• Mapping the Mind

    Junior computer science and mathematics double major Brooke Guo analyzes neural connections to understand the causes of complex brain conditions like schizophrenia.  When Brooke Guo arrived at the University of Maryland as a freshman in 2022, she knew she wanted to help people and work in a health-related field someday.… Read More

  • Four Science Terps Awarded 2025 Goldwater Scholarships

    Four undergraduates in the University of Maryland’s College of Computer, Mathematical, and Natural Sciences (CMNS) have been awarded 2025 scholarships by the Barry Goldwater Scholarship and Excellence in Education Foundation, which encourages students to pursue advanced study and research careers in the sciences, engineering and mathematics.  Over the last 16 years, UMD’s nominations… Read More

  • Announcing the Winners of the Frontiers of Science Awards

    Congratulations to our colleagues who won the 2025 Frontiers of Science Award: - Dan Cristofaro-Gardiner, for his join paper with Humbler and Seyfaddini: “Proof of the simplicity conjecture”, Annals of Mathematics 2024. - Dima Dolgopyat & Adam Kanigowski, for their joint paper with Federico Rodriguez Hertz: “Exponential mixing implies Bernoulli”, Annals of Mathematics… Read More

  • 2024 Putnam Results

    We are very excited to report that our MAryland Putnam team ranked 7th among 477 institutions that participated in the 2024 Putnam math competition. Our team members this year were Daniel Yuan, Isaac Mammel, and Clarence Lam. Daniel Yuan ranked 26th among 3,988 participants. Clarence Lam and Isaac Mammel were recognized for… Read More

  • From Math Olympiads to Diplomacy: Meet Visiting Math Professor Qendrim Gashi

    Maryland Global, published a great interview with our visiting professor (and diplomat), Qendrim Gashi. The interview is available at https://marylandglobal.umd.edu/about/news/math-olympiads-diplomacy-meet-visiting-math-professor-qendrim-gashi Read More
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Description

The course is a solid introduction to the formulation and manipulation of probability models, leading up to a rigorous proof of the law of large numbers and the central limit theorem. The emphasis is on concepts: sets and combinatorics allow a precise mathematical formulation of probability models, multivariable calculus supplies machinery for changing variables and calculating probabilities and average values relating to vectors of real-valued random variables, and limit theorems allow event-occurrences which are individually unpredictable to become predictable in the aggregate.

Prerequisites

1 course with a minimum grade of C- from (MATH240, MATH461, MATH341); and 1 course with a minimum grade of C- from (MATH340, MATH241).


Level of Rigor

Advanced


Sample Textbooks

A First Course in Probability, by Sheldon Ross


Applications



If you like this course, you might also consider the following courses



Additional Notes

Crosslisted with SURV410

Students interested in grad school in AMSC should consider this course

Students interested in grad school in MATH should strongly consider this course

Students interested in grad school in STAT should strongly consider this course

Topics

Text of Ross, chapters 1-8 including:

Axioms of Probability and basic properties

Combinatorial problems

Conditional probability

Random variables and distributions in one and several variables, including change-of-variable techniques

Expectation and conditional expectation

Moments

Moment generating functions

Law of Large Numbers and Central Limit Theorem

Optional Topics from among:

Characteristic functions

Fourier transforms

Borel-Cantelli Lemma

Meaning of convergence with probability 1

Filling in missing steps of the book's proof of the Central Limit Theorem

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