Creative programming. Assessing and improving mathematical algorithms with students

Abstract

Mathematics and algorithms have a common history dating back to ancient times. Since the
beginning of mathematics, with the theorems, concepts, and definitions of mathematics, we also find
algorithms that accompany many of the oldest proofs of mathematics, such as Euclid's Algorithm, the Sieve
of Eratosthenes, etc. Mathematics and algorithms are two highly intertwined disciplines that form the
backbone of today's modern science and technology. While mathematics provides the theoretical framework
for understanding abstract concepts and solving complex problems, algorithms provide practical methods
for applying mathematical ideas and solving real-world problems efficiently. Nowadays, with the rapid
development of technology, the advancement of computing skills, and the use of artificial intelligence,
mathematics is helping the development of algorithms, and algorithms are also helping mathematicians
understand the most complex and difficult mathematical problems, including working on conjectures. In the
process of developing a computer program, for example, Python, it is very important for students to
understand that everything starts with math and reasoning to reach a clear and complete understanding of
the problem, then the process of solving the problem and writing codes in any language, Python, Java, C++,
Basic, etc. In this article, we will consider one of the oldest and most popular problems in mathematics, the
Euclidean algorithm, solved in different Python programs to check the complexity time for each and
encourage students to do creative programming.