Mathematics, as a discipline, is one of the fundamentals of computers. It is one among the vital elements applied in computer science and its studies. It could be said that these two fields are tangled, and one is non-existent without the other. How is this so? Many Computer operations and functions heavily rely on mathematical understanding for programming. In addition to that, it is also true that computers use binary digits and heavily depend on algorithms, which cannot be achieved without employing the use of mathematics. This essay is going to explain different scopes and impact of mathematics on computer science. These include programming techniques in both mathematics and computers that are applied in computer graphics, game playing for maths learning, the impact that modern maths has had on computer games, computer support for mathematics learning and finally logic, maths and sets for computing.
Thesis: Mathematics and computers are intertwined in that, mathematic improves the understanding of computer, and computers improve the understanding of mathematics.
One of the ways mathematics relates to computers is through computer programming skills, computer graphics, and programming language. In the contemporary world, the involvement of mathematical ideas plays a major role in forming the framework for comprehending certain mathematical concepts in computer graphics. For instance, Coding language learners experiment and explore programming languages and data through mastering of mathematical skills. This approach demystifies both the application of maths and shows how relevant it is to the concept of 2D and 3D computer graphics. The use of these concepts helps in understanding geometric transformations to visualize 2D and 3D graphic scenes (Vince 158). Geometry is a basic mathematical unit taught to students at many academic levels. It gives students the ability to translate, scale and rotate an object at different angles with the use of a computer. These transformations are later presented in different ways, which involve both mathematical calculations, such as matrices and complex transformations. For instance, understanding or mathematics helps the computer programmers to "transform the geometry of the problem into a much simpler domain defined around the origin of the coordinate space" (Comninos 173) Therefore, applying geometry to computer graphics gives meaning to students with a minimum prerequisite mathematical knowledge.
The other technique that shows the relationship between maths and computers is the computer programming languages. Mostly used programming languages such as C and C++ engage mathematical concepts in their coding (Comninos 441). The use of binary codes and other coded formulas help to have a clear understanding of how data is written, fetched and transferred to the computers. Examples of these codes are the 4-bit, 8-bit and 16-bit binary codes, which have frequently found use in solving algorithmic problems. Using many of these codes aids to experiment with different computer programs and also exploring data, and hence mastering techniques used in mathematics.
Another way that mathematics impact computers is by computer support for learning mathematics. Various studies have shown that the essence of this is to create a conducive learning atmosphere that is centered on recreational studying objects to inspire learners to develop a positive attitude towards math. Interactive Instructors of Recreational Mathematics (IIRM) software is a software that was developed to serve this purpose. This has been effective especially with the incorporation of playful learning objects that are meant to enhance the learner's mathematical knowledge and promote positive maths attitudes (Fengfeng and Grabowski 256; Lopez-Morteo and López 639).
Electronic learning of mathematics is a more effective method of learning compared to the traditional one. This learning environment provides a cooperative workspace that is designed for interaction between learners, as well as learners and their workspace. Since this invention was meant to enhance mathematical skills using computer-based materials, students have been able to develop gradually a wonderful mathematical thought. For instance, argues that Teams-Games-Tournament (TGT) Corporation promotes higher positive maths attitudes compared to the interpersonal competition, but not in enhancing maths performance (Fengfeng and Grabowski 257). Moreover, the introduction of playful learning tools has proven to be a more fun and interesting way to learn.
Computer and maths connection is evident in how the use of computer games and other interactive programs helps students to develop a more positive approach towards mathematics. With this type of learning, students understand how important mathematics is and how significant it is to their everyday life. For instance, "can motivate learners through fantasy, being contextually relevant and appropriately difficult" (Fengfeng and Grabowski 257). Such approaches, when directly applied to formal education can be of great benefit in improving students' performance in mathematics. Moreover, providing them with motivational elements is one among many useful ways that students can be helped, not only to develop a good learning culture towards mathematics but also other subjects in general.
