M.Sc. in Informatics Engineering

Hellenic Mediterranean University

Applied Mathematics

Module Title: Applied Mathematics

Teaching hours: 52
Credits: 7,5
Semester: 1st
Instructor: Mageiropoulos Emmanouel Professor

Course Objectives

PART A .Review of Linear Algebra I
■  Linear  spaces (of finite dimension).and Matricial  Calculus
1 Linear independence and basis
2 Column space and  nullspace. .
3 LU  and QR   decomposition
4.1 Elimination matrices and LU decomposition
6.The Fundamental Theorem of Linear Algebra
7.Eigenvalues  and eigenvectors
8.Diagonalization  and powers of A
9 Symmetric matrices
10.Singular value  decomposition (Cholesky  factorization)

■ Algebraic derivation and special topics of Numerical Linear Algebra.
1.The SVD   Analysis
2.The Principal Axes Theorem and its Geometric interpretation.
3.The Least squares approximations
4.Useful  Inequalities
5,Review  of Comlex  Numbers & the  n Primitive Roots of Unity

PART B . Review of Probability Theory  I. 
1. Probability space , Conditional probability ,Independence  and Random variables
2. Examples of random variables
3. Expectation and moments
4.Function  of random variables
5 Joint statistics   and Conditional expectation
6. Gaussian random variables
7.Estimation  and Estimators
8. Markov chains. . . . . .

PART C.Some Important Distributions
1. Bernoulli trials
2 Binomial random variables
3 Geometric random variables
4 Poisson random variables
5. Poisson process
6. Uniform random variable
7. Exponential random variable
8. Gamma random variable

PART D. Basic Theory of the Discrete Fourier Transform
1.The Discrete vs the Continuous FT
2.The Fast FT (in the sense ofCooley & Tuckey)
3.The “Butterfly”  Flow Chart (in the sense of G.Strang)
4.Discrete Convolutions

PART E. Examples and Applications
(a) In  Greek and/or translated from the English edition
1.D.Karayannakis, “Introductory Linear Algebra & Applications”, Ziti press,2013
2.G.Strang, “Introductory Linear Algebra & Applications”, Crete University Press,2013
3.Hoel, Port& Stone,”Introductory Probability Theory”, Crete University Press, 2011
4.V.Dougalis, Noutsos & Hadzidimos,
(b)In English
Master Vibot  & Computer Vision Module: Applied Mathematics
Université de Bourgogne – IUT Le Creusot, Laboratoire LE2I, UMR CNRS 6306.

Short Description_Applied Mathematics.pdf