This website houses notes from my studies at the University of Liverpool. If you see any errors or issues, please do open an issue on this site's GitHub.
Adversarial search is a method of reaching a goal while making moves against another player. This allows the agent to react to the moves of another player. In search we make all moves. In games we play against an unpredictable opponent: Solution is a strategy specifying a move for every...
Union The union of two sets $A$ and $B$ is the set: \(A\cup B = \{x\vert x\in A\ \text{or} \in B\}\) This is the same as logical OR ($+$) Example Suppose \(A=\{4,7,8\},\ B=\{4,9,10\}\) Then \(A\cup B = \{4,7,8,9,10\}\) In bit vectors you just perform a logical OR on both of...
Subsets A set $B$ is called a subset of a set $A$ if every element of $B$ is an element of $A$. This is denoted by $B\subseteq A$. Examples \(\begin{aligned} \{3,4,5\}&\subseteq\{1,5,4,2,1,3\}\\ \{3,3,5\}&\subseteq\{3,5\}\\ \{5,3\}&\subseteq\{3,5\} \end{aligned}\) graph TB subgraph A B(B) end Venn diagram of $B$ subset $A$. Therefore, $\forall$ sets $A$,...
Notation for Sets A set is a collection of objects, called the elements of the set. $\{7,5,3\}$ We have written down the element of each set and contained them between the braces $\{\}$. Repetitions and orderings don’t matter in sets hence $\{7,5,3\}$ is the same as $\{5,3,3,3,7\}$. We write $a\in...
Cracking the Caesar Cipher In order to crack a Caesar Cipher you can use the fact that, in English, each letter isn’t used equally. From this you can shift around the letters until you find a shift that fits the distribution of the English language. As a result of this...
The Caesar Cipher The Caesar Cipher is a shift method of encoding. This shifts every letter forward by three and wraps around when z is reached. There is no particular reason to shift by three and you can shift by any number between zero and 25. Shifting by 13 would...
Referencing is a description that identifies an information source, whereas citation is the use of a reference in text. It is not a good practice to simply list all your references at the end of a document without a connection. Need to clearly mark what is your own work and...
The purpose of referencing is to show how work extends the current state-of-the-art knowledge in the area, proof originality of work, give credit to other people’s work, support and validate arguments made and demonstrate familiarity with work done in the area. Culture of Citing For fiction there might be sources...
How to we form our knowledge? Generally we form our personal collection of facts from sources that we meet in our every day life. This means that a good proportion of the knowledge we might think that we have is composed of myths. This is especially found in news articles....
Definitions of Supplementary Statements Conjectures are built on other conjectures. They can be subdivided into the following parts: Theorem A very important true statement. Proposition A less important by still interesting statement. Lemma A true statement used to prove other statements. Corollary A simple consequence of a theorem or a...