interested in the working of computer programs and systems
I am a student who has always been interested in the working of computer programs and systems, ever since middle school, I have tried to teach myself programming and coding languages. These past weeks my mathematics class had become very interesting when I learnt that mathematical induction is the technique used as the foundation of correctness proofs of computer programs. The mathematical induction technique is used to prove that a property P (n) holds natural for every natural number n.
This mathematical concept postulates that once we find the base number, then you can go as high as you want in establishing the subsequent steps. The first step is to prove that the base case property holds figure 0, then the second and subsequent stages called the induction stage shows that if a property contains a natural number n, then it holds for the next number n+1. The model then is used to establish the truth of the property for all the natural numbers that are greater than or equal to the starting number (Akosy and Bayram, 1996). I have used the mathematical induction technique in automatic bug fixing in computer programs.
The other concept that interests me is the analysis of algorithms which provides theoretical estimates for the resources needed by an algorithm that solves a given computational problem. The study of algorithms is yet another concept that I have used in computers in establishing the amount of time, storage and resources needed to execute a model. An efficient algorithm is one with small function values compared to the growth of the input. When doing run time analysis, this concept is used to gauge how long a program takes to execute.