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30-Day Sprint

· 30 days

An intense one-month plan through every topic and coding problem — brain teasers, probability, stochastic calculus, statistics, finance, options, portfolio risk and coding. About five a day, mixed so each topic keeps coming back instead of being crammed once.

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

1

Day 1

Coding · Brain teasers · Calculus

Two SumLeetCode

Algorithms & NumericalGoogleDE Shaw

Coin Toss — Two Heads

ProbabilityJane Street

Trailing Zeros in 100!

Brain TeasersGoldman SachsJ.P. Morgan

Put-Call Parity

FinanceGoldman SachsMorgan Stanley

Definite Integral of x²

Calculus & Linear AlgebraGoldman Sachs

2

Day 2

Coding · Options · Portfolio

Delta of an ATM Call

Options & GreeksOptiverIMC Trading

Portfolio & RiskGoldman SachsAQR Capital

Variance of Uniform(0,1)

StatisticsGoldman SachsCitadel

Variance of Brownian Motion

Stochastic ProcessesGoldman SachsMorgan Stanley

Monte Carlo — Estimate π

Algorithms & NumericalGoldman SachsTwo Sigma

3

Day 3

Brain teasers · Calculus · Finance

ProbabilityGoldman SachsMorgan Stanley

Clock Hands at 3:15

Brain TeasersMorgan StanleyBarclays

Zero-Coupon Bond Price

FinanceGoldman SachsPIMCO

Limit of sin(x)/x

Calculus & Linear AlgebraGoldman SachsMorgan Stanley

Delta of a Forward

Options & GreeksOptiverIMC Trading

4

Day 4

Coding · Brain teasers · Portfolio

Newton’s Method for √2

Algorithms & NumericalGoldman SachsJane Street

Flips Until First Head

ProbabilityOptiverIMC Trading

Nim GameLeetCode

Algorithms & NumericalJane StreetSIG / Susquehanna

Portfolio & RiskGoldman SachsAQR Capital

Brain TeasersJane StreetGoldman Sachs

5

Day 5

Calculus · Finance · Options

Futures Fair Value

FinanceGoldman SachsOptiver

StatisticsTwo SigmaAQR Capital

Flips Until Two Heads in a Row

Stochastic ProcessesJane StreetCitadel

Geometric Series

Calculus & Linear AlgebraGoldman Sachs

Most Negative Put Delta

Options & GreeksGoldman SachsOptiver

6

Day 6

Coding · Brain teasers · Finance

Product of Array Except SelfLeetCode

Algorithms & NumericalTwo SigmaHRT

Two Dice Sum to 7

ProbabilityOptiverIMC Trading

Last Digit of 2^100

Brain TeasersGoldman SachsMorgan Stanley

Duration & Price Sensitivity

FinanceGoldman SachsJ.P. MorganPIMCO

Kth Largest ElementLeetCode

Algorithms & NumericalTwo SigmaDE Shaw

7

Day 7

Coding · Calculus · Options

Limit of (1+1/n)^n

Calculus & Linear AlgebraGoldman SachsMorgan Stanley

Sign & Peak of Vega

Options & GreeksOptiverIMC Trading

ProbabilityGoldman SachsMorgan Stanley

Two-Asset Portfolio Volatility

Portfolio & RiskGoldman SachsAQR Capital

Maximum Subarray (Kadane)LeetCode

Algorithms & NumericalTwo SigmaDE Shaw

8

Day 8

Brain teasers · Finance · Probability

Variance of a Sum

StatisticsGoldman SachsMorgan Stanley

Gambler’s Ruin

Stochastic ProcessesJane StreetSIG / Susquehanna

Handshakes at a Party

Brain TeasersGoldman Sachs

Perpetuity Value

FinanceGoldman SachsJ.P. Morgan

Expected Rolls for a Six

ProbabilityOptiverIMC Trading

9

Day 9

Coding · Brain teasers · Calculus

L'Hôpital — (eˣ−1)/x

Calculus & Linear AlgebraGoldman SachsMorgan Stanley

Options & GreeksOptiverCitadel Securities

Random Pick with WeightLeetCode

Algorithms & NumericalCitadelTwo Sigma

Value at Risk (Normal)

Portfolio & RiskGoldman SachsMorgan StanleyMillennium Management

Two Eggs, 100 Floors

Brain TeasersGoogleGoldman Sachs

10

Day 10

Coding · Calculus · Finance

FinanceGoldman SachsMorgan Stanley

At Least One Six

ProbabilitySIG / SusquehannaOptiver

Shuffle an Array (Fisher-Yates)LeetCode

Algorithms & NumericalTwo SigmaDE Shaw

Derivative of ln(x)

Calculus & Linear AlgebraGoldman Sachs

How Dear Can a Call Be?

