Mathematics BSc
Course description
2013.

Symbolic mathematical programs
Hours
lect+pc
Credits
lect+pc
Assessment Specialization Course code
lect/pc
Semester Status
0 + 2 0 + 2 term grade pure math. mm1c2sp3m 3 optional
applied math. mm1c2sp3a 3 compulsory
Course coordinator
Strong Weak Prerequisites
Practice class
Strong:
Strong:
Algebra2L (mm1c1al2)
Prerequisites
Basics of programming.
Course objectives
By the end of this course, students will be able to
• understand the concepts of symbolic algebraic systems;
• use these systems in their studies and in research;
• solve mathematical problems by applying symbolic computations.
Literature
• A. Heck: Introduction to Maple. Springer, 3rd edition, 2003.
• A. Iványi (ed.): Algorithms in Informatics, Vol1, part II, Computer Algebra. 2007.
Syllabus
• Overview of symbolic algebraic systems. Introduction to symbolic and algebraic computations, Maple, Sage.
• Maple:
• 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.
• Sage:
• 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.
• Case studies:
• High precision computations, number theory, RSA, prime tests.
• Linear algebra, algebraic structures, graphs.