Symbolic mathematical programs
|0 + 2||0 + 2||term grade||pure math.||mm1c2sp3m||3||optional|
Programming fundamentalsL (im1c1pn2)
Syllabus designed by:
Basics of programming.
- understand the concepts of symbolic algebraic systems;
- use these systems in their studies and in research;
- solve mathematical problems by applying symbolic computations.
By the end of this course, students will be able to
- A. Heck: Introduction to Maple. Springer, 3rd edition, 2003.
- A. Iványi (ed.): Algorithms in Informatics, Vol1, part II, Computer Algebra. 2007.
- Overview of symbolic algebraic systems. Introduction to symbolic and algebraic computations, Maple, Sage.
- Usage, tool structure, mathematical capabilities.
- Representing data and basic algorithms.
- Language structure: expressions, forms, patterns, procedures, input and output.
- Numbers, mathematical functions, polynomials and rational functions, solving equations.
- Numeric and symbolic operations.
- Elements of programming: language constructs, control flow, data types, tables and arrays, operators, memory representation.
- Drawing in 2 and 3 dimensions, graphics, animation.
- Library structure.
- The interactive shell.
- Programming language: assignments, arithmetic, functions, algebra and calculus, drawing.
- Python/Sage scripts, compilation, data types, tuples, tables, sequences, sets, iterators, control flow.
- Interfaces: PARI, GAP, Singular, Maxima.
- High precision computations, number theory, RSA, prime tests.
- Linear algebra, algebraic structures, graphs.