Undergraduate courses

MEM-101 Calculus I

  • Classification: Compulsory
  • Year/Semester: 1st/Fall
  • ECTS/Contact hours: 8/5
  • Lecture/Lab hours: 4/2
  • Prerequisites: None
  • Teaching method: Lectures, recitation sessions
  • Assessment method: Final examination, midterm exam

Course content

  • Sequences, limits of sequences, properties.
  • Functions, elementary functions, limits of functions, properties.
  • Continuity. The maximum value theorem. The intermediate value theorem.
  • The derivative of a function, properties. Chain rule, inverse function rule. The theorems of Fermat and Rolle, the mean value theorem. Higher derivatives. Graphing using first and second derivatives. L'Hôpital's rule.
  • Definite integrals, properties, examples.
  • Indefinite integrals, the fundamental theorem of calculus. Integration techniques. Applications in computing areas, volumes, etc. Improper integrals.
  • Series, convergence, absolute convergence. Convergence tests. Power series, radius of convergence. Taylor series.

Recommended Reading

  • R.L. Finney, M.D. Weir, F.R. Giordano. Thomas' Calculus. Pearson. 2002.
  • Mιχάλης Παπαδημητράκης. Απειροστικός Λογισμός. Σημειώσεις. Τμήμα Μαθηματικών, Πανεπιστήμιο Κρήτης, 2013.
  • Tom Apostol. One-Variable Calculus, with an Introduction to Linear Algebra. Wiley. 1991.
  • D. Hughes-Hallet, A.M. Gleason, W.G. McCallum. Calculus. John Wiley & Sons, Inc. 2012.

MEM-102 Geometry and Linear Algebra

  • Classification: Compulsory
  • Year/Semester: 1st/Fall
  • ECTS/Contact hours: 8/5
  • Lecture/Lab hours: 4/2
  • Prerequisites: None
  • Teaching method: Lectures, recitation sessions
  • Assessment method: Final examination, midterm exam

Course content

  • Geometric vectors in the plane, linear combinations, projection and inner product. Change of coordinate system, lines in the plane.
  • Vectors in space, cross product. Coordinate system, lines and planes in space.
  • Vectors, matrices, solution of systems of linear equations by elimination. Inverse matrices.
  • Linear subspaces of Rn. Linear independence. Bases. Linear transformations from Rm to Rn.
  • Norm and orthogonality. Orthogonal subspaces. Orthogonal projections.
  • Determinants, properties, techniques of computation, applications.
  • Eigenvalues and eigenvectors, matrix diagonalization.

Recommended Reading

MEM-103 Foundations of Mathematics

  • Classification: Compulsory
  • Year/Semester: 1st/Fall
  • ECTS/Contact hours: 7/5
  • Lecture/Lab hours: 4/2
  • Prerequisites: None
  • Teaching method: Lectures, recitation sessions
  • Assessment method: Final examination, midterm exam

Course content

  • Introduction to sets, relations, equivalence relations, functions.
  • Introduction to mathematical logic and mathematical proofs.
  • The natural numbers. Mathematical induction. The arithmetic of natural numbers, their ordering and well-ordering. The fundamental theorem of arithmetic.
  • Complex numbers, polar form, roots of unity, applications in trigonometry.
  • Finite sets and counting, introduction to combinatorics.
  • Introduction to cardinal numbers. Countable and uncountable sets. Cantor's diagonal argument.

Recommended Reading

  • I. Stewart and D. Tall. The Foundations of Mathematics. Oxford University Press, 2015.
  • Χρήστος Κουρουνιώτης. Θεμέλια των Μαθηματικών, Σημειώσεις.
  • Αντώνης Τσολομύτης. Σύνολα και Αριθμοί: Μία εισαγωγή στα Μαθηματικά. Leader Books, 2004. Κωδικός βιβλίου στον Εύδοξο: 50659157

MEM-104 Computer Programming I

  • Classification: Compulsory
  • Year/Semester: 1st/Fall
  • ECTS/Contact hours: 7/5
  • Lecture/Lab hours: 4/2
  • Prerequisites: None
  • Teaching method: Lectures, computer labs
  • Assessment method: Final examination, computer lab assignments

Course content

  • Structure and applications of a Computer.
  • Introduction to Linux operating system.
  • Basic programming principles and the Python computer language.
  • Data types (characters, integers, floats, boolean).
  • Flow control of a program (if-then-else commands). Loops (for and while commands).
  • Structured types and sequences (strings, lists, tuples).
  • Functions.
  • Files.
  • Modules and applications with Python using modules: math (mathematical library), pylab, matplotlib (plotting).

Recommended Reading

  • John V. Guttag. Introduction to computation and programming using Python. MIT Press, 2013.
  • Δημήτριος Καρολίδης. Μαθαίνετε εύκολα python. Εκδόσεις Καρολίδη, 2016.
  • Tony Gaddis. Starting out with Python. Pearson, 2015.
  • Ν. Αβούρης, Κ. Σγράμπας, Β. Πάλιουρας, Μ. Κούκιας. Εισαγωγή στους Υπολογιστές με τη γλώσσα Python Εκδότης Εταιρεία Αξιοποίησης και Διαχείρισης Περιουσίας Πανεπιστημίου Πατρών, 2η έκδοση 2013. Κωδικός Βιβλίου στον Εύδοξο: 33154040.
  • Γεώργιος Μάνης. Εισαγωγή στον προγραμματισμό με αρωγό τη γλώσσα Python. Εκδότης Ελληνικά Ακαδημαϊκά Ηλεκτρονικά Συγγράμματα και Βοηθήματα - Αποθετήριο "Κάλλιπος", 2016 (ηλεκτρονικό βιβλίο). Κωδικός Βιβλίου στον Εύδοξο: 320152
  • Κωνσταντίνος Μαγκούτης και Χρήστος Νικολάου. Εισαγωγή στον αντικειμενοστραφή προγραμματισμό με Python. Εκδότης Ελληνικά Ακαδημαϊκά Ηλεκτρονικά Συγγράμματα και Βοηθήματα - Αποθετήριο "Κάλλιπος", 2016 (ηλεκτρονικό βιβλίο). Κωδικός Βιβλίου στον Εύδοξο: 320102.
  • Hans Peter Langtangen. Python Scripting for Computational Science. Εκδότης Heal-Link/Σύνδεσμος Ελληνικών Ακαδημαϊκών Βιβλιοθηκών, 2η έκδοση 2006 (ηλεκτρονικό βιβλίο). Κωδικός Βιβλίου στον Εύδοξο: 174838.
  • Magnus Lie Hetland. Beginning Python. Εκδότης Heal-Link/Σύνδεσμος Ελληνικών Ακαδημαϊκών Βιβλιοθηκών (ηλεκτρονικό βιβλίο). Κωδικός Βιβλίου στον Εύδοξο: 170352.

MEM-105 Calculus II

  • Classification: Compulsory
  • Year/Semester: 1st/Spring
  • ECTS/Contact hours: 8/5
  • Lecture/Lab hours: 4/2
  • Prerequisites: MEM-101, MEM-102
  • Teaching method: Lectures, recitation sessions
  • Assessment method: Final examination, midterm exam

Course content

  • Circles, ellipses, hyperbolas, parabolas. Spheres, ellipsoids, cylinders, cones, paraboloids, hyperboloids.
  • Polar, cylindrical, and spherical coordinates.
  • Smooth curves, tangent vectors.
  • Functions of many variables, limits and continuity.
  • Partial derivatives, directional derivatives. Tangent planes, normal vectors. Higher partial derivatives.
  • Curves, velocity and acceleration vectors. Arclength.
  • Taylor's theorem. Extrema of real functions of many variables.
  • The implicit function theorem, the inverse function theorem. Constrained optimization, Lagrange multipliers.

Recommended Reading

  • J.E. Marsden and A.J. Tromba. Vector Calculus. W. H. Freeman. 2011.
  • R.L. Finney, M.D. Weir, F.R. Giordano. Thomas' Calculus. Pearson. 2002.
  • Tom Apostol. Multi-Variable Calculus and Linear Algebra with Applications to Differential Equations and Probability. Wiley, 1969.
  • Ν. Δανίκας και Μ.Γ. Μαριάς. Μαθήματα Διαφορικού Λογισμού πολλών μεταβλητών. Εκδόσεις Ζήτη, 2003.
  • Μ.Γ. Μαριάς και Ν. Μαντούβαλος. Μαθήματα Ολοκληρωτικού Λογισμού πολλών μεταβλητών. Εκδόσεις Ζήτη, 2002.
  • D. Hughes-Hallet, A.M. Gleason, W.G. McCallum. Calculus. John Wiley & Sons, Inc. 2012.

MEM-106 Linear Algebra I

  • Classification: Compulsory
  • Year/Semester: 1st/Spring
  • ECTS/Contact hours: 8/5
  • Lecture/Lab hours: 4/2
  • Prerequisites: MEM-102
  • Teaching method: Lectures, recitation sessions
  • Assessment method: Final examination, midterm exam

Course content

  • Vector spaces. Linear subspaces. Linear independence, basis, dimension. Sum of subspaces.
  • Linear transformations, kernel, image, isomorphisms.
  • Direct sums of vector spaces. Quotient spaces. Isomorphism theorems. Dual spaces.
  • The matrix of a linear transformation with respect to given ordered bases. Change of bases.
  • Invariant subspaces. Characteristic polynomials. Algebraic and geometric multiplicity of eigenvalues. The Caley-Hamilton theorem. Triangularizable matrices.
  • Norm and inner product. Gramm-Schmidt orthonormalization. Diagonalization of symmetric and hermitian matrices.

