Introduction to Symbolic Mathematics (MAE644)

• Ελληνική Έκδοση
• Undergraduate Courses Outlines
• Outline Modification (available only for faculty members)
• Department of Mathematics
• Save as PDF or Print (to save as PDF, pick the corresponding option from the list of printers, located in the window which will popup)

General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Undergraduate
Course Code	MAE644
Semester	6
Course Title	Introduction to Symbolic Mathematics
Independent Teaching Activities	Lectures and laboratory exercises (Weekly Teaching Hours: 3, Credits: 6)
Course Type	Special Background
Prerequisite Courses	-
Language of Instruction and Examinations	Greek
Is the Course Offered to Erasmus Students	Yes
Course Website (URL)	See eCourse, the Learning Management System maintained by the University of Ioannina.

Learning Outcomes

Learning outcomes

The course is an introduction to symbolic mathematical computations (computer algebra) and programming using a language for processing symbolic mathematical expressions, such as Mathematica. The course examines basic concepts in symbolic algebraic computations and emphases is given on finding the solution of a problem in closed form (exact solution) as opposed to a numerical solution (approximate solution). Using a symbolic language the course examines tools / commands to solve problems from different areas of Mathematics (Calculus, Algebra, Geometry, Statistics, etc.) and how to graphically show the results of solving a problem. Also programming methods are examined which can be used for the solution of a problem in addition to using just ready commands. Much of the course is to present the possibilities and tools available in a programming language for symbolic processing of mathematical expressions. After completing the course the student: Has an understanding of the basic concepts of the symbolic processing of mathematical expressions. Can use software packages for symbolically processing mathematical expressions and design/implement procedures using these packages for solving a problem in a closed form. Can present and explain the solution to a problem using graphics.

General Competences

Working independently Teamwork Analysis of Problem Data Can use a computer algebra programming language to solve a problem and if possible to visualize data and solution. May solve problems in various disciplines with appropriate mathematical modeling.

Syllabus

1. Symbolic mathematical manipulation systems
2. Introduction to Mathematica
3. Representation of symbolic mathematical expressions
4. Numerical computations
5. Symbolic computations
6. Symbolic manipulation of mathematical expressions
7. Basic functions of Mathematica
8. Lists
9. Patterns and transformation rules
10. Input / Output and Files
11. Functions
12. Structures for program flow control (assignment, selection, loops, etc)
13. Programming with Mathematica
14. Graphics
15. Factorization
16. Solving equations and systems
17. Differentiation
18. Integration
19. Series
20. Linear algebra
21. Basic algorithms in symbolic mathematics

Teaching and Learning Methods - Evaluation

Delivery	Face to face
Use of Information and Communications Technology	Yes
Teaching Methods	Activity Semester Workload Lectures 39 Self study 78 Exercises, projects 33 Course total 150
Student Performance Evaluation	Written final exam (70%) comprising: questions about the processing of symbolic mathematical expressions using programming languages for this purpose Term project (teams) (30%) students in groups do a term project which basically consists of using Mathematica to work on a specific mathematical topic (presentation of concepts, problem solving, etc.)

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:

• SCHAUM'S MATHEMATICA, EUGENE DON, 2006, Publicer KLEIDARITHMOS (translation)
• Mathematics and programming with Mathematica, Karampetakis Nikolaos, Stamatakis Stylianos, Psomopoulos Evangelos, 2004, Publicer Ziti Pelagia & Co.
• Wolfram, S., The Mathematica Book, 5 Edition, Wolfram Media.
• Abell, M., Braselton, J., Mathematica by Example, 2d Edition, Academic Press, 1997.
• Gaylord, R., Kamin, S., Wellin, P., An Introduction to Programming with Mathematica, 2d Edition, Telos Springer-Verlag, 1996.
• Gray, J., Mastering Mathematica - Programming Methods and Applications, 2d Edition, Academic Press, 1998.
• http://www.wolfram.com/
• http://library.wolfram.com/