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Quant Researcher Plan

· 24 days

A deep plan for research interviews (Two Sigma, D. E. Shaw, Citadel): probability theory, statistics and inference, stochastic calculus, calculus and linear algebra, and the heaviest coding load — dynamic programming, graphs, sampling and Monte Carlo. Topics interleave daily so nothing fades. Light on pure brain teasers and options.

Sign in to track your progress — each day checks off as you solve its problems.

1

Day 1

Coding · Calculus · Probability

Two SumLeetCode

Algorithms & NumericalGoogleDE Shaw

Coin Toss — Two Heads

ProbabilityJane Street

Definite Integral of x²

Calculus & Linear AlgebraGoldman Sachs

Variance of Uniform(0,1)

StatisticsGoldman SachsCitadel

2

Day 2

Coding · Calculus · Probability

Variance of Brownian Motion

Stochastic ProcessesGoldman SachsMorgan Stanley

Monte Carlo — Estimate π

Algorithms & NumericalGoldman SachsTwo Sigma

ProbabilityGoldman SachsMorgan Stanley

Limit of sin(x)/x

Calculus & Linear AlgebraGoldman SachsMorgan Stanley

3

Day 3

Coding · Probability · Statistics

Newton’s Method for √2

Algorithms & NumericalGoldman SachsJane Street

Flips Until First Head

ProbabilityOptiverIMC Trading

Nim GameLeetCode

Algorithms & NumericalJane StreetSIG / Susquehanna

StatisticsTwo SigmaAQR Capital

4

Day 4

Coding · Calculus · Probability

Flips Until Two Heads in a Row

Stochastic ProcessesJane StreetCitadel

Geometric Series

Calculus & Linear AlgebraGoldman Sachs

Product of Array Except SelfLeetCode

Algorithms & NumericalTwo SigmaHRT

Two Dice Sum to 7

ProbabilityOptiverIMC Trading

5

Day 5

Coding · Calculus · Probability

Kth Largest ElementLeetCode

Algorithms & NumericalTwo SigmaDE Shaw

Limit of (1+1/n)^n

Calculus & Linear AlgebraGoldman SachsMorgan Stanley

ProbabilityGoldman SachsMorgan Stanley

Maximum Subarray (Kadane)LeetCode

Algorithms & NumericalTwo SigmaDE Shaw

6

Day 6

Calculus · Probability · Statistics

Variance of a Sum

StatisticsGoldman SachsMorgan Stanley

Gambler’s Ruin

Stochastic ProcessesJane StreetSIG / Susquehanna

Expected Rolls for a Six

ProbabilityOptiverIMC Trading

L'Hôpital — (eˣ−1)/x

Calculus & Linear AlgebraGoldman SachsMorgan Stanley

7

Day 7

Coding · Calculus · Probability

Random Pick with WeightLeetCode

Algorithms & NumericalCitadelTwo Sigma

At Least One Six

ProbabilitySIG / SusquehannaOptiver

Shuffle an Array (Fisher-Yates)LeetCode

Algorithms & NumericalTwo SigmaDE Shaw

Derivative of ln(x)

