Fourier Series
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Recap: Example: Minimum Cardinality Problem, Interpretation As Convex Relaxation, Interpretation Via Convex Envelope, Weighted And Asymmetric L_1 Heuristics, Regressor Selection, Sparse Signal Reconstruction, L_1-Norm Methods For Convex-Cardinality Problems Part II, Total Variation Reconstruction, Total Variation Reconstruction, TV Reconstruction, L_2 Reconstruction, Iterated Weighted L_1 Heuristic, Sparse Solution Of Linear Inequalities,...more
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A glimpse of the mystery of the Universe as we approximate e^x with an infinite series.
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Approximating cos x with a Maclaurin series.
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Suppose you have a perfect model of contingent mortgage prepayments, like the one built in the previous lecture. You are willing to bet on your prepayment forecasts, but not on which way interest rates will move. Hedging lets you mitigate the extra risk, so that you only have to rely on being right about what you know. The trouble with hedging is that there are so many things that can happen over the 30-year life of a mortgage. Even if...more
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Winblad explains that very few Series A investments were done in 2002. However, a lot more were done in 2003 and will be done in 2004, she says. The reasons for the decline since 2000 include: restart dollars were competing with the A round dollars; corporate investors disappeared (excpet Intel); and individual investing declined. Additionally, during this era, VCs were doing deals individually, creating twice as many A round deals and...more
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The lecture covers a number of mathematical concepts. The Taylor series is introduced and its properties discussed, supplemented by various examples. Complex numbers are explained in some detail, especially in their polar form. The lecture ends with a discussion of simple harmonic motion.
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About the Introduction to Computer Science Series at Stanford, The Philosophy, Why take CS106B?, Logistics of the Course, Introducing C++
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Correction To The End Of The CLT Proof, Discussion Of The Convergence Of Integrals; Approaches To Making A More Robust Definition Of The Fourier Transform, Examples Of Problematic Signals, How To Approach Solving The Problem; Choosing Basic Phenomena To Use To Explain Others, Identifying The Best Class Of Signals For Fourier Transforms; + Their Properties, The Definition Of The Class Of Rapidly Decreasing Functions, Rationale For Why...more
