The role of mathematics in learning computer science
Baydjanov Maksudbek islamdjanovich (PhD),
Vice-rector for Academic Matters
Radjikhodjaeva Elvira Rashidovna,
Head of “Information Technology” department “Информационные технологии”
Chay Zoya Serggevna (PhD)
Associate professor of “Information Technology” department
The things of this world cannot be made known
without a knowledge of mathematics.
Roger Bacon
There are important innovations in technology, which are often based on new algorithms and mathematical theorems, even from abstract areas of mathematics. Mathematics plays an important role in computer science, providing fundamental tools for developers and professionals working with computer systems and algorithms. One of the key areas where mathematics finds application is in algorithmic thinking.
Developing efficient algorithms requires an understanding of mathematical concepts such as logic, discrete mathematics, and graph theory. Mathematical methods help analyze the complexity of algorithms and optimize their performance. Without mathematical knowledge, it is impossible to solve problems related to information retrieval, automatic text processing and bioinformatics, as well as to develop software systems and create Internet services. One of the directions in the field of computer science is “new mathematics” for working with large amounts of data (Big Data).
The importance of mathematical knowledge for the training of engineering personnel in the field of information technology is associated with their widespread use in the study of general professional and specialized disciplines. Mathematical concepts are actively used in such subjects as “Fundamentals of Programming”, “Software Engineering”, “Network Information Systems and Information Systems Management”, “Computers and Network Technologies”, “Database Management Systems”, “Algorithmizing and Programming” and others.
Another important area where mathematical knowledge is needed is cryptography and information security. Mathematical algorithms are used to encrypt data and ensure the security of information systems. Knowledge of the laws of number theory and algebra allows you to develop cryptographic protocols and analyze their reliability against hacking.
Machine learning and artificial intelligence
Using mathematical analysis, models are created and optimized, gradients are estimated and differential equations are solved:
Optimization. Machine learning models are often optimized using gradient descent. The goal of such optimization is to find a set of model parameters that minimize a certain loss function.
Estimation of gradients. In the backpropagation algorithm, which is used to train neural networks, the gradients of the loss function relative to the network’s weights and biases are calculated using a chain rule.
Solving differential equations. Many problems in machine learning and AI involve solving differential equations that describe the rate at which a system changes over time. Solving these equations allows us to model a wide range of physical and biological systems, from the spread of disease to the behavior of financial markets.
Data science and data analysis
In this area, you also cannot do without mathematical analysis – it is used in the development of regression, classification and data clustering algorithms. Here are just a few examples of how different aspects of mathematical analysis allow you to solve applied problems:
Derivatives help you understand how a function changes depending on its input.
Integrals – allow you to calculate all accumulated changes in a function.
Multivariate calculus – used to analyze functions of many variables, which is important for understanding complex data sets.
Optimization – allows you to find the minimum or maximum of a function, or, in other words, the best solution to a problem.
Differential equations – help to model and predict complex events and processes.
Machine learning algorithms are based on mathematical models and statistical methods. Linear algebra, mathematical optimization, and probabilistic models play an important role in developing and improving machine learning models. In addition, mathematics is the basis for computer graphics and data visualization. Geometry and algebra are used to describe and display three-dimensional objects, and numerical methods help analyze and visualize complex data.
Thus, knowledge of applied mathematics becomes an important tool, providing the necessary tools and concepts for developing effective algorithms, ensuring information security, developing machine learning models and creating data visualizations. Mathematics education helps develop professional competencies among future information technology specialists, and also contributes to increasing the competence and success of computer science specialists.
And if we take such a mathematical discipline as probability theory and mathematical statistics, then today there is not a single area of human activity in which probabilistic statistical methods are not used. For example, only the Law of Large Numbers (LBN) is applied in business, banking, insurance, investing, business development planning and performance assessment, forecasting.
LBN is a law that allows you to understand what the most likely result of an experiment will be if it is carried out repeatedly, and the greater the number of such experiments, the closer the result will be to the mathematical expectation. Moreover, the LBN is a pattern that allows one to predict the outcome of complex events over a “long distance,” which is very important in predicting and assessing risks in any human activity.
In insurance, the LBN helps calculate the insurance bonus. Over a long period of time, even accidents obey this law. In medicine, statistics make it possible to identify the average incidence of illness by month and, depending on this, to develop supply standards for medical institutions.
Bernoulli’s law of large numbers proves that over a large number of experiments, the frequency of a certain event is equal to the probability of its occurrence. There is also the law of large numbers, in which the mathematical expectation can be many times very different from the average value of the exponential result (which happens very rarely).
Predicting future outcomes is not the only application of LBN!
Application in banking. If clients have collectively deposited a certain amount S into the account, then the bank keeps part of this amount ready in case clients want to cash out the funds, and puts part of it into turnover. The LBN allows you to calculate the share of funds that can be put into turnover. The percentage of customers who can simultaneously demand a refund is calculated, and based on this, the reservation rate is determined.
In lending – to justify the interest on the loan. According to the LBN, the bank can predict what proportion of borrowers will not repay a previously received loan, on the basis of which interest is assigned for the use of loan funds.
Mathematical disciplines are an integral part of education in the field of information technology. They are the basis for the successful study of other professional and specialized subjects. Knowledge in mathematics allows you to develop professional and general skills. Improving the mathematical education of future specialists in the IT field contributes to effective professional activity not only in the industrial sphere, but also in the social and research spheres. Understanding modern mathematics, mathematical methods and logical thinking allows you to successfully solve various applied problems.
Mathematics plays a central role in our daily lives. It penetrates into many areas of our activities, including the IT industry, artificial intelligence, finance, medicine and biology. Mathematics helps us create mathematical models for new technologies, allowing us to predict and optimize their behavior and effectiveness. This allows us to create more innovative and effective solutions.
Mathematical models play an important role in the development of new technologies and innovations. They allow you to predict the behavior of complex systems, analyze data and optimize processes. Thanks to mathematical models, we can create more efficient and safer technologies that will change the world around us.
