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Master in Mathematics – MODULES

HOU > Master in Mathematics (MSM) > Master in Mathematics – MODULES

MSM70: FUNDAMENTAL THEORIES AND METHODS IN MATHEMATICS

Module code: MSM70

ECTS Credit Points: 30

Module Type: Compulsory

Year: 1st

Language: Greek

Module Outline

Module general description: The objective of the module MSM70 is to teach fundamental mathematical knowledge and techniques from Analysis, Linear Algebra, Probability Theory, and Statistics, in order for students to obtain the necessary foundations to successfully participate in the thematic units of the second term of studies. Lessons will focus on fundamental mathematical principles and familiarization with calculations.

Curriculum of the Module: In particular, the curriculum of MSM70 includes the following topics:

Metric spaces (topology of metric spaces, sequences, continuity). Complete metric spaces. Fixed point theorems. Completion of metric spaces. Normed vector spaces. Matrices. Eigenvalues – Eigenvectors. Linear Systems. Probability. Conditional probability and independence. Discrete random variables.

Learning Outcomes: Upon successful completion of the module MSM70 “Fundamental Theories and Methods in Mathematics”, students will have developed the following skills:

  • Knowledge and understanding of the fundamental topological properties of Metric Spaces, such as convergence, continuity, completeness, connectedness and compactness,
  • Knowledge and understanding of the fundamental theorems of Linear Algebra, in particular the theorems concerning the structure and properties of finitedimensional vector spaces, linear transformations, matrices, and linear systems of equations,
  • Ability to utilize the tools of Linear Algebra in modelling physical problems,
  • Ability to implement the aforementioned tools to solve linear systems of differential equations, study Markov chains, and in linear programming,
  • Knowledge of the fundamental concepts of Probability Theory and discrete random variables, and the ability to apply the theory in modeling physical problems,
  • Ability to make calculations using the forenamed mathematical tools.

General Learning Outcomes: Upon successful completion of MSM70, students will have obtained the following:

  • Comprehension of the basic mathematical theories,
  • Attainment of the necessary mathematical knowledge to successfully participate in the other thematic units of the curriculum

Subjects Covered:

  • Real Analysis
  • Linear Algebra
  • Elements of Stochastic Mathematics

Prerequisites: There are no prerequisite courses.

Evaluation: Students are assigned to submit six (6) written assignments during the academic year. The average grade of the six (6) written assignments, weighted at 30%, is taken into consideration for the calculation of the final grade. The grade of written assignments is activated only with a score equal to or above the pass level (≥5) in the final or resit exams.

The grade of the final or the resit exams shall be weighted at 70 % for the calculation of the final grade.

MSM71: MATHEMATICAL MODELS IN THE PHYSICAL SCIENCES

Module code: MSM71

ECTS Credit Points: 30

Module Type: Compulsory

Year: 1st

Language: Greek

Module Outline

Module general description: The module MSM71 aims to provide knowledge on mathematical methods and tools for the analysis of mathematical models in Physical Sciences and Modern Technology.

Curriculum of the Module: In particular, the curriculum of THE MSM71 includes the following topics:

Ordinary Differential Equations (ODEs) and Systems of ODEs: Qualitative theory. Phase plane, equilibrium point characterization, Bifurcations, Lyapunov method for studying stability, Sturm theory, Sturm Liouville boundary value problems (BVP).

Partial Differential Equations (PDEs): First order PDEs: Methods for solving linear and non-linear PDEs, classical solutions, weak solutions, shock waves. Second order Linear PDEs: classification, methods of solution: method of separation of variables, Fourier and Laplace integral transforms, Poisson Integral, Green’s method. Properties of harmonic functions. Extreme values theorems. Green’s function for BVPs.

Linear Operators: Duality and conjugate operators. Green’s method for BVPs with linear operator. Existence of solution via alternative Fredholm theorem.