Recommended Reading

  • Δ. Βάρσος, Δ. Δεριζιώτης, Γ. Εμμανουήλ, Μ. Μαλιάκας, Α. Μελάς, Ο. Ταλέλλη. Μία εισαγωγή στη Γραμμική ‘Αλγεβρα. Εκδόσεις Σοφία, 2012. Κωδικός Βιβλίου στον Εύδοξο: 22768417.
  • Gilbert Strang. Introduction to Linear Algebra. Wellesley Cambridge Press. 2016.
  • Gilbert Strang. Linear Algebra and Its Applications. Cengage Learning. 2006.
  • Θ. Θεοχάρη-Αποστολίδη, Χ. Χαραλάμπους, Χ. Βαβατσούλας. Εισαγωγή στη Γραμμική ‘Αλγεβρα. Εκδότης Χ.Χαραλάμπους, 2006.
  • Χρήστος Κουρουνιώτης. Γραμμική Άλγεβρα. Σημειώσεις. Πανεπιστήμιο Κρήτης.
  • Χρήστος Κουρουνιώτης. Γραμμική Άλγεβρα Ι. Ανοικτά Ακαδημαϊκά Μαθήματα Πανεπιστημίου Κρήτης.

MEM-107 Computer Programming ΙΙ

  • Classification: Compulsory
  • Year/Semester: 1st/Spring
  • ECTS/Contact hours: 7/5
  • Lecture/Lab hours: 4/2
  • Prerequisites: MEM-104
  • Teaching method: Lectures, computer labs
  • Assessment method: Final examination, computer lab assignments

Course content

  • Debugging in Python.
  • Basic functions (polynomial, factorial, Fibonacci numbers etc), Dictionary, Recursion.
  • Algorithms and implementations in Python: Linear search, Binary search, Bisection method, selection sort, insertion sort, merge sort, "divide and conquer" algorithms.
  • Applications: Sorting of a list of names.
  • Obect-oriented programming: Introduction and applications for a class in Python, Objects, Class construction, Methods, Inheritance, Applications (fractions, figures, vectors, etc).
  • numpy module and applications: Calculations with vectors, matrices, Solutions of linear systems (Gauss elimination), Plotting with Pylab in 2 and 3 dimensions, Histograms, Random numbers, graphs.

Recommended Reading

  • John V. Guttag. Introduction to computation and programming using Python. MIT Press, 2013.
  • Δημήτριος Καρολίδης. Μαθαίνετε εύκολα python. Εκδόσεις Καρολίδη, 2016.
  • Tony Gaddis. Starting out with Python. Pearson, 2015.
  • Κωνσταντίνος Μαγκούτης και Χρήστος Νικολάου. Εισαγωγή στον αντικειμενοστραφή προγραμματισμό με Python. Εκδότης Ελληνικά Ακαδημαϊκά Ηλεκτρονικά Συγγράμματα και Βοηθήματα - Αποθετήριο "Κάλλιπος", 2016 (ηλεκτρονικό βιβλίο). Κωδικός Βιβλίου στον Εύδοξο: 320102.
  • Hans Peter Langtangen. Python Scripting for Computational Science. Εκδότης Heal-Link/Σύνδεσμος Ελληνικών Ακαδημαϊκών Βιβλιοθηκών, 2η έκδοση 2006 (ηλεκτρονικό βιβλίο). Κωδικός Βιβλίου στον Εύδοξο: 174838.
  • Magnus Lie Hetland. Beginning Python. Εκδότης Heal-Link/Σύνδεσμος Ελληνικών Ακαδημαϊκών Βιβλιοθηκών (ηλεκτρονικό βιβλίο). Κωδικός Βιβλίου στον Εύδοξο: 170352.

MEM-108 Calculus III

  • Classification: Compulsory
  • Year/Semester: 2nd/Fall
  • ECTS/Contact hours: 8/5
  • Lecture/Lab hours: 4/2
  • Prerequisites: MEM-102, MEM-105
  • Teaching method: Lectures, recitation sessions
  • Assessment method: Final examination, midterm exam

Course content

  • Vector fields, divergence, curle, differential vector calculus.
  • Double and triple integrals. Improper double and triple integrals.
  • Plane and space curves.
  • Line integrals, surface integrals, the integral theorems of vector calculus.

Recommended Reading

  • J.E. Marsden and A.J. Tromba. Vector Calculus. W. H. Freeman. 2011.
  • W.E. Boyce and C. DiPrima. Elementary Differential Equations and Boundary Value Problems. Wiley, 2012.

MEM-211 Analysis I

  • Classification: Compulsory
  • Year/Semester: 2nd/Fall
  • ECTS/Contact hours: 8/5
  • Lecture/Lab hours: 4/2
  • Prerequisites: MEM-101
  • Teaching method: Lectures, recitation sessions
  • Assessment method: Final examination, midterm exam

Course content

  • Axiomatic foundation of the reals. The completeness axiom.
  • Sequences of real numbers. The definition of the limit. Elementary properties. Subsequences. Cauchy sequences. liminf, limsup.
  • Series of real numbers. Convergence tests. Absolute and conditional convergence. Rearrangements and products.
  • Functions of one variable. Accumulation points. Limits of a function. Continuous functions. The maximum value theorem. The intermediate value theorem. Continuity of the inverse.
  • Derivatives. The mean value theorem. Chain rule, the inverse function theorem. Taylor's theorem. L’Hôpital's rule. Convex functions.

Recommended Reading

  • Walter Rudin. Principles of Mathematical Analysis. McGraw-Hill Education.
  • Σ. Νεγρεπόντης, Σ. Γιωτόπουλος, Ε. Γιαννακούλιας. Απειροστικός Λογισμός. Πρώτος τόμος. Εκδόσεις ΣΥΜΜΕΤΡΙΑ, 1999.
  • Michael Spivak. Calculus. Publish or Perish. 2008.
  • Μ. Παπαδημητράκης και Ι. Σαραντόπουλος. Πραγματικές συναρτήσεις και μετρικοί χώροι. Αποθετήριο Συγγραμμάτων «Κάλλιπος», 2015.

MEM-221 Algebra I

  • Classification: Compulsory (Math), Elective (ApplMath)
  • Year/Semester: 2nd/Fall
  • ECTS/Contact hours: 8/5
  • Lecture/Lab hours: 4/2
  • Prerequisites: MEM-102, MEM-103
  • Teaching method: Lectures, recitation sessions
  • Assessment method: Final examination, midterm exam

Course content

  • Review of the basics of set theory.
  • The integers, divisibility, euclidean division, gcd, lcm. The fundamental theorem of arithmetic.
  • Groups. The integers and the integers mod n as cyclic groups.
  • Group homomorphisms. The classification of cyclic groups. Subgroups, cosets, Lagrange's theorem.
  • Rings. Integral domains, fields. Subrings. Ring homomorphisms.
  • The theorems of Fermat and Euler. Congruences.
  • Polynomial rings.

Recommended Reading

  • John B. Fraleigh. A First Course in Abstract Algebra. Pearson. 2002.
  • Δ. Βάρσος, Δ. Δεριζιώτης, Γ. Εμμανουήλ, Μ. Μαλιάκας, Α. Μελάς, Ο. Ταλέλλη. Μια εισαγωγή στην ‘Αλγεβρα. Εκδόσεις Σοφία, 2013. Κωδικός Βιβλίου στον Εύδοξο: 22768509.

MEM-251 Numerical Analysis

  • Classification: Compulsory (ApplMath), Elective (Math)
  • Year/Semester: 2nd/Fall
  • ECTS/Contact hours: 8/5
  • Lecture/Lab hours: 4/2
  • Prerequisites: MEM-101, MEM-102, MEM-107
  • Teaching method: Lectures, computer labs
  • Assessment method: Final examination, computer lab assignments

Course content

  • Introduction (floating point arithmetic, rounding and truncation error).
  • Root-finding method (bisection method, fixed point theorems, fixed point iteration/general iteration method, Newton method and secant method).
  • Systems of (linear) equations (Gauss elimination for linear systems, partial pivoting, vector and matrix norms, mode indicator, of linear system, introduction to stability of linear systems, introduction to iterative methods).
  • Interpolation and approximation (Lagrange polynomials, Newton representations of Lagrange polynomial, Hermite interpolation, linear and cubic polynomials/interpolation of continuous functions and piecewise linear and cubic polynomials).
  • Numerical integration (Newton-Cotes integration formulas, trapezoidal rule, Simpson’s rule, composite numerical integration, Gauss-Legendre integration).
  • Lab projects, implementation and analysis of the algorithms and programming languages.

