Band structure of metals and semiconductors, electron transport, electron scattering mechanisms, 2 dimensional electron gases, Si technology (FET, SSD memory), semiconductor heterostructure (semiconductor laser, MEMT), nanoelectronics, single electron transistor. – Magnetic materials, origin of magnetic momentum and interaction between moments, magnetic structures. Magnetism of metals, spin polarized bands, spintronics devices (spin valve, MRAM). Spin transistor, magnetic semiconductors.
– Jenő Sólyom: Fundamentals of the Physics of Solids (Springer 2007) – Thomas Ihn: Semiconductor Nanostructures: Quantum States and Electronic (2009)

Differential equations: Separable d.e., first order linear d.e., higher order linear d.e. of constant coefficients. Series: Tests for convergence of numerical series, power series, Taylor series.
Functions of several variables: Limits, continuity. Differentiability, directional derivatives, chain rule. Higher partial derivatives and higher differentials. Extreme value problems. Calculation of double and triple integrals. Transformations of integrals, Jacobi matrix.
Analysis of complex functions: Continuity, regularity, Cauchy - Riemann partial differential equations. Elementary functions of complex variable, computation of their values. Complex contour integral. Cauchy - Goursat basic theorem of integrals and its consequences. Integral representation of regular functions and their higher derivatives (Cauchy integral formulae).

Based on the quantum mechanics, solid-state physics and statistical physics courses in the Physics BSc studies, this course gives an introduction to theoretical methods used for describing magnetic ordering, excitations and transport in spin systems on the nanoscale. The course will cover the following topics: Atomistic spin Hamiltonians and types of interactions (Heisenberg, Dzyaloshinsky-Moriya, magnetocrystalline anisotropy, symmetry considerations). Themicromagnetic model and its connection to the atomistic description. Long-range magnetic order (ferromagnetism, antiferromagnetism, spin spirals) and solitons (domain walls, vortices, skyrmions). Dynamics of spin systems (Landau-Lifshitz-Gilbert equation, thermal noise). Excitations of ordered magnetic systems (linear spin-wave theory,Mermin-Wagner theorem). Topological magnon insulators. Magnon-magnon interactions based on Green's functiontheory. Interaction of magnetic configurations with spin-polarized currents and thermal gradients (spin transfer torque, magnonic spin current, transversal transport coefficients). Lifetimes of metastable magnetic configurations. Phase transitions (mean-field theory, spin-wave expansion). The theoretical methods discussed in the lecture will be practiced in computer simulations performed during the tutorials.

Curves,reparameterization, length. Tangent line, osculating planes, curves of general type. Frenet frame, Frenet's formulas, curvatures. The fundamental theorem of curve theory. Plane curves: osculating circle, evolute, involutes, parallel curves. Rotation number, Hopf's theorem. Convex curves, the four vertex theorem. Curves in space: osculating, normal and rectifying planes, geometrical interpretation of curvatures.Hypersurfaces,parameterization, tangent plane, normal curvature, Meusnier's theorem. Fundamental forms, Weingarten map. Principal Axis Theorem, principal curvatures, Gaussian and mean curvature. Umbilical points, surfaces of rotation, ruled surfaces. Gauss frame, Christoffel symbols, Gauss and Codazzi–Mainardi equations. The fundamental theorem of hypersurface theory, Theorema Egregium. Tensor fields, Riemannian curvature tensor, Bianchi identity.
Manfredo Do Carmo: Differential Geometry of Curves and Surfaces
Szőkefalvi-Nagy Gyula, Gehér László, Nagy Péter: Differenciálgeometria (1979)Balázs Csikós: Differential GeometryV.T. Vodnyev: Differenciálgeometriai feladatgyűjtemény

The main goal of this course is to demonstrate the ways how the game theory and evolutionary game theory describe real-life situations affecting human behavior, economics, and biological systems. After a brief survey of the basic concept of the traditional game theory (e.g., games, strategies, Nash equilibrium, etc.) we will study evolutionary games that combine the concepts of game theory with the spirit of Darwinism. We will discuss the decomposition of games and also the potential games related to physical systems. Using simple multi-agent mathematical models we will investigate the effects supporting the maintenance of cooperative behavior in the situations of different social dilemmas (e.g., prisoner's dilemma or public goods game) when the individual interests prefer defection to cooperation. The predictions of the mathematical models will be contrasted with human and animal experiments. Finally we study systems where the evolution is controlled by the competition between different spatial strategy associations.

