for academia, mathematics, music, art and philosophy

Bracket Notation for Mathematical Proofs

The bracket notion for mathematical proofs is an adaptation of the Fitch notation for Gentzen's natural deduction proof system. It has led to the development of the SOFiA proof assistant. This post brings together some videos explaining the bracket notation and the first-order formal language for mathematics in the context of the bracket notation.

1. General Overview

~ 20 min

2. Building Blocks for Statements

~ 1 hour

3. Examples of Forming Statements

~ 40 min

4. Examples of Forming Statements (Continued)

~ 35 min

5. Concluding Quantified Statements

~ 35 min

6. Concluding from Quantified Statements

~ 1 hour

Read More

Category Theory Course 2022

Here you will find the content for the Category Theory course given under the National Graduate Academy NGA-Coursework of the CoE-MaSS. The lectures are on Saturdays 9:00-11:00. 

Register here to receive the Zoom link for joining the lectures

There is also a Discord channel for this course, which you can find on the Discord server of the NGA-Coursework project. 

This is a video-based course aimed at post-graduate students and as well academics interested to learn about category theory, with live participation of the audience shaping the content of the course. For a reading course at the South African honors level, see:

For an introduction to category theory for non-mathematicians and undergraduate students, see:

Lecture 1: Categories

Lecture 2: Functors

Lecture 3: Natural Transformations

Lecture 4: Adjunctions

Lecture 5: Limits

Lecture 6: Duality

Lecture 7: Yoneda Embedding

Lecture 8: Equivalence of Categories

9. Exponentiation

10. Universal constructions

Read More