Options & GreeksJane StreetAkuna Capital

11

Day 11

Coding · Brain teasers · Probability

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

Horse Race — Top 3

Brain TeasersGoogleTwo Sigma

12

Day 12

Coding · Calculus · Finance

Coupon Equals Yield

FinanceGoldman SachsPIMCO

Rand10() from Rand7()LeetCode

Algorithms & NumericalJane StreetOptiver

Sum of First 10 Squares

Calculus & Linear AlgebraJane StreetTwo Sigma

Find the Put from Parity

Options & GreeksGoldman SachsMorgan Stanley

CVaR / Expected Shortfall

Portfolio & RiskAQR CapitalTwo Sigma

13

Day 13

Coding · Brain teasers · Finance

Birthday Problem

ProbabilityGoldman SachsCitadel

Brain TeasersGoogleTwo Sigma

FinanceBarclaysMorgan Stanley

Coin Change (DP)LeetCode

Algorithms & NumericalGoogleDE Shaw

StatisticsTwo SigmaDE Shaw

14

Day 14

Coding · Calculus · Options

Random Walk Recurrence

Stochastic ProcessesTwo SigmaDE Shaw

Trace = Sum of Eigenvalues

Calculus & Linear AlgebraTwo SigmaGoldman Sachs

Delta of a Deep ITM Call

Options & GreeksIMC TradingOptiver

Drunk Passenger

ProbabilityJane StreetCitadel

Online Stock SpanLeetCode

Algorithms & NumericalCitadel SecuritiesHRT

15

Day 15

Coding · Brain teasers · Finance

Brain TeasersGoogleJane Street

Duration and a Rate Move

FinancePIMCOBlackRock

Diversification & Sharpe

Portfolio & RiskAQR CapitalCitadel

Time-Based Key-Value StoreLeetCode

Algorithms & NumericalTwo SigmaJump Trading

Bayes — Disease Test

ProbabilityGoldman SachsTwo Sigma

16

Day 16

Coding · Calculus · Options

Determinant = Product of Eigenvalues

Calculus & Linear AlgebraTwo SigmaDE Shaw

Straddle Breakeven

Options & GreeksSIG / SusquehannaAkuna Capital

Range of Correlation

StatisticsGoldman SachsCitadel

Quadratic Variation of BM

Stochastic ProcessesGoldman SachsTwo Sigma

Best Time to Buy and Sell Stock IILeetCode

Algorithms & NumericalOptiverJane Street

17

Day 17

Brain teasers · Calculus · Finance

Mislabeled Jars

Brain TeasersJane StreetOptiver

Real Rate of Return

FinancePIMCOCitadel

Broken Stick Triangle

ProbabilityJane StreetCitadel

Maximum Drawdown

Portfolio & RiskCitadelTwo SigmaMan Group

Approximate cos(0.1)