Recommended Reading

  • Γ.Δ. Ακρίβης και Β. Δουγαλής. Εισαγωγή στην Αριθμητική Ανάλυση. Πανεπιστημιακές Εκδόσεις Κρήτης, 1997.
  • G.E. Forsythe, M.A. Malcolm, C.B. Moler. Computer Methods for Mathematical Computations. Prentice Hall, Inc., 1977.

MEM-109 Physics I

  • Classification: Compulsory
  • Year/Semester: 2nd/Fall
  • ECTS/Contact hours: 7/5
  • Lecture/Lab hours: 4/2
  • Prerequisites: MEM-101
  • Teaching method: Lectures, recitation sessions
  • Assessment method: Final examination, midterm exam

Course content

  • Introduction to Mechanics. Motion in one dimension. Motion in two dimensions: Circular motion.
  • Newton's laws of motion. Simple forms of forces in one dimension.
  • Kinetic energy and work. Conservative forces. Potential energy.
  • Motion in two and three dimensions. Central forces. Law of universal gravitation.
  • Dynamics of a system of particles. Linear momentum. Collisions.
  • Angular momentum and torque.
  • Rotation of a rigid body. Rolling motion.
  • Angular momentum. Energy of a system of particles.
  • Oscillations. Resonance.
  • Waves. Transverse waves in a string.
  • Superposition principle. Standing waves.
  • Sound waves.

Recommended Reading

  • R.A. Serway, J.W. Jewett. Physics for Scientists and Engineers, Volume 1. Engage Learning. 2013.
  • D. Halliday, R. Resnick, J. Walker. Fundamentals of Physics, Volume 1. Wiley.
  • H.D. Young and R.A. Freedman. University Physics with Modern Physics. Addison-Wesley, 2011.

MEM-212 Analysis II

  • Classification: Compulsory
  • Year/Semester: 2nd/Spring
  • ECTS/Contact hours: 8/5
  • Lecture/Lab hours: 4/2
  • Prerequisites: MEM-211
  • Teaching method: Lectures, recitation sessions
  • Assessment method: Final examination, midterm exam

Course content

  • Uniform continuity. Uniformly continuous functions on intervals.
  • The Riemann integral. The definition of Darboux. The criterion of Riemann. Basic properties.
  • Integrability of continuous and monotone functions.
  • Sequences of functions. Pointwise and uniform convergence. Examples. The Weierstrass approximation theorem.
  • Series of functions. The Weierstrass criterion. Power series. Radius of convergence. Abel's theorem.
  • Metric spaces. Euclidean spaces, spaces of continuous functions. Open and closed sets. Limit of a sequence. Limit and continuity of a function. Completeness. Compactness.

Recommended Reading

  • Walter Rudin. Principles of Mathematical Analysis. McGraw-Hill Education.
  • Σ. Νεγρεπόντης, Σ. Γιωτόπουλος, Ε. Γιαννακούλιας. Απειροστικός Λογισμός. Tόμος ΙΙα. Εκδόσεις ΣΥΜΜΕΤΡΙΑ, 1999.
  • Σ. Νεγρεπόντης, Σ. Γιωτόπουλος, Ε. Γιαννακούλιας. Απειροστικός Λογισμός. Tόμος ΙΙβ. Εκδόσεις ΣΥΜΜΕΤΡΙΑ, 1999.
  • Michael Spivak. Calculus. Publish or Perish. 2008.
  • Μ. Παπαδημητράκης και Ι. Σαραντόπουλος. Πραγματικές συναρτήσεις και μετρικοί χώροι. Αποθετήριο Συγγραμμάτων «Κάλλιπος», 2015.

MEM-271 Differential Equations

  • Classification: Compulsory
  • Year/Semester: 2nd/Spring
  • ECTS/Contact hours: 8/5
  • Lecture/Lab hours: 4/2
  • Prerequisites: MEM-105
  • Teaching method: Lectures, recitation sessions
  • Assessment method: Final examination, midterm exam

Course content

Part I (ordinary differential equations)

  • Introduction with examples from Physics.
  • Equations with separable variables and equations that can be reduced to them.
  • Complete equations, integrating factor.
  • Linear equations of first order and equations that can be reduced to them (Bernoulli, Riccati).
  • Linear equations of higher order, general solution. Linear equations of higher order with constant coefficients, Euler equation.
  • Non-homogeneous linear equations, method of variation of parameters, method of undetermined coefficients.

Part II (Differential equations with partial derivatives with two independent variables)

  • Introduction with examples from Physics.
  • Equations of first order, systems of equations of first order.
  • Classification of equations of second order.
  • Wave equation, the Cauchy problem, d’Alembert formula.
  • Fourier series (basic notions).
  • Fourier method for the Wave equation and diffusion equation, Dirichlet and Neumann boundary conditions. Laplace equation.

Recommended Reading

  • Στέφανος Τραχανάς. Συνήθεις Διαφορικές Εξισώσεις. Πανεπιστημιακές Εκδόσεις Κρήτης, 1989.
  • Ν. Αλικάκος και Γ. Καλογερόπουλος. Συνήθεις διαφορικές εξισώσεις. Σύγχρονη εκδοτική, 2003.
  • Γ. Παντελίδης, Δ. Κραββαρίτης, Ν. Χατζησάββας. Συνήθεις Διαφορικές Εξισώσεις. Εκδόσεις Ζήτη, 1990.

MEM-261 Probability Theory

  • Classification: Compulsory
  • Year/Semester: 2nd/Fall
  • ECTS/Contact hours: 8/5
  • Lecture/Lab hours: 4/2
  • Prerequisites: MEM-105
  • Teaching method: Lectures, recitation sessions
  • Assessment method: Final examination, midterm exam

Course content

  • Probability and basic properties, independence, conditional probability, Bayes formula.
  • Discrete random variables, expected value, variance.
  • Binomial, Bernoulli, geometric and Poisson distributions.
  • Continuous random variables, expected value, variance, moment-generating functions. Uniform, normal, and exponential distributions.
  • Multivariate random variables.
  • Independence, conditional distribution (of discrete and continuous random variables), calculations for multivariate normal random variables.

Recommended Reading

  • P.G. Hoel, S.C. Port, C.J. Stone. Introduction to Probability Theory. Houghtion Mifflin, 1972.
  • Γ. Γ. Ρουσσάς. Θεωρία Πιθανοτήτων. Εκδόσεις Ζήτη, 1992.
  • Χαράλαμπος Χαραλαμπίδης. Θεωρία πιθανοτήτων και εφαρμογές. Εκδόσεις Συμμετρία, 2009.

MEM-222 Algebra II

  • Classification: Compulsory (Math), Elective (ApplMath)
  • Year/Semester: 2nd/Spring
  • ECTS/Contact hours: 8/5
  • Lecture/Lab hours: 4/2
  • Prerequisites: MEM-106, MEM-221
  • Teaching method: Lectures, recitation sessions
  • Assessment method: Final examination, midterm exam

Course content

  • Integral domains, irreducible elements, relatively prime elements. The ring of polynomials with coefficients in a field, unique factorization. Gauss's lemma, Eisenstein's criterion.
  • Ideals, prime ideals, maximal ideals. Quotient rings, the isomorphism theorem.
  • Finite fields.
  • Permutation groups, cycles. The sign of a permutation. The alternating group. Cayley's theorem.
  • Direct products of groups.
  • Group homomorphisms and their kernels, normal subgroups. Quotient groups, the isomorphism theorem.
  • Transformation groups.

Recommended Reading

  • John B. Fraleigh. A First Course in Abstract Algebra. Pearson. 2002.
  • Δ. Βάρσος, Δ. Δεριζιώτης, Γ. Εμμανουήλ, Μ. Μαλιάκας, Α. Μελάς, Ο. Ταλέλλη. Εισαγωγή στη Γραμμική ‘Αλγεβρα, τόμος Β. Εκδόσεις Σοφία, 2013. Κωδικός Βιβλίου στον Εύδοξο: 22768509.

MEM-202 Analytic Geometry

  • Classification: Elective
  • Year/Semester: 1st/Spring
  • ECTS/Contact hours: 8/4
  • Lecture/Lab hours: 4/0
  • Prerequisites: None
  • Teaching method: Lectures
  • Assessment method: Final examination

Course content

  • Vectors in the plane and in space, circles, spheres, ellipses, hyperbolas, parabolas, conic sections, surfaces in space, geometric inversion in the plane.

Recommended Reading

  • Στυλιανός Ανδρεαδάκης. Αναλυτική Γεωμετρία. Εκδόσεις Συμμετρία, 1999.
  • Στ. Ηλιάδης, Σ. Ζαφειρίδου, Δ. Γεωργίου. Αναλυτική Γεωμετρία. Αυτοέκδοση, Πάτρα, 2008.

MEM-203 Euclidean Geometry

  • Classification: Elective
  • Year/Semester: 3rd/Fall
  • ECTS/Contact hours: 8/3
  • Lecture/Lab hours: 4/0
  • Prerequisites: None
  • Teaching method: Lectures
  • Assessment method: Final examination

Course content

  • Selections from books 1-6 and 11-13 of Euclid's Elements, with some newer results, and a brief overview of the attempts to prove the Parallel Postulate.

