The following videos are for a discrete mathematics module I am currently tutoring.
The first five sections are on this page. The second five sections are currently on this page.
This material is going to be moved to https://mathsatstatslab.wordpress.com/ very soo.
Section 1 : Number Systems
Link for Tutorial Sheet (Currently being written)
- Binary Number Conversion
- Binary Addition Adding two binary numbers
- Binary Subtraction (using Borrowing Method)
- Binary Subtraction (using 2’s complement Method)
- Binary Multiplication (using Left Shifting)
- Hexadecimal Number Conversion
- Converting Hexadecimal Numbers With Fractions to Decimal Form
- Converting Decimal Fractions to Hexadecimal
- Adding Hexadecimal Numbers
- Spreadsheet Commands Checking your answers on a spreadsheet.
- Number Sets Natural Numbers, Integers, Rational Numbers and Real Numbers.
- Irrational Numbers : exercise involving irrational numbers.
- Repeating Decimals
Section 2 : Set Theory
Set theory is a fundamental concept throughout mathematics. Intuitively a set is a collection of objects, which are called elements. Although this seems like a simple idea, it has some far reaching consequences throughout all of mathematics.
Link for Tutorial Sheet
- Rules of Inclusion
- Listing Method
- Elements and Subsets in Set Theory
- Set Difference and Symmetric Difference
- Power Set
- Binary Strings
Section 3 : Logic
Link for Tutorial Sheet for section 3.
- Introduction to Truth Tables
- Logic Truth Tables
- Proofs using Truth Tables : Using truth tables to prove that two statements are equivalent
- Logic Networks (Example 1)
- Logic Networks (Example 2)
Section 4 : Functions
Link for Tutorial Sheet for section 4.
- Arrow Diagrams for Functions (One-to-One and Onto)
- Properties of Functions (Example 1) One-to-One, Onto and Invertible Functions
- Properties of Functions (Example 2) One-to-One, Onto and Invertible Functions
- Floor and Ceiling Functions
- Laws of Logarithms
- Mathematical Function Exercise Logarithms and Cube Root Functions
- Binary Strings and Functions
Section 5 : Graphs
Graph theory is the study of points and lines. In particular, it involves the ways in which sets of points, called vertices, can be connected by lines, called edges.
Graphs are classified according to their complexity, the number of edges allowed between any two vertices, and whether or not directions are assigned to edges.
Link for Tutorial Sheet for section 5
- Degree Sequence of a Graph
- Complete Graphs
- Regular Graphs
- Adjacency List: Using an adjacency list to construct a graph.
- Paths and Cycles in Graph Theory
- Non-Isomorphic Graphs