Calculus & Linear AlgebraJane StreetOptiver

18

Day 18

Coding · Brain teasers · Finance

Covered Call Max Profit

Options & GreeksMorgan StanleyIMC Trading

Gas StationLeetCode

Algorithms & NumericalJane StreetCitadel

Burning Ropes — 45 Minutes

Brain TeasersGoldman SachsMorgan Stanley

Black-Scholes ATM Call

FinanceGoldman SachsMorgan Stanley

ProbabilitySIG / SusquehannaOptiver

19

Day 19

Coding · Calculus · Options

Jump GameLeetCode

Algorithms & NumericalGoogleDE Shaw

Variance of a Scaled Variable

StatisticsGoldman Sachs

Expectation of GBM

Stochastic ProcessesGoldman SachsMorgan Stanley

Eigenvalues of a 2×2

Calculus & Linear AlgebraGoldman SachsCitadel

Gamma Near Expiry

Options & GreeksOptiverIMC Trading

20

Day 20

Coding · Brain teasers · Finance

Predict the WinnerLeetCode

Algorithms & NumericalJane StreetOptiver

ProbabilityJane StreetDE Shaw

Bridge Crossing

Brain TeasersGoogleJane Street

Risk-Neutral Probability

FinanceGoldman SachsJ.P. Morgan

Kelly Criterion

Portfolio & RiskCitadelJane Street

21

Day 21

Coding · Brain teasers · Calculus

LRU CacheLeetCode

Algorithms & NumericalTwo SigmaHRT

Gaussian Integral

Calculus & Linear AlgebraGoldman SachsTwo Sigma

Options & GreeksOptiverSIG / Susquehanna

Expected Max of Two Dice

ProbabilityOptiverIMC Trading

Ants on a Triangle

Brain TeasersGoldman SachsOptiver

22

Day 22

Coding · Finance · Portfolio

Gordon Growth Model

FinanceGoldman SachsMorgan Stanley

Longest Increasing SubsequenceLeetCode

Algorithms & NumericalTwo SigmaDE Shaw

Correlation of X and X²

StatisticsTwo SigmaDE Shaw

Expected Flips for HTH

Stochastic ProcessesJane StreetSIG / Susquehanna

VaR Time Scaling

Portfolio & RiskGoldman SachsMorgan Stanley

23

Day 23

Coding · Brain teasers · Calculus

Russian Roulette — Spin?

ProbabilityJane StreetCitadel

Derivative of xˣ

Calculus & Linear AlgebraJane StreetCitadel

Early Exercise of a Call

Options & GreeksGoldman SachsMorgan Stanley

Course ScheduleLeetCode

Algorithms & NumericalGoogleDE Shaw

Brain TeasersGoogle

24

Day 24

Coding · Calculus · Finance

Implied Forward Rate

FinanceJ.P. MorganBarclays

Expected Min of Two Dice

ProbabilityOptiverSIG / Susquehanna

Number of IslandsLeetCode

Algorithms & NumericalGoogleTwo Sigma

Integral of x·e^(−x)

Calculus & Linear AlgebraGoldman SachsTwo Sigma

25

Day 25

Brain teasers · Options · Statistics

Delta of an ATM Straddle

Options & GreeksOptiverIMC TradingSIG / Susquehanna

Covariance of a Linear Transform

StatisticsGoldman SachsAQR Capital

Random Walk — Expected Steps

Stochastic ProcessesJane StreetTwo Sigma

Brain TeasersGoldman SachsMorgan Stanley

26

Day 26

Coding · Finance · Portfolio

Forward Price with a Dividend Yield

FinanceJ.P. MorganCitadel

Minimum-Variance Weight

Portfolio & RiskAQR CapitalBlackRock

Trapping Rain WaterLeetCode

Algorithms & NumericalJane StreetCitadel Securities

Poisson — No Arrivals

ProbabilityTwo SigmaJump Trading

27

Day 27

Coding · Brain teasers · Calculus

Sliding Window MaximumLeetCode

Algorithms & NumericalHRTJump Trading

Integrate x·eˣ

Calculus & Linear AlgebraGoldman SachsMorgan Stanley

Value of a Box Spread

Options & GreeksOptiverCitadel Securities

Brain TeasersJane StreetOptiver

28

Day 28

Coding · Finance · Probability

FX Forward by Interest Parity

FinanceGoldman SachsBarclays

Exponential Survival

ProbabilityDE ShawMorgan Stanley

Median of Two Sorted ArraysLeetCode

Algorithms & NumericalGoogleTwo Sigma

Variance of the Sample Mean

StatisticsTwo SigmaDE Shaw

29

Day 29

Calculus · Options · Portfolio

Expected Running Max of BM

Stochastic ProcessesGoldman SachsDE Shaw

Annualizing Sharpe

Portfolio & RiskTwo SigmaAQR Capital

Maximize x^(1/x)

Calculus & Linear AlgebraJane StreetSIG / Susquehanna

Worst Case with a Protective Put

Options & GreeksBarclaysJ.P. Morgan

30

Day 30

Coding · Brain teasers · Finance

12 Balls, One Odd

Brain TeasersCitadelJane StreetTwo Sigma

Present Value of an Annuity

FinanceMorgan StanleyJ.P. Morgan

Expected Max of Two Uniforms

ProbabilityJane StreetCitadel

Find Median from Data StreamLeetCode

Algorithms & NumericalTwo SigmaCitadel