Research has shown that for years, mathematics and maths related subjects have recorded the lowest performance in the education system (Lopez-Morteo and Lo´pez 619). For this reason, various solutions had to be sought after to foster the learning of mathematics. With all the propositions that were tabled, incorporating computer games was seen as a powerful and effective tool to nurture mathematics learning. The reason for this choice was that computers were seen to have great appeal to motivate learners when used in classrooms. Gaming, as opposed to what others think, has more positive effects on learning. It is known to facilitate the rate of thinking and finding a different approach to solving problems. As mentioned in the journal, Game playing for maths learning, "Mathematics literature has acknowledged the positive effects of cooperative learning in improving achievement, attitudes, [and] higher-order thinking skills" (Fengfeng and Grabowski 250). This illustrates that effective gaming participants, especially the TGT, recorded greater performances and improvement in attitudes towards maths than the non-gaming students. However, students may have individual differences in socio-economic status, gender, and ability in math, involving computers in learning has increasingly developed students' positive attitude towards mathematics (Fengfeng and Grabowski 256). Furthermore, the use of computer games in studying mathematics also benefits those students who are disadvantaged socio-economically
Integration of games to learning institutions has remarkably assisted in reforming the educational system. For instance, the use of modern mathematics on computer games has proven to be an effective tool for learning. This has been so especially in teaching complex and difficult to grasp procedures. Reinforcing skills for mastery, adopting multiple ways of learning, creating personal satisfaction and motivation and providing interactive ways to make decisions, are some of the ways the learning procedure has been made more understandable.
Incorporating DimensionMTM games, for instance, had incredible effects on students' motivation. According to Kebritchi et al. students like playing these games for various reasons. One reason is that the game changed students' class environment, entertain and alter their moods. They have also found solving problems and learning maths in these games to be attractive (Kebritchi et al. 435). Besides, they have found the challenges, exploration and adventure traits of the game to be utterly interesting. However, prior knowledge of maths, computer and English language does not count at the end in motivating learners who participates in playing these games (Kebritchi et al. 436). Gradually, those students with a minimum knowledge of both maths and computer skills were able to learn and gain the required skills. Surprisingly, the results indicated that the performance of students who had less passion for mathematics was comparable or even higher than those that had prior knowledge of it.
Others studies have suggested that the study of information science and computers requires basic mathematic tools for both critical thinking and logical calculations. According to Makinson, there are two aspects of mathematical language: the qualitative and quantitative thinking. As a quantitative part, maths language is equipped with principles that involve probability and counting. The qualitative part, on the other hand, involves itself much with concepts such as induction, relation, functions and an extensive array of sets and logics (Makinson 123). The concepts of recursion and induction, for instance, are widely employed in computer science. Induction plays a role in proving facts (sets) about positive integers while recursion defines functions (sets) on the equivalent topic.
In addition to sets, more mathematic tools and methods such as combinatorics and propositional logic are employed in computing. Propositional logics, which can also be termed as quantificational, is a computing language used to express complex truth functions in a more possible and transparent way which can be understood (Makinson 238). Combinatorics, on the other hand, is useful in counting things. It deals with merging objects that are of a finite set through particular constraints like graphs. The correlation between mathematics and computers is again seen here since students can assimilate these mathematical concepts for computing to build a better understanding.
Conclusion
Works Cited
Comninos, Peter. Mathematical and Computer Programming Techniques for Computer Graphics. London: Springer Science & Business Media, 2010. Print.
Kebritchi, Mansureh, Atsusi Hirumi, and Haiyan Bai. "The effects of modern mathematics computer games on mathematics achievement and class motivation." Computers & Education 55.2 (2010): 427-443. Print.
Ke, Fengfeng, and Barbara Grabowski. "Gameplaying for maths learning: cooperative or not?" Br J Educ Technol 38.2 (2007): 249-259. Print.
Lopez-Morteo, Gabriel, and Gilberto López. "Computer support for learning mathematics: A learning environment based on recreational learning objects." Computers & Education 48.4 (2007): 618-641. Print.
Makinson, D. Sets, logic and maths for computing. London: Springer, 2008. Print.
Vince, John. Mathematics for Computer Graphics. 4th ed. London: Springer Science & Business Media, 2013. Print.
