Logic and functions
- 2.5 hours on-demand video
- 5 articles
- 3 downloadable resources
- Full lifetime access
- Access on mobile and TV
- Certificate of Completion
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- What logic is and its role in mathematics, especially proofs
- What sets and functions are and their role as the foundation of mathematics
- Understand the connection between logical statements and sets and use the concept of functions to describe this connection
- This is the foundation of mathematics so no prerequisite knowledge.
- An aspiration to learn mathematics
- Good attitude and discipline
- Persistence and above average mathematical maturity
[Under construction: get in early and influence the creation of the course at a lower price!] We talk about logic as the glue that holds the ideas of mathematics together. We give a working definition for logical statements and then derive many fundamental results from them treating logic as a mathematical subject! The idea of proof and its manifestations are discussed in detail. We then study sets and functions on them and immediately we are able to re-express our working definition of logical statements using the idea of functions. We proceed develop the basic theory of functions naturally all the while doing exercises and proofs. We conclude with a statement that beautifully summarizes all of the topics involved and their connections: it involves defining two functions that represent the relationship between the set of logical statements on a set and the set of all subsets of that set and then proving that there is some sort of symbiosis between these theories.
- Students of mathematics
- Year 10, 11 and 12 students planning on studying Extension 2 maths for the HSC
- Gifted year 5-9 students
Logic is the glue that holds mathematical theories together. Functions and sets is one of the first key topics that a mathematician learns. We can even analyse the logic we learn mathematically using functions.
Improvements scheduled per student: suggestions welcome, functional equations and harder topics put here, missing lectures identified and plugged, new intro video, solutions to some exercises, price adjustment
Defined temporarily to be things which assign true and false values to members of a set
Below in the resources tab is a set of exercises that will help you master the topic and motivate your learning.