Calculus & Linear AlgebraGoldman Sachs

8

Day 8

Coding · Probability · Statistics

Central Limit Theorem

StatisticsGoldman SachsMorgan Stanley

Covariance of Brownian Motion

Stochastic ProcessesGoldman SachsTwo Sigma

Best Time to Buy and Sell StockLeetCode

Algorithms & NumericalTwo SigmaDE Shaw

Roll Until All Six Faces

ProbabilityGoogleTwo Sigma

9

Day 9

Coding · Calculus · Probability

Rand10() from Rand7()LeetCode

Algorithms & NumericalJane StreetOptiver

Sum of First 10 Squares

Calculus & Linear AlgebraJane StreetTwo Sigma

Birthday Problem

ProbabilityGoldman SachsCitadel

Coin Change (DP)LeetCode

Algorithms & NumericalGoogleDE Shaw

10

Day 10

Calculus · Probability · Statistics

StatisticsTwo SigmaDE Shaw

Random Walk Recurrence

Stochastic ProcessesTwo SigmaDE Shaw

Trace = Sum of Eigenvalues

Calculus & Linear AlgebraTwo SigmaGoldman Sachs

Drunk Passenger

ProbabilityJane StreetCitadel

11

Day 11

Coding · Probability

Online Stock SpanLeetCode

Algorithms & NumericalCitadel SecuritiesHRT

Time-Based Key-Value StoreLeetCode

Algorithms & NumericalTwo SigmaJump Trading

Bayes — Disease Test

ProbabilityGoldman SachsTwo Sigma

12

Day 12

Calculus · Statistics · Stochastic

Determinant = Product of Eigenvalues

Calculus & Linear AlgebraTwo SigmaDE Shaw

Range of Correlation

StatisticsGoldman SachsCitadel

Quadratic Variation of BM

Stochastic ProcessesGoldman SachsTwo Sigma

13

Day 13

Coding · Calculus · Probability

Best Time to Buy and Sell Stock IILeetCode

Algorithms & NumericalOptiverJane Street

Broken Stick Triangle

ProbabilityJane StreetCitadel

Approximate cos(0.1)

Calculus & Linear AlgebraJane StreetOptiver

14

Day 14

Coding · Probability

Gas StationLeetCode

Algorithms & NumericalJane StreetCitadel

ProbabilitySIG / SusquehannaOptiver

Jump GameLeetCode

Algorithms & NumericalGoogleDE Shaw

15

Day 15

Calculus · Statistics · Stochastic

Variance of a Scaled Variable

StatisticsGoldman Sachs

Expectation of GBM

Stochastic ProcessesGoldman SachsMorgan Stanley

Eigenvalues of a 2×2

Calculus & Linear AlgebraGoldman SachsCitadel

16

Day 16

Coding · Probability

Predict the WinnerLeetCode

Algorithms & NumericalJane StreetOptiver

ProbabilityJane StreetDE Shaw

LRU CacheLeetCode

Algorithms & NumericalTwo SigmaHRT

17

Day 17

Coding · Calculus · Probability

Gaussian Integral

Calculus & Linear AlgebraGoldman SachsTwo Sigma

Expected Max of Two Dice

ProbabilityOptiverIMC Trading

Longest Increasing SubsequenceLeetCode

Algorithms & NumericalTwo SigmaDE Shaw

18

Day 18

Probability · Statistics · Stochastic

Correlation of X and X²

StatisticsTwo SigmaDE Shaw

Expected Flips for HTH

Stochastic ProcessesJane StreetSIG / Susquehanna

Russian Roulette — Spin?

ProbabilityJane StreetCitadel

19

Day 19

Coding · Calculus · Probability

Derivative of xˣ

Calculus & Linear AlgebraJane StreetCitadel

Course ScheduleLeetCode

Algorithms & NumericalGoogleDE Shaw

Expected Min of Two Dice

ProbabilityOptiverSIG / Susquehanna

20

Day 20

Coding · Calculus · Statistics

Number of IslandsLeetCode

Algorithms & NumericalGoogleTwo Sigma

Integral of x·e^(−x)

Calculus & Linear AlgebraGoldman SachsTwo Sigma

Covariance of a Linear Transform

StatisticsGoldman SachsAQR Capital

21

Day 21

Coding · Probability · Stochastic

Random Walk — Expected Steps

Stochastic ProcessesJane StreetTwo Sigma

Trapping Rain WaterLeetCode

Algorithms & NumericalJane StreetCitadel Securities

Poisson — No Arrivals

ProbabilityTwo SigmaJump Trading

22

Day 22

Coding · Calculus · Probability

Sliding Window MaximumLeetCode

Algorithms & NumericalHRTJump Trading

Integrate x·eˣ

Calculus & Linear AlgebraGoldman SachsMorgan Stanley

Exponential Survival

ProbabilityDE ShawMorgan Stanley

23

Day 23

Coding · Statistics · Stochastic

Median of Two Sorted ArraysLeetCode

Algorithms & NumericalGoogleTwo Sigma

Variance of the Sample Mean

StatisticsTwo SigmaDE Shaw

Expected Running Max of BM

Stochastic ProcessesGoldman SachsDE Shaw

24

Day 24

Coding · Calculus · Probability

Maximize x^(1/x)

Calculus & Linear AlgebraJane StreetSIG / Susquehanna

Expected Max of Two Uniforms

ProbabilityJane StreetCitadel

Find Median from Data StreamLeetCode

Algorithms & NumericalTwo SigmaCitadel