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Mathematical depth — probability theory, statistics, stochastic calculus and the numerical tools behind alpha research (Two Sigma, DE Shaw, Citadel).
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01Probability Theory
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Coin Toss — Two HeadsNext up
Probability
Birthday Problem
Probability
Roll Until All Six Faces
Probability
Drunk Passenger
Probability
Bayes — Disease Test
Probability
Broken Stick Triangle
Probability
Hat Check
Probability
Top Two Aces
Probability
Expected Max of Two Dice
Probability
02Statistics & Inference
0/503Stochastic Processes & Itô
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Gambler’s Ruin
Stochastic Processes
Flips Until Two Heads in a Row
Stochastic Processes
Expectation of GBM
Stochastic Processes
Variance of Brownian Motion
Stochastic Processes
Covariance of Brownian Motion
Stochastic Processes
Expected Flips for HTH
Stochastic Processes
Random Walk Recurrence
Stochastic Processes
04Calculus & Linear Algebra
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Definite Integral of x²
Calculus & Linear Algebra
Limit of sin(x)/x
Calculus & Linear Algebra
Eigenvalues of a 2×2
Calculus & Linear Algebra
Gaussian Integral
Calculus & Linear Algebra
Derivative of xˣ
Calculus & Linear Algebra
Maximize x^(1/x)
Calculus & Linear Algebra
Geometric Series
Calculus & Linear Algebra
Limit of (1+1/n)^n
Calculus & Linear Algebra
Integral of x·e^(−x)
Calculus & Linear Algebra
05Algorithms & Numerical
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Two SumLeetCode
Algorithms & Numerical
Best Time to Buy and Sell StockLeetCode
Algorithms & Numerical
Maximum Subarray (Kadane)LeetCode
Algorithms & Numerical
Monte Carlo — Estimate π
Algorithms & Numerical
Newton’s Method for √2
Algorithms & Numerical
Product of Array Except SelfLeetCode
Algorithms & Numerical
Kth Largest ElementLeetCode
Algorithms & Numerical
Trapping Rain WaterLeetCode
Algorithms & Numerical
Sliding Window MaximumLeetCode
Algorithms & Numerical
Random Pick with WeightLeetCode
Algorithms & Numerical
Shuffle an Array (Fisher-Yates)LeetCode
Algorithms & Numerical
Rand10() from Rand7()LeetCode
Algorithms & Numerical
Coin Change (DP)LeetCode
Algorithms & Numerical
Median of Two Sorted ArraysLeetCode
Algorithms & Numerical
Longest Increasing SubsequenceLeetCode
Algorithms & Numerical
Find Median from Data StreamLeetCode
Algorithms & Numerical
Course ScheduleLeetCode
Algorithms & Numerical
Number of IslandsLeetCode
Algorithms & Numerical
LRU CacheLeetCode
Algorithms & Numerical