Scientific Computing: Computational Sciences

The study of Computer Science isn't really the study of the science of computers. Some computer topics include hardware, programming, and algorithms. Some science topics include Physics, Chemistry, and Biology. Although different, computers are used in these science topics in real-life situations. It would make sense to call this Computer Science, the study of usage of computers in different sciences, but it isn't. It can, however, be thought of as computational science, which, again, is "concerned with constructing mathematical models and quantitative analysis techniques and using computers to analyze and solve scientific problems." Some real-life computational sciences include computational physics, chemistry, and biology.

Computational physics is "the study and implementation of numerical algorithms to solve problems in physics for which a quantitative theory already exists." The different theories based on mathematical modeling provide predictions of a system's behavior. Sometimes, the solution is hard to solve by hand, so a computer comes in place by approximating the solution. The numerical approximations are written as large, finite mathematical algorithms; the computer would perform the operations and approximate the solution and error.

Computational chemistry is "a branch of chemistry that uses computer simulation to assist in solving chemical problems." Theoretical chemistry methods are used, along with computer programs, to "calculate the structures and properties of molecules and solids." Sometimes, these problems can't be solved analytically. Computational results are obtained by chemical experiments, which can help predict chemical phenomena.

Computational biology involves "the development and application of data-analytical and theoretical methods, mathematical modeling and computational simulation techniques to the study of biological, behavioral, and social systems." Also known as bioinformatics, it uses biological data to develop algorithms and relations in different biological systems. The use of computers helped biologists store and access large amounts of data. Computational biology has been used in different ways such as sequencing the human genome, creating models of the human brain, and modeling different biological systems.

Computational sciences have helped scientists do many different things. Even though it involves similar ideas and concept, it can be used very differently in different fields.

Scientific Computing: Mathematical Analysis

Math used to be fun. The hardest thing about it was counting up to 100. The numbers also had weird shapes, so that also added to its difficulty. Then, we learned how to combine numbers in different ways: addition, subtraction, multiplication, and division. With these simple operations, you would think that it was all there was. Next thing you know, letters are added with the numbers, which was also known as Algebra. As you progressed through higher math and encountered weird symbols, which are still as unknown to me like the Egyptian Hieroglyphics, eventually, you encounter the highest level of math by the average student: Calculus, which helps enable you to solve real-life situations. After your last Calculus class, you would think there is no more math to learn. Nope. The math after Calculus is basically math problems that you will almost never encounter and use in your daily life. An example would be computational science.

Computational science is "concerned with constructing mathematical models and quantitative analysis techniques and using computers to analyze and solve scientific problems." It involves different theories to approach certain problems. Since math can be tedious to do by hand, computers are used to analyze mathematical models. Programs are made just so models can be studied by inputting different parameters. Some examples of different real-life models used include graph theory and mathematical optimization.

Numerical analysis is a very common method used in computational science. It is "the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis." Numerical analysis usually involves getting results that are not exact, since it is not always possible. It is more about obtaining approximate solutions. An example would be ; you would not get an exact number.

Related to computational science, there is also symbolic computation, also known as computer algebra. It is "a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expressions and other mathematical objects." The solutions are usually exact numbers with expressions that contain variables with no given value. An example would be the equality symbol:

Even though we almost never use higher level math, it is still applied in some fields or in some real-life situations without us even knowing it. Since we are in a computer-related field, it would be a plus if we can understand some simple mathematical models.