Syllabus

Round 1 · PRIORAMS Derive Prior | Syllabus & ScopePreparation guide for the first online round.

What Round 1 Tests

Round 1 tests reasoning under pressure, mathematical intuition, probabilistic thinking, algorithmic problem solving, and strategic decision making.

It does not test rote memorization.

Reasoning under pressureMathematical intuitionProbabilistic thinkingAlgorithmic problem solvingStrategic decision making

Topics You Should Be Comfortable With

Probability & Expected Value

  • conditional probability
  • linearity of expectation
  • intuitive EV reasoning
  • distributions/basic variance intuition

Combinatorics

  • counting
  • constructive thinking
  • parity/invariants
  • recurrence intuition

Game Theory & Brain Teasers

  • adversarial reasoning
  • optimal play
  • strategic simplification
  • puzzle solving

Algorithms & Programming

  • implementation
  • greedy
  • DP intuition
  • basic data structures
  • Codeforces Div2 C/D level thinking

Market Microstructure Basics

  • bid/ask
  • spread
  • order flow intuition
  • matching logic
  • simple trading/game simulations

Suggested Practice

Competitive Programming

  • Solve Div2 A-D regularly on Codeforces
  • Focus more on reasoning than memorizing templates

Puzzles & Quant Teasers

  • estimation problems
  • probability puzzles
  • game strategy questions
  • mental models

Recommended Resources

  • Project Euler
  • Brilliant.org
  • Chess Programming Wiki for strategic/system thinking
  • Green Book / classic quant interview puzzles
  • YouTube channels around probability, game theory, and mathematical thinking
Important Note

AMS Derive is designed to reward original thinking and problem solving ability over memorized tricks.

You do NOT need prior finance or trading experience to perform well. Anything requiring financial context or prerequisite knowledge will be described in the question for people who do not already know it.

Round 2 · POSTERIORAMS Derive Posterior | Syllabus & ScopeA programming contest built around quantitative reasoning, probability, inference, and market microstructure.

The Posterior round will be a programming contest with problems designed around quantitative reasoning, probability, inference, and market microstructure.

No prior finance knowledge required — only quantitative thinking through code.

Topics & Problem Areas

Probability & Expected Value

  • conditional probability
  • expected value & variance
  • linearity of expectation
  • probability distributions
  • modular arithmetic for probabilities
  • random processes & stopping conditions

Example areas

  • probability of ruin
  • expected stopping time
  • success probability of a strategy
  • Markov-style state transitions

Dynamic Programming under Uncertainty

  • DP over states
  • optimal stopping
  • threshold-based decisions
  • maximizing expected reward
  • minimizing expected loss
  • position/state transitions with costs

Example areas

  • choosing when to stop
  • deciding whether to act or wait
  • trading/position DP with transaction costs
  • optimizing decisions over a sequence of signals

Bayesian Inference & Signal Reliability

  • Bayes' theorem
  • posterior updates
  • likelihoods & log probabilities
  • hidden states / regimes
  • model selection from observed data

Example areas

  • identifying which signal is reliable
  • updating belief after observations
  • detecting hidden regimes
  • choosing the best predictor from noisy history

Simulation-Inspired Problems

  • exact probability DP
  • recurrence relations
  • expected value equations
  • state transition models

Example areas

  • queue fill probability
  • random walks
  • absorbing states
  • repeated trials with changing state

Market Microstructure & Execution

  • limit & market orders
  • order book matching
  • best bid / best ask & spread
  • queue priority
  • partial fills & cancellations

Example areas

  • maintaining an order book
  • simulating trades
  • calculating executed volume
  • estimating whether an order gets filled

Risk, Cost & Overfitting

  • transaction costs & slippage-like penalties
  • risk-adjusted reward
  • variance penalty
  • overfitting intuition
  • choosing among noisy strategies

Example areas

  • strategy survives before cost but fails after
  • selecting signals without overfitting
  • maximizing reward under risk/cost constraints

Required Programming Skills

  • arrays, maps, priority queues, sets
  • sorting and binary search
  • dynamic programming
  • graph / state transitions
  • modular arithmetic
  • floating-point precision
  • simulation-to-DP conversion
  • efficient implementation under constraints
What Is Not Required
finance theoryoptions pricingstock market knowledgeprior trading experiencemachine learning librariesadvanced economics
Round 3 · CONVERGENCEAMS Derive Convergence | Syllabus & ScopeInvite-only, on-site finals hosted on Codeforces. Problems span puzzles, probability, and stochastic reasoning.