Integral Equations of Fredholm and Volterra type: existence of solution via  alternative Fredholm theorem, or fixed point theorem, iterative methods (Successive Approximations, solvent kernel via iterative kernels or Fredholm determinants), Characteristic values and eigenfunctions. Separable kernels and symmetric kernels (Hilbert–Schmidt theory) Fourier and Laplace Integral transform methods. Transformation of integral equations to BVPs or to Initial Value Problems and vice versa.

Learning Outcomes: Upon successful completion of MSM70 “Mathematical Models in the Physical Sciences”, students will have developed the following skills:

  • Ability to investigate Boundary Value problems, involving Ordinary Differential Equations (ODEs) or ODE systems, to find a unique solution and determine its stability,
  • Ability to identify and categorize Partial Differential Equations (PDEs) and Integral Equations (IEs), in order to correctly solve them,
  • Ability to apply analytical methods for their solution, such as the Separation of Variables method wherever applicable, the use of integral transformations and the use of the fundamental solution of the corresponding Differential Operator,
  • Ability to investigate and find a subspace in which a problem defined by a general linear operator is solvable,
  • Ability to study a mathematical problem consisting of an ODE or a PDE and auxiliary conditions as to its well-posedness, i.e., the existence, uniqueness and stability of its solution
  • Ability to construct a consistent mathematical model to describe a physical process, such as equilibrium potential, diffusion of a substance, wave propagation, etc.,
  • and formulate the corresponding mathematical Boundary and/or Initial Value Problem,
  • Ability to construct the Green’s function of a Boundary Value problem, using analytical methods,
  • Ability to use the Green’s function in addition to the appropriate integral representations and transformations to solve a Boundary Value Problem.

General Learning Outcomes: Upon successful completion of MSM71, students will have obtained the following:

  • Ability to express a mathematical problem in mathematical terms,
  • Ability to organize and utilize the knowledge they have obtained through studying and solving individual problems.
  • Ability to comprehend and present the modern literature on PDEs, IEs, and their applications in the Natural sciences.

Prerequisites: There are no prerequisite courses.

Subjects Covered:

  • Methods for the Analysis of Mathematical Models in Science and Modern Technology
  • Differential Equations
  • Integral Equations

Evaluation: Students are assigned to submit six (6) written assignments during the academic year. The average grade of the six (6) written assignments, weighted at 30%, is taken into consideration for the calculation of the final grade. The grade of written assignments is activated only with a score equal to or above the pass level (≥5) in the final or resit exams.

The grade of the final or the resit exams shall be weighted at 70 % for the calculation of the final grade.

MSM80: COMPUTATIONAL METHODS AND SOFTWARE IN MATHEMATICS

Module code: MSM80

ECTS Credit Points: 20

Module Type: Compulsory

Year: 2nd

Language: Greek

Module Outline

Module general description: The principal aim of the module MSM80 is to provide the student with substantial experience in using scientific software packages for symbolic and numerical computations for teaching and research, in order to solve problems stemming from natural sciences corroborating a variety of analytical and computational methods.

Curriculum of the Module: In particular, the curriculum of MSM80 includes the following topics:

Introduction to basic software commands and the Wolfram Language: Definition of functions, symbolic and numerical computation of series and integrals.  Functions of several variables, derivatives and partial derivatives. Basic commands for graphical representations, plots of parametric curves in 2D and 3D. Basic commands for handling linear algebra problems (matrix calculus, determinants, eigenvalues and eigenvectors). Lists. Basic symbolic and numerical solving commands for ordinary differential equations. Introduction to the mathematical theory of dynamical systems – Study of non-linear phenomena using software (limit cycles and chaotic phenomena). Basic commands for the study of power series and Fourier series – Implementations of representations by using the software capabilities. Introduction to finite difference numerical methods for partial differential equations. Eigenvalue problems and studies with relevant software commands. Study of partial differential equations by using the software capabilities: Implementations of the representations of the solutions for elliptic, parabolic and hyperbolic equations – Nonlinear problems (nonlinear wave propagation phenomena, reaction-diffusion equations and relevant topics) – Calculus of variations and mathematical software. Integral transformations and mathematical software.