The building blocks of nowadays electronic devices have already reached a few tens on nanometers sizes, and further miniaturization requires the introduction of novel technologies. At such small length-scales the coherent behavior and the interaction of electrons, together with the atomic granularity of matter induce several striking phenomena, that are not observed at the macroscopic scale. The course gives an introduction to a broad set of nanoscale phenomena covering the following topics: characteristic length-scales; basic concepts of quantum transport, conductance quantization; coherent and incoherent transport, interference phenomena in nanostructures; mesoscopic phenomena in atomic and molecular nanojunctions; quantized Hall effect; noise phenomena in nanostructures; graphene nanostructures, 2D heterostructures; quantum dots.

Permutation groups, group actions.Conjugacy, normaliser, centraliser, centre, class equation, Cauchy's theorem. Automorphisms of groups, semidirect product, wreath product.Sylow's theorems. Finite p-groups. Nilpotent and solvable groups. Description of finite nilpotent groups. Transfer, existence of normal p-complement. Free groups, defining relations. Free Abelian groups.Fundamental theorem of finitely generated Abelian groups, applications. Linear groups, classical groups.Representations. Group algebra, Maschke's theorem, Schur's lemma, Wedderburn-Artin theorem.Characters, orthogonality relations, induction, Frobenius reciprocity. Clifford theory. Applications: Burnside's theorem, Frobenius kernel, character tables.
I M Isaacs, Algebra, A graduate course, Brooks/Cole, 1994
I.M. Isaacs, Character theory of finite groups, Dover, 1994

Introduction: point groups, fundamental theorems on finite groups, representations, character tables. Optical spectroscopy: selection rules, direct product representations, factor group. Electronic transitions: crystal field theory, SO(3) and SU(2) groups, correlation diagrams, crystal double groups. Symmetry of crystals: space groups, International Tables of Crystallography. Electronic states in solids: representations of space groups, compatibility rules.

The course aims to learn the programming through understanding the Python language. Introduction to programming and Python language, data types, expressions, input, output. Control structures: if, while. Flowchart, structogram, Jackson figures. Complex control structures. Fundamental algorithms (sum, selection, search extrema, decision..., many practical examples). Lists. For cycle. Newer algorithms (sorting, splitting into two lists...). Exception handling. Abstraction of a part of the program, name it, using as a building block = function. Function call process, parameters, local variables, passing by value. Abstraction: complex data types from simple ones, for example fraction (numerator + denominator), complex numbers (real & imaginary part). OOP concepts: object, method. File management. Command-line arguments. Recursion (painting of an area, building a labyrinth). Algorithms efficiency, quick sorting, binary search versus linear search, O(n). Data structures: binary tree (algorithms), effectiveness: search trees (Morse tree). Mathematical libraries. Modules.

The aim of the course is to understand the basic elements of C++ language fundamental in effective scientific calculations. Compiling C++ programs, programming environments for C++. Input/Output. Built-in data types: int, double, char, bool, complex. Control commands: if, switch, for, while, do. Exception handling(recall Python). Functions. Extending operators (fractions struct), references (a += b, cout << fraction, cin >> fractions). Object-oriented programming in C++: object, class, encapsulation, member functions, constructors, destructors (in complex class with re + im or r + fi data members). Using arrays in C++. Pointers, relationship with arrays. File management. Basic algorithms: search, sort, etc. Command-line arguments. Dynamic memory management, new[], delete[]. Inheritance. Templates. Libraries. Header files.
– E. Scheinerman: C++ for Mathematicians. An Introduction for Students and Professionals, CRC Press

The mathematics of integers: divisibility, division with remainder, greatest common divisor, Euclidean algorithm, irreducible and prime numbers, the fundamental theorem of number theory. Linear Diophantine equations, modular arithmetic, complete and reduced residue systems, solving linear congruences. Fields of prime order. Irreducibility of polynomials and unique factorization. Schönemann-Eisenstein criterion. Multivariate polynomials, complete and elementary symmetric polynomials, relations between roots and coefficients.
Cayley-Hamilton theorem. Bilinear forms, symmetric and symplectic bilinear functions. Standard form, signature, principal axis theorem. Quadratic forms. Classification of local extrema, geometric applications and illustration. Unitary and normal matrices, complex spectral theorem. Polar decomposition, applications of SVD, pseudoinverse and its properties. Normal forms of matrices, existence, uniqueness and computation, generalized eigenvectors, Jordan chain and Jordan basis. Norms of real and complex vectors, matrix norms, basic properties and computation, functions of matrices (convergence only mentioned and illustrated), exponential functions of matrices. Vector spaces over arbitrary fields. Existence of basis, dimension, infinite dimensional examples (function spaces, etc.), isomorphism of vector spaces. Notion, properties, isomorphism of Euclidean space. Dual space. Applications of vector spaces over a finite field in coding theory, cryptography, combinatorics.
S Roman: Advanced Linear Algebra. Springer 2008.
R. Irving: Integers, Polynomials, and Rings - A Course in Algebra. Springer 2004.

