# An Algorithmic Introduction to Probability and its Applications

## MATH 231

Official description: Probabilistic concepts and modeling introduced and explored through developing and implementing computational algorithms. Topics include Probability models, random variables with discrete and continuous distributions, independence, joint distributions, conditional distributions including binomial, multinomial, Gaussian, Poisson. Expectations, functions of random variables, central limit theorem, Poisson Limit theorem, Order Statistics, Bayesâ€™ formula, and Markov Chains. Many examples will drawn from algorithms used in modeling and data science. Requires ability to write basic computer programs. Recommended pre/corequisite: Mathematics 218 or 221. Not open to students who have taken Mathematics 228L, 230, or 340, Statistics 230, 231, or 240L.

Further information: This course:

• Covers all of the core material in Math 230 and introduces additional topics such as Markov chains and random trees
• Reinforces ideas being taught by grounding them in computational algorithms
• Introduces ideas from Monte Carlo sampling, stochastic modeling, machine learning and statistics
• Builds intuition and understanding by mixing computational experiments with conceptual explanations
• Provides a solid foundation for future machine learning, stochastic modeling, CS, Stats, or Math classes
• Requires single variable calculus and linear algebra, as well as an ability to program in or learn Python.

Questions? Contact Prof. Jonathan Mattingly at jonm@math.duke.edu.

Probabilistic concepts and modeling introduced and explored through developing and implementing computational algorithms. Topics include Probability models, random variables with discrete and continuous distributions, independence, joint distributions, conditional distributions including binomial, multinomial, Gaussian, Poisson. Expectations, functions of random variables, central limit theorem, Poisson Limit theorem, Order Statistics, Bayes' formula, and Markov Chains. Many examples will drawn from algorithms used in modeling and data science. Requires ability to write basic computer programs. Recommended pre/corequisite: Mathematics 218 or 221. Not open to students who have taken Mathematics 228L, 230, or 340, Statistics 230, 231, or 240L.

#### Notes

New in Spring 2024.

#### Prerequisites

Not open to students who have taken MATH 228L, MATH 230, MATH 340, STA 230, STA 231, or STA 240L

• QS
Spring Only