Learning Outcomes: The successful completion of the module MSM80 “Computational methods and software for Mathematics” provides the opportunity for the student to develop the following skills

  • Familiarization with the Mathematica software package and practical experience solving mathematical problems.
  • Ability to use the software to teach mathematics at various educational levels
  • Ability to study various linear and non-linear problems and solve them using the software.
  • Ability to use Fourier series methods and then numerical methods for solving ordinary differential equations.
  • Ability to use methods of dimensional analysis and perturbation theory to study otherwise unexaminable problems through the use of software packages.
  • Ability to utilize methods drawn from the theory of variations by solving boundary value problems for functionals.
  • Ability to develop the basic theory and methods of partial differential equations to solve problems primarily through the use of the software package.
  • Ability to solve numerical problems of partial differential equations through the finite difference method.

General Learning Outcomes: Upon successful completion of MSMB80, students will have obtained the following:

  • Ability to study and solve problems relating to the Natural sciences with various methods of applied mathematics,
  • Ability to utilize software packages for both teaching and research purposes,
  • Ability to organize and apply the knowledge they have obtained to solve individual problems.

By learning to use the software package, students will obtain a valuable asset for writing both their diploma theses and scientific papers in the fields of Mathematics and the Natural Sciences in general.

Subjects Covered:

  • Computational Mathematics (Numerical & symbolic computing techniques & methods using computing systems – packages).
  • Computational Applications in Mathematical Modeling.
  • Educational software.

Prerequisites: There are no prerequisite courses.

Evaluation: Students are assigned to submit six (6) written assignments during the academic year. The average grade of the six (6) written assignments, weighted at 30%, is taken into consideration for the calculation of the final grade. The grade of written assignments is activated only with a score equal to or above the pass level (≥5) in the final or resit exams.

The grade of the final or the resit exams shall be weighted at 70 % for the calculation of the final grade.

MSM81: HISTORICAL EVOLUTION AND MATHEMATICAL EDUCATION

Module code: MSM81

ECTS Credit Points: 20

Module Type: Compulsory for division C

Division: Mathematics Education

Year:2nd

Language: Greek

Module Outline

Module general description: The module MSM 81 aims to present the historical evolution of fundamental mathematical concepts as well as diachronic and contemporary trends in Mathematics Education.

Learning Outcomes: Upon successful completion of MSMB81 “History and Teaching of Mathematics”, students will have developed the following skills:

  • Ability to critically assess contemporary questions in Mathematics philosophy
  • In-depth knowledge of the evolution of mathematical concepts, structures, and fields
  • Knowledge of the factors driving the evolution of Mathematics

More particularly, learning outcomes are the following:

  • Ability to discern the differences between Logicism, Formalism, and Intuitionism, in addition to the influence of typical results of Logic on these philosophical schools of thought.
  • Ability to analyze issues of ontology connected with the schools of mathematical philosophical thought.
  • Ability to manage the truth values of mathematical claims within the philosophical school to which they belong.
  • Ability to relate philosophical questions about the nature of Mathematics to their teaching practice.
  • Ability to examine the structure of an axiomatic system, scrutinize its consistency, and understand the evolution of its axiomatic foundation.

Students are required to actively participate at two levels: a) in the search for reputable literature from free sources (open access journals) that supplements the arguments and critical assessment of their positions, and b) in the application of the knowledge they have obtained in practical teaching circumstances.

Students will obtain the ability to base their assertions not only on their existing experience, but also on references to reputable sources.

The unit offers students the opportunity to develop their ability to manage the knowledge they have obtained, edit scientific papers, and write critical, scientifically documented assertions.

Furthermore, students shall become acquainted with assessing scientific papers drawn from journals and drawing key positions and conclusions from them.

To better connect the aforementioned subjects, students will write “case studies”.

Finally, a separate part of the unit dedicated to the interaction between modern Mathematics and Cognitive Science.

Subjects Covered:

  • Historical Evolution of Fundamental Mathematical Concepts
  • Diachronic and Contemporary Trends in Mathematics Education
  • Foundations of Mathematics & Modern Mathematical Theories

Evaluation: Submission of six (6) written assignments during the academic year, the weighted average grade of which constitutes a 33 percent of each student’s grade, if a pass grade (≥5) is obtained in the final or resit examination. The grade of the final or the resit exams is weighted at 67% for the calculation of the final grade.

