These are the notes from a course taught at Cornell in Spring 2009. They are a record of what was covered in the lectures. Many results were copied out of books and other sources, as noted in the text. The course had three parts: (1) An introduction to finite-dimensional algebras (lectures 1-12) (2) Gabriel’s Theorem (lectures 13-16) (3) Auslander-Reiten theory (lectures 17-27). Thanks to C. H....

These are the first version of suggested lecture notes for a second level course on advanced topics in database systems for master's students of Computer Science. A prerequisite in algorithms and an exposure to database systems are required. Additional reading may require exposure to mathematical logic which seems to be getting outdated going by newer editions of Computer Science theory books. ...

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I think Mr. Yang Peng's lecture has made a great contribution to our understanding of the similarities and differences between God in ancient Chinese books Bible. It is very specific real. The "seven characteristics" he summarized, summed up attributes Bible or Christianity into seven characteristics, which quite accurate: an adjective front, noun back, adjectives are indispensable (if have tim...

We give, for the first time, the English translation of a manuscript by Ettore Majorana, which probably corresponds to the text for a seminar lecture delivered at the University of Naples in 1938, where he lectured on theoretical physics. Some passages reveal a physical interpretation of quantum mechanics which anticipates for several years the Feynman approach in terms of path integrals, indep...

These lecture notes are meant to serve as a short introduction to implicit computational complexity for those students who have little or no knowledge of recursion theory and proof theory. They have been obtained by enriching and polishing a set of notes the author wrote for a course (on the same subject) he gave at ESSLLI 2010. These notes are definitely not meant to be comprehensive nor exhau...

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References Most of the material in these lecture notes is discussed in greater detail in the following two books, which I recommend you study if you are interested in quantum computation. 1. M. Nielsen and I. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, 2000. 2. A. Kitaev, A. Shen, and M. Vyalyi. Classical and Quantum Computation, volume 47 of Graduate Studie...

As it will be clear, the proof of [MSS13] although not being long is very involved and has several novel ideas. So, we start with a significantly simpler setup and we prove relatively weaker statements. As the ideas become more clear we will go over the actual ideas in [MSS13]. The materials of this lecture are based on the work of Batson, Spielman and Srivastava [BSS14] and lecture notes of Ni...