ZURAB JANELIDZE'S BLOG

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Slides for the presentation at the NITheCS innauguration event  

Worgologi is a unique game of logic, language, and discovery, where players journey through an ancient African-inspired world, uncovering wisdom by forming words on a grid according to guiding axioms. Developed by Zurab Janelidze and Nino Mekanarishvili, the game combines storytelling with deductive reasoning to foster mathematical thinking and curiosity, inviting players to explore the beauty of structured thought in a culturally rich setting. Purchase Worgologi using bank transfer: Purchase Worgologi with PayPal: Select Worgologi packaging (shipping prices not included) In a box (bag included) $20,00 USD In a bag $15,00 USD Collection Collect from store (email zurabj@gmail.com for address) Ship the pr...

Outline: In this course we will explore various topics in category theory. The choice of topics can range from basic to advanced and will depend on the existing knowledge of the subject among the participants. Category theory provides a unifying language for conceptualising phenomena across different disciplines, including subjects within pure mathematics, as well as some aspects of quantum physics, computer science, biology, and others. Skills outcome: This course introduces students to basic concepts of category theory, which are useful when applying category theory as a language of conceptualisation in various disciplines. Upon completing the course, you would have gained the skills of making sense of, working with and applying these concepts. Prerequisites: Experience with mathematical thinking and working with a symbolic language (e.g., experience with mathematical formalisms).  See the previous courses (not required): Category Theory 2022  - an NGA course, Categor...

Outline: In this course we will explore various topics in category theory. The choice of topics can range from basic to advanced and will depend on the existing knowledge of the subject among the participants. Category theory provides a unifying language for conceptualising phenomena across different disciplines, including subjects within pure mathematics, as well as some aspects of quantum physics, computer science, biology, and others. Skills outcome: This course introduces students to basic concepts of category theory, which are useful when applying category theory as a language of conceptualisation in various disciplines. Upon completing the course, you would have gained the skills of making sense of, working with and applying these concepts. Prerequisites: Experience with mathematical thinking and working with a symbolic language (e.g., experience with mathematical formalisms). Anyone interested in the course is advised to look through the notes and videos on  https://www....

Emerging Perspectives in Mathematics II

Some notes from Abstract Algebra Session 2 (more info to appear soon, including link to the video).

So I wanted to check how well will ChatGPT-4 perform with the theorem-proving (in a variant of incidence geometry) that I give to second-years at the start of Foundations of Abstract Mathematics I... it takes a few weeks for the students to master the new, axiomatic approach to mathematics -- and precision of proofs that comes with it. For ChatGPT-4 it was a breeze at first, but then it started to mess up. It was, however, after some effort, able to correct its mistakes once they were pointed out. Below is the record of our conversation.  I will state some axioms and then ask you to prove theorems based on them. Please do not use any of your previous knowledge in the proofs, just the axioms. Sure, please state the axioms and the theorems you would like me to prove. Axiom 1. A point may only lie on a line or a plane, and a line may only lie on a plane. If a point lies on a line which lies on a plane, then the point lies in the same plane. Thank you for providing the axiom. Plea...

Use mathematical induction to show that n^2-n is always divisible by 2. To prove that n^2 - n is always divisible by 2 using mathematical induction, we'll follow these steps: Base case (n=1): Show that the statement is true for the lowest value of n. Inductive step: Assume that the statement is true for n=k (k is an arbitrary positive integer), and show that it is also true for n=k+1. Base case (n=1): When n=1, the expression becomes: 1^2 - 1 = 0 Since 0 is divisible by 2, the statement holds for n=1. Inductive step: Assume that the statement is true for n=k, i.e., k^2 - k is divisible by 2. We can write: k^2 - k = 2m, where m is an integer. Now, we need to prove that the statement is true for n=k+1. So, let's consider the expression for (k+1)^2 - (k+1): (k+1)^2 - (k+1) = k^2 + 2k + 1 - k - 1 = k^2 + k Now, we want to show that k^2 + k is divisible by 2. To do this, we can rewrite the expression using the assumption that k^2 - k is divisible by 2: k^2 + k = (k^2 - k) + 2k = 2m ...