Aims and Scope

To teach students the basic concepts in Probability, as well as essential techniques of Computational Mathematics.

 

Course Description

Part A, Probability: Sets, Definition and axioms of Probability, Permutations and combinations, Conditional probability, Random variables, Distributions.

Part B, Computational Mathematics: Solution of nonlinear equations, Solution of systems of linear equations, Polynomial interpolation, Numerical integration, Initial value problems for ordinary differential equations.

 

Learning Objectives

Upon successful completion of this course students are expected to:

·         Follow the concepts of experiments, events and probabilities. To calculate permutations and combinations. To compute conditional probabilities. To identify random variables as discrete or continuous, find the expected value and the variance of a random variable, and use basic distributions.

·         Be able to analyze and implement algorithms for finding roots of nonlinear functions, and for solving systems of linear equations. Use polynomial interpolation for the reconstruction of an unknown function whose graph passes through a given set of points. Evaluate definite integrals. Solve numerically initial value problems for o.d.e.’s.

·         Have acquired a solid mathematical background on the topics and the techniques discussed in this course, and be able to use them in order to solve applied problems.

·         Enhance their research and analytical thinking abilities.

 

Bibliography

In Greek:  

1.       Ουρ. Χρυσαφίνου, Α. Μπουρνέτας, Ε. Βαγγελάτου, Σημειώσεις Πιθανοτήτων και Στατιστικής, Αθήνα, 2006.

2.       P.G. Hoel, S.C. Port., C.J. Stone, Εισαγωγή στη Θεωρία Πιθανοτήτων, Πανεπιστημιακές Εκδόσεις Κρήτης, 2008.

3.       Γ.Χ. Ζιούτας, Πιθανότητες και στοιχεία στατιστικής για μηχανικούς, Εκδόσεις Ζήτη, 2004.

4.       Α. Μπράτσος, Εφαρμοσμένα Μαθηματικά, Εκδόσεις Α. Σταμούλη, Αθήνα, 2011.

5.       Γ.Δ. Ακρίβης, Β.Α. Δουγαλής, Εισαγωγή στην Αριθμητική Ανάλυση, Πανεπιστημιακές Εκδόσεις Κρήτης, 2008.

 

In English:

1.       S.M. Ross, Introduction to Probability and Statistics for Engineers and Scientists, 3^rd ed., Elsevier, 2004.

2.       S. Ross, A First Course in Probability, 8^th ed., Prentice Hall, 2010.

3.       R.L. Burden, J.D. Faires, Numerical Analysis, 9^th ed., Brooks/Cole, 2011.

3.       E. Süli, D. Mayers, An Introduction to Numerical Analysis, Cambridge University Press, 2006.