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1 Table of Contents Chapter 1 General Principles Build a broad knowledge base Practice your interview skills Listen carefully Speak your mind Make reasonable assumptions...2 Chapter 2 Brain Teasers Problem Simplification... 3 Screwy pirates...3 Tiger and sheep Logic Reasoning... 5 River crossing...5 Birthday problem...5 Card game...6 Burning ropes...7 Defective ball...7 Trailing zeros...9 Horse race...9 Infinite sequence Thinking Out of the Box Box packing...10 Calendar cubes...11 Door to offer...12 Message delivery...13 Last ball...13 Light switches...14 Quant salary Application of Symmetry Coin piles...15 Mislabeled bags...16 Wise men Series Summation Clock pieces...18 Missing integers...18 Counterfeit coins I The Pigeon Hole Principle Matching socks...21 Handshakes...21 Have we met before?...21 Ants on a square...22 Counterfeit coins II...22
2 Contents 2.7 Modular Arithmetic...23 Prisoner problem Division by Chameleon colors Math Induction...27 Coin split problem Chocolate bar problem Race track Proof by Contradiction...31 Irrational number Rainbow hats Chapter 3 Calculus and Linear Algebra Limits and Derivatives...33 Basics of derivatives Maximum and minimum L Hospital s rule Integration...36 Basics of integration Applications of integration Expected value using integration Partial Derivatives and Multiple Integrals Important Calculus Methods...41 Taylor s series Newton s method Lagrange multipliers Ordinary Differential Equations...46 Separable differential equations First-order linear differential equations Homogeneous linear equations Nonhomogeneous linear equations Linear Algebra...50 Vectors QR decomposition Determinant, eigenvalue and eigenvector Positive semidefinite/definite matrix LU decomposition and Cholesky decomposition Chapter 4 Probability Theory Basic Probability Definitions and Set Operations...59 Coin toss game Card game Drunk passenger ii
3 A Practical Guide To Quantitative Finance Interviews N points on a circle Combinatorial Analysis Poker hands...65 Hopping rabbit...66 Screwy pirates Chess tournament...68 Application letters...69 Birthday problem th digit...71 Cubic of integer Conditional Probability and Bayes formula Boys and girls...73 All-girl world?...74 Unfair coin...74 Fair probability from an unfair coin...75 Dart game...75 Birthday line...76 Dice order...78 Monty Hall problem...78 Amoeba population...79 Candies in a jar...79 Coin toss game...80 Russian roulette series...81 Aces...82 Gambler s ruin problem...83 Basketball scores...84 Cars on road Discrete and Continuous Distributions Meeting probability...88 Probability of triangle...89 Property of Poisson process...90 Moments of normal distribution Expected Value, Variance & Covariance Connecting noodles...93 Optimal hedge ratio...94 Dice game...94 Card game...95 Sum of random variables...95 Coupon collection...97 Joint default probability Order Statistics Expected value of max and min...99 Correlation of max and min Random ants Chapter 5 Stochastic Process and Stochastic Calculus iii
4 Contents 5.1 Markov Chain Gambler s ruin problem Dice question Coin triplets Color balls Martingale and Random walk Drunk man Dice game Ticket line Coin sequence Dynamic Programming Dynamic programming (DP) algorithm Dice game World series Dynamic dice game Dynamic card game Brownian Motion and Stochastic Calculus Brownian motion Stopping time/ first passage time Ito s lemma Chapter 6 Finance Option Pricing Price direction of options Put-call parity American v.s. European options Black-Scholes-Merton differential equation Black-Scholes formula The Greeks Delta Gamma Theta Vega Option Portfolios and Exotic Options Bull spread Straddle Binary options Exchange options Other Finance Questions Portfolio optimization Value at risk Duration and convexity Forward and futures Interest rate models iv
5 A Practical Guide To Quantitative Finance Interviews Chapter 7 Algorithms and Numerical Methods Algorithms Number swap Unique elements Horner's algorithm Moving average Sorting algorithm Random permutation Search algorithm Fibonacci numbers Maximum contiguous subarray The Power of Two Power of 2? Multiplication by Probability simulation Poisonous wine Numerical Methods Monte Carlo simulation Finite difference method v
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