This course is about numerical methods. We are NOT going to discuss ALL the theory related to numerical methods (for example how to solve differential equations). We are just going to consider the concrete implementations and numerical principles.
The first section is about matrix algebra and linear systems: such as matrix multiplication, gaussian elimination and applications of these approaches, such as Google's PageRank algorithm.
Then we will talk about numerical integration. How to use techniques like trapezoidal rule, Simpson formula and Monte-Carlo method - my personal favourite.
The last chapter is about solving differential equations with Euler's-method and Runge-Kutta approach. We will consider examples such as the pendulum problem.
Hope you will like it!
My name is Balazs Holczer. I am from Budapest, Hungary. I am qualified as a physicist and later on I decided to get a master degree in applied mathematics. At the moment I am working as a simulation engineer at a multinational company. I have been interested in algorithms and data structures and its implementations especially in Java since university. Later on I got acquainted with machine learning techniques, artificial intelligence, numerical methods and recipes such as solving differential equations, linear algebra, interpolation and extrapolation. These things may prove to be very very important in several fields: software engineering, research and development or investment banking. I have a special addiction to quantitative models such as the Black-Scholes model, or the Merton-model. Quantitative analysts use these algorithms and numerical techniques on daily basis so in my opinion these topics are definitely worth learning.