# A Collection of Short Lectures on Discrete Mathematics

Listen to the videos prior to attending class. Print the handouts and annotate them with your own notes. Solve the problems that accompany the lectures. Be prepared to ask and answer questions in class.

## Naming Systems

• Introduction to Naming Systems,  Handout,  <-a href=../Problems/NamingSystems.pdf">Problems
• String Length Needed to Name n Things,  HandoutProblems

## Number Systems

• Introduction to Number Systems,  HandoutProblems
• Horner's Rule for Converting Natural Numbers to Decimal Notation,  HandoutProblems
• Repeated Remaindering for Converting Decimal Numbers to Another Base,  HandoutProblems
• Conversions Among Binary, Octal, and Hexadecimal,  HandoutProblems
• Repsenting Positive and Negative Integers,  HandoutProblems
• Ten's Complement Number Systems,  HandoutProblems
• Two's Complement Number Systems,  HandoutProblems
• Biased Numbers for Representing Integers,  HandoutProblems
• Floating Point Numbers,   HandoutProblems

## Number Theory

• Introduction to Number Theory,  HandoutProblems
• Fundamental Theorems about the Integers,  HandoutProblems
• Modular Numbers,  HandoutProblems
• An Algebra of Modular Numbers,  HandoutProblems
• Linear Congruence Equations,  HandoutProblems
• The Extended Eucliean Algorithm,  HandoutProblems

## Proofs

• Introduction to Proofs,  Handout,  Problems
• Direct Proofs,  Handout,  Problems
• Indirect Proofs,  Handout,  Problems
• Proofs By Contradiction,  Handout,  Problems

William Shoaff <wds@cs.fit.edu>