A week-by-week plan for every seat.

Start the daily mental-math habit and refresh core probability.

• Do 10 mental math questions daily, speed over elegance → go
• Work through 8 easy probability questions (difficulty 1–2) → go
• Read: expected value and linearity of expectation until instinctive
• Learn the fast conversions: odds ↔ probability, fractions ↔ decimals

Price any simple bet in under a minute.

• Daily mental math drill (keep streak alive) → go
• Solve 10 EV-based probability questions (dice, cards, coins) → go
• First market-making questions: fair pricing of simple games → go
• Practice saying answers out loud, interviews are verbal

Recognize the classic puzzle archetypes on sight.

• Daily mental math drill → go
• Solve 12 brainteasers across difficulty 2–4 → go
• For each puzzle solved, write the reusable pattern in one line

Understand spreads, quoting, and why you move your market.

• Daily mental math drill → go
• Work through 10 market-making questions → go
• Learn the three costs a spread covers: adverse selection, inventory, processing
• Practice 'make me a market on X' with a friend, quote, get filled, requote

Update beliefs correctly and quickly.

• Daily mental math drill → go
• Solve 10 Bayes / conditional probability questions → go
• Revisit every question you got wrong so far, redo from scratch

Handle the follow-ups: informed flow, inventory, sizing.

• Daily mental math drill → go
• Solve difficulty 4–5 market-making questions → go
• Learn Kelly sizing and why traders bet fractions of it → go
• Read the position sizing concept → go

Simulate test conditions: timed, no paper, out loud.

• Timed drills: 80 mental math questions in 8 minutes, daily → go
• Brainteaser marathon: 10 in one sitting, explaining answers aloud → go
• Mixed set: alternate probability and market-making questions → go

Full interview simulation plus the human part.

• Two full mock interviews with a friend (math + games + market making)
• Prepare your 'why trading' story and 2–3 decision-under-uncertainty stories
• Light daily drills only, arrive fresh → go

Rebuild fundamentals rigorously, not just by pattern matching.

• Solve 8 probability questions at difficulty 1–3 → go
• Review distributions: binomial, geometric, Poisson, normal, exponential
• Master linearity of expectation with 3 hat-check style problems → go

Random walks, Markov chains, and conditioning tricks.

• Solve 10 questions: random walks, gambler's ruin, Markov chains → go
• Write out the first-step conditioning technique from memory
• Attempt 2 difficulty-5 probability questions without hints → go

Estimators, bias, variance, and MLE cold.

• Solve 10 statistics questions on estimators and MLE → go
• Derive the MLE for Bernoulli, normal, and uniform by hand
• Understand bias-variance through the sample variance example

Hypothesis testing and confidence intervals without hand-waving.

• Solve 10 questions on testing, p-values, power, CIs → go
• Write one paragraph: what a p-value is and is not
• Study the classic traps: peeking, multiple testing, Simpson's paradox → go

OLS assumptions, interpretation, and failure modes.

• Solve the regression question set → go
• Read: overfitting and walk-forward concepts → go
• Explain omitted variable bias with a markets example

Clean Python for arrays, hashing, and data manipulation.

• Solve 10 coding questions at difficulty 1–3 → go
• Time yourself: 25 minutes per problem, then study the solution
• Redo any problem where your solution was messier than the model answer → go

DP, heaps, streaming data, the researcher's toolkit.

• Solve 8 coding questions at difficulty 3–4 (DP, heaps, streams) → go
• Implement median-from-stream and moving average from scratch → go
• Write a clean Monte Carlo simulation of a random walk → go

Speak the language of strategies and risk.

• Read 5 core concepts: Sharpe, drawdown, vol targeting, position sizing, transaction costs → go
• Study 3 strategies end-to-end in the database → go
• For one strategy, list every way its backtest could be fooling you → go

Cover the classics researchers still get asked.

• Solve 10 brainteasers, writing the pattern for each → go
• Mixed probability/statistics review: 8 questions from your weak areas → go

Have one piece of work you can defend for 30 minutes.

• Pick a simple signal idea and test it properly (train/test split, costs)
• Write a 1-page summary: hypothesis, method, result, what would change your mind
• Have someone technical poke holes in it, fix the holes

Difficulty 4–5 across all topics.

• Solve 6 hard probability questions → go
• Solve 5 hard statistics questions → go
• Solve 4 hard coding questions under time pressure → go

Simulate the full loop and polish your research story.

• Two full mock interviews: math round + coding round + research discussion
• Rehearse presenting your project: 5-minute and 20-minute versions
• Light review only in the final two days

The bread-and-butter patterns at full speed.

• Solve 10 coding questions: arrays, hashing, two pointers → go
• For each, state time/space complexity before running anything

Stream-shaped thinking, the quant-dev signature.

• Solve the sliding window and prefix sum question sets → go
• Implement max drawdown over a price series in O(n) → go

Monotonic stacks and classic list manipulation.

• Solve 8 questions: stacks, monotonic stack, queues, lists → go
• Implement max-in-sliding-window two ways (deque vs heap) and compare

Never fumble a boundary condition again.

• Solve the binary search question set including rotated arrays → go
• Write binary search from memory five days in a row, zero bugs allowed

Recognize the state, write the recurrence, then optimize.

• Solve 8 DP questions from easy to hard → go
• For two problems, write both memoized and bottom-up versions

LRU cache, streaming medians, order books.

• Solve the design questions: LRU, min-stack, median from stream → go
• Sketch an order book: data structures, operations, complexities → go

Floating point, overflow, and why naive code loses money.

• Solve the numerical-pitfall questions → go
• Profile one of your earlier solutions and make it measurably faster
• Read up on memory layout and cache-friendliness basics (C++ if targeting HFT)

Enough probability to pass the math screen comfortably.

• Solve 10 probability questions at difficulty 1–3 → go
• Implement 3 simulation questions and verify against the closed-form answer → go

Difficulty 4–5 coding plus brainteaser coverage.

• Solve 6 hard coding questions under a 35-minute timer each → go
• Solve 6 brainteasers, devs get these too → go

Full-loop simulation including the systems conversation.

• Two mock coding interviews, thinking aloud the entire time
• Prepare to discuss one system you built: design choices, tradeoffs, failures
• Light review only in the final two days