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.
Course Overview
Boolean Logic
- Introduction to Boolean Logic (3:05 min),
Handout,
Problems
- Truth Assignments (4:35 min) ,
Handout,
Problems
- Boolean Functions (13:27 min) ,
Handout,
Problems
- Conditional Statements (11:26 min),
Handout,
Problems
- Boolean Laws (7:19 min),
Handout,
Problems
- Truth Tables (15:06 min),
Handout,
Problems
- Normal Forms,
Handout,
Sets
- Introduction to Sets (6:11 min),
Handout,
Problems
- Set Operations (15:24 min),
Handout,
Problems
- Diagramming Set Operations (5:00 min),
Handout,
Problems
- Cardinality of a Set (3:42 min),
Handout,
Problems
- Subsets of a Set (6:14 min),
Handout,
Problems
- Cartesian Products (4:26 min),
Handout,
Problems
- Partitions of a Set (5:37 min),
Handout,
Problems
Predicate Logic
Sequences
- Introduction to Sequences (6:09 min),
Handout,
Problems
- The Alice Sequence (2:35 min),
Handout,
Problems
- The Gauss Sequence (3:24 min),
Handout,
Problems
- The Triangular Sequence (3:33 min),
Handout,
Problems
- The Pyramidal Sequence and Higher-Order Sequences,
Handout,
Problems
- The Doubling Sequence (5:13 min),
Handout,
Problems
- The Mersenne Sequence (3:04 min),
Handout,
Problems
- The Fibonacci Sequence (7:24 min),
Handout,
Problems
- Harmonic Numbers,
Handout,
Problems
Recursion
Mathematical Induction
Relations
- Introduction to Relations (7:09 min),
Handout,
Problems
- Representing Relations (5:23 min),
Handout,
Problems
- Counting Relations (3:57 min),
Handout,
Problems
- The Reflexive Property,
Handout,
Problems
- The Symmetric Property,
Handout,
Problems
- The Antisymmetric Property,
Handout,
Problems
- The Transitive Property,
Handout,
Problems
- Equivalence Relations,
Handout,
Problems
- Counting Equivalence Relations (Stirling's Identity of the Second Kind),
Handout,
Problems
- Partial Orders,
Handout,
Problems
Functions
- Introduction to Functions,
Handout,
Problems
- Counting Functions,
Handout,
Problems
- Functions that are Onto,
Handout,
Problems
- Functions that are One-to-One,
Handout,
Problems
- The Inverse of a Function,
Handout,
Problems
- Logarithms and Exponentials,
Handout,
Problems
- Polynomials,
Handout,
Problems
- Using Horner's Rule to Compute the Value of a Polynomial,
Handout,
Problems
- The Floor and Ceiling Function,
Handout,
Problems
- The Quotient and Remainder (Mod $n$) Functions,
Handout,
Problems
- The Greatest Common Divisor Function,
Handout,
Problems
- Permutations,
Handout,
Problems
- Representing Permutations and Cyclic Notation,
Handout,
Problems
- Counting Cyclic Permutations (Stirling's Identity of the First Kind),
Handout,
Problems
Naming Systems
- Introduction to Naming Systems,
Handout,
<-a href=../Problems/NamingSystems.pdf">Problems
- String Length Needed to Name n Things,
Handout,
Problems
Number Systems
- Introduction to Number Systems,
Handout,
Problems
- Horner's Rule for Converting Natural Numbers to Decimal Notation,
Handout,
Problems
- Repeated Remaindering for Converting Decimal Numbers to Another Base,
Handout,
Problems
- Conversions Among Binary, Octal, and Hexadecimal,
Handout,
Problems
- Repsenting Positive and Negative Integers,
Handout,
Problems
- Ten's Complement Number Systems,
Handout,
Problems
- Two's Complement Number Systems,
Handout,
Problems
- Biased Numbers for Representing Integers,
Handout,
Problems
- Floating Point Numbers,
Handout,
Problems
Number Theory
- Introduction to Number Theory,
Handout,
Problems
- Fundamental Theorems about the Integers,
Handout,
Problems
- Modular Numbers,
Handout,
Problems
- An Algebra of Modular Numbers,
Handout,
Problems
- Linear Congruence Equations,
Handout,
Problems
- The Extended Eucliean Algorithm,
Handout,
Problems
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>
Last modified: Thu Apr 4 15:27:20 2013