Random Variables
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This is a math course aimed at students with life science majors covering elementary probability, probability distributions, random variables, and limit theorems.
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According to the rational expectations hypothesis, traders know the probabilities of future events, and value uncertain future payoffs by discounting their expected value at the riskless rate of interest. Under this hypothesis the best predictor of a firm's valuation in the future is its stock price today. In one famous test of this hypothesis, it was found that detailed weather forecasts could not be used to improve on contemporaneous...more
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Decomposition Applications, Rate Control Setup, Rate Control Problem, Rate Control Lagrangian, Aside: Utility Functions, Rate Control Dual, Dual Decomposition Rate Control Algorithm, Generating Feasible Flows, Convergence Of Primal And Dual Objectives, Maximum Capacity Violation, Single Commodity Network Flow Setup, Network Flow Problem, Network Flow Lagrangian, Network Flow Dual, Recovering Primal From Dual, Dual Decomposition Network...more
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Heap Management - How Information about Allocations are Stored in the Heap
Stanford / Computer Science
Heap Management - How Information about Allocations are Stored in the Heap, Result of Freeing Memory Improperly, Actual Sizes of Heap Allocations - Nearest Power of 2, Management of Free Blocks on the Heap by Storing Addresses in the Blocks of Free Memory, Algorithms for Choosing Which Free Block to Allocate, How the Heap's Free List Can Be Updated When Memory is Freed, How Adjacent Free Blocks Are Combined To Avoid Fragmentation,...more
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Scheme Memory Model - How Scheme Instructions Synthesize Linked Lists Behind the Scenes and Perform Operations on Them, Two Different Ways of Laying Out A List In Memory, One With Memory Aliasing and One Without, The Scheme Equivalent of "..." (Functions With Multiple Arguments), Writing A Generic Map Function, Modifying the Unary-Map Function to Handle Multiple Arguments By Adding A . to the List of Arguments, Extending Unary-Map to An...more
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Moving from C Code Generation to C++ Code Generation: Basic Swap Example
Stanford / Computer Science
Moving from C Code Generation to C++ Code Generation: Basic Swap Example, Code Generation for the Pointer Swap Function, Code Generation for the C++ Version Of Swap Using References, Which Are Treated as Automatically Dereferenced Pointers, Local Variables Declared as References, Difference Between References and Pointers, Effect Of Declaring a Class on Memory in the Stack, Class Methods, Which Take a "This" Pointer as An invisible First...more
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Guest Lecturer: Sasha Rush, Haskell History, Safeguards in Haskell that Avoid Runtime Errors, Expressive Functions in Haskell, Speed of Haskell, Haskell Fibonacci Sequence in One Line Using Lazy Evaluation, How Lazy Evaluation Allows if Statements, Haskell Types, User-defined Data Types, Representing the Null Type in Haskell, List Types, Strings as Lists and Recursive Type Definitions, List Functions and Pattern Matching, Type Variables...more
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Several theories in finance relate to stock price analysis and prediction. The efficient markets hypothesis states that stock prices for publicly-traded companies reflect all available information. Prices adjust to new information instantaneously, so it is impossible to "beat the market." Furthermore, the random walk theory asserts that changes in stock prices arise only from unanticipated new information, and so it is impossible to...more
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Aliasing Demonstration With Music, Transition To Discrete! The DFT, The Plan For Transitioning To Discrete Time, Creating A Discrete Signal From F(T) Creating A Discrete Version Of The Fourier Transform Of The Sampled Version Of F(T), Summary Of What We Just Did, Summary Of Results (Formulas), Moving From Continuous To Discrete Variables, Final Result: The DFT
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Complementary Slackness, Karush-Kuhn-Tucker (KKT) Conditions, KKT Conditions For Convex Problem, Perturbation And Sensitivity Analysis, Global Sensitivity Result, Local Sensitivity, Duality And Problem Reformulations, Introducing New Variables And Equality Constraints, Implicit Constraints, Semidefinite Program
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readInt() and readDouble(), The Division Operator w.r.t ints and Doubles, Order of Precedence for Operators, Type Casting, Shorthands, Constants, The Boolean Data Type, Value Comparisons, Boolean Expressions, Short Circuit Evaluation, Statement Blocks, Scope of Variables, Cascading if, The Switch Statement, The For Loop, The While Loop
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Thinking Recursively, Procedural vs Functional Recursion, Fractal Code, Live Demo: Fractal Example, Another Recursive Graphic: Mondrian Art, Random Pseudo-Mondrian and the Code, Hanois Towers : Classic Recursion Example, Tower Code, Live Demo, Permutations, Permute Code, Tree of Recursive Calls
