Introduction to Symbolic Mathematics (MAE644)

Undergraduate Courses Outlines - Department of Mathematics

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)	-

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

Symbolic mathematical manipulation systems
Introduction to Mathematica
Representation of symbolic mathematical expressions
Numerical computations
Symbolic computations
Symbolic manipulation of mathematical expressions
Basic functions of Mathematica
Lists
Patterns and transformation rules
Input / Output and Files
Functions
Structures for program flow control (assignment, selection, loops, etc)
Programming with Mathematica
Graphics
Factorization
Solving equations and systems
Differentiation
Integration
Series
Linear algebra
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. Additionally:

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/