flynn017

As with Bull Graphs, House Graphs are simple graphs (not the Graph Theoretic definition) which have been neglected. They may not be interesting or yield any important findings to professional research mathematicians, but I haven't been able to find a paper or website which lists or shows any of the House Graphs properly at all. My intention is simply to state and prove of these properties. Please note I'm not a professional mathematician and I'm not even studying for a Mathematics degree (Computer Science), and therefore may make mistakes or misunderstandings. There are two main variants of House Graphs, and in this article I will listing the Vertex Colouring and Edge Colouring properties of such graphs. The two graphs are the House Graph and the House-X Graph. House Graph House-X Graph Both of the graphs are simple graphs, and the same number of vertices. In terms of the structure of the graph, the only difference between the graphs are the number of edges. The number edge...

This post is a little irrelevant to general contents of my blog, but I found this to be a interesting geometry problem and it does have some ties with Computational Geometry, which is form a of theoretical computer science. There is additionally some connection with Computational Complexity Theory too. The Bin Packing Problem isn't difficult to explain, and yet can be difficult to find a optimal solution. With Discrete Mathematics, I personally find that the branches within this field are more accessible but the problems are difficult enough to be interesting and form a field of serious mathematical study. I'm only a amateur mathematician and a student, so if there are any problems then please highlight them in the comments section. Bin Packing Problem: The Bin Packing Problem is an example of a optimization problem which has a surprisingly large number of applications, especially in logistics and data management. The Bin Packing Problem asks to minimize the number of bins need...

I thought I would create a list of Maths topics which were relevant for those who are wishing to study Computer Science. I've seen most people on online communities referring to topics which have very little relevance or completely pointless in relation to Computer Science. This list is based upon my experiences and a friend who studies Computer Science at University. I've listed the most popular Computer Science fields and their Maths topics below. General Computer Science: These are the topics which you will typically study in your first year, and therefore will have to do. Graph Theory Linear Algebra (Matrices and Vectors) Calculus I and maybe some Calculus II  Analytical Geometry Set Theory Big O Notation Radicals, Logarithms and Polynomials Logic Computer Graphics:  I'm not too sure about Graphics, but these are the subjects which do have some relevance. Fractal Geometry Linear Algebra Analytical Geometry Differentiable Geometry Hyperbolic Geometry Differential Equati...

Graph Theory Related Concepts: Before explaining the concept of Red and Black Trees and some of the algorithm analysis related to Red and Black Trees. It's best to have a understanding of some basic Graph Theory, such as what is a tree and the colouring nodes (or vertices). Graph Theory is my favorite area of Mathematics, and has many applications in Computer Science and other subjects. Graph Theory is a very visual form of Mathematics, much like Geometry, and for those who enjoy those types of Mathematics may also enjoy Graph Theory. A graph G is a ordered pair (V,E), with V being the graph's set of vertices and E being the the graph's set of edges which connect each vertex. Most graphs will have this basic structure, and it's the connections within the vertices which give graph their interesting properties. Hypergraphs are very interesting type of graph in my opinion, and sit between the boundary of Set Theory and Graph Theory. I may talk about more in the future. Hy...

This is going to be a short description of the difference between P and NP time complexity classes, and what the time complexity classes are based upon. These are used for Computational Complexity and Algorithm Analysis. Computability Theory is mainly concerned with what is computable, rather than how feasible that computation is. The P and NP time complexity classes are commonly based upon Deterministic and Non-Deterministic Turing Machines. These machines use similar mathematical notation to other models of computation, but are slightly more complex and have a larger application to other areas of Computer Science, and that is one of the reasons why I prefer to look at Turing Machines rather than Finite-State Automata. The P complexity class is a class of decision problems (Yes or No on some input), which are solvable within Polynomial Time on a Deterministic Turing Machine. It is given by P(n) or just P , where is the number of inputs. On the other hand, NP is the complexity class o...

Automata are abstract models of automatic machines which tend to have a very limited number of states they can be in. We use Automata without even knowing it, the most common example I can think of is the use of compilers with programming languages. In this post I'm going to be looking at Deterministic and Non-Deterministic Finite State Automata, and Regular Languages. Firstly, I believe it would be best to give an introduction to the concept of Formal Languages which are processed by these abstract models of computation which represent real life computers in our modern age. All the Formal Languages are defined within the Chomsky Hierarchy, which defines which languages can be computed by which machines. It takes the following format. The hierarchy gives the types of languages classes, and what machines they can be computed by. For example, Finite Automata can only recognise Regular Languages and not Context-Free Languages. So what is the formal definition of a Formal Language? Reg...

I'm still in a hiatus at the moment, but I may write the occasional blog post now and again (during the hiatus) like in this example. I will be giving a brief insight into the concept of Qubits which is the analogue to Classical Bits (1's and 0's). The only real difference between the two types, is that Qubits can be manipulated and controlled by the laws of Quantum Mechanics such as Superposition and Quantum Entanglement; the Spin states are also of great importance here since the control of the Spin will help create strings of information which are studied in Quantum Information Theory. Before reading this post, I will assume you have some mathematical knowledge of Linear Algebra and Dirac Notation. Otherwise, I'll explain the concepts as a I write about the fundamentals of Qubits. Firstly, let's look at the concept of Spin. Spin is a very important concept for Qubits. Spin is the angular momentum of a particle intrinsic (property of itself) to it's body. Spin...