Logic and functions
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Logic and functions

Build a foundation to learn mathematics
0.0 (0 ratings)
Course Ratings are calculated from individual students’ ratings and a variety of other signals, like age of rating and reliability, to ensure that they reflect course quality fairly and accurately.
13 students enrolled
Created by Dr Michael Sun
Last updated 5/2020
English
Current price: $13.99 Original price: $19.99 Discount: 30% off
5 hours left at this price!
30-Day Money-Back Guarantee
This course includes
  • 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 you'll learn
  • 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
Requirements
  • 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
Description

[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.

Who this course is for:
  • Students of mathematics
  • Year 10, 11 and 12 students planning on studying Extension 2 maths for the HSC
  • Gifted year 5-9 students
Course content
Expand all 34 lectures 02:25:10
+ Introduction
5 lectures 13:28

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


Preview 03:30

Defined temporarily to be things which assign true and false values to members of a set

Preview 02:11
Logic def
1 question

Negation or NOT takes a statement and reverses all of the true and false values

Logic of NOT
03:36

AND takes in two statements and outputs a single statement whose value is T whenever both the original statements are T and F otherwise.

OR takes in two statements and outputs a single statement whose value is T whenever one of the original statement is T and F when both are F

Logic of AND and OR
04:09
Logic of IMPLIES
00:02
Logic op
1 question
+ Logic of proofs
3 lectures 00:06
Logic behind direct proof
00:01
Logic behind contraposition
00:02
Logic behind argument by contradiction
00:02
Logic proof
1 question
+ Functions from sets
8 lectures 59:22

Below in the resources tab is a set of exercises that will help you master the topic and motivate your learning.

Preview 01:57
onto
03:13
Examples of things thought of as functions
06:18
natural functions
04:44
+ Composition of functions
5 lectures 16:52
composition defined
00:58
inverse functions defined
10:48
invertible is one to one
02:49
invertible is onto
01:14
+ Functions as graphs
9 lectures 24:39
Representing functions as graphs
03:45
graphs 1.2
02:50
graphs 1.3
01:25
graphs1.4
01:26
1.last
02:58
graphs 2.1
01:51
graphs 2.2
03:01
graphs 2.3
02:36
swap
04:47
+ Relating with functions
3 lectures 30:40
Correspondence between logical statements and subsets
07:31
countability
15:23
Countability 2
07:46
+ Exercises
1 lecture 00:02
Exercises on sets and functions
00:02