1. Intro: about methods of algorithm design, analysis of algorithms,
    and  computational complexity of
    algorithms and problems
  2. Divide-and-Conquer: description of 
    the method, examples of problems and algorithms (see examples 12
  3. Greedy  method: description,
  4. Iterative improvement: descr., examples
  5. Dynamic programming: descr., examples  
  6. Backtracking: description, examples
  7. Branch&Bound: description, examples
  8. Linear programming: descr., Simplex algorithm, examples
  9. Selected advanced data structures
  10. NP-hard computational problems: lower bounds on time complexity, informally
    about P, NP and NP-hard problems;
  11. Methods of solving NP-hard problems:   heuristic algorithms,  approximation algorithms, randomized algorithms,
     parameterized algorithms, exact
    exponential algorithms, examples
  12. Example  problems and algorithms: advanced sorting & Heapsort, Quicksort;     selection problem & linear algorithms;        matrix multiplication & Strassen
    alg.; Discrete Fourier Transformation & FFT alg; string matching
    &  Knuth-Morris-Pratt;
     elementary and other graph problems and
    algorithms (searching a graph; topological sort; maximum
    flow & Ford-Fulkerson alg.; shortest paths &  algorithms of  Bellman-Ford,  and 
    ; selected problems from computational geometry.

Tutorial:  Students will  use
the topics given during the lectures to independently solve practical problems
(with the assistance of the
TAs if needed)
.  They will implement several
smaller programs (home works) as well as larger programs (seminars), and
present them at the tutorial.