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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).

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01Probability Theory

21
Coin Toss — Two Heads
ProbabilityJane Street
53%Easy24
Birthday Problem
ProbabilityGoldman SachsCitadel
52%Medium23
Roll Until All Six Faces
ProbabilityGoogleTwo Sigma
41%Medium26
Drunk Passenger
ProbabilityJane StreetCitadel
55%Medium28
Bayes — Disease Test
ProbabilityGoldman SachsTwo Sigma
55%Medium29
Broken Stick Triangle
ProbabilityJane StreetCitadel
43%Medium31
Hat Check
ProbabilityJane StreetDE Shaw
72%Medium30
Top Two Aces
ProbabilitySIG / SusquehannaOptiver
63%Medium33
Expected Max of Two Dice
ProbabilityOptiverIMC Trading
41%Medium

02Statistics & Inference

176
Central Limit Theorem
StatisticsGoldman SachsMorgan Stanley
74%Easy172
Correlation of X and X²
StatisticsTwo SigmaDE Shaw
74%Medium173
Variance of Uniform(0,1)
StatisticsGoldman SachsCitadel
71%Easy174
OLS Slope
StatisticsTwo SigmaAQR Capital
90%Easy175
Variance of a Sum
StatisticsGoldman SachsMorgan Stanley
63%Easy183
Width of a 95% Confidence Interval
StatisticsGoldman SachsBlackRock
45%Easy187
A One-Sample z-Statistic
StatisticsMorgan StanleyGoldman Sachs
75%Easy184
From Correlation to R²
StatisticsTwo SigmaAQR Capital
60%Easy185
Correlation of X with X + Y
StatisticsJane StreetCitadel
57%Medium186
Median of an Exponential
StatisticsDE ShawJump Trading
64%Medium182
The German Tank Problem
StatisticsTwo SigmaDE Shaw
69%Medium188
Simpson’s Paradox
StatisticsTwo SigmaCitadel
69%Medium

03Stochastic Processes & Itô

47
Gambler’s Ruin
Stochastic ProcessesJane StreetSIG / Susquehanna
72%Medium46
Flips Until Two Heads in a Row
Stochastic ProcessesJane StreetCitadel
44%Medium48
Expectation of GBM
Stochastic ProcessesGoldman SachsMorgan Stanley
59%Hard49
Variance of Brownian Motion
Stochastic ProcessesGoldman SachsMorgan Stanley
69%Easy50
Covariance of Brownian Motion
Stochastic ProcessesGoldman SachsTwo Sigma
65%Medium51
Expected Flips for HTH
Stochastic ProcessesJane StreetSIG / Susquehanna
45%Hard52
Random Walk Recurrence
Stochastic ProcessesTwo SigmaDE Shaw
69%Medium58
Two Poisson Streams
Stochastic ProcessesJump TradingHRT
70%Medium57
Hitting 3 Before 0
Stochastic ProcessesCitadelMorgan Stanley
77%Medium59
How Long Until Ruin or Riches
Stochastic ProcessesOptiverSIG / Susquehanna
57%Medium56
The Ballot Problem
Stochastic ProcessesJane StreetDE Shaw
47%Hard60
Half-Life of Mean Reversion
Stochastic ProcessesAQR CapitalMillennium Management
64%Medium61
Reflection Principle for the Maximum
Stochastic ProcessesCitadelDE Shaw
50%Hard

04Calculus & Linear Algebra

62
Definite Integral of x²
Calculus & Linear AlgebraGoldman Sachs
78%Easy63
Limit of sin(x)/x
Calculus & Linear AlgebraGoldman SachsMorgan Stanley
91%Easy64
Eigenvalues of a 2×2
Calculus & Linear AlgebraGoldman SachsCitadel
80%Medium65
Gaussian Integral
Calculus & Linear AlgebraGoldman SachsTwo Sigma
43%Medium66
Derivative of xˣ
Calculus & Linear AlgebraJane StreetCitadel
83%Medium67
Maximize x^(1/x)
Calculus & Linear AlgebraJane StreetSIG / Susquehanna
51%Hard68
Geometric Series
Calculus & Linear AlgebraGoldman Sachs
86%Easy69
Limit of (1+1/n)^n
Calculus & Linear AlgebraGoldman SachsMorgan Stanley
55%Easy70
Integral of x·e^(−x)
Calculus & Linear AlgebraGoldman SachsTwo Sigma
74%Medium