Convergence is the on-site final, solved individually as a Codeforces contest. It covers puzzles, probability, the Kelly criterion, random walks, Monte Carlo simulation, expected value, and Bayesian questions.

Same Codeforces format as the earlier rounds — judged on accepted solutions, now at IIT.

Invite-only, on-site at IITIndividual — solved alone, not in teamsHosted on Codeforces (ICPC-style)Top 2 advance to a live 1v1 round on Codeforces

Topics & Problem Areas

Puzzles & Brain Teasers

  • estimation and Fermi problems
  • logic and constraint puzzles
  • adversarial / strategic reasoning
  • structured simplification of unfamiliar problems

Example areas

  • derive a result from first principles
  • reason about an underspecified setup
  • find the optimal strategy in a novel game

Probability & Expected Value

  • conditional probability
  • linearity of expectation
  • variance & higher moments
  • distributions and tail behaviour

Example areas

  • expected payoff of a strategy
  • probability of an outcome under uncertainty
  • comparing risky alternatives by EV

The Kelly Criterion

  • optimal bet sizing
  • log-growth maximisation
  • edge vs. variance trade-offs
  • fractional Kelly and risk control

Example areas

  • sizing a bet given edge and odds
  • long-run growth vs. drawdown reasoning
  • allocating across simultaneous bets

Random Walks & Stochastic Processes

  • simple and biased random walks
  • hitting times and absorbing states
  • martingales & stopping times
  • Brownian motion intuition

Example areas

  • probability of ruin
  • expected time to hit a boundary
  • drift vs. diffusion reasoning

Monte Carlo Simulation

  • estimating quantities by sampling
  • convergence and error intuition
  • variance reduction ideas
  • when to simulate vs. derive in closed form

Example areas

  • approximate a hard probability
  • estimate an expected value via sampling
  • reason about simulation accuracy

Bayesian Reasoning

  • Bayes' theorem
  • priors, likelihoods & posteriors
  • belief updating from evidence
  • inference under noisy observations

Example areas

  • update a belief after new data
  • identify the most likely hidden state
  • reason about reliability of a signal
Important Note

Convergence is solved individually, not in teams. Finalists are evaluated on adaptability, structured reasoning, and modeling under uncertainty.

You may carry a one-page formula sheet into the finals.

01

Mathematics

Probability & InferenceSample spaces, Conditional probability, Bayes theorem, Discrete and continuous distributions, PMF / PDF / CDF, Joint distributions, Linearity of expectation, Moments, MGFs, Tail bounds
Stochastic ProcessesMarkov chains, Transition matrices, Stationary distributions, Random walks, Martingales, Brownian motion intuition
Analytical FoundationsDerivation over formula recall, First-principles reasoning, Modeling under uncertainty, Structured proof construction
02

Algorithms

Graph TheoryBFS, DFS, Shortest paths, Trees, Flows and matchings
Dynamic ProgrammingOptimal substructure, State design, DP on sequences, DP on trees, DP on graphs
OptimizationGreedy algorithms, Exchange arguments, Constraint handling, Expected-cost minimization
03

Quant Concepts

Order BooksBid-ask structure, Limit and market orders, Price impact intuition
Pricing IntuitionNo-arbitrage reasoning, Risk-neutral thinking, Relative valuation
Arbitrage LogicIdentifying mispricing, Constructing hedges, Reasoning about market efficiency

Research & Application

01Stochastic processes & probabilistic modeling
02Algorithmic game theory & market mechanisms
03High-performance computing & architecture
04Advanced combinatorics & number theory
05Competitive programming with mathematical depth
06Quantitative finance & strategy simulation
Learning Hub

Want to master these concepts?

Check out our curated repository of high-signal resources, books, and problem sets to build your first-principles foundation.

View Resources