MSM82: APPLIED MATHEMATICAL MODELING

Module code: MSM82

ECTS Credit Points: 20

Module Type: Optional Mandatory (Students choose between course modules MSM82 and MSM84)

Division: Applied Mathematics

Year: 2nd

Language: Greek

Module Outline

Module general description: The course aims to give students a detailed and practical introduction to basic concepts of Mathematical Modeling and specifically to the concepts of dimensional analysis, scaling, perturbation methods (regular perturbation methods, multiple scales methods, boundary layer method) with the use certain case studies. Additionally the process of mathematical modelling is applied to present the basic concepts of acoustic scattering and tumor growth, as well as the application of electroencephalography (EEG) and magnetoencephalography (MEG). Finally an introduction of the basic concepts of simulation and the programming package OCTAVE is presented.

Curriculum of the Module: The curriculum of MSMΒ82 includes the following topics:

  • Introduction to Mathematical Modelling. Basic Concepts.
  • Methods of Mathematical Modelling, Dimensional Analysis, Scaling,
  • Perturbation Methods (Regular Perturbation Methods, Poincare Lindstedt Method, Multiple Scales Method, Boundary Layer Theory). Applications Mathematical Models for Diffusion Phenomena.
  • Distributions, Green’s functions, PDE’s of 1st order, Shocks, Mathematical Modelling of Traffic Flow.
  • Euler’s equations for fluid motion. Derivation of Helmholtz equation. Acoustic Scattering integral representations, Basic Theorems, Low Frequency Scattering
  • Mathematical models for Electroegephalography (EEG) and Magnetoencephalography (MEG).
  • Basic concepts on simulation. Discrete and Continuous models. Simulation Algorithms.
  • Language Programming OCTAVE (MATLAB)

Learning Outcomes:  Upon successful completion of MSM82 “Applied Mathematical Standardization”, students will have developed the following skills:

  • Ability to describe in mathematical terms processes that occur in problems of physics, the biomedical sciences, and continuous-medium engineering.
  • Ability to identify and express the dominant mechanisms of physical and biological phenomena, including fluid flow, blood flow, electrochemical nerve impulses, cancer tumor growth, etc.
  • Ability to analyze, reproduce, and develop mathematical models related to the Natural Sciences, Medicine and Technology, through applications in wave propagations and scattering as well as heat and mass transfer.
  • Ability to apply analytical methods to solve mathematical problems that express phenomena (separation of variables, techniques for solving integral equations, perturbation methods, calculus of variations, etc.)
  • Ability to perform parametric studies and draw conclusions regarding model stability and accuracy
  • Ability to use mathematical packages (e.g. Mathematica, Matlab, etc.) to validate obtained results, make predictions, and further develop a mathematical model or investigate a process.
  • Ability to construct simulation models in Octave-Matlab
  • Ability to evaluate a mathematical model through estimation of its solution as derived from its analytical and/or numerical processing and from the corresponding simulation model.

General Learning Outcomes: Upon successful completion of MSM82, students will have:

  • Obtained incentives for research in mathematical physics, continuum mechanics, and mathematical standardization
  • Obtained experience and the ability to apply mathematical methods in the standardization of processes from various scientific fields
  • Learned to identify the mathematical model that exists within a physical process or phenomenon
  • Obtained the ability to present a scientific paper or conclusion to both a scholarly and a general audience.
  • Learned to communicate with scientists and mechanics from various different fields

Subjects Covered:

  • Mathematical modelling
  • Simulation
  • Applications of mathematical modelling in Science, Medicine, and Technology

Prerequisite Courses: Successful completion of MSM71.

Evaluation: Students are assigned to submit six (6) written assignments during the academic year. The average grade of the six (6) written assignments, weighted at 30%, is taken into consideration for the calculation of the final grade. The grade of written assignments is activated only with a score equal to or above the pass level (≥5) in the final or resit exams.