05Algorithms & Numerical

78
Two SumLeetCode
Algorithms & NumericalGoogleDE Shaw
Easy86
Best Time to Buy and Sell StockLeetCode
Algorithms & NumericalTwo SigmaDE Shaw
Medium83
Maximum Subarray (Kadane)LeetCode
Algorithms & NumericalTwo SigmaDE Shaw
Medium87
Monte Carlo — Estimate π
Algorithms & NumericalGoldman SachsTwo Sigma
65%Easy88
Newton’s Method for √2
Algorithms & NumericalGoldman SachsJane Street
79%Easy79
Product of Array Except SelfLeetCode
Algorithms & NumericalTwo SigmaHRT
Medium81
Kth Largest ElementLeetCode
Algorithms & NumericalTwo SigmaDE Shaw
Medium80
Trapping Rain WaterLeetCode
Algorithms & NumericalJane StreetCitadel Securities
Hard82
Sliding Window MaximumLeetCode
Algorithms & NumericalHRTJump Trading
Hard84
Random Pick with WeightLeetCode
Algorithms & NumericalCitadelTwo Sigma
Medium85
Shuffle an Array (Fisher-Yates)LeetCode
Algorithms & NumericalTwo SigmaDE Shaw
Medium89
Rand10() from Rand7()LeetCode
Algorithms & NumericalJane StreetOptiver
Medium90
Coin Change (DP)LeetCode
Algorithms & NumericalGoogleDE Shaw
Medium91
Median of Two Sorted ArraysLeetCode
Algorithms & NumericalGoogleTwo Sigma
Hard100
Longest Increasing SubsequenceLeetCode
Algorithms & NumericalTwo SigmaDE Shaw
Medium101
Find Median from Data StreamLeetCode
Algorithms & NumericalTwo SigmaCitadel
Hard102
Course ScheduleLeetCode
Algorithms & NumericalGoogleDE Shaw
Medium103
Number of IslandsLeetCode
Algorithms & NumericalGoogleTwo Sigma
Medium99
LRU CacheLeetCode
Algorithms & NumericalTwo SigmaHRT
Medium
Follow as a 24-day schedule

Interleaved, easy → hard, mixed daily

1
Day 1

Coding · Statistics · Stochastic

78
Two SumLeetCode
Algorithms & NumericalGoogleDE Shaw
Easy49
Variance of Brownian Motion
Stochastic ProcessesGoldman SachsMorgan Stanley
69%Easy173
Variance of Uniform(0,1)
StatisticsGoldman SachsCitadel
71%Easy
2
Day 2

Coding · Calculus · Probability

62
Definite Integral of x²
Calculus & Linear AlgebraGoldman Sachs
78%Easy21
Coin Toss — Two Heads
ProbabilityJane Street
53%Easy87
Monte Carlo — Estimate π
Algorithms & NumericalGoldman SachsTwo Sigma
65%Easy
3
Day 3

Coding · Statistics · Stochastic

46
Flips Until Two Heads in a Row
Stochastic ProcessesJane StreetCitadel
44%Medium174
OLS Slope
StatisticsTwo SigmaAQR Capital
90%Easy88
Newton’s Method for √2
Algorithms & NumericalGoldman SachsJane Street
79%Easy
4
Day 4

Coding · Calculus · Probability

63
Limit of sin(x)/x
Calculus & Linear AlgebraGoldman SachsMorgan Stanley
91%Easy23
Roll Until All Six Faces
ProbabilityGoogleTwo Sigma
41%Medium79
Product of Array Except SelfLeetCode
Algorithms & NumericalTwo SigmaHRT
Medium
5
Day 5

Coding · Statistics · Stochastic

47
Gambler’s Ruin
Stochastic ProcessesJane StreetSIG / Susquehanna
72%Medium175
Variance of a Sum
StatisticsGoldman SachsMorgan Stanley
63%Easy81
Kth Largest ElementLeetCode
Algorithms & NumericalTwo SigmaDE Shaw
Medium
6
Day 6

Calculus · Probability · Stochastic

50
Covariance of Brownian Motion
Stochastic ProcessesGoldman SachsTwo Sigma
65%Medium68
Geometric Series
Calculus & Linear AlgebraGoldman Sachs
86%Easy24
Birthday Problem
ProbabilityGoldman SachsCitadel
52%Medium
7
Day 7

Coding · Statistics

83
Maximum Subarray (Kadane)LeetCode
Algorithms & NumericalTwo SigmaDE Shaw
Medium176
Central Limit Theorem
StatisticsGoldman SachsMorgan Stanley
74%Easy84
Random Pick with WeightLeetCode
Algorithms & NumericalCitadelTwo Sigma
Medium
8
Day 8

Calculus · Statistics · Stochastic

52
Random Walk Recurrence
Stochastic ProcessesTwo SigmaDE Shaw
69%Medium183
Width of a 95% Confidence Interval
StatisticsGoldman SachsBlackRock
45%Easy69
Limit of (1+1/n)^n
Calculus & Linear AlgebraGoldman SachsMorgan Stanley
55%Easy
9
Day 9

