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Quant Researcher

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Mathematical depth — probability theory, statistics, stochastic calculus and the numerical tools behind alpha research (Two Sigma, DE Shaw, Citadel).

Sign in to track your progress — each problem checks off as you solve it.

01Probability Theory

18
Coin Toss — Two Heads
ProbabilityJane Street
Easy21
Birthday Problem
ProbabilityGoldman SachsCitadel
Medium20
Roll Until All Six Faces
ProbabilityGoogleTwo Sigma
Medium23
Drunk Passenger
ProbabilityJane StreetCitadel
Medium25
Bayes — Disease Test
ProbabilityGoldman SachsTwo Sigma
Medium26
Broken Stick Triangle
ProbabilityJane StreetCitadel
Medium28
Hat Check
ProbabilityJane StreetDE Shaw
Medium27
Top Two Aces
ProbabilitySIG / SusquehannaOptiver
Medium30
Expected Max of Two Dice
ProbabilityOptiverIMC Trading
Medium

02Statistics & Inference

138
Central Limit Theorem
StatisticsGoldman SachsMorgan Stanley
Easy134
Correlation of X and X²
StatisticsTwo SigmaDE Shaw
Medium135
Variance of Uniform(0,1)
StatisticsGoldman SachsCitadel
Easy136
OLS Slope
StatisticsTwo SigmaAQR Capital
Easy137
Variance of a Sum
StatisticsGoldman SachsMorgan Stanley
Easy

03Stochastic Processes & Itô

39
Gambler’s Ruin
Stochastic ProcessesJane StreetSIG / Susquehanna
Medium38
Flips Until Two Heads in a Row
Stochastic ProcessesJane StreetCitadel
Medium40
Expectation of GBM
Stochastic ProcessesGoldman SachsMorgan Stanley
Hard41
Variance of Brownian Motion
Stochastic ProcessesGoldman SachsMorgan Stanley
Easy42
Covariance of Brownian Motion
Stochastic ProcessesGoldman SachsTwo Sigma
Medium43
Expected Flips for HTH
Stochastic ProcessesJane StreetSIG / Susquehanna
Hard44
Random Walk Recurrence
Stochastic ProcessesTwo SigmaDE Shaw
Medium

04Calculus & Linear Algebra

48
Definite Integral of x²
Calculus & Linear AlgebraGoldman Sachs
Easy49
Limit of sin(x)/x
Calculus & Linear AlgebraGoldman SachsMorgan Stanley
Easy50
Eigenvalues of a 2×2
Calculus & Linear AlgebraGoldman SachsCitadel
Medium51
Gaussian Integral
Calculus & Linear AlgebraGoldman SachsTwo Sigma
Medium52
Derivative of xˣ
Calculus & Linear AlgebraJane StreetCitadel
Medium53
Maximize x^(1/x)
Calculus & Linear AlgebraJane StreetSIG / Susquehanna
Hard54
Geometric Series
Calculus & Linear AlgebraGoldman Sachs
Easy55
Limit of (1+1/n)^n
Calculus & Linear AlgebraGoldman SachsMorgan Stanley
Easy56
Integral of x·e^(−x)
Calculus & Linear AlgebraGoldman SachsTwo Sigma
Medium

05Algorithms & Numerical

64
Two SumLeetCode
Algorithms & NumericalGoogleDE Shaw
Easy72
Best Time to Buy and Sell StockLeetCode
Algorithms & NumericalTwo SigmaDE Shaw
Medium69
Maximum Subarray (Kadane)LeetCode
Algorithms & NumericalTwo SigmaDE Shaw
Medium73
Monte Carlo — Estimate π
Algorithms & NumericalGoldman SachsTwo Sigma
Easy74
Newton’s Method for √2
Algorithms & NumericalGoldman SachsJane Street
Easy65
Product of Array Except SelfLeetCode
Algorithms & NumericalTwo SigmaHRT
Medium67
Kth Largest ElementLeetCode
Algorithms & NumericalTwo SigmaDE Shaw
Medium66
Trapping Rain WaterLeetCode
Algorithms & NumericalJane StreetCitadel Securities
Hard68
Sliding Window MaximumLeetCode
Algorithms & NumericalHRTJump Trading
Hard70
Random Pick with WeightLeetCode
Algorithms & NumericalCitadelTwo Sigma
Medium71
Shuffle an Array (Fisher-Yates)LeetCode
Algorithms & NumericalTwo SigmaDE Shaw
Medium75
Rand10() from Rand7()LeetCode
Algorithms & NumericalJane StreetOptiver
Medium76
Coin Change (DP)LeetCode
Algorithms & NumericalGoogleDE Shaw
Medium77
Median of Two Sorted ArraysLeetCode
Algorithms & NumericalGoogleTwo Sigma
Hard86
Longest Increasing SubsequenceLeetCode
Algorithms & NumericalTwo SigmaDE Shaw
Medium87
Find Median from Data StreamLeetCode
Algorithms & NumericalTwo SigmaCitadel
Hard88
Course ScheduleLeetCode
Algorithms & NumericalGoogleDE Shaw
Medium89
Number of IslandsLeetCode
Algorithms & NumericalGoogleTwo Sigma
Medium85
LRU CacheLeetCode
Algorithms & NumericalTwo SigmaHRT
Medium
Follow as a 24-day schedule

Interleaved, easy → hard, mixed daily

1
Day 1

Coding · Calculus · Probability

64
Two SumLeetCode
Algorithms & NumericalGoogleDE Shaw
Easy48
Definite Integral of x²
Calculus & Linear AlgebraGoldman Sachs
Easy18
Coin Toss — Two Heads
ProbabilityJane Street
Easy
2
Day 2