The grade of the final or the resit exams shall be weighted at 70 % for the calculation of the final grade.

Students have the right to participate in the final/resit exams if (a) at least 50% of the potentially excellent grade has been obtained when adding the total of the six (6) assignments and (b) at least four (4) of the six (6) written assignments have been submitted.

MSM83: ANALYSIS

Module code: MSM83

ECTS Credit Points: 20

Module Type: Optional Mandatory (Students choose between course modules MSM83 and MSM85)

Division: Pure Mathematics

Year: 2nd

Language: Greek

Module Outline

Module general description: The Module MSM83 discusses advanced elements of Functional Analysis and Operator Theory.

Curriculum of the Module: In particular, the curriculum of MSM83 includes the following topics:

Metric spaces (topology of metric spaces, sequences, continuity). Complete metric spaces. Fixed point theorems, Cantor, Baire. Completion of metric spaces. Normed vector spaces. Banach spaces. Continuous linear operators and linear functionals in normed spaces, norm of a linear operator, dual space and examples. Inner product spaces. Hilbert spaces (orthogonality, Riesz representation theorem, orthonormal bases). Linear operators on Hilbert spaces (adjoints, orthogonal projections, normal, hermitian and compact operators). Hahn-Banach theorem. Reflexive spaces. The principle of uniform boundedness. Open mapping theorem and bounded inverse theorem. Closed graph theorem. Locally convex spaces. Separation theorems. Continuous functionals in Schwartz spaces. Bounded linear operators on Βanach spaces (dual and compact operators). Banach algebras. Spectrum in Banach algebras. Ideals. Spectrum of bounded linear operators in Banach spaces (e.g point, approximate). Spectral theory of compact operators in Banach (or Hilbert) spaces. Unbounded operators in Hilbert spaces (closed, closable, symmetric, hermitian).

Learning Outcomes: Upon successful completion of MSM83 “Analysis”, students will have developed the following skills:

  • Knowledge and understanding of the fundamental theorems of Functional Analysis, such as the Hahn-Banach Theorem, the Homomorphic Barrier Theorem, and the Open Representation Theorem
  • Knowledge of the basics of the theory of normed spaces
  • Knowledge of the basics of the theory of classical Banach spaces
  • Knowledge of the basics of the theory of Hilbert spaces
  • Knowledge and comprehension of the basics of the theory of blocked linear operators in Hilbert spaces
  • Ability to apply techniques from Functional Analysis and Operator Theory to the study of problems from Differential Equation Theory

General Learning Outcomes: Upon successful completion of MSM83, students will have:

  • Understood the basic concepts and techniques of Mathematical Analysis
  • Obtained the ability to apply these techniques to problems in other fields of mathematics

Subjects Covered:

  • Elements of Operator Theory
  • Functional Analysis

Prerequisites: There are no prerequisite courses.

Evaluation: Students are assigned to submit six (6) written assignments during the academic year. The average grade of the six (6) written assignments, weighted at 30%, is taken into consideration for the calculation of the final grade. The grade of written assignments is activated only with a score equal to or above the pass level (≥5) in the final or resit exams.

The grade of the final or the resit exams shall be weighted at 70 % for the calculation of the final grade.

MSM84: STOCHASTIC MATHEMATICS

Module code: MSM84

ECTS Credit Points: 20

Module Type: Optional Mandatory (Students choose between course modules MSM84 and MSM82)

Division: Applied Mathematics

Year: 2nd

Language: Greek

Module Outline

Module general description: This course includes basic Probability theory and theory of Stochastic processes and also Applications in Stochastic Modelling.