Coding · Probability · Stochastic

26
Drunk Passenger
ProbabilityJane StreetCitadel
55%Medium85
Shuffle an Array (Fisher-Yates)LeetCode
Algorithms & NumericalTwo SigmaDE Shaw
Medium57
Hitting 3 Before 0
Stochastic ProcessesCitadelMorgan Stanley
77%Medium
10
Day 10

Coding · Statistics

86
Best Time to Buy and Sell StockLeetCode
Algorithms & NumericalTwo SigmaDE Shaw
Medium184
From Correlation to R²
StatisticsTwo SigmaAQR Capital
60%Easy89
Rand10() from Rand7()LeetCode
Algorithms & NumericalJane StreetOptiver
Medium
11
Day 11

Calculus · Probability · Stochastic

64
Eigenvalues of a 2×2
Calculus & Linear AlgebraGoldman SachsCitadel
80%Medium28
Bayes — Disease Test
ProbabilityGoldman SachsTwo Sigma
55%Medium58
Two Poisson Streams
Stochastic ProcessesJump TradingHRT
70%Medium
12
Day 12

Coding · Statistics · Stochastic

187
A One-Sample z-Statistic
StatisticsMorgan StanleyGoldman Sachs
75%Easy90
Coin Change (DP)LeetCode
Algorithms & NumericalGoogleDE Shaw
Medium59
How Long Until Ruin or Riches
Stochastic ProcessesOptiverSIG / Susquehanna
57%Medium
13
Day 13

Coding · Calculus · Probability

99
LRU CacheLeetCode
Algorithms & NumericalTwo SigmaHRT
Medium65
Gaussian Integral
Calculus & Linear AlgebraGoldman SachsTwo Sigma
43%Medium29
Broken Stick Triangle
ProbabilityJane StreetCitadel
43%Medium
14
Day 14

Coding · Statistics · Stochastic

172
Correlation of X and X²
StatisticsTwo SigmaDE Shaw
74%Medium60
Half-Life of Mean Reversion
Stochastic ProcessesAQR CapitalMillennium Management
64%Medium100
Longest Increasing SubsequenceLeetCode
Algorithms & NumericalTwo SigmaDE Shaw
Medium
15
Day 15

Coding · Statistics

182
The German Tank Problem
StatisticsTwo SigmaDE Shaw
69%Medium102
Course ScheduleLeetCode
Algorithms & NumericalGoogleDE Shaw
Medium
16
Day 16

Calculus · Probability

66
Derivative of xˣ
Calculus & Linear AlgebraJane StreetCitadel
83%Medium30
Top Two Aces
ProbabilitySIG / SusquehannaOptiver
63%Medium
17
Day 17

Coding · Stochastic

48
Expectation of GBM
Stochastic ProcessesGoldman SachsMorgan Stanley
59%Hard103
Number of IslandsLeetCode
Algorithms & NumericalGoogleTwo Sigma
Medium
18
Day 18

Statistics · Stochastic

185
Correlation of X with X + Y
StatisticsJane StreetCitadel
57%Medium51
Expected Flips for HTH
Stochastic ProcessesJane StreetSIG / Susquehanna
45%Hard
19
Day 19

Coding · Calculus

80
Trapping Rain WaterLeetCode
Algorithms & NumericalJane StreetCitadel Securities
Hard70
Integral of x·e^(−x)
Calculus & Linear AlgebraGoldman SachsTwo Sigma
74%Medium
20
Day 20

Coding · Probability

31
Hat Check
ProbabilityJane StreetDE Shaw
72%Medium82
Sliding Window MaximumLeetCode
Algorithms & NumericalHRTJump Trading
Hard
21
Day 21

Statistics · Stochastic

186
Median of an Exponential
StatisticsDE ShawJump Trading
64%Medium56
The Ballot Problem
Stochastic ProcessesJane StreetDE Shaw
47%Hard
22
Day 22

Coding · Calculus

91
Median of Two Sorted ArraysLeetCode
Algorithms & NumericalGoogleTwo Sigma
Hard67
Maximize x^(1/x)
Calculus & Linear AlgebraJane StreetSIG / Susquehanna
51%Hard
23
Day 23

Probability · Statistics

33
Expected Max of Two Dice
ProbabilityOptiverIMC Trading
41%Medium188
Simpson’s Paradox
StatisticsTwo SigmaCitadel
69%Medium
24
Day 24

Coding · Stochastic

61
Reflection Principle for the Maximum
Stochastic ProcessesCitadelDE Shaw
50%Hard101
Find Median from Data StreamLeetCode
Algorithms & NumericalTwo SigmaCitadel
Hard