The titles with star are not in the 113-1 CSE215 Data Structure Course syllabus. Most content in part (I) had existed in 112-1 CSE131 C Programming I, so I will use C language to do the implementation as much as possible. Part (I) - basic concept and linear data structure Basic Concepts Arrays (Link) List Stacks Queues

FoundationsA Brief Introduction to Algorithms Growth of Functions Probabilistic Analysis and Randomized Algorithms Sorting and Order Statistics Heapsort Quicksort Medians and Order Statistics

PART (II) - 04 Other parts in this series $\rightarrow$ Data Structure - Syllabus What is hashing Hashing is a technique used in data structures that efficiently stores and retrieves data in a way that allows for quick access. It involves mapping data to a specific index in a hash table using a hash function that enables fast retrieval of information based on its key. Performance Comparison of Arrays and Trees Array<br>(Sorted) Array<br>( Not Sorted)

There are big-O, big-Omega, big-Theta, little-o and little-omega in this page QQ 1. Big-O :::info Defnition: $$ O(g(n))={f(n)|\exists c, n_0, s.t. 0\le f(n)\le cg(n)\forall n\ge n_0} $$ in human language, the alien's language above means:

Basic Variance $Var(X)=E[X^2]-E[X]^2$ Advance PMF v.s PDF v.s CDF PMF (Probability Mass function) A PMF is a mathematical function that gives the probability that a discrete random variable is exactly equal to a specific value. It is used in statistics to describe the distribution of discrete random variables. $p(x) = P(X=x)$, $p(x)$ is PMF

Topics flowchart LR LG(Linear Geometry)-->LS(Linear Space)-->LF(Linaer Function) Linear GeometrySystems of Linear Equations Linear Space Vector Spaces Linaer Function

中山大學資訊工程學系全英班 我的第一場面試，當天頗熱，前面有兩個人沒報到，中間我覺得我算回答的2266的，不過教授人都還不錯，很和善。 不同於一般班，我們是個別面試，分為數理面向及英文面向各兩位教授，沒有自我介紹（人家準備了的說…）。 然後對其他考生的觀察的部分，女生大部份穿的像辦公室OL，男生從全套西裝到稍微不那麼正式的短袖襯衫我都有看到，然後我還在路上（不確定哪個系的）穿格子襯衫+牛仔褲。 數理面向 以抽籤選題，給五分鐘解題，解完題後教授會問你解題思路及為什麼選擇這個解法，題目及問答皆為英文。 題目 求以下式之三根（有給選項）

Simple operations Matrix addition I think most of us learnt it in high school, so let's just give an example. :::info what is result of $\left[ {\begin{array}{cc} 1 & 2 & 3\ 4 & 5 & 6 \ \end{array} } \right]+ \left[ {\begin{array}{cc} 1 & 3 & 5\

Linear Algebra - Introduction Systems of Linear Equations Linear Algebra - Vector Linear Algebra - Vector and Set of Vectors Linear Algebra - Systems of Linear Equations Vector Spaces Linear Algebra - Vector Space Linear Algebra - Subspace

# Linear Algebra - Matrix Inverse

https://hackmd.io/@benny-liu/SkuD7zJBJx 幸運地，抑或者是不幸地，我這學期暈船了。 註: 暈船，指快速喜歡上一個人，或對某人產生強烈迷戀，並且通常是指不可能有結果的愛情。 這邊就不提狗血戀愛腦的部分了，在暈船以來差不多一個月的時間，剛好會遇到一次月經，這時候我發現一件非常有趣的現象，在暈船時，我的月經血量會比平常多更多，而更奇妙的事，在血量增多的同時，我的經痛卻減少了。這時我想到，會不會是暈船時，大腦中的某些激素造成了這一現象。 本筆記分三段: 「暈船時的大腦狀態」、「是甚麼影響我的月經呢?」，最後是「我的結論」。

