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Introduction to Symbolic Mathematics (MAE644): Διαφορά μεταξύ των αναθεωρήσεων

Introduction to Symbolic Mathematics (MAE644): Διαφορά μεταξύ των αναθεωρήσεων

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(Νέα σελίδα με '=== General === {| class="wikitable" |- ! 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...')
 
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[[Undergraduate Courses Outlines]] - [https://math.uoi.gr  Department of Mathematics]
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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

  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

  • 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/
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