Recommended Reading

  • Α. Πούλος και Γ. Θωμαΐδης. Διδακτική της Ευκλείδιας Γεωμετρίας. Εκδόσεις Ζήτη, 2006.
  • Πάρης Πάμφιλος. Ελλάσον Γεωμετρικόν. Πανεπιστημιακές Εκδόσεις Κρήτης, 2012.

MEM-204 Number Theory

  • Classification: Elective
  • Year/Semester: 3rd/Spring
  • ECTS/Contact hours: 8/5
  • Lecture/Lab hours: 4/0
  • Prerequisites: MEM-103
  • Teaching method: Lectures
  • Assessment method: Final examination

Course content

  • Integers and rational numbers.
  • Number-theoretic functions.
  • The Euler function and the Moebius function.
  • Linear congruences. Algebraic congruences.
  • Primitive roots. Indices.
  • Legendre and Jacobi symbols.
  • Special diophantine equations.

Recommended Reading

  • Δ.M. Πουλάκης. Θεωρία Αριθμών. Εκδόσεις Ζήτη, Θεσσαλονίκη, 1997.
  • Π.Γ. Τσαγκάρη: Θεωρία Αριθμών, 3η έκδοση. Εκδόσεις Συμμετρία, Αθήνα, 2010.

MEM-205 Descriptive Statistics

  • Classification: Elective
  • Year/Semester: 1st/Spring
  • ECTS/Contact hours: 8/4
  • Lecture/Lab hours: 2/2
  • Prerequisites: None
  • Teaching method: Lectures, recitation sessions
  • Assessment method: Final examination, computer lab assignments

Course content

  • Statistical analysis of performance data. Non-Cartesian coordinates systems.
  • Numerical descriptive measures. Measures of central tendency and variability.
  • Quantitative data analysis (description of two-Quantitative traits). Introduction to correlation and linear regression analysis.
  • Basic concepts of correlation and linear regression analysis.
  • Non-linear adjustments.
  • Time series, analysis, seasonality.
  • Statistical indicators.

Recommended Reading

  • Κ. Τραχανάς, Α. Τσεβάς. Περιγραφική Στατιστική, θεωρία, παραδείγματα, ασκήσεις. Εκδόσεις Σταμούλη, 1998
  • E. Δημητριάδης. Στατιστική επιχειρήσεων με εφαρμογές σε SPSS και LISREL. Εκδόσεις Κριτική, 2012.

MEM-XXX History of Mathematics

  • Classification: Elective
  • Year/Semester: 3rd/Spring
  • ECTS/Contact hours: 6/3
  • Lecture/Lab hours: 3/0
  • Prerequisites: None
  • Teaching method: Lectures
  • Assessment method: Final examination

Course content

  • Egyptian and Babylonian mathematics. Greek mathematics. Thales, Pythagoras, the famous problems of classical greek mathematics. Euclid's Elements, after Euclid (Apollonius, Archimedes, ...). Brief overview of the history of mathematics after the hellenistic period.
  • The revival of greek mathematics in the first centuries after Christ. Diophantus, Ptolemy, Pappus, Proclus. Brief overview of mathematics in China and India. Arabic mathematics and western middle ages. Renaissance mathematics, Cardano, Tartaglia and Ferrari. The beginnings of modern mathematics: Vieta, Napier, Briggs, Galileo, Kepler, Cavalieri. The era of Fermat και Descartes. Various topics, depending on the instructor, on the forerunners of calculus, Newton and Leibnitz, the mathematicians of the eras of Bernoulli and Euler, Lagrange, Gauss, Cauchy, etc.

Recommended Reading

  • H.N.L. Bunt, J.S. Phillip, D.J. Bedient. Οι ιστορικές ρίζες των στοιχειωδών Μαθηματικών. Εκδόσεις Πνευματικός.
  • B.L. van Der Waerden. Η αφύπνιση της επιστήμης. Πανεπιστημιακές Εκδόσεις Κρήτης, 2000.
  • V. J. Katz. Ιστορία των Μαθηματικών. Πανεπιστημιακές Εκδόσεις Κρήτης, 2013.
  • Γ. Χριστιανίδης, Δ. Διαλέτης. Διαμάχες για την Ιστορία των Αρχαίων Ελληνικών Μαθηματικών. Πανεπιστημιακές Εκδόσεις Κρήτης, 2006.

MEM-213 Complex Analysis

  • Classification: Elective
  • Year/Semester: 3rd/Fall
  • ECTS/Contact hours: 8/4
  • Lecture/Lab hours: 4/0
  • Prerequisites: None
  • Teaching method: Lectures
  • Assessment method: Final examination, midterm exam

Course content

  • Topology of the complex plane.
  • Analytic functions, line integrals, and power series.
  • Cauchy's integral theorem and applications.

Recommended Reading

  • James W. Brown and Ruel V. Churchill. Complex variables and Applications. 9th ed., McGraw-Hill, 2013.
  • Stephen D. Fisher. Complex Variables. 2nѕ ed., Dover Publications, 1999.
  • Joseph Bak and Donald Newman. Complex Analysis. Springer, 2010.
  • Σάββας Τερσένοβ. Αναλυτικές συναρτήσεις και μερικές εφαρμογές τους. Δίαυλος Α.Ε., 1998.

MEM-217 Harmonic Analysis

  • Classification: Elective
  • Year/Semester: 4th/Fall
  • ECTS/Contact hours: 7/5
  • Lecture/Lab hours: 4/2
  • Prerequisites: MEM-211, MEM-212
  • Teaching method: Lectures, recitation sessions
  • Assessment method: Final examination, midterm exam

Course content

  • Fourier series, convergence theorems.

Recommended Reading

  • E. Stein and R. Shakarchi. Fourier Analysis, an introduction. Princeton University Press, 2003.
  • T. Korner. Fourier Analysis. Cambridge University Press, 1988.

MEM-214 Real Analysis

  • Classification: Elective
  • Year/Semester: 4th/Eaρινό
  • ECTS/Contact hours: 8/4
  • Lecture/Lab hours: 4/0
  • Prerequisites: MEM-211, MEM-212
  • Teaching method: Lectures
  • Assessment method: Final examination

Course content

  • Outer Lebesgue measure in R.
  • Measurable sets, Lebesgue measure.
  • The Lebesgue integral.
  • Convergence theorems.
  • Comparison with the Riemann integral.

Recommended Reading

MEM-215 Functional Analysis

  • Classification: Elective
  • Year/Semester: 4th/Spring
  • ECTS/Contact hours: 8/4
  • Lecture/Lab hours: 4/0
  • Prerequisites: MEM-106, MEM-212
  • Teaching method: Lectures
  • Assessment method: Final examination

Course content

  • Normed spaces, Banach spaces.
  • Inner product spaces.
  • Hilbert spaces with emphasis on the geometric side of the theory and on the role of completeness.
  • The dual space.
  • The Hahn-Banach theorem.

Recommended Reading

  • Erwin Kreyszig. Introductory Functional Analysis. Wiley, 1989
  • Σ. Νεγρπόντης, Θ. Ζαχαριάδης, Ν. Καλαμίδας, Β. Φαρμάκη. Γενική Τοπολογία και Συναρτησιακή Ανάλυση. Εκδόσεις Συμμετρία, 1997.
  • George F. Simmons. Introduction to Topology and Modern Analysis. Krieger Publishing Company, 2003.

MEM-216 Analysis of several variables

  • Classification: Elective
  • Year/Semester: 4th/Spring
  • ECTS/Contact hours: 8/4
  • Lecture/Lab hours: 4/0
  • Prerequisites: MEM-211, MEM-212, MEM-108
  • Teaching method: Lectures
  • Assessment method: Final examination

Course content

  • Differentiability of a function of several variables.
  • The inverse and implicit function theorems.
  • Higher derivatives.
  • Change of variables in multiple integrals.
  • Differential forms.
  • Stokes' theorem.

Recommended Reading

  • Michael Spivak. Calculus On Manifolds. Westview Press, 1971.

MEM-223 Linear Algebra II

  • Classification: Elective
  • Year/Semester: 3rd/Fall
  • ECTS/Contact hours: 8/4
  • Lecture/Lab hours: 4/0
  • Prerequisites: MEM-102, MEM-106
  • Teaching method: Lectures
  • Assessment method: Final examination

Course content

  • Vector spaces. Subspaces. Linear independence, basis, dimension. Sum of subspaces.
  • Linear maps, Subspaces related to a linear map. Composition. Isomorphisms.
  • Direct sum of vector spaces. Quotient space. Isomorphism theorems. Dual spaces.
  • Matrix of a linear map in a basis. Change of basis.
  • Invariant subspaces. Characteristic polynomial of a matrix. Algebraic and geometrical multiplicity of eigenvalues. Caley-Hamilton theorem. triangularisation of a matrix.
  • Norm and scalar product. Gramm-Schmidt orthonormalisation. Diagonalisation of symmetric and of hermitian matrices.

