Using the Maple computer algebra system to study mathematical induction

Abstract

Mathematical induction is one of the main methods of the proof that students study and use it in their studies in higher education. This important method, in addition to mathematics, is widely used in computer science and a number of other related disciplines. However, even if the principles of proof using the method of induction are taught, understood and mastered by students well, many students have great difficulty with algebraic transformations necessary for proving, for example, finding the inductive step. The use of the Maple computer algebra system allows students to overcome this obstacle and, more attention and effort to pay to understanding the concept of proofs using the method of mathematical induction. In addition, students can prove more complex algebraic statements, and their activities can be of a pronounced research nature.

Increasing the competence of future economists to improve the effectiveness of training in the context of achieving the principles of sustainable development

“…Researchers also suggest that additional free time enables the teacher, depending on the level of students' training, to: pay more attention to the demonstration of the essence of the problem (Olenev et al, 2020); place additional emphasis on the sequence and logic of problem solution (Ochkov, Bogomolova, 2015), allocate more time to developing students' problemsolving skills by increasing the number of problems (Ochkov, Bogomolova, 2015), diversify the problem statement, show various possible formulations of one problem (Kramarski, Hirsch, 2003), demonstrate the solution of problems of increased complexity (Kramarski, Hirsch, 2003), explore non-standard approaches to problem analysis and show the equivalence of the obtained results (Taylor, 2008).…”

“…The pedagogical experience of using Mathematica (Chen et al, 2009), Maple (Olenev et al, 2020), MatLab (Zhaparov, Guvercin, 2012), and MathCAD (Abdullaeva, Sultonova, 2020;Etcuban et al, 2019;Lashchenko, 2020) environments shows that, as a rule, students do not need such multifunctional systems to conduct research in their specialty areas.…”

Inclusión educativa desde el enfoque de derechos humanos: propuesta pedagógica controversial

“…Permite al usuario obtener soluciones paso a paso para diversos problemas matemáticos, tales como álgebra, cálculo, matrices y ecuaciones diferenciales. Se puede trabajar en línea, desde una computadora o a través de una aplicación que se instala también en dispositivos móviles (Olenev et al, 2020).…”

Improving the Learning and Teaching of Mathematical Logic Elements Using Maple

“…Maple software is a computer algebra system (CAS, or Symbolic Algebra System [SAS]), in other words, a program that can represent information in symbolic or algebraic form. In addition, Maple CAS allows one to produce accurate analytical solutions to many mathematical problems (Kumar & Kumaresan, 2008;Olenev, Kirichek, Potekhina & Pelikh, 2020;Olenev, Shuvaev, Migacheva, Kulevskaya & Nazarenko, 2020;Shingareva & Lizárraga-Celaya, 2009). Currently, Maple is a robust system that can be used to solve almost any mathematical problem in a university course, and even more so in a school mathematics course.…”