Yue's Notes

Some latex tests

Consider a $n \times m$ chessboard… $$ \int{f(x)dx} $$Since $94 = 4 + 5x$ for some $x \in \mathbb{N}$, my claim is that the first player wins when it chooses $4$ in the beginning. Then, whenever the second player choose $a, x \in\set{1, 2, 3, 4}$, the first player just add it to 5. So choose $5-a$. By doing this, the first player always reaches $10x + 9$ or $10x + 4$ for $x \in \mathbb{N}$. Since $94$ is included, the first player must win. ...

My Math 417 review notes

I have had a wonderful summer as I have been able to take Math 417 with Professor Chales Rezk. He is a very very good teacher and I have learnt a lot from him. Thanks! These are the notes I have taken during the course. It includes the greate Theorems, Lemmas and Propositions that we have learnt in the course. Previous Next / [Downlaod] View the PDF file here.

413_basic counting

The four basic counting principle Suppose that a set $S$ is partitioned into pairwise disjoint parts $S_1, S_2, ..., S_n$. Addition principle: $$ |S| = |S_1| + |S_2| + ... + |S_m| $$Ex: Path counting: In a $3 \times 3$ grid, if you can move 1 step upward or 1 step to the right. How many ways do we have to move from bottom-left to top-right corner? The idea is to break this problem into smaller problems. Addition principle guarrantees that we can add the numbers together. ...