Differential calculus of functions of several variables: partial derivatives, differentiability, tangent plane. Derivatives of composite functions. Local and global maxima / minima. Inverse function, implicit function. Double and triple integrals. (5 weeks)
Numerical series, power series, Taylor series. (2 weeks)
Laplace and Fourier transform. (1 week)
Linear algebra. Vectors, applications in geometry. Systems oflinear equations. (3 weeks).
Differential equations (separable differential equations, first order linear differential equations, second order linear differential equations with constant coefficients). (3 weeks)

Limit, continuity, partial derivatives and differentiability of functions of multiple variables. Equation of the tangent plane. Local extrema of functions of two variables. Gradient and directional derivative. Divergence, rotation. Double and triple integrals and their applications. Polar coordinates. Substitution theorem for double integrals. Curves in the 3D space, tangent line, arc length. Line integral. 3D surfaces. Separable differential equations, first order linear differential equations. Algebraic form of complex numbers. Second order linear differential equations with constant coefficients. Taylor polynomial of exp(x), sin(x), cos(x). Eigenvalues and eigenvectors of matrices.

Algebra of vectors in plane and in space. Arithmetic of complex numbers. Infinite sequences. Limit of a function, some important limits. Continuity. Differentiation: rules, derivatives of elementary functions. Mean value theorems, l’Hospital’s rule, Taylor theorem. Curve sketching for a function, local and absolute extrema. Integration: properties of the Riemann integral, Newton-Leibniz theorem, antiderivatives, integration by parts, integration by substitution. Integration in special classes of functions. Improper integrals. Applications of the integral.

Solving systems of linear equations:elementary row operations, Gauss-Jordan- and Gaussian elimination. Homogeneous systems of linear equations. Arithmetic and rank of matrices. Determinant:geometric interpretation, expansion of determinants. Cramer's rule, interpolation, Vandermonde determinant. Linear space,subspace, generating system, basis, orthogonal and orthonormal basis. Linear maps, linear transformations and their matrices. Kernel, image, dimension theorem. Linear transformationsand systems of linear equations. Eigenvalues, eigenvectors, similarity, diagonalizability. Infinite series:convergence, divergence, absolute convergence. Sewuences and series of functions, convergence criteria, power series, Taylor series. Fourier series:axpansion, odd and even functions. Functions in several variables:continuity, differential and integral calculus, partial derivatives, Young's theorem. Local and global maxima / minima. Vector-vector functions, their derivatives, Jacobi matrix. Integrals: area and volume integrals.

Topics:The course covers introductions to two disciplines: Quantum Mechanics and Solid State Physics. After the semester students should be able to understand the basic principles behind these two disciplines and solve some simple quantum mechanical and solid state physics problems. This will contribute to the understanding of the workings of modern electronics and nanotechnology. To follow the course no higher mathematics than algebra and the basics of the differential and integral calculus is required.
Detailed thematics:
Quantum Mechanics. Blackbody radiation, photoelectric effect, Compton effect, stability and line spectra of atoms, Frank-Hertz experiment, Time dependent and independent Schrödinger's equation, stationary states, wave function, "wave - particle duality", electron diffraction, two-slit experiment, uncertainty relations, electron wavefunction probability distribution in an atom, solving the Schrödinger equation, tunneling, the ammonia molecule, electron emission from metals, perturbation calculus, selection rules, operator calculus, eigenstate problems, measurement, quantum mechanics of the hydrogen atom, quantum numbers, H spectrum and selection rules, electron spin, Zeeman-effect, Stern-Gerlach experiment, spin-orbit coupling, atoms with more than one electron, the exclusion principle, indistinguishable particles, periodic table of elements, buildup of shells, Hund's rule, valence and core electrons, molecules, molecular orbitals, chemical bonding, H-H bond, H2+ molecule ion, bonding and anti-bonding states, orbital hybridisation, heteronuclear molecules, sp3 hybridization, rotation and vibration of molecules, Franck-Condon principle, Rayleigh and Raman scattering, Stokes and anti-Stokes scattering, Statistical physics. Classical and quantum statistics. Distribution functions, distinguishable and indistinguishable particles, photon gas, Einstein model, laser principle. Solid State Physics. Short and long range ordering, amorphous and crystalline solids, crystal structures, lattices (point lattice and basis), symmetries and unit cells, primitive, conventional and Wigner-Seitz cells, primitive vectors, Miller indexes, Bravais lattices, close packing structures, reciprocal lattice, k-space, X-ray diffraction, Laue formulae, classical physical models for crystals: lattice vibrations, monatomic and diatomic linear chain model, boundary conditions, form of the solution, dispersion relation, generalization for 3 dim., QM handling of lattice vibrations, phonons, momentum and energy of phonons, relative to the momentum and energy of Bloch electrons, specific heat of solids, equipartition principle and the Debye model, specific heat from electrons, conductors and insulators, band theory of solids, formation of bands, insulators, conductors, real band structures, conduction models,Drude model, collision time, mean free path, Wiedmann-Franz law, Sommerfeld model of metals, Fermi energy, electrons and holes, equivalence of electron and hole conductivity in a completely filled band, metals with hole conduction, work function, thermionic emission, contact potential, crystal potential, double layer at the surface, Bloch functions, Hartree-Fock method, dispersion relation, Brillouin zone, reduced zone picture, kinematics of electrons and holes, Bloch oscillations, effective mass, tight binding model, semiconductors, intrinsic conductivity, density of states in the conduction and valence bands, position of the Fermi level, donors and acceptors, charge carrier concentrations, extrinsic conductivity, Fermi level in doped semiconductors, p-n junction, application of p-n junctions, diode, (MOS)FET, bipolar transistors, Schottky and ohmic structures, characteristics.

