Syllabus
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
Round I · PRIOR
Sample Problem
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