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
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.