Algebra, Probability, Statistics

Description

This course is intended to teach basic concepts in algebra and probability and statistics. The algebra topics include:

·        Euclidean division

·        Extended Euclidean algorithm

·        Greatest common divisor

·        Congruences

·        Chinese remainder theorem

·        Public key crypto-systems

The probability and statistics topics include:

·        Probability theory

·        Counting rules

·        Random variables

·        Discrete and continuous random variables and their distributions (uniform, binomial, hypergeometric, Poisson, exponential, and normal)

·        Descriptive statistics

·        Linear regression

·        Sampling distributions

Confidence intervals for the mean     

Compétences visées

By the end of this course, students should be able to:

·        Do simple number theory proofs

·        Find integer solutions to Linear Diophantine equations

·        Solve systems of congruences

·        Encrypt and decrypt using the RSA crypto-system

·        Understand the basics of probability and counting rules

·        Distinguish between different probability distributions and apply them in solving probability problems

·        Describe data numerically and graphically

·        Apply linear regression analysis to given data