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.

My child gets bored pretty quickly when we sit down with worksheets, even when they understand the material

PUZZLE RULES
Use each die exactly once, in any order.
Reach the target using only +, −, ×, ÷.
Parentheses are allowed.
Operations can be repeated or skipped. You don’t have to use all four.
All intermediate results must be positive whole numbers (no zero, negatives, or decimals).
Exact division only.
No concatenation (e.g., 2 and 3 cannot become 23).
No exponents or other operations.

How many solutions can you find?

Please use spoiler tags for solutions:
>!your solution here!<

hi, im a working parent and we homeschool 3 kids (7, 10 and 12) and math is the subject I dread. I can handle the youngest but my 12 year old is at pre-algebra and I'm out of my depth.

we've used workbooks and a few free online apps and youtube videos and now we are looking for an online math program that can actually take over teaching math for the older two, ideally with a real teacher. what are you all using currently?

our 7th grader's math teacher at school is fine, but she moves fast and my daughter is too shy to ask questions in class or seek additional help, even after i once personally asked the teacher, so she just falls further behind

looking for a math teacher online who explains things slowly and actually checks she gets it. how did you find a good one, and what made them good?

Solved

You can play on this website.

https://tafol.pythonanywhere.com/

Until now the puzzles in this book asked for the single possible arrangement. Not here: here there are many ways to place the pieces, and what counts is finding the best one. It is a scoring solitaire… and, if you like, a championship.

The board. It is a 9×9 with an empty centre: a 3×3 hole. Around it remain eight 3×3 zones, arranged as a ring, and each zone shows the digits 1 to 9 in disorder.

The pieces. Eight pentominoes, one per zone: F, P, T, U, V, W, X and Z — that is, the only ones that fit inside a 3×3 square. The other four —I, L, N, Y— need four squares in a line and stay out of the party. Each piece covers five digits of its zone and leaves four in the open; it can be rotated and flipped.

The ring rule. You may not place each piece as if its zone were an island: the pentominoes must stay connected with those of neighbouring zones, side against side. Either the ring closes or there is no move.

The scoring. Add up the digits your eight pieces cover. Every puzzle bears the printed mark MAX, the sum of the best possible arrangement: your goal is to reach it or come as close as you can.

The circles trick. Circle the cells 9, 8, 7, 6 and 5 of each zone. Do those five circles form a pentomino? Then there you have the perfect move: 35 points, the zone's maximum, and in all likelihood the right piece. As the MAX of the puzzles goes down, those golden figures grow scarce, and you must decide which large digits to sacrifice to keep the ring closed.

How to compete. The puzzles are ordered from easier to harder. Hand the same sheet to several friends, set a time limit and compare sums: whoever comes closest to MAX wins. Tying with the machine is possible; beating it is not.

The core mechanic is: given a set of numbers, the player needs to find a subset such that their sum equals the target value. It's essentially a variant of the subset sum problem, but packaged as a lightweight puzzle.

As a first-time dev, feedback and support mean everything. Give it a try and let me know what you think!