Introduction to Computational Mathematics (MAE742A)

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School of Science

Academic Unit

Department of Mathematics

Level of Studies


Course Code




Course Title

Introduction to Computational Mathematics

Independent Teaching Activities

Lectures (Weekly Teaching Hours: 3, Credits: 6)

Course Type

Special Background

Prerequisite Courses -
Language of Instruction and Examinations


Is the Course Offered to Erasmus Students

Yes (in English)

Course Website (URL) See eCourse, the Learning Management System maintained by the University of Ioannina.

Learning Outcomes

Learning outcomes

Science is based on two major pillars, both theoretical and experimental. However, over the last few decades scientific computing has emerged and recognized as the third pillar of science. Now, in most scientific disciplines, theoretical and experimental studies are linked to computer analysis. In order for the graduate student to be able to stand with claims in the modern scientific and work environment, knowledge in computational techniques is considered a necessary qualification.
The course aims to introduce the student into the field of computational mathematics, emphasizing the implementation of numerical methods using computers. The student will be able to familiarize himself with Matlab and Python programming languages, the most widespread for performing scientific calculations. Working autonomously and in groups, the student will be required to implement computational methods related to the fields of numerical analysis and numerical linear algebra.
Specifically, the objectives of this laboratory course are:

  • Familiarity with Matlab and Python programming languages to implement numerical methods and graphical design of the numerical solutions
  • Implementation of polynomial interpolation and function approximation
  • Apply numerical integration
  • Solving linear and nonlinear equations
  • Solving systems of linear equations
  • Study of direct and iterative methods.
General Competences

The course aims to enable the student to:

  • Search, analyze and synthesize data and information, using the available technologies
  • Work autonomously
  • Work in a team
  • Promote free, creative and inductive thinking


  • Vector and matrix definition and calculations
  • Basic commands and functions
  • Graphic representation of the numerical results
  • Polynomial interpolation: Lagrange Method, Newton's Method
  • Numerical integration: Simple and generalized types of numerical integration, rectangular rule, trapezoid rule, Simpson rule, Gauss integration
  • Numerical solution of non-linear equations: iterative methods, bisection method, fixed point method, Newton's method
  • Numerical solution of linear systems - Direct methods: Gauss elimination, LU decomposition.

Teaching and Learning Methods - Evaluation


In the laboratory

Use of Information and Communications Technology Use of scientific computing software packages
Teaching Methods
Activity Semester Workload
Lectures 39
Study of bibliography 39
Laboratory exercises 39
Home exercises (project) 33
Course total 150
Student Performance Evaluation
  • Weekly assignments
  • Final project
  • Written examination at the end of the semester

Attached Bibliography

See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:

  • Introduction to Numerical Analysis, G.D. Akrivis, V.A. Dougalis, 2010 (in Greek).
  • Numerical Linear Algebra, V. Dougalis, D. Noutsos, A. (in Greek).
  • A Primer on Scientific Programming with Python, H. P. Langtangen, Springer-Verlag Berlin Heidelberg, 5 Edition, 2016.
  • Programming for Computations- MATLAB/Octave, S. Linge, H. P. Langtangen, Springer International Publishing, 2016 (in Greek).