SUGGESTED TALK TOPICS

Below you can find list of suggested talk topics for oncoming SMS session. That's only a set of problems, that seems to be intresting. In your talk it would be good to say something about algorithm's complexity - sometimes it will be the only truly mathematical aspect of your speech.

Introductory topics:

1. Definition of algorithm. Algorithm complexity.
   
2. Proofs of algorithm correctness.
   
3. Turing mashine.
   
4. ASorting algorithms.

Data structures:

1. Axiomatic approach to data structures. Examples.
   
2. Binary trees, binary tree lookup orderings. Binary search.
   
3. Basic data structures: list, heap, FIFI queue, priority queue.
   
4. BST and AVL trees.

Geometria obliczeniowa:

1. Convex hull problem. Graham algorithm, Jarvis march.
   
2. Voronoi diagrams.
   
3. Robot track planning.
   
4. Art gallery problem.

Graph theory:

1. Graph theory basics. Graph representation.
   
2. Minimal spanning trees..
   
3. Shortest path problem Dijkistra algorithm, Ford-Bellmann algorithm.
   
4. Maximal flow problem.
   
5. Graph coloring.

Differential equations:

1. Numerical methods od DE solving. Euler method, backward Euler method, Runge-Kutta methods. Complexity comparison of thee methods.

Artificial inteligence:

1. Neural networks.
   
2. Genetic algorithms.

Cryptography:

1. Mathematical background of cryptography. Euclidean algorithm. Finite fields. Chinese remainder theorem. Fermat's little theorem.
   
2. Diffi-Hellmann protocol. RSA algorithm.
   
3. Natural number factorisation.

Others:

1. Information theory elements. Entropy.
   
2. Polynomials multiplication methods. Karatsuba algorithm, FFT.

Literature:

1. Introduction to algorithms. Third edition. T. H. Cormen
   
2. Algorithms, 4th edition. Robert Sedgewick and Kevin Wayne'
   
3. Geometria obliczeniowa. Algorytmy i zastosowania. M.Berg, M.Kreveld
   
4. Metody Numeryczne. Postawy teoretyczne, aspekty praktyczne i algorytmy. E. Majchrzak, B. Mochnacki
   
5. Sieci neuronowe. S. Osowski
   
6. An introduction to neural networks. Ben Krose, Patrick van der Smagt
   
7. Cryptography and Data Security. Dorothy Elizabeth Robling Denning