exploring infinity within

AI Tutor Prompt

Any student who wishes to take help from AI models could try to use this prompt, which makes them behave like your personal tutor. (It may feel annoying at first but this actually ensures that one does not outsource thinking to AI!)

Please act like my maths tutor at every step. Do only the task I tell you. Do not anticipate the next step at any point, and do not give me a hint unless I ask for one.

If I ask a Yes/No type question and the answer is yes, respond in at most one line. If the answer is no, indicate in one line exactly where my reasoning is wrong.

If my response lacks precision, do not complete it for me. Ask exactly one question that may help me realise what is missing.

If it is clear that I understand the mathematical idea, do not make me spend time guessing notation, variable names, or obvious arithmetic details.

If I say that I am stuck or do not know how to proceed, give me only the minimum help needed to restart my thinking. Prefer exactly one focused question rather than telling me the next step directly.

Once I have identified all the important logical steps correctly, tell me that the proof or solution is complete and then write a clean complete version using the ideas that I developed.

Unless you have worked with me on a project for at least a month, please do not ask me to write a letter of recommendation for you. I take writing one such letter very seriously which makes it a time-consuming process.

Courses taught at IIT Kanpur

MTH101A Mathematics-I, Odd term 19-20
MTH111M Single variable calculus, Odd term 24-25, Odd term 26-27
MTH202A Set theory and Discrete Mathematics Odd term 22-23
MTH302A Set theory and logic, Odd term 17-18, 18-19, 23-24
MTH613A Rings and Modules, Even term 21-22
MTH619 Representation theory of quivers, Odd term 25-26
MTH642A Topics in model theory, Odd term 18-19, 21-22
MTH661A Introduction to sheaves and topos theory, Even term 17-18
MTH666A Category theory, Odd term 17-18, Even term 19-20, Logic Webinar 20, Even term 23-24, Even term 25-26
MTH678A Techniques in combinatorics, Even term 18-19, Odd term 20-21, Even term 22-23, Even term 24-25
MTH724A An introduction to algebraic K-theory, Even term 20-21
ETH111 Introduction to Practical Ethics Even term 22-23 (Feedback), Even term 23-24 (Feedback), Even term 24-25 (Feedback), Even term 25-26 (Feedback)

Tutorials at IIT Kanpur

MSO201A Probability and Statistics, Even term 17-18
MTH102A Linear algebra and Differential equations, Even term 18-19

NPTEL MOOC (Massive Online Open Course)

Set Theory and Mathematical Logic, January-April

Category Theory, July-November

Maths Circle India

1) Modules 74-77, March-April 25

Other facilitators: Garima Chauhan, Rohun Easwer, Mihir Mittal, Sam K Mathew

2) Modules 95-99, May -July 26 (Picture of survivors)

Other facilitators: Annoy Sengupta, Rohun Easwer, Hrishik Gupta, Jayaprathap N

Other courses

Representation theory of bound quiver algebras, CIMPA-funded AESiM Flavours of Representation Theory at North-Eastern Hill University, Shillong, July 25.
Auslander-Reiten theory, Virtual AIS on Representations of quivers and BGG category O for semi-simple Lie algebras, Dec. 24.
Categorical syntax-semantics dualities, ISLA 2022 Part-I, hybrid mode, May 22.
Completeness and compactness theorems in propositional and predicate logic, ISLA 2020, virtual mode, Dec. 20.
Measure theory, Annual Foundation School-II, Bhaskaracharya Pratishthana, Pune, June 19.
Topology, Annual Foundation School-I, Bhaskaracharya Pratishthana, Pune, Dec. 17, Dec. 18.
Model theory, PG level, Indian School on Logic and Applications (ISLA), Vellore VIT, Sept.-Oct. 18
Introduction to elliptic curves (with G. Terzo), UG level, Second university of Naples, Caserta, Italy, Fall 15
Algebraic K-theory, UG level, Second university of Naples, Caserta, Italy, Spring 15
K-theory of model-theoretic structures, Invited short, Leeds university, March 14
Category theory and Topos theory, Invited graduate level, Pune University, Summer 11
Fundamentals of discrete Fourier transforms for digital image processing, Invited short, Fergusson college and Garware college, Pune, July 11

Tutorials as a TA at University of Manchester

MTH10101, MTH10222, MTH20302, MTH20101, 0B2, 0F2, 0N1, 1E1, 1E2

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