angular correlations of decay products, etc. must be precisely calculated. A rough outline of the talk is available here: http://nilaykumar.com/NilayLHCHiggsAugust31.pdf