The course introduces the hardware building blocks of modern information technologies from traditional semiconductor architectures to the the most up-to-date concepts, technologies and devices. Topics: History of semiconductor devices and semiconductor industry. Advanced silicon technologies from crystal growth to micromachining and nanofabrication techniques. Si devices from traditional MOS FETs to trigate transistors or CCD sensors. Memory devices (SRAM, DRAM, flash). Si solar cells. Compound semiconductors, band engineering, two dimensional electron gas systems, quantum wells, light emitting and laser diodes, high electron mobility transistors, GaN technology. Organic semiconductors: polymer solar cells, OLEDs, printed electronics. Perovskite solar cells. Sensors and actuators: MEMS, physical, chemical, biological sensors, actuators, robotic applications, biointerfaces, artificial skin and nose. Novel device platforms: spintronic devices and resistive switching memories. Novel computing architectures: brain inspired computing, in memory computing, hardware implementation of artificial neural networks.

Basic Number Theory: Divisibility, greatest common divisor, Euclid's algorithm, congruences, Chinese remainder theorem, Hensel lifting, primitive roots, discrete logarithm, quadratic residues, Legendre and Jacobi symbol. Law of quadratic reciprocity.
Analytic Number Theory: Prime numbers and its properties, primes of special forms. Primes in arithmetic progressions, gaps between primes, Bertrand's postulate, the Prime Number Theorem. The Riemann zeta function, Riemann Hypothesis, Dirichlet characters. The generating function and its applications, partitions. Sieve methods, application of Brun's sieve to estimate the number of  twin primes, Goldbach's conjecture. Additive and multiplicative arithmetic functions. Additive Number Theory: Sumsets, direct and inverse problems. Sum-product estimates. 
Combinatorial Number Theory: Schnirelman density, Schur's theorem,  van der Waerden's theorem, Szemerédi's theorem about arithmetic progressions. Zero-sum combinatorics: the polynomial method, Combinatorial Nullstellensatz, applications. 
Diophantine equations: sum of two, three, four squares, representations as the sums of k-th powers, Waring problem.  Fermat's last theorem.  Mordell equation. The abc conjecture.
Miscellaneous modern topics (sketch only): Number Theory in Cryptography: The RSA and the ElGamal scheme. Primality tests. Diophantine Approximation Theory: Continued fractions. Pell equation. Wiener attack against RSA. p-adic numbers.
 

The aim of the course is to provide an overview of the methods of optical measurement technology and to present the latest procedures and results.
Topics: Elements of optical measurement systems. Light sources, detectors, recording materials. Measurement technology of the properties of optical elements. Measurement of angle, length, parallelism with classical optical and coherent optical methods. Heterodyne and phase-shift interferometry. Holographic and speckle pattern interferometry. Digital holography. Optical data processing methods in speckle pattern measurement technology. Photoelasticity. Fiber optic sensors. Color measurement, measurement technology based on color detection.