Recommended Reading

  • Gilbert Strang. Linear Algebra and Its Applications. Cengage Learning. 2006.
  • Δ. Βάρσος, Δ. Δεριζιώτης, Γ. Εμμανουήλ, Μ. Μαλιάκας, Α. Μελάς, Ο. Ταλέλλη. Μία εισαγωγή στη Γραμμική ‘Αλγεβρα, τόμος Ι. Εκδόσεις Σοφία, 2008.
  • Δ. Βάρσος, Δ. Δεριζιώτης, Γ. Εμμανουήλ, Μ. Μαλιάκας, Α. Μελάς, Ο. Ταλέλλη. Μία εισαγωγή στη Γραμμική ‘Αλγεβρα, τόμος ΙI. Εκδόσεις Σοφία, 2008.
  • Θ. Θεοχάρη-Αποστολίδη, Χ. Χαραλάμπους, Χ. Βαβατσούλας. Εισαγωγή στη Γραμμική ‘Αλγεβρα. Εκδότης Χ.Χαραλάμπους, 2006.
  • Στυλιανός Ανδρεαδάκης. Γραμμική Άλγεβρα. Εκδόσεις Συμμετρία, Αθήνα, 1991.
  • Χρήστος Κουρουνιώτης. Γραμμική Άλγεβρα ΙΙ. Σημειώσεις. Πανεπιστήμιο Κρήτης, 2014.

MEM-224 Group Theory

  • Classification: Elective
  • Year/Semester: 4th/Fall
  • ECTS/Contact hours: 8/4
  • Lecture/Lab hours: 4/0
  • Prerequisites: MEM-221
  • Teaching method: Lectures
  • Assessment method: Final examination, midterm exam

Course content

  • Generators, dihedral groups, permutation groups.
  • Isomorphisms, Cayley's theorem.
  • Products of groups. Quotient groups.
  • Group actions.
  • Cauchy's theorem.
  • Counting orbits.
  • The Sylow Theorems. The classification of groups of order ≤ 15.
  • Selection of topics e.g.: Solvable groups, abelian groups, introduction to representation theory.

Recommended Reading

  • M.A. Armstrong. Groups and Symmetry. Springer, 1988.
  • Θ. Θεοχάρη-Αποστολίδη. Εισαγωγή στη Θεωρία Ομάδων. Α.Π.Θ., Θεσσαλονίκη, 1991.
  • Δημήτριος Νταής. Ομάδες. Σημειώσεις παραδόσεων. Ηράκλειο Κρήτης, 2009.
  • Πάρης Πάμφιλος. Εισαγωγή στη Θεωρία Ομάδων. Σημειώσεις παραδόσεων. Ηράκλειο Κρήτης, 2002.

MEM-226 Theory of Rings and Modules

  • Classification: Elective
  • Year/Semester: 4th/Eaρινό
  • ECTS/Contact hours: 8/4
  • Lecture/Lab hours: 4/0
  • Prerequisites: MEM-222
  • Teaching method: Lectures
  • Assessment method: Final examination

Course content

  • Rings. Subrings, ideals. Prime and maximal ideals.
  • Euclidean domains, principal ideal domains, unique factorization domains.
  • Modules, submodules, quotient modules, morphisms and direct sums of modules, torsion and free modules, decomposition theorems.

Recommended Reading

  • Στυλιανός Ανδρεαδάκης. Εισαγωγή στην Άλγεβρα. Εκδόσεις Συμμετρία, 1986.

MEM-227 Field Theory

  • Classification: Elective
  • Year/Semester: 4th/Eaρινό
  • ECTS/Contact hours: 8/4
  • Lecture/Lab hours: 4/0
  • Prerequisites: MEM-222
  • Teaching method: Lectures
  • Assessment method: Final examination

Course content

  • Finite field extensions. Algebraic numbers.
  • Ruler and compass constructions and the classical unsolvable problems.
  • Splitting fields.
  • The Galois group of a finite field extension. The Fundamental Theorem of Galois Theory.
  • Solvability of algebraic equations.
  • Unsolvability of the general polynomial equation of degree ≥ 5.

Recommended Reading

  • J. Rotman. Galois Theory. Springer, 2013.
  • Στυλιανός Ανδρεαδάκης. Θεωρία Galois. Εκδόσεις Συμμετρία, 1999.

MEM-231 Differential Geometry

  • Classification: Elective
  • Year/Semester: 4th/Spring
  • ECTS/Contact hours: 8/4
  • Lecture/Lab hours: 4/0
  • Prerequisites: MEM-102, MEM-105
  • Teaching method: Lectures
  • Assessment method: Final examination

Course content

  • Curves and surfaces in Euclidean space. Introduction to the intrinsic geometry of surfaces.

Recommended Reading

  • Barrett O'Neil. Elementary Differential Geometry. Academic Press, 2006.
  • Δημήτρης Κουτρουφιώτης, Στοιχειώδης Διαφορική Γεωμετρία, Εκδόσεις Leader Books, 2006.
  • M.P. do Carmo. Differential geometry of curves and surfaces. Prentice-Hall, 1976.
  • Andrew Pressley. Elementary Differential Geometry. Springer, 2010.

MEM-232 Topology

  • Classification: Elective
  • Year/Semester: 4th/Spring
  • ECTS/Contact hours: 8/4
  • Lecture/Lab hours: 4/0
  • Prerequisites: MEM-103, MEM-211, MEM-212
  • Teaching method: Lectures
  • Assessment method: Final examination

Course content

  • Points and sets in euclidean spaces (open sets, closed sets, interior, closure, boundary). Generalization to abstract topological spaces.
  • Continuous functions, metric spaces, products, Hausdorff spaces, sequences, countability properties, compactness, connectedness, quotient spaces.
  • If time permits, depending on the instructor, topics among: Separation properties and metrizability, Baire spaces, introduction to homotopy theory.

Recommended Reading

  • Χ.Γ. Καρυοφύλλης, Χ. Κωνσταντιλάκη-Σαββοπούλου. Τοπολογία Ι. Εκδόσεις Ζήτη, 1985.
  • Χ.Γ. Καρυοφύλλης, Χ. Κωνσταντιλάκη-Σαββοπούλου. Τοπολογία ΙI. Εκδόσεις Ζήτη, 1986.
  • Σ. Νεγρπόντης, Θ. Ζαχαριάδης, Ν. Καλαμίδας, Β. Φαρμάκη. Γενική Τοπολογία και Συναρτησιακή Ανάλυση. Εκδόσεις Συμμετρία, 1997.

MEM-233 Geometry

  • Classification: Elective
  • Year/Semester: 4th/Spring
  • ECTS/Contact hours: 8/4
  • Lecture/Lab hours: 4/0
  • Prerequisites: MEM-102
  • Teaching method: Lectures
  • Assessment method: Final examination

Course content

  • Euclid's axioms. Hilbert's axioms. Consistency.
  • Absolute geometry. Euclidean geometry. Basic results. Conic sections. Pencils of circles.
  • Spherical geometry. Projective geometry.
  • Hyperbolic geometry. Hyperbolic distance, angle of parallelism. Geodesics, circles. Hyperbolic area.

Recommended Reading

  • Χρόνης Στράντζαλος. Η εξέλιξη των Ευκλείδειων και των Μη Ευκλείδειων Γεωμετριών. Εκδόσεις Καρδαμίτσα, 1987.
  • Πάρης Πάμφιλος. Ελλάσον Γεωμετρικόν. Πανεπιστημιακές Εκδόσεις Κρήτης, 2012.

MEM-241 Discrete Mathematics

  • Classification: Elective
  • Year/Semester: 1st/Spring
  • ECTS/Contact hours: 8/4
  • Lecture/Lab hours: 4/0
  • Prerequisites: MEM-103
  • Teaching method: Lectures
  • Assessment method: Final examination

Course content

  • Basics of set theory.
  • Mathematical induction. Propositional calculus.
  • Formal languages.
  • Discrete probability.
  • Relations and functions.
  • Graphs. Trees.
  • Time complexity of algorithms.
  • Discrete numeric functions and generating functions.

Recommended Reading

  • C.L. Liu. Elements of Discrete Mathematics. Mcgraw-Hill College, 1985.
  • Kenneth H. Rosen. Discrete Mathematics and Its Applications. William C Brown Pub, 1998.
  • Susanna S. Epp. Discrete Mathematics with Applications . Cengage Learning, 2010.

MEM-XXX Set Theory

  • Classification: Elective
  • Year/Semester: 4th/Spring
  • ECTS/Contact hours: 8/4
  • Lecture/Lab hours: 4/0
  • Prerequisites: MEM-103
  • Teaching method: Lectures
  • Assessment method: Final examination

Course content

  • Brief review of basic concepts (algebra of sets, relatioins and functions, etc.).
  • Construction of the set of natural numbers.
  • Ordinal numbers and their arithmetic.
  • The axiom of choice.
  • Cardinal numbers and their arithmetic.

Recommended Reading

  • Κορνηλία Κάλφα. Αξιωματική Θεωρία Συνόλων. Εκδόσεις Ζήτη, 1996.
  • Paul R. Halmos. Αφελής Συνολοθεωρία. Εκδόσεις Εκκρεμές, 2002.