PART (II) - 03 Other parts in this series $\rightarrow$ Data Structure - Syllabus Sorting Algorithms A Sorting Algorithm is used to rearrange a given array or list of elements according to a comparison operator on the elements. The comparison operator is used to decide the new order of elements in the respective data structure. Sorting Terminology In-place Sorting: An in-place sorting algorithm uses constant space for producing the output (modifies the given array only) or copying elements to a temporary storage. Examples: Selection Sort, Bubble Sort Insertion Sort and Heap Sort. Internal Sorting: Internal Sorting is when all the data is placed in the main memory or internal memory. In internal sorting, the problem cannot take input beyond its size. Example: heap sort, bubble sort, selection sort, quick sort, shell sort, insertion sort.

https://hackmd.io/@benny-liu/Syi9ifIZkl Week06 運動與知覺 射箭(複合弓)很困難嗎? flowchart LR 1([內在動機])-->2([計畫])-->3([訊息傳遞])-->4([精細控制])-->5([動作結果]) 內在動機 我要把箭射到黃心。 計畫

可以使用Ctrl+F直接尋找題目 SELECT 01. 顯示所有圖書館內書籍的資料(資料表Allbooks)。 SELECT * FROM allbooks; 02. 在圖書館內的書籍中，請列出分類為 “電腦” 的書籍。 SELECT allbooks.* FROM allbooks, category WHERE cate=category.cid AND category.catename="電腦";

Definition for all vectors $\vec{u}$, $\vec{v}$, $\vec{w} \in V$, and $r$,$s\in\mathbb{R}$, if rule explain rule explain $\vec{v}+\vec{w}\in V$ close under addition

Definition For all vector space,a subspace is a subset that is itself a vector space, under the inheriate operation. Lemma If $W$ is a vector space, $V\subseteq W$, $\forall$ $\vec{v},\vec{w}\in V, r\in V$ $\vec{0}\in V$ $\vec{v}+\vec{w}\in V$ $r\vec{v}\in V$

We gonna expalin Linear Equations and its extentions, such as ker(),row(), pivot, leading variables & free variables Linear Equations In mathematics, a linear equation is an equation that may be put in the form $c_1x_1+c_2x_2...c_nx_n=a$, and $c_1,c_2...c_n$ are the coefficients, which are often real numbers. When there are a lot of equetions to slove we simply list them down. $$\begin{cases} c_{11}x_1+c_{12}x_2...c_{1n}x_n=a_1 \ c_{21}x_1+c_{22}x_2...c_{2n}x_n=a_2 \ \vdots\

Basis Definition A basis for vector space is a sequence of vector that is linearly independent and that spans the space. Examples basis of $\mathbb{R}^n={\left[ {\begin{array}{} 1\0\0\\vdots\0\end{array} } \right],\left[ {\begin{array}{} 0\1\0\\vdots\0\end{array} } \right],...,\left[ {\begin{array}{} 0\0\0\\vdots\1\end{array} } \right]}$ basis of $V={\left[ {\begin{array}{} x\y\z\end{array} } \right]\mid x+y+z=0}$ is ${\left[ {\begin{array}{} -1\1\0\end{array} } \right],\left[ {\begin{array}{} -1\0\1\end{array} } \right]}$ Dimension Definition

Definition In any vector space, a set of vector is 'linear independent' if none of its element is a linear combination of others from the set. Otherwise, it is it is linear dependent. Lemma If a linear combination of an independent set of vectors equals $\vec{0}$, then all coefficiant is 0. $$c_1u_1+c_2u_2+...+c_du_d=\vec{0}\rightarrow c_1=c_2=...=c_d=0$$ For a linear independent set ${u_1,u_2,...u_d}$ $$ker(\left[ {\begin{array}{} |&|&...&|\u_1 & u_2 & ... & u_d\|&|&...&| \end{array} } \right])=\vec{0}$$

Linear Combination Given a set of vectors S, $S={u_1,u_2,...,u_n }$, Linear combination of S is $$c_1u_1+c_2u_2+...+c_nu_n\text{ , such that }c_1,c_2,...,c_n\in\mathbb{R}$$ Span Span(S) is linear combiantion of S $$Span(S)={c_1u_1+c_2u_2+...+c_nu_n|c_1,c_2,...,c_n\in\mathbb{R}}$$ How to show vector is in a span or not? Let's just took some examples.