Curriculum of the Module: A detailed description of the course content follows

  • Probability Theory: Random experiments and probability spaces, conditional probability and independent events, discrete and continuous random variables (rv), probability mass function and probability density function of a rv, cumulative distribution function, expectation and variance, the most important discrete and continuous random variables, distribution for a function of a rv, multidimensional rvs and distributions, independence of variables, covariance and correlation, generating functions, laws of large numbers, Central Limit Theorem.
  • Stochastic Processes: Stochastic processes in discrete and continuous time, with discrete and continuous values, Markov property, Markov processes in discrete and continuous time, transition and stationary probabilities, Poisson process, random walks, martingales, renewal processes.
  • Stochastic Modelling:
  • queuing models with one and multiple serves, exponential models, queueing networks,
  • reliability theory, structure functions, reliability of a system with independent components, system lifetime,
  • Brownian motion: definition and properties, application to gambler’s ruin problem, variations of Brownian motion, applications in finance.

Learning Outcomes: Upon successful completion of MSM84 “Stochastic Mathematics”, students will have developed the following skills:

  • Knowledge of the basics of Probability Theory: probability space, random variables, independence, the function of probability distribution, law of large numbers, central limit theorem,
  • Knowledge of the basics of stochastic process theory: discrete stochastic processes, Markov chains, random walks,
  • Knowledge of the basics of Stochastic Modelling theory: queueing theory, reliability theory,
  • Ability to apply their obtained knowledge in modelling of problems from other disciplines: finance, environmental sciences, engineering, etc.

General learning outcomes: Upon successful completion of MSM84, students will have obtained the following:

  • Knowledge of the basic concepts of Probability Theory and Stochastic Process Theory, and capacity to comprehend the stochastic modelling of problems from other disciplines.
  • Knowledge of the techniques necessary to construct and study stochastic models and ability to apply them in practice.

Subjects Covered:

  • Probability Theory
  • Stochastic Processes
  • Stochastic Modeling

Prerequisites: There are no prerequisite courses.

Evaluation: Students are assigned to submit six (6) written assignments during the academic year. The average grade of the six (6) written assignments, weighted at 30%, is taken into consideration for the calculation of the final grade. The grade of written assignments is activated only with a score equal to or above the pass level (≥5) in the final or resit exams.

The grade of the final or the resit exams shall be weighted at 70 % for the calculation of the final grade.

MSM85: ALGEBRA AND GEOMETRY

Module code: MSM85

ECTS Credit Points: 20

Module Type: Optional Mandatory (Students choose between course modules MSM85 and MSM83)

Division: Pure Mathematics

Year: 2nd

Language: Greek

Module Outline

Module general description: Module MSΜB85 discusses the basic elements of Number Theory and its applications in Cryptography, the basic elements of Group Theory and the theory of Euclidean spaces and their isometry groups.

Curriculum of the Module: In particular, the curriculum of the MSM85 includes the following topics:

Number Theory and Algebraic Structures

a). Euclidean Division  – Arithmetic Algorithms – Fast Multiplication – Greatest Common Divisor – Least Common Multiple – Euclidean Algorithm – Primes– Primitive Analysis and Applications.

b). Monoids – Groups – Subgroups – Cyclic Groups – Group Morphisms – Rings – Polynomials – Greatest Common Divisor – Euclidean Algorithm – Polynomial over a Field – Irreducible Polynomials.

c). Congruences – Linear Congruences – The Euler φ function – Order of an Integer mod n – Finite Fields.

d) Integer Factorization Algorithms – Primality Tests – Αlgorithms for the Computation of Discrete Logarithm.

Cryptography and Codes

Fundamentals of Cryptology – RSA, Rabin and  ElGamal cryptosystems – Digital Signatures RSA, Rabin and DSA – Diffie-Hellman key protocol– Error Correcting Codes – Linear Codes – Generator Matrices – Control Matrices – Decoding.

Affine Geometry

Affine Spaces – Barycenter – Affine Subspaces – Affine Frames – Affine Maps – Affine Groups – Multilinear Maps – Multiaffine Maps – Polynomial Curves – Berstein Polynomials – Bézier Form of a Polynomial Curve – De Casteljau Algorithm – Subdivision Algorithm –  De Boor Algorithm – Derivatives of Polynomial Curves  – Joining Polynomial Curves.