MEM-243 Logic

  • Classification: Elective
  • Year/Semester: 4th/Spring
  • ECTS/Contact hours: 8/4
  • Lecture/Lab hours: 4/0
  • Prerequisites: MEM-103
  • Teaching method: Lectures
  • Assessment method: Final examination

Course content

  • Propositional calculus: Tautological implications, formal proofs, completeness, adequate sets of connectives.
  • Predicate calculus: Logical implications, formal proofs, completeness.
  • First order theories.
  • Elimination of quantifiers.
  • Elements of model theory.

Recommended Reading

  • Μπρανισλάβ Μπόριτσιτς. Λογική και Απόδειξη. Εκδόσεις Ζήτη, 1995.
  • Αθανάσιος Τζουβάρας. Στοιχεία Μαθηματικής Λογικής. Εκδόσεις Ζήτη, 1998.
  • Herbert B. Enderton. A Mathematical Introduction to Logic. Academic Press, 2001.

MEM-244 Applied Algebra

  • Classification: Elective
  • Year/Semester: 4th/Eaρινό
  • ECTS/Contact hours: 8/4
  • Lecture/Lab hours: 4/0
  • Prerequisites: MEM-221
  • Teaching method: Lectures
  • Assessment method: Final examination

Course content

  • Euclidean domains.
  • Unique factorization domains.
  • Construction of fields via euclidean domains.
  • Finite fields.
  • Cyclotomic fields. Factorization of polynomials with coefficients in a finite field.
  • Elements of coding theory.

Recommended Reading

MEM-245 Introduction to cryptography

  • Classification: Elective
  • Year/Semester: 4th/Fall
  • ECTS/Contact hours: 8/4
  • Lecture/Lab hours: 4/0
  • Prerequisites: MEM-221
  • Teaching method: Lectures
  • Assessment method: Final examination

Course content

  • Classical cryptography. Study of the following cryptosystems: transposition, substitution, affine, Vigenère, Hill, permutation, stream ciphers. Cryptoanalysis of all the above cryptosystems.
  • RSA and factorization, public-key cryptography. The RSA cryptosystem. Encryption, "attack", cryptoanalysis, factorization algorithm.
  • Other public-key cryptosystems: ElGamal and discrete logarithm, finite field, elliptic curve, knapsack.
  • Signatures.

Recommended Reading

  • Δ.Μ. Πουλάκης. Κρυπτογραφία: Η επιστήμη της ασφαλούς επικοινωνίας. Εκδόσεις Ζήτη, Θεσσαλονίκη 2004.

MEM-252 Numerical Solution of Ordinary Differential Equations

  • Classification: Elective
  • Year/Semester: 3rd/Spring
  • ECTS/Contact hours: 8/4
  • Lecture/Lab hours: 4/2
  • Prerequisites: MEM-101, MEM-102, MEM-107, MEM-108
  • Teaching method: Lectures, computer labs
  • Assessment method: Final examination, computer lab assignments

Course content

  • Numerical methods for the initial value problem for ordinary differential equations. Euler’s methods, Runge-Kutta, multistep methods.
  • Consistency, stability and convergence. Error analysis and estimation.
  • Applications in Physics and Biology.
  • Finite difference and element methods for the two-point boundary value problem.
  • Lab projects.

Recommended Reading

  • Μιχαήλ Ν. Βραχάτης. Αριθμητική Ανάλυση: Συνήθεις Διαφορικές Εξισώσεις. Εκδόσεις Κλειδάριθμος, 2012.
  • G.E. Forsythe, M.A. Malcolm, C.B. Moler. Computer Methods for Mathematical Computations. Prentice Hall, Inc., 1977.
  • C. Pozrikidis. Numerical Computation in Science and Engineering. Oxford University Press, 2008.
  • Γ.Δ. Ακρίβης και Β. Δουγαλής. Αριθμητικές Μέθοδοι για Συνήθεις Διαφορικές Εξισώσεις. Πανεπιστημιακές Εκδόσεις Κρήτης, 2006.
  • Στέφανος Τραχανάς. Συνήθεις Διαφορικές Εξισώσεις. Πανεπιστημιακές Εκδόσεις Κρήτης, 1989.

MEM-253 Numerical Solution of Partial Differential Equations

  • Classification: Elective
  • Year/Semester: 4th/Fall
  • ECTS/Contact hours: 8/4
  • Lecture/Lab hours: 4/2
  • Prerequisites: MEM-101, MEM-102, MEM-107, MEM-108
  • Teaching method: Lectures, computer labs
  • Assessment method: Final examination, computer lab assignments

Course content

  • Finite difference and element methods in piecewise linear polynomial approximation for the two-point boundary value problem with various boundary conditions.
  • Finite difference methods for the Poisson equation.
  • Finite difference and element methods/method for initial and boundary value problems for evolutionary partial differential equations (heat equation, wave equation, first order hyperbolic type, Schrodinger equation).
  • Lab projects, implementation and analysis of the algorithms and programming languages.

Recommended Reading

  • C. Pozrikidis. Numerical Computation in Science and Engineering. Oxford University Press, 2008.
  • Γ.Δ. Ακρίβης και Β. Δουγαλής. Αριθμητικές Μέθοδοι για Συνήθεις Διαφορικές Εξισώσεις. Πανεπιστημιακές Εκδόσεις Κρήτης, 2006.
  • Στέφανος Τραχανάς. Μερικές Διαφορικές Εξισώσεις. Πανεπιστημιακές Εκδόσεις Κρήτης, 2001.
  • Γ. Ακρίβης και Ν. Αλικάκος. Μερικές Διαφορικές Εξισώσεις. Σύγχρονη Εκδοτική, Αθήνα 2012

MEM-254 Numerical Linear Algebra

  • Classification: Elective
  • Year/Semester: 4th/Spring
  • ECTS/Contact hours: 8/4
  • Lecture/Lab hours: 4/2
  • Prerequisites: MEM-101, MEM-102, MEM-106, MEM-107, MEM-108
  • Teaching method: Lectures, computer labs
  • Assessment method: Final examination, computer lab assignments

Course content

  • Vector and matrix norms
  • Sensitivity of linear systems. Matrix condition number and analysis of linear systems in the presence of disturbances/ analysis of linear systems in the presence of actuator saturation and L2-disturbances/theorem of disturbance of linear system.
  • LU decomposition. Round-off (error) analysis of Gaussian estimation.
  • Cholesky decomposition. Linear systems with positive fixed matrix, area and sparse matrices/efficient approximate solution of sparse linear systems/an introduction to sparse matrices.
  • Iterative methods: Jacobi, Gauss-Seidel, conjugate gradient method, preconditioning techniques (for large linear systems).
  • Linear least squares problems. Rectangular matrices. QR decomposition. Householder transformation,. Singular value decomposition (SVD).
  • The eigenvalue-eigenvector problem.
  • Lab projects, implementation and analysis of the algorithms and programming languages.

Recommended Reading

  • Γ.Δ. Ακρίβης και Β. Δουγαλής. Αριθμητικές Μέθοδοι για Συνήθεις Διαφορικές Εξισώσεις. Πανεπιστημιακές Εκδόσεις Κρήτης, 2006.
  • Νικόλαος Μισυρλής. Αριθμητική Ανάλυση. Αυτοέκδοση, Αθήνα, 2009.

MEM-255 Approximation Theory and Applications

  • Classification: Elective
  • Year/Semester: 4th/Spring
  • ECTS/Contact hours: 8/5
  • Lecture/Lab hours: 4/2
  • Prerequisites: MEM-211, MEM-106, MEM-107
  • Teaching method: Lectures, computer labs
  • Assessment method: Final examination, computer lab assignments

Course content

  • Optimal approximations. Existence- uniqueness. Optimal approximations in Euclidean spaces.
  • Normal equations - Fourier representation - Orthogonal polynomials.
  • Uniform approximation: characterization of optimal uniform approximations and calculation with Remez methods.
  • Interpolation in one and two dimensions. Interpolation with splines. Approximation properties of splines.
  • Numerical integration: Newton-Cotes, Romberg, Gauss.
  • Lab projects, implementation and analysis of the algorithms and programming languages.

Recommended Reading

  • Γ.Δ. Ακρίβης και Β. Δουγαλής. Αριθμητικές Μέθοδοι για Συνήθεις Διαφορικές Εξισώσεις. Πανεπιστημιακές Εκδόσεις Κρήτης, 2006.
  • F. Scheid. Schaum's Outline of Numerical Analysis. McGraw-Hill, 1989.

MEM-262 Parametric Statistics

  • Classification: Elective
  • Year/Semester: 3rd/Fall
  • ECTS/Contact hours: 8/5
  • Lecture/Lab hours: 4/2
  • Prerequisites: MEM-101, MEM-102, MEM-261
  • Teaching method: Lectures, computer labs
  • Assessment method: Final examination, computer lab assignments

Course content

  • Modes of stochastic convergence, Slutsky’s theorem, stabilization theorem, the theory of dispersion models.
  • Parametric statistical models, statistical sampling (theory), statistical functions, occupancy statistics, statistical stability, statistical criteria.
  • Estimator: Parametric spaces, methods of moments, maximum likelihood estimation, least squares estimation, Bayes’ estimators and minimum-variance unbiased estimator. Cramer-Frechet-Rao inequality, efficient estimators, asymptotic behavior of estimators, confidence intervals.
  • Statistical hypothesis testing: parametric assumptions, Neyman-Pearson theory, likelihood-ratio test and asymptotic behavior, asymptotic theory of testing statistical hypothesis, testing of normality, linear regression model.
  • Lab projects, implementation of methods using statistical software.

