注意：AI写的
A Book That Truly Opened My Mind
If you ask me to recommend a book, I won’t choose an easy storybook. Instead, I’d like to talk about a university textbook called Combinatorics. I’m a Grade 8 student who loves competitive programming. Many people think this book must be terribly hard. But to be honest, once you get into it, you’ll find it quite simple — and it has truly opened my mind.
I’ve read several chapters so far, and the ideas inside are just amazing. The book introduces things like generating functions, group theory, and Burnside’s lemma, which turn messy counting problems into beautiful patterns. It also explains Lucas’ theorem, abelian groups, and even Ramanujan’s congruences — names that sound scary, but the book makes them surprisingly clear. What’s more, it shows how the Fast Fourier Transform and the Fast Walsh Transform are connected to counting, and something called a reduced residue system becomes a natural tool instead of just a weird definition. There’s even a chapter on block designs, which feels like solving a perfectly designed puzzle.
Now I can’t even play chess normally anymore. Seriously, when I look at a chessboard, I don’t see black and white pieces. I see a perfect 8×8 binary matrix. When someone says, “Let’s play five-in-a-row,” my first thought isn’t “Where should I put my stone?” It’s “In how many ways can we color an n×n grid with two colors without getting five consecutive squares of the same color?” And when the board is symmetric, I automatically start calculating orbits using Burnside’s lemma in my head.
What I love most is that the book doesn’t just teach formulas. It teaches a way of thinking. Before, I would only try to list all possibilities by brute force, but now I can use Burnside’s lemma to count symmetries, or use generating functions to see hidden rules. Many problems that used to confuse me now seem easy and fun. It’s as if the book gave me a new pair of eyes to look at math.
So, if you are someone who enjoys solving puzzles or programming problems, I truly recommend this book. Don’t be frightened by the word “university” or those big names. With a little patience, you’ll find many parts are actually quite simple and super exciting. It’s a book that opens your mind, not just your textbook.
P.S. Don’t worry, I’m not dropping out of middle school. I just read the first few chapters for fun. My math grades are still normal — well, mostly.
P.P.S. Actually, I also prepared a version about Algebraic Topology. Do you need it?
P.P.P.S. Don’t even get me started on Go. I once spent three hours trying to calculate the number of legal Go positions. I gave up at 10^170.
P.P.P.P.S. To my English teacher: I promise this is not a math homework submission. But if you want, I can teach you Burnside’s lemma during lunch.