MATH 7241. Probability 1 (4 Hours)

Course Outline:

1. Introduction to Probability Theory

• • Basic concepts of probability spaces
  • Definitions and properties of random variables

1. Markov Chains

• • Classification of Markov chains
  • Applications of Markov chains in data analytics

1. Law of Large Numbers and Central Limit Theorem

• • Theoretical foundations of large numbers and central limit theorem
  • Applications in the theory of random walks and Brownian motion

Assignments and Assessments:

• Probability theory problem sets
• Markov chain analysis projects
• Midterm exam
• Final project: Modeling a real-world scenario using probability theory

This detailed course outline provides a structured progression of topics for each core unit. Assignments and assessments are included to reinforce learning, and the final projects offer students the opportunity to apply their knowledge to real-world scenarios. Let me know if you have any specific preferences or modifications you'd like to make to this outline before we proceed to the elective courses and thesis/project options.

Lesson Summary

MATH 7241. Probability 1 (4 Hours)

Course Outline:

• Introduction to Probability Theory
• Basic concepts of probability spaces
• Definitions and properties of random variables
• Markov Chains
• Classification of Markov chains
• Applications of Markov chains in data analytics
• Law of Large Numbers and Central Limit Theorem
• Theoretical foundations of large numbers and central limit theorem
• Applications in the theory of random walks and Brownian motion

Assignments and Assessments:

• Probability theory problem sets
• Markov chain analysis projects
• Midterm exam
• Final project: Modeling a real-world scenario using probability theory

This detailed course outline provides a structured progression of topics for each core unit. Assignments and assessments are included to reinforce learning, and the final project offers students the opportunity to apply their knowledge to real-world scenarios.

Let me know if you have any specific preferences or modifications you'd like to make to this outline before we proceed to the elective courses and thesis/project options.