Recommended Reading

  • Γεώργιος Γ. Ρούσσας, Γεώργιος Σταματέλος. Στατιστική συμπερασματολογία, τόμος Ι. 2η έκδοση. Εκδόσεις Ζήτη, 1994.
  • Γεώργιος Γ. Ρούσσας, Γεώργιος Σταματέλος. Στατιστική συμπερασματολογία, τόμος ΙI. Εκδόσεις Ζήτη, 1992.
  • Χ. Δαμιανού, Μ. Κούτρας. Εισαγωγή στη Στατιστική, Μέρος Ι. Εκδόσεις Σ. Αθανασόπουλος & ΣΙΑ Ο.Ε., 1998.

MEM-263 Stochastic Processes

  • Classification: Elective
  • Year/Semester: 4th/Fall
  • ECTS/Contact hours: 8/4
  • Lecture/Lab hours: 4/0
  • Prerequisites: MEM-101, MEM-261
  • Teaching method: Lectures
  • Assessment method: Final examination

Course content

  • Definition of a discrete time stochastic process and its distribution.
  • Markov chains.
  • Transition probabilities.
  • Class structure.
  • Recurrence and transience.
  • Ergodic theorem random walks.
  • Invariant distributions and convergence to equilibrium.
  • Markov chains of continuous time. Poisson distribution.

Recommended Reading

  • Θεόφιλος Ν. Κάκκουλος. Στοχαστικές Ανελίξεις. Εκδόσεις Σ. Αθανασόπουλος & ΣΙΑ Ο.Ε., 1995.
  • Ουρανία Χρυσαφίνου. Εισαγωγή στις Στοχαστικές Ανελίξεις. Εκδόσεις Σοφία Α.Ε., 2012
  • Δημήτρης Φακίνος. Ουρές Αναμονής. Εκδόσεις Συμμετρία, 2008.
  • Δημήτριος Γ. Κωνσταντινίδης. Θεωρία Στοχαστικών Διαδικασιών, Μέρος Α'. Εκδόσεις Σύγγραμμα, 2009.
  • Σοφία Καλπαζίδου. Στοιχεία θεωρίας στοχαστικών ανελίξεων. Εκδόσεις Ζήτη, 1996.

MEM-264 Applied Statistics

  • Classification: Elective
  • Year/Semester: 3rd/Spring
  • ECTS/Contact hours: 8/5
  • Lecture/Lab hours: 4/2
  • Prerequisites: MEM-101, MEM-102, MEM-261
  • Teaching method: Lectures, computer labs
  • Assessment method: Final examination, computer lab assignments

Course content

  • Sampling distribution.
  • Evaluation of generalized linear model assumptions using randomization. Dispersion analysis.
  • Graphical methods in statistics, test of normality and transformation, model assessment.
  • Exploratory statistics.
  • Examples of biology, Medicine, Econometrics, etc.
  • Lab projects, implementation of methods using statistical software.

Recommended Reading

  • Γεώργιος Γ. Ρούσσας, Γεώργιος Σταματέλος. Στατιστική συμπερασματολογία, τόμος ΙI. Εκδόσεις Ζήτη, 1992.
  • Χ. Δαμιανού, Μ. Κούτρας. Εισαγωγή στη Στατιστική, Μέρος Ι. Εκδόσεις Σ. Αθανασόπουλος & Σια Ο.Ε., 1998.
  • M.R. Spiegel, L.J. Stephens. Statistics. Schaum's Outline of Statistics, 1998.
  • Ε. Μπόρα-Σέντα, Χρόνης Θ. Μωυσιάδης. Εφαρμοσμέη Στατιστική. Εκδόσεις Ζήτη, 1990.
  • Χαράλαμπος Γναρδέλλης. Εφαρμοσμένη Στατιστική. Εκδόσεις Παπαζήση, 2003.

MEM-272 Ordinary Differential Equations

  • Classification: Elective
  • Year/Semester: 3rd/Fall
  • ECTS/Contact hours: 8/4
  • Lecture/Lab hours: 4/0
  • Prerequisites: MEM-271, MEM-212
  • Teaching method: Lectures
  • Assessment method: Final examination

Course content

  • First order differential equations. Existence and uniqueness of the solution of the initial value problem. Local and global existence, a priori estimates. Continuous dependence of a solution on the data. Differentiability of solutions.
  • Systems of differential equations. Existence and uniqueness of solutions. Reduction of a system of equations to a single high order equation and vice versa.
  • Systems of linear differential equations. Wronskian determinant. General solution. Systems with constant coefficients. Nonhomogeneous systems.
  • Boundary-value problems. Existence and uniqueness of the solution. Green's function.
  • Theory of stability. Elementary types of rest points. Lyapunov's theorems on stability and asymptotic stability. Test for stability based on first approximation.

Recommended Reading

  • Στέφανος Τραχανάς. Συνήθεις Διαφορικές Εξισώσεις. Πανεπιστημιακές Εκδόσεις Κρήτης, 1989.
  • Ν. Αλικάκος και Γ. Καλογερόπουλος. Συνήθεις διαφορικές εξισώσεις. Σύγχρονη εκδοτική, 2003.
  • Γ. Παντελίδης, Δ. Κραββαρίτης, Ν. Χατζησάββας. Συνήθεις Διαφορικές Εξισώσεις. Εκδόσεις Ζήτη, 1990.

MEM-273 Partial Differential Equations

  • Classification: Elective
  • Year/Semester: 4th/Spring
  • ECTS/Contact hours: 8/4
  • Lecture/Lab hours: 4/0
  • Prerequisites: MEM
  • Teaching method: Lectures
  • Assessment method: Final examination

Course content

  • Sturm-Liouville problems. Basic partial differential equation (PDE).
  • Orthogonality-L2 spaces-Fourier series. Trigonometric Fourier series.
  • Heat equation. Laplace equation. Wave equation.
  • Fourier transform.

Recommended Reading

  • Γ. Ακρίβης και Ν. Αλικάκος. Μερικές Διαφορικές Εξισώσεις. Σύγχρονη Εκδοτική, Αθήνα 2012
  • David J. Logan. Applied Mathematics. Wiley, 2013.
  • Στέφανος Τραχανάς. Μερικές Διαφορικές Εξισώσεις. Πανεπιστημιακές Εκδόσεις Κρήτης, 2001.

MEM-274 Methods of Applied Mathematics

  • Classification: Elective
  • Year/Semester: 3rd/Fall
  • ECTS/Contact hours: 8/4
  • Lecture/Lab hours: 4/0
  • Prerequisites: MEM-101, MEM-105
  • Teaching method: Lectures
  • Assessment method: Final examination

Course content

  • Perturbation methods, Canonical perturbations, singular perturbations.
  • Analysis of boundary layers, WKB approximation.
  • Asymptotic series of integrals.
  • Green's functions, integral equations, initial-value and boundary-value problems in Mathematical Physics.

Δεξιότητες για χρήση μαθηματικών μεθόδων σε προβλήματα επιστημών.

Recommended Reading

  • David J. Logan. Applied Mathematics. Wiley, 2013.
  • Ιωάννης Βεργάδος. Μαθηματικές Μέθοδοι Φυσικής, τόμος Ι. Πανεπιστημιακές Εκδόσεις Κρήτης, 2004.

MEM-280 Physics II

  • Classification: Elective
  • Year/Semester: 2nd/Spring
  • ECTS/Contact hours: 7/4
  • Lecture/Lab hours: 4/2
  • Prerequisites: MEM-109, MEM-105, MEM-108
  • Teaching method: Lectures, recitation sessions
  • Assessment method: Final examination

Course content

  • Electric fields, Coulomb's law.
  • Lines of electric field and Gauss's law. Distribution charges. Conductors in electrostatic equilibrium.
  • Electric potential.
  • Capacitors and capacitance. Dielectrics, Energy stored in an electric field.
  • Electric current. Resistance and circuits of continuous current. Motion of charges in a conductor.
  • Simple model for electrical resistance. Kirchhoff's laws. Charging of a capacitor.
  • Properties of the magnetic field and motion of charge in magnetic field: Lorentz force.
  • Sources of magnetic field. Biot-Savart law.
  • Ampere's law, displacement current.
  • Induction. Faraday's law and the notion of the electromotive force.
  • nature of light and the diffraction index. Diffraction, Dispersion, Snell's law.
  • Geometrical optics.

Recommended Reading

  • R.A. Serway, J.W. Jewett. Physics for Scientists and Engineers, Volume 2. Brooks Cole. 2012.
  • D. Halliday, R. Resnick, J. Walker. Fundamentals of Physics, Volume 2. Wiley. 2015.
  • H.D. Young and R.A. Freedman. University Physics with Modern Physics. Addison-Wesley, 2011.

