Time And Space Complexity Analysis
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This course is the natural successor to Programming Methodology and covers such advanced programming topics as recursion, algorithmic analysis, and data abstraction using the C++ programming language, which is similar to both C and Java. If you've taken the Computer Science AP exam and done well (scored 4 or 5) or earned a good grade in a college course, Programming Abstractions may be an...more
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Complexity; log, linear, quadratic, exponential algorithms
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According to Musk, some causes of the high costs in space exploration are: The energy to launch a rocket into space is very high, all the calculations have to be right and this is very expensive given the low launch rate. His final analysis is that rockets should be a lot cheaper and presently there are a lot of inefficiencies.
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Algorithm Analysis, Evaluating the Performance, Analysis of Codes: Statement Counts, Another Example (Statement Count Contd.), Comparing Algorithm, Big-O Notation, Big-O to Predict the Time of Execution, Best/Worst/Average Case, Analysis of Recursive Algorithms, Another Example : Towers of Hanoi, A Tabulation for Different Algorithms, Growth Patterns, Application of Algorithm Analysis to Sorting, Selection Sort, Selection Sort Code
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Musk does not recommend space travel to a first time entrepreneur. It is better to start with something that requires low capital.
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In this introductory lecture, Professor Lewin discuses basic units, dimensions, measurements and associated uncertainties, dimensional analysis, and scaling arguments. Further, he explains why a measurement is meaningless without knowledge of its uncertainty, using data collected by Galileo Galilei as an example. He begins to dive into dimensional analysis, reasoning that the time from...more
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The four-vector is introduced that unifies space-time coordinates x, y, z and t into a single entity whose components get mixed up under Lorentz transformations. The length of this four-vector, called the space-time interval, is shown to be invariant (the same for all observers). Likewise energy and momentum are unified into the energy-momentum four-vector.
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Previous Knowledge Recommended (Matlab), The Fourier Series, Analysis V. Synthesis, Periodic Phenomena And The Fourier Series -Periodicity In Time And Space -Reciprocal Relationship Between Domains, The Reciprocal Relationship Between Frequency And Wavelength
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The Factor Analysis Model,0 EM for Factor Analysis, Principal Component Analysis (PCA), PCA as a Dimensionality Reduction Algorithm, Applications of PCA, Face Recognition by Using PCA
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A perennial favorite is the idea of time travel. What would happen if we could go back in time and alter the future a la “Back to the Future”? The great narrative of the history of life has a complexity rife with subplots and twists, many of which we will never uncover. Yet somehow the story of life on Earth began with a prebiotic ooze and ended with the awe-inspiring diversity of life we...more
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Interior-Point Methods (Cont.), Example, Barrier Method (Review), Complexity Analysis Via Self-Concordance, Total Number Of Newton Iterations, Generalized Inequalities, Logarithmic Barrier And Central Path, Barrier Method, Course Conclusion, Further Topics
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