The course aims to thoroughly cover the basic principles and methods of calculus and linear algebra that are considered to be essential to the qualified financial analyst/ accountant today. In order to achieve this goal, this course develops aspects of algebra, analysis, and differential and integral calculus, which are the mathematical background of quantitative tools of modern financial and accounting theory.

,  Undergraduate 
(A+)
, Eastern Macedonia and Thrace Institute of Technologie

Christos Kourouniotis  Undergraduate 
(A+)
Department of Mathematics and Applied Mathematics, University of Crete

Numerical Analysis
Konstantinos Kleidis  Undergraduate 
(A)
Department of Mechanical Engineering, TEI of Central Macedonia
Errors calculations: Basic concepts, types of errors, error propagation in numerical calculations. Approximate expressions functions: The coincident polynomial and polynomials of Taylor and Mc Laurin, applications in numerical problem solving methods  complete functions in nonclosed form. Numerical solution of algebraic equations: Finding roots  method of regula falsi, method of NewtonRaphson. Numerical interpolation: Linear interpolation full insertion by the method of Newton. Dual linear interpolation. Numerical differentiation: Linear derivation, complete derivatization by means of coincident polynomial Newton. Numerical integration: trapezoidal method, method of Cotes. Numerical solution of firstorder differential equations: The method of Euler, the method of Taylor, the method of RungeKutta 2nd and 4th order.

Electrical Circuits
Anastasios Mpalouktsis  Undergraduate 
(A)
Department of Computer Engineering, TEI of Central Macedonia
Historical data. Conductors, insulators, semiconductors. Law of Coulomb. Maintaining cargo. Electric field. Electric field strength. Electric Resources.
Electric Current and Resistance. Law of Ohm. Connecting elements in series and parallel. Energy transfer to an electrical circuit. Notations electrical quantities. Units of measurement. Multiples and submultiples.
Signals and waveforms. Nonperiodic signals. Magazines signals. Modulated signals. Back & Active signal value. Electric circuit. Linearity, causality, temporal immutability.
Independent and dependent sources. Internal resistance. Log ideals sources. Connecting actual sources. Voltage divider. Divider current. Wheatstone Bridge.
Solving circuits. Laws of Kirchhoff. Process loops. Examples.
Process nodes. Examples.
Superposition theorem. Theorem of substitution. Theorem of Tellegen.
Theorems of Thevenin & Norton. Examples.
Solving circuits with dependent sources. Examples.
Transformations star  triangle. Maximum power transfer theorem. Straight burden and dynamic element resistance.
Complex resistors. Composite circuits. Voltage & Vectors intensity. Power in complex circuits. Examples.
Circuits coordination with passive components. In a series  parallel. Range transit zone. Quality factor. Frequency transfer function. Examples.
Time response circuits. Circuits RC. Circuit RLC.
Stability circuits.
Transformers. An ideal, real and hybrid transformer.
Graphic measurement performances. Errors of measurements. Straight least squares.
Detection Instruments. Gauges. Multimeters. Oscilloscope.

Linear Algebra II
Nikolaos Marmaridis, Ioannis Beligiannis  Undergraduate 
(A)
Department of Mathematics, University of Ioannina
Sum and direct sum of subspaces.
The polynomial rings R[t] and C[t].
Eigenvalues, eigenvectors, and eigenspaces.
Diagonalization and triangulation of endomorphisms and square matrices.
Minimal polynomial and the CayleyHamilton Theorem.
Applications to linear recurrent sequences, computation of powers and inverse of a matrix.
Symmetric bilinear forms and inner products.
Euclidean spaces.
Orthonormal bases and the GramSchmidt orthogonalization process.
Orthogonal subspaces and orthogonal complements.
Orthogonal matrices and isometries.
Adjoint of an endomorphism and of a square matrix.
Selfadjoint endomorphisms and symmetric matrices.
The spectral theorem for selfadjoint endomorphisms (Euclidean case) and symmetric matrices.
Geometric interpretation of isometries. Positive and nonnegative endomorphisms. Norm of a matrix.
Quadratic forms and principal axes. Classification of quadratic surfaces.
Hermitian spaces.
Hermitian and unitary matrices.
The spectral theorem for selfadjoint endomorphisms (Hermitian case) and Hermitian matrices.

Algebraic Structure I
Nikolaos Marmaridis, Ioannis Beligiannis  Undergraduate 
(A)
Department of Mathematics, University of Ioannina
Definition Grous  Groups transfers  Cyclic Groups  Generators  Lateral Classes  Theorem Lagrange  homomorphism Groups  Groups quotient  Rings and Bodies  Integral Locations  Theorems of Fermat and Euler  polynomial rings  homomorphism of Rings  Rings quotient

Basic introduction to agricultural experimentation. Introduction to Statistics. Descriptive Statistics. Theoretical probability distributions. Sampling distributions. Measures of dispersion. Estimation. Statistical Inference. Statistical significance tests. Hypothesis testing. Simple linear regression. Demonstrate use of statistical packages.

Group Theory
Nikolaos Marmaridis  Undergraduate 
(A)
Department of Mathematics, University of Ioannina
Groups, subgroups, cyclic groups, direct products, symmetric groups, conjugation, centralizer, normal subgroups, quotient groups, homomorphisms. Finitely generated abelian groups. Sylow theorems and applications. Semidirect and wreath products. Free and solvable groups. Upper and lower central series. Nilpotent groups.

With the help of computer and using the statistical program SPSS,
this course applies the statistical theory developed in the courses "Introduction to Statistics", "Statistical Inference" and "Regression and Analysis of Variance."
