This course explores topics in discrete mathematics including the language of logic, set theory, enumeration, probability, and statistics. Basic elements of probability and statistics will be used to solve problems involving the organization, description, and interpretation of data. Furthermore, it explores topics in Euclidean geometry. Emphasis will be placed on the development of clarity and understanding of mathematical processes and ideas, the application of these ideas to problem-solving and the communication of these ideas to other people.
- 1: Basic Language of Mathematics
- Mathematical sentences are critical to any mathematical discussion, which are used to express ideas. A mathematical statement is a declarative sentence that is either true or false, but not both. A statement is sometimes called a proposition. The key to constructing a good mathematical statement is that there must be no ambiguity. To be a statement, a sentence must be true or false. It cannot be both.
- 3: Number Patterns
- Numbers can be organized into many different sequences. These sequences have patterns which can be used to predict the next number in the pattern. Misunderstandings may occur when we list few numbers in the sequence. Therefore it is wise to define sequences in terms of an explicit formula for the n ^th term.
- 4: Basic Concepts of Euclidean Geometry
- At the foundations of any theory, there are truths, which are taken for granted and can't be proved or disproved. These are called axioms. The first axiomatic system was developed by Euclid in his books called "Elements". The most basic terms of geometry are point, line, and plane. A point has no dimension (length or width), but it does have a location. A line is straight and extends infinitely in the opposite directions. A plane is a flat surface that extends indefinitely.
- 6: Introduction to Statistics
- Descriptive statistics is the branch of statistics used in describing the data (via graphs, tables or sample stats like mean). Inferential statistics is the branch that deals with inferring/estimating population characteristics from sample data.
- 6.1: Qualitative Data and Quantitative Data
- 6.2: Descriptive Statitics:Measures of Center, Measures of Variation and the Five -Number Summary
- 6.3: Introduction to Statistical Calculations using Microsoft EXCEL
- 6.4: Binomial distribution and Normal Distribution
- 6.E: Introduction to Statistics (Exercises)
- 7: Rational Reasoning
- We all have faced a situation when need to be able to change from one unit of measurement to another unit of measurement. In this section, we discuss a method of converting units called dimensional analysis.
Pamini Thangarajah (Mount Royal University, Calgary, Alberta, Canada)