Math and programming and coding are actually closely related. In fact, many people think programming is just a more technical form of math. But the truth is that coding can be much easier if you understand some basic math concepts.
If you are new to the term mathematical programming and wish to learn more about this field of science, here are a few short points you should know.
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The difference between mathematical and computer programming
While computer programming includes the use of computer algorithms to solve a certain problem, mathematical programming differs extensively. It can be used by students in many different fields such as data analysis, statistics and even business.
Math programming may seem overwhelming at first for those who struggle with college math. In order to learn programming, but had difficulties with mathematics, I could ask for help to solve my math problem, which helps me in understanding how to deal with a difficult mathematical task later. It helps make sense of the mathematics that will be used in coding. In addition, math learning improves the quality of thinking that is essential to programming.
Linear programming
Among several types of mathematical programming, Linear is one of the most commonly used. It is a method that allows one to achieve the optimum results when faced with a problem that has linear constraints. In its standard form, linear programming consists of three elements:
- Linear function
- Constraints
- Variables
To put this in a practical perspective, we can observe an imaginary farming problem that we should solve. A farmer could own a piece of land where he could plant corn, wheat, or a combination of these crops. There is a limited amount of fertilizers and pesticides that could be used, and each crop requires a distinctive amount of resources. To assure the maximum profit, we need to decide what crops to plant and the optimal ratio considering the constraints we have.
We could express our problem in linear form and use it to come up with the optimal farming decision.
Network flow programming
Network flow is a type of graph where both edges have a capacity and a flow. Also, each edge receives a flow, but it can’t surpass the capacity. Therefore, with network flow programming, the goal is to create a flow that is restrained by the edge capacity. There are numerous types of network flow problems, including the following:
- Maximum flow problem – When we need to maximize the total flow from source to sink terminal.
- Minimum cost flow – when we need to achieve maximum flow at the minimum expense.
- Multi-commodity flow – when we need to provide the flow of different commodities concerning the overall capacity.
- Nowhere-zero flow – where flow amounts must be non-zero values.
In real life, we have examples of network flow problems virtually everywhere. If a certain factory was to ship products to another town via intermediate cities, network flow could facilitate the shipping process. Using known constraints, the factory could decide the optimal shipping routes and packing methods. This way, the company would ensure that each shipment is being used to its full capacity at the minimum expense.
Nonlinear programming
This type of mathematical programming allows finding a solution to a problem constrained by nonlinear variables. This means that the changes in the input value of these constraints are not proportional to the changes in the output value.
Let’s say a certain company needs to make a transportation choice when there are multiple options available. A company could transport their goods via air, land, or sea, and for each of these options, there are subgroups of available options. Here, the decision-making process is not only restricted by the type of transport. The capacity of each transport choice and a series of other constraints determine the outcome.
Other real-life applications of nonlinear programming include the following activities:
- Data fitting
- Engineering design
- Process control
- Economic planning
One of the main uses for nonlinear programming is a convex optimization. It is a process of minimizing costs while maximizing revenue. A good example is flight scheduling. One needs to minimize the costs of fuel or crew while securing a maximum number of passengers. The same goes for inventory management, where we need to maintain a certain stock value while minimizing the costs.
Conclusion
Numerous online courses teach computer programming. Some people can even learn how to code on their own. When it comes to mathematical programming, the situation is difficult. You need strong control of mathematics to succeed in this area. However, once you master mathematical programming, you will never have to worry about making a wrong choice. This field of science will help you make the optimal decision using mathematical models and available data.
Author Bio:
Michael Stoddard is a freelance content writer engaged in tech and academic writing. His work is based on actual information from relevant sources. As a writer, Michael aims to deliver practical pieces of data that his audience can implement in everyday life.