Coding · Stochastic

41
Variance of Brownian Motion
Stochastic ProcessesGoldman SachsMorgan Stanley
Easy73
Monte Carlo — Estimate π
Algorithms & NumericalGoldman SachsTwo Sigma
Easy
3
Day 3

Coding · Statistics

135
Variance of Uniform(0,1)
StatisticsGoldman SachsCitadel
Easy74
Newton’s Method for √2
Algorithms & NumericalGoldman SachsJane Street
Easy
4
Day 4

Calculus · Probability

49
Limit of sin(x)/x
Calculus & Linear AlgebraGoldman SachsMorgan Stanley
Easy20
Roll Until All Six Faces
ProbabilityGoogleTwo Sigma
Medium
5
Day 5

Coding · Stochastic

65
Product of Array Except SelfLeetCode
Algorithms & NumericalTwo SigmaHRT
Medium38
Flips Until Two Heads in a Row
Stochastic ProcessesJane StreetCitadel
Medium
6
Day 6

Coding · Calculus

67
Kth Largest ElementLeetCode
Algorithms & NumericalTwo SigmaDE Shaw
Medium54
Geometric Series
Calculus & Linear AlgebraGoldman Sachs
Easy
7
Day 7

Coding · Probability

21
Birthday Problem
ProbabilityGoldman SachsCitadel
Medium69
Maximum Subarray (Kadane)LeetCode
Algorithms & NumericalTwo SigmaDE Shaw
Medium
8
Day 8

Coding · Statistics

136
OLS Slope
StatisticsTwo SigmaAQR Capital
Easy70
Random Pick with WeightLeetCode
Algorithms & NumericalCitadelTwo Sigma
Medium
9
Day 9

Calculus · Stochastic

39
Gambler’s Ruin
Stochastic ProcessesJane StreetSIG / Susquehanna
Medium55
Limit of (1+1/n)^n
Calculus & Linear AlgebraGoldman SachsMorgan Stanley
Easy
10
Day 10

Coding · Probability

23
Drunk Passenger
ProbabilityJane StreetCitadel
Medium71
Shuffle an Array (Fisher-Yates)LeetCode
Algorithms & NumericalTwo SigmaDE Shaw
Medium
11
Day 11

Coding

72
Best Time to Buy and Sell StockLeetCode
Algorithms & NumericalTwo SigmaDE Shaw
Medium75
Rand10() from Rand7()LeetCode
Algorithms & NumericalJane StreetOptiver
Medium
12
Day 12

Calculus · Probability

50
Eigenvalues of a 2×2
Calculus & Linear AlgebraGoldman SachsCitadel
Medium25
Bayes — Disease Test
ProbabilityGoldman SachsTwo Sigma
Medium
13
Day 13

Statistics · Stochastic

137
Variance of a Sum
StatisticsGoldman SachsMorgan Stanley
Easy42
Covariance of Brownian Motion
Stochastic ProcessesGoldman SachsTwo Sigma
Medium
14
Day 14

Coding

76
Coin Change (DP)LeetCode
Algorithms & NumericalGoogleDE Shaw
Medium85
LRU CacheLeetCode
Algorithms & NumericalTwo SigmaHRT
Medium
15
Day 15

Calculus · Probability

51
Gaussian Integral
Calculus & Linear AlgebraGoldman SachsTwo Sigma
Medium26
Broken Stick Triangle
ProbabilityJane StreetCitadel
Medium
16
Day 16

Coding · Stochastic

44
Random Walk Recurrence
Stochastic ProcessesTwo SigmaDE Shaw
Medium86
Longest Increasing SubsequenceLeetCode
Algorithms & NumericalTwo SigmaDE Shaw
Medium
17
Day 17

Coding · Statistics

138
Central Limit Theorem
StatisticsGoldman SachsMorgan Stanley
Easy88
Course ScheduleLeetCode
Algorithms & NumericalGoogleDE Shaw
Medium
18
Day 18

Calculus · Probability

52
Derivative of xˣ
Calculus & Linear AlgebraJane StreetCitadel
Medium27
Top Two Aces
ProbabilitySIG / SusquehannaOptiver
Medium
19
Day 19

Coding · Stochastic

89
Number of IslandsLeetCode
Algorithms & NumericalGoogleTwo Sigma
Medium40
Expectation of GBM
Stochastic ProcessesGoldman SachsMorgan Stanley
Hard
20
Day 20

Coding · Calculus

66
Trapping Rain WaterLeetCode
Algorithms & NumericalJane StreetCitadel Securities
Hard56
Integral of x·e^(−x)
Calculus & Linear AlgebraGoldman SachsTwo Sigma
Medium
21
Day 21

Coding · Probability

28
Hat Check
ProbabilityJane StreetDE Shaw
Medium68
Sliding Window MaximumLeetCode
Algorithms & NumericalHRTJump Trading
Hard
22
Day 22

Coding · Statistics

134
Correlation of X and X²
StatisticsTwo SigmaDE Shaw
Medium77
Median of Two Sorted ArraysLeetCode
Algorithms & NumericalGoogleTwo Sigma
Hard
23
Day 23

Calculus · Stochastic

43
Expected Flips for HTH
Stochastic ProcessesJane StreetSIG / Susquehanna
Hard53
Maximize x^(1/x)
Calculus & Linear AlgebraJane StreetSIG / Susquehanna
Hard
24
Day 24

Coding · Probability

30
Expected Max of Two Dice
ProbabilityOptiverIMC Trading
Medium87
Find Median from Data StreamLeetCode
Algorithms & NumericalTwo SigmaCitadel
Hard