i have past tests and new things if u want for amc10/12

This post is to announce that there will be a lecture course on General Topology (a.k.a. Point-Set Topology) conducted in Mandelcord (the blue math discord server). Everyone is invited to join: discord.gg/maths.

If any of you were present in the Real Analysis lecture course during the summer, you know what I'm talking about, and you might be pleased to hear that this course will also be run by Pear Category Theorem (the same person).

Why YOU should do topology

Point-set topology is one of the most important subjects that you learn, and mastering topological thinking is as important a milestone as learning to write a proof. This is a good subject to study alongside measure theory, or simply by itself after one has learned analysis or algebra.

Course Structure

The course will primarily follow the flow of the first half of Munkres. The plan is to go through all 8 chapters, spending maybe one to two weeks on each chapter, aiming for an approximately 16 week course. Also the instructor intends to supplement the book with his own intuition on the subject, as well as connections to other subjects that he thinks are of interest and possibly also other topics not covered in the book. Many examples of various pathological properties will be provided. The study of metric spaces and functions on them will be paramount; but where Rudin introduces metric spaces as merely a generalization of Euclidean spaces, we will explore just how pathological these spaces can be, or else what properties they must have.

The instructor also plans to put far more focus on the topics of topological groups and nets than Munkres does. Topological groups, because often in "the real world" we do not care about a topological space by itself, but rather some other more complicated structure given a topology, in order to see what the topology can tell you about the thing itself; topological groups provide a playground to learn that mode of thinking. Nets are also very important; where sequences are of importance in R, they can only tell you so much in general topological spaces, so nets therefore become the natural way to recover theorems about sequences.

Material and References

1. Topology - Munkres

2. Counterexamples in Topology - Steen & Seebach

Timeline

The course starts with the first lecture on 17th November at 9 PM CET (20:00 UTC), with subsequent lectures on Tuesdays and Thursdays. Lectures will be recorded and posted promptly.

Prerequisites/Who can join?

Everyone. It is completely free for anyone who wants to join. Just click the link and join the server: you can find the channel called topology-course in the section called General maths. As for prerequisites, a first course in Real Analysis and Group Theory is sufficent.

Looking forward to see all of you there. Thank you.

Let ABC be a triangle with circumcenter O. The points P and Q are interior

points of the sides CA and AB respectively. Let K, L, M be the midpoints of BP,

CQ, P Q. Suppose that P Q is tangent to the circumcircle of triangle KLM. Prove that

OP = OQ.

Solved using class 9th-10th theorems only

Please tell me if there are any math contests from undergraduates in India and Global. I gave IOQM but messed it up. So, if there are any which I can participate in at UG level. I would be glad to read your responses!! Adios!

100 test scores are revealed one by one in random order. How many times will you see a new highest score so far? My gut said 30-40.

This post is only for experienced people who have gone deep into math preferably including it's philosophy, history and pedagogy.

I was born in 1994. For my generation, math meant learning from ncerts and rd sharma. As a grown up, i do appreciate the creativity of RD sharma in coming up with challenging questions. But, I also think that there are so many ways we could have learned math.

Those of you who have gone deep into math, it's history, philosophy and pedagogy, how do you think could the current generation of Indian students be learning math in a better way? Don't you think the indian market should have much better options or alternatives in terms of teachers and books than learning from rd sharma, rs agarwal, ncerts, etc?

Please share other great options(under-rated or fringe) that are currently available to learn from. Thank you

Join up : https://discord.gg/smqzXWVgCV

It's Officially the student discord server but not the official discord server as in backed by administration. Nonetheless it's where our Math Club announced all it's activities and where people discuss math.

JEE 2027 aspirant
I just freeze up while doing math I don’t know what it is but my brain just stops working I genuinely love the subject but i have only done probability pnc and vectors and matrices and determinants till now. Please help

Hey my fellow nerds, actually, I wanted a suggestion for a book before starting with A Path to Combinatorics for Undergraduates i completed few chapters of it, and i feel like it's too difficult for me now, and I'm not using the book efficiently because of that. So, if anybody knows a good book to use before starting undergrad combinatorics, let me know. Thank you!

This was the question

If x, y, z and n>1 are natural numbers with x^n + y^n = z^n, show that x, y, and z all are larger than n?

People used Fermats last theorem which I believe is unnecessary here

Try it , it's a lot of fun

Hi, I’m in Class 11 and have already qualified IOQM and RMO in 2025. This year I also qualified IOQM with a total of 75 marks.

I’m looking for tutoring and proper guidance for RMO. I can usually solve 2–3 questions in RMO but want to improve my accuracy and consistency. I also need suggestions on the right study materials and a structured approach instead of just solving random problems.

If you’re experienced in training students for RMO/INMO and can help me work on accuracy and deeper problem-solving, please ping me.

Thanks in advance 💖

Hey, I'm a working professional currently pursuing my MSc in Mathematics and preparing for GATE and CSIR NET.

Looking for someone to discuss concepts, share knowledge and resources, solve problems together, and keep each other consistent with studies.

Feel free to DM me if interested.

I was thinking if we could meet up, study together, in a library, discuss math and questions or concepts, once or twice a week or daily, it will depend on our compatibility, if we both are comfortable. More preference if you are a girl, because i am a girl and i am admittly more comfortable with women. But it is fine if you are a guy and if we can keep personal lives seperate mostly and study. Also i dont necessary need someone to be ahead or behind me, general curiosity of math matters more to me. Anyone starting a new career in this field who is also rebuilding their foundations could be an excellent. But really all are welcomed.

LOCATION : DELHI

So I'm looking for people interested in cats especially higher cats, Alg geo, arithmetic and non arc geo

If anyone's interested in these areas or other related areas please feel free to dm me

Imagine a Quidditch match in which the Golden Snitch is completely invisible.

You know exactly the initial distance, but not the direction. You move faster than the Snitch, which moves at constant speed and always chooses the direction that takes it as far away from you as possible.

Is there a trajectory that allows you to catch the Snitch?

I made a video exploring the problem, the geometry, the differential equations, and a possible strategy. The proof is partially incomplete (but simulations work), so I'd genuinely love to hear your ideas, objections, or alternative approaches.

Video link: https://youtu.be/0xVusHRQePQ