Probability (MATH-0265)

Spring 2026 · MATH 0265 · Tufts University · 3 credits · Undergraduate

Introduction to probability theory based on one semester of graduate real analysis. Random objects as measurable maps, construction of probability spaces using the Carathéodory extension theorem, independence, Kolmogorov zero-one law, expected value and variance, Chebyshev and Markov inequalities, the weak and strong laws of large numbers, distribution functions and density functions, random walks and Markov chains, weak convergence and the portmanteau theorem, characteristic functions and the classical central limit theorem, conditional probability and expectation, martingales, the Wiener process. Optional additional topics include the Lindeberg central limit theorem, the Kolmogorov-Gnedenko generalized central limit theorem, continuous-time random walks, entropy, stochastic integrals, Itô’s lemma, and the Black-Scholes equation. Prerequisites: Math 235; or permission of instructor. Recommendation: Math 165 or equivalent recommended but not required

Course codes: MATH-0265, MATH 0265, MATH0265, MATH-265, MATH 265, MATH265

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