Learning Outcomes: Upon successful completion of MSM85 “Algebra and Geometry”, students will have developed the following skills:

  • Knowledge of the basic elements of Number Theory
  • Knowledge of the applications of Number Theory in Cryptography
  • Knowledge and comprehension of Group Theory
  • Knowledge of the structure of Euclidean spaces
  • Knowledge of the theory of the isometric groups of Euclidean spaces, in particular dimensions 2 and 3.
  • Ability to calculate and study groups of symmetries of simple geometric shapes

General Learning Outcomes: Upon successful completion of MSM85, students will have obtained the following:

  • Knowledge and comprehension of the fundamental concepts of Number Theory and its applications in Cryptography
  • Knowledge of the structure of Euclidean spaces and their isometric groups
  • Knowledge of the interaction between Group Theory and Geometry in the study of Euclidean Spaces

Subjects Covered:

  • Number Theory
  • Group Theory
  • Groups and Geometry

Prerequisites: There are no prerequisite courses.

Evaluation: Students are assigned to submit six (6) written assignments during the academic year. The average grade of the six (6) written assignments, weighted at 30%, is taken into consideration for the calculation of the final grade. The grade of written assignments is activated only with a score equal to or above the pass level (≥5) in the final or resit exams.

The grade of the final or the resit exams shall be weighted at 70 % for the calculation of the final grade.

MSM86 POSTGRADUATE THESIS

Module code: MSM86

ECTS Credit Points: 20

Module Type: Compulsory

Year: 2nd

Language: Greek

Module Outline

General Description: The purpose of the Module MSMDE is to synthesize knowledge acquired during the student’s studies, through the elaboration of the Postgraduate Diploma Thesis.

The topics of the Diploma Theses concern Mathematical Science and its Applications. They are related to the specialized cognitive areas of the five Modules of the postgraduate program MSM.  Also, topics can be proposed by both the Coordinators and the Instructors of the Program and they are subject to the approval of the Academic Committee of the Program. The approved topics are posted on the University’s website, before the beginning of the period of submission of the relevant statement by the students.

The M.D.E. can be theoretical-synthetic, applied-experimental or a combination of the two.

A) In theoretical-synthetic theses, students should understand a scientific topic or problem, applying for its study scientific knowledge and experience gained from the Study Program, in combination with a review of proposed literature. They should also be able to write their results and present them in public. .

B) In the applied – experimental projects, students should understand an applied scientific problem, present the tools and methodology for dealing with it and elaborate the process of solving it. They should also be able to write their findings and present them with scientific competence in public.

Therefore, the Module MSMDE, through the elaboration of the Diploma Thesis, provides the opportunity for synthesis and utilization of the knowledge acquired during the studies.

The scientific responsibility for preparing the D.E. is assigned to a three-member Evaluation Committee (EC), one member of which is responsible for the supervision and support of the student (Supervisor), in accordance with the prevailing ethics and scientific practice and respecting the principles of Open and Distance Education and Adult Education.

Learning Outcomes: Upon completion of the Module MSMDE, students will be able to:

  • Implement a literature review on a scientific topic in the area of Mathematics, using bibliographic sources and relevant search tools
  • search, collect, verify, process critically-synthetically and effectively present information
  • analyze a complex problem by identifying the basic knowledge and tools required to solve it.
  • plan the activities that lead to solving the problem, by synthesizing knowledge and skills from different subjects.
  • realize, evaluate and improve the solution to the problem.
  • cooperate smoothly in the context of scientific / research work, demonstrating responsibility and developing communication skills.
  • effectively and creatively utilize the online / digital tools / media for the writing / editing / publication of their texts.
  • write a comprehensive scientific dissertation, in which the problem, methodology and results of their work will be analyzed
  • Present and publicly support their work.

General Regulation for Preparing Graduate Dissertations in PC with an annual Module Correspondence

For more information regarding the Specifications – Useful Material for writing Master’s Theses and uploading a Thesis at the H.O.U. Repository, you can go to the Digital Training Area http://study.eap.gr and especially to the Program of Studies section.

Prerequisites: The presentation of the Postgraduate Thesis takes place after the successful completion of the program’s Course Modules.

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