MEM-281 Theory of Fluids

  • Classification: Elective
  • Year/Semester: 4th/Spring
  • ECTS/Contact hours: 8/4
  • Lecture/Lab hours: 4/0
  • Prerequisites: MEM-101, MEM-105, MEM-108, MEM-271
  • Teaching method: Lectures
  • Assessment method: Final examination

Course content

  • The physical properties of fluids.
  • Conservation laws of mass, momentum, angular momentum and energy.
  • Ideal fluids.
  • Vorticity and vortex lines.
  • Euler and Navier Stokes equations.
  • Potential flow, special solutions through complex functions.
  • Stokes flow.
  • Prandtl boundary layer and Ekman boundary layer.

Recommended Reading

  • Αντώνης Λιακόπουλος. Μηχανική Ρευστών. Εκδόσεις Τζιόλα, 2011.
  • Γ.Δ. Μπόζης, Ι. Χατζηδημητρίου. Εισαγωγή στη μηχανική των συνεχών μέσων. Εκδόσεις Τζιόλα, 1990.

MEM-282 Mathematical Modelling

  • Classification: Elective
  • Year/Semester: 3rd/Fall
  • ECTS/Contact hours: 8/4
  • Lecture/Lab hours: 4/2
  • Prerequisites: MEM-106, MEM-108, MEM-271
  • Teaching method: Lectures, recitation sessions
  • Assessment method: Final examination

Course content

  • Dimensional analysis, dimensionless variables and parameters.
  • Fundamental notions of theoretical mechanics: Newton's laws of motion.
  • Variational calculus and Euler-Lagrange equations.
  • Conservation laws. Application to the modelling of mechanical systems.
  • Models for the dynamics of point vortices in fluids and of charges in an electric and magnetic field.
  • Linear and nonlinear systems of differential equations and stability of fixed points.
  • Population models in Biology. Dynamics of two interacting species.
  • Project on mathematical modelling.

Recommended Reading

  • David J. Logan. Applied Mathematics. Wiley, 2013.
  • B. Barnes, G.R. Fulford. Mathematical Modeling with case studies. CRC press, Taylor and Francis group, 2002.
  • G.R. Fowles. Analytical mechanics. CBS College Publishing, 1986.
  • Σ. Κομηνέας, Ε. Χαρμανδάρης. Μαθηματική Μοντελοποίηση. Εκδότης Ελληνικά Ακαδημαϊκά Ηλεκτρονικά Συγγράμματα και Βοηθήματα - Αποθετήριο "Κάλλιπος", 2016.

MEM-283 Mathematical Models of Classical Physics

  • Classification: Elective
  • Year/Semester: 4th/Fall
  • ECTS/Contact hours: 8/4
  • Lecture/Lab hours: 4/0
  • Prerequisites: MEM-101, MEM-105, MEM-108, MEM-271
  • Teaching method: Lectures
  • Assessment method: Final examination

Course content

  • Introduction in the foundation and in the equations of mathematical models in areas of classical mathematical physics with applications from the theory of diffusion, the mechanics of continuous media (fluid mechanics, linear theory of elasticity), optics, electromagnetism, etc.

Recommended Reading

MEM-284 Wave Propagation

  • Classification: Elective
  • Year/Semester: 4th/Fall
  • ECTS/Contact hours: 8/4
  • Lecture/Lab hours: 4/0
  • Prerequisites: MEM-101, MEM-105, MEM-108, MEM-271
  • Teaching method: Lectures
  • Assessment method: Final examination

Course content

  • Waves and 1st order PDEs.
  • Hyperbolic systems, and the nonlinear wave equation.
  • Wave equation in two and three dimensions.
  • Propagation in layered and non-homogeneous media.
  • geometric optics.
  • Dispersive linear waves.
  • Asymptotic behaviour, group velocity and amplitude equations.
  • Energy propagation.
  • Multi-scale problems and homogenisation.
  • WKB method and paraxial approximation.

Recommended Reading

MEM-287 Mathematical Theory of Materials

  • Classification: Elective
  • Year/Semester: 4th/Fall
  • ECTS/Contact hours: 8/4
  • Lecture/Lab hours: 4/0
  • Prerequisites: MEM-271
  • Teaching method: Lectures
  • Assessment method: Final examination

Course content

  • Elements of tensor algebra.
  • Elements of vector and tensor calculus.
  • Geometrical analysis of deformations.
  • Motions. Material and spatial descriptions.
  • Axioms of mass conservation, linear and angular momentum balance.
  • Cauchy's stress tensor.
  • Material form of balance laws.
  • Power theorem.
  • Examples of constitutive laws.

Recommended Reading

MEM-289 Mathematical Biology

  • Classification: Elective
  • Year/Semester: 4th/Fall
  • ECTS/Contact hours: 8/4
  • Lecture/Lab hours: 4/2
  • Prerequisites: MEM-271
  • Teaching method: Lectures, laboratory classes
  • Assessment method: Final examination

Course content

  • Continuous and discrete population models for a single species.
  • Continuous and discrete models for interacting populations.
  • Evolution and diffusion of biological systems.
  • Modeling and Simulations of biomolecular systems.
  • Biological waves.
  • Dynamics and models for diseases.
  • Pattern formation in biology.
  • Modeling the dynamics of marital interaction.

Recommended Reading

  • J.D. Murray. Mathematical Biology, I. An Introduction. Springer, 1993.
  • Σ. Κομηνέας, Ε. Χαρμανδάρης. Μαθηματική Μοντελοποίηση. Εκδότης Ελληνικά Ακαδημαϊκά Ηλεκτρονικά Συγγράμματα και Βοηθήματα - Αποθετήριο "Κάλλιπος", 2016.

MEM-291 Design and Analysis of Algorithms

  • Classification: Elective
  • Year/Semester: 3rd/Fall
  • ECTS/Contact hours: 8/4
  • Lecture/Lab hours: 4/2
  • Prerequisites: MEM
  • Teaching method: Lectures, computer labs
  • Assessment method: Final examination, computer lab assignments

Course content

  • Principles of design and analysis of algorithms. Algorithmic complexity.
  • Sorting, Finding and Counting algorithms.
  • Dynamic programming.
  • Greedy algorithms.
  • Graph algorithms.
  • Minimum spanning trees and shortest path algorithms.
  • Matrices, number theroy and combinatorics, networks.
  • Computer labs: Desing and implementation of algorithms.

Recommended Reading

  • T.H. Cormen, CH.E. Leiserson, R.L. Rivest, C. Stein. Introduction to Algorithms. The MIT Press, 2009.
  • G. J. E. Rawlings. Αλγόριθμοι: Ανάλυση και Σύγκριση. Εκδόσεις Κριτική, 2004.
  • Anany Leviten. Ανάλυση και σχεδίαση αλγορίθμων. Εκδόσεις Τζιόλα, 2007.

MEM-292 Data Structures

  • Classification: Elective
  • Year/Semester: 3rd/Fall
  • ECTS/Contact hours: 8/4
  • Lecture/Lab hours: 4/0
  • Prerequisites: HY-150
  • Teaching method: Lectures, computer labs
  • Assessment method: Final examination, computer lab assignments

Course content

  • Design and analysis of data structures.
  • Building blocks: arrays, linked lists, trees.
  • Fundamental functions of a data structure (insertion, deletion, counting, finding).
  • Implementation of fundamental functions: catalogs, stacks, queues, priority queues, dictionaries, hash tables.
  • Advanced implementation issues: binomial trees, splay trees, Fibonacci trees
  • Ζητήματα καταχώρησης σχέση δεδομένων.

Recommended Reading

  • Robert Sedgewick. Αλγόριθμοι σε C, Μέρη 1-4 (Θεμελιώδεις Έννοιες, Δομές Δεδομένων, Ταξινόμηση, Αναζήτηση). 3η Αμερικάνικη έκδοση. Εκδόσεις Κλειδάριθμός 2005.
  • Γ. Φρ. Γεωργακόπουλος. Δομές Δεδομένων. Πανεπιστημιακές Εκδόσεις Κρήτης, 2012.
  • S. Sahnii. Δομές Δεδομένων, Αλγόριθμοι και Εφαρμογές στη C++. Εκδόσεις Τζιόλα, 2004.

MEM-293 Optimization Theory

  • Classification: Elective
  • Year/Semester: 4th/Fall
  • ECTS/Contact hours: 8/4
  • Lecture/Lab hours: 4/0
  • Prerequisites: MEM-101, MEM-105, MEM-102
  • Teaching method: Lectures
  • Assessment method: Final examination

Course content

  • Linear Programming.
  • Simplex method.
  • Duality, Sensitivity.
  • Non linear programming.
  • Convex programming.

Recommended Reading

  • Δ. Φακίνος, Α. Οικονόμου. Εισαγωγή στην Επιχειρησιακή Έρευνα. Θεωρία και Ασκήσεις. Εκδόσεις Συμμετρία, 2003.
  • F. Hillier, G. Lieberman. Introduction to Operations Research. McGraw Hill, 2012.
  • Gilbert Strang. Linear Algebra and Its Applications. Cengage Learning. 2006.

MEM-200 Diploma Thesis

  • Classification: Elective
  • Year/Semester: 4th/Fall/Spring
  • ECTS/Contact hours: 12/6
  • Lecture/Lab hours: 0/0
  • Prerequisites: All compulsory courses
  • Teaching method: Supervision
  • Assessment method: Written and oral examination