Electromagnetic waves in vacuum and in a medium; complex dielectric function, interfaces, reflection and transmission. Optical conduction in dipole approximation; linear response theory, Kramers-Kronig relation, sum rules. Simple optical models of metals and insulators; Drude model, Lorentz oscillator. Optical phonons, electron-phonon interaction. Optical spectroscopes: monochromatic- and Fourier transformation spectrometers. Optical spectroscopy of interacting electron systems: excitons, metal-insulator transition, superconductors. Magneto optics: methods and current applications.

The aim of the course is to maintain the students' programming skills through programming problems associated with the topics of Algorithm Theory course helping the understanding of the basic concepts of algorithms.
– M. L. Hetland: Python Algorithms, Mastering Basic Algorithms in the Python Language, Apress, 2010.

Physical fundamentals of generating ionizing radiations: radioactivity, radioactive decay, operation of equipment for generating ionizing radiations. Definition of doses. Biological effects of ionizing radiations: deterministic and stochastic effects, somatic and genetic effects. Control of applications of ionizing radiations in connection with the explanation of generic principles of radiation  protection (justification, optimization, and individual limitations). Procedures and conditions of generating ionizing radiations: external and internal exposure situations, natural and artificial radioactivity. Practical implementation of radiation protection: workplace and environmental radiation protection, monitoring, management and disposal of radioactive wastes, applications of radiation shielding. management of nuclear and radiological emergencies. 
H. Cember, T.E. Johnson: Introduction to Health Physics 

Random matrix theory provides an insight of how one can achieve information relatively simply about systems having very complex behavior. The subject based on the knowledge acquired in quantum mechanics and statistical physics together with some knowledge of probability theory provides an overview of random matrix theory. The Dyson ensembles are defined with their numerous characteristics, e.g. the spacing distribution, the two-level correlation function and other quantities derived thereof. Then the thermodynamic model of levels is obtained together with several models of transition problems using level dynamics. Among the physical applications the universality classes are identified in relation to classically integrable and chaotic systems. The problem of decoherence is studied as well. Then the universal conductance fluctuations in quasi-onedimensional disordered conductors are investigated. Other models are investigated: the disorder driven Anderson transition and the random interaction model of quantum dot conductance in the Coulomb-blockade regime. We use random matrix models to investigate chirality in two-dimensional and Dirac systems and the normal-superconductor interface. The remaining time we cover problems that do not belong to strictly physical systems: EEG signal analysis, covariance in the stock share prize fluctuations, mass transport fluctuations, etc.

Magnetic phenomena are considered as electron correlation effects. This course builds heavily on knowledge gained by successful completion of the course “Modern solid state physics”. The following topics are discussed: Landau levels in magnetic field, magnetism of extended electron states, magnetism of atoms and ions, magnetite, direct exchange, kinetic exchange, Mott transition, Mott insulators, mean field theory of magnetic ordering, the ferromagnetic Heisenberg model, the antiferromegnetic Heisenberg model.

Introductory course to experimental physics, with special emphasis on the physical phenomena and demonstrations.
Temperature and the Zeroth Law of Thermodynamics. Temperature scales. The concept and description of the ideal gas. Thermodynamic state and processes. Heat, specific heat, latent heat, internal energy, and the First Law of Thermodynamics. Generalized work. Processes with ideal gas. The kinetic theory of gases, description of pressure, temperature, internal energy, and molar specific heat of an ideal gas. Equipartition of Energy. Real gases and the van der Waals gas. The barometric formula and the Boltzmann distribution. The Maxwell distribution of molecular speeds and its measurement. The mean free path approximation, diffusion, heat transfer, and viscosity. Closed cycles with ideal gas and the Carnot cycle. Heat engines and heat pumps. The Second Law of Thermodynamics, the Carnot principle, reversible, and irreversible processes. The thermodynamic temperature scale. Examples of heat engines. The Clausius inequalities, the entropy, principle of entropy growth. The fundamental equation of thermodynamics, thermodynamic potentials, their differential relations, and the Maxwell relations. The Third Law of Thermodynamics and its consequences. Phase changes in gases, the Clausius–Clapeyron equation. Principles of statistical physics: micro- and macro-states, the statistical description of entropy, quantum statistics.
– Raymond A. Serway, John W. Jewett: Physics for Scientists and Engineers (Cengage Learning; 10th edition, 2018) ISBN 978-1337553278 Ch 19-22
– Raymond A. Serway , Clement J. Moses, Curt A. Moyer: Modern Physics (Thomson Learning, 2005, 3rd Edition), ISBN 0-534-49339-4
– Herman Gewirtz, Jonathan S. Wolf: Barron's SAT Subject Test in Physics 9th Edition (Barron’s, 2010) ISBN 978-0-7641-4353-3 ezt nem tudom, ezt egy tesztkönyv?