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| BILL5230 | Symbolic Mathematics and Programming | 3+0+0 | ECTS:7.5 | | Year / Semester | Fall Semester | | Level of Course | Second Cycle | | Status | Elective | | Department | DEPARTMENT of COMPUTER ENGINEERING | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | -- | | Co-Lecturer | None | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | This course aims to introduce the basic concepts of symbolic programming, including selected topics in symbolic algebra, expression parsing, function evaluation, expression formatting, formal grammars, expression derivation and integration, using the object-oriented and functional programming languages. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | represent mathematical notations in a programming environment | 1,3 | 1,3 | | PO - 2 : | develop formal grammars for various mathematical expressions | 1,3 | 1,3 | | PO - 3 : | write a content recognizer from some particular grammar | 1,3 | 1,3 | | PO - 4 : | write programs that format mathematical expressions in a more readable way | 1,3 | | | PO - 5 : | code math expression evaluators | 1,3,4 | 1,3 | | PO - 6 : | code the simplifiers and expanders for simple mathematical expressions | 1,3 | 1,3 | | PO - 7 : | code symbolic solvers for a simple system of linear equations | 1,3 | 1,3 | | PO - 8 : | write programs that take symbolic derivatives and indefinite integrals | 1,3 | 1,3 | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), PO : Learning Outcome | | |
| Mathematical notations: symbolic representations, function symbols, conceptual symbols, equations and variables.
Formal grammars: CFG notation, mathematical expression structures, expression parsing, procedural and data abstraction, content recognizers,
Expression formatting: Formatting concepts, latex language, PDF documents, a simple language for expression representation, expression formatters.
Expression evaluation: Evaluation methods, interpreters, symbolic algebra, the evaluation of mathematical expressions and functions, writing expression evaluators in the Java language.
Expression manipulation: Algebraic and symbolic simplification, the simplification and expansion of mathematical expressions, symbolic expression simplifiers and expanders.
Linear equations: The solution of systems of linear equations, symbolic equation solvers.
Derivation and Integration: Polynomial expressions, logarithmic expressions, trigonometric expressions, mathematical functions, symbolic derivators and integrators.
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Mathematical notations: symbolic representations, function symbols, conceptual symbols, equations and variables. | | | Week 2 | Mathematical notations: symbolic representations, function symbols, conceptual symbols, equations and variables. | | | Week 3 | Formal grammars: CFG notation, mathematical expression structures, expression parsing, procedural and data abstraction, content recognizers. | | | Week 4 | Formal grammars: CFG notation, mathematical expression structures, expression parsing, procedural and data abstraction, content recognizers. | | | Week 5 | Expression formatting: Formatting concepts, latex language, PDF documents, a simple language for expression representation, expression formatters. | | | Week 6 | Expression formatting: Formatting concepts, latex language, PDF documents, a simple language for expression representation, expression formatters. | | | Week 7 | Expression evaluation: Evaluation methods, interpreters, symbolic algebra, the evaluation of mathematical expressions and functions, writing expression evaluators in the Java language. | | | Week 8 | Expression evaluation: Evaluation methods, interpreters, symbolic algebra, the evaluation of mathematical expressions and functions, writing expression evaluators in the Java language. | | | Week 9 | Midterm exam | | | Week 10 | Expression manipulation: Algebraic and symbolic simplification, the simplification and expansion of mathematical expressions, symbolic expression simplifiers and expanders. | | | Week 11 | Expression manipulation: Algebraic and symbolic simplification, the simplification and expansion of mathematical expressions, symbolic expression simplifiers and expanders. | | | Week 12 | Linear equations: The solution of systems of linear equations, symbolic equation solvers. | | | Week 13 | Linear equations: The solution of systems of linear equations, symbolic equation solvers. | | | Week 14 | Derivation and Integration: Polynomial expressions, logarithmic expressions, trigonometric expressions, mathematical functions, symbolic derivators and integrators. | | | Week 15 | Derivation and Integration: Polynomial expressions, logarithmic expressions, trigonometric expressions, mathematical functions, symbolic derivators and integrators. | | | Week 16 | End-of-term exam | | | |
| 1 | Cohen, J. S., 2003; Computer Algebra and Symbolic Computation: Mathematical Methods, AK Peters, Ltd. 472 p. | | | |
| 1 | Tan, K. S., Steeb, W. H., Hardy, Y., 2007; SymbolicC : An introduction to Computer Algebra Using Object-Oriented Programming, Springer, Enlarged 2nd ed., 692 p | | | 2 | Heck, A., 2003; Introduction to Maple, Springer, 3rd ed., 848 p. | | | 3 | Geddes, K. O., Czapor, S. R., Labahn, G., 1992; Algorithms for Computer Algebra, 1st ed., 608 p. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 8 | 12/11/2015 | 2 | 30 | | Homework/Assignment/Term-paper | 10 | 19/11/2015 | 5 | 20 | | End-of-term exam | 16 | 06/01/2016 | 2 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 3 | 14 | 42 | | Sınıf dışı çalışma | 5 | 14 | 70 | | Arasınav için hazırlık | 15 | 1 | 15 | | Arasınav | 2 | 1 | 2 | | Ödev | 30 | 1 | 30 | | Dönem sonu sınavı için hazırlık | 20 | 1 | 20 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 181 |
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