Physical sciences
The candidate answers examination questions formulated by the committee based on a list of topics: a general list and a specific list of topics selected by the candidate. These lists constitute sets of topics and are not lists of questions. The committee then uses them to formulate specific examination questions.
1. Fundamentals of classical and relativistic mechanics with elements of gravity
- Momentum conservation principle
- Angular momentum conservation principle
- Energy conservation principle
- Galileo and Lorentz transformations
- Mass-energy equivalence, examples
- Newtonian gravity and its generalisations
2. Electromagnetism
- Charge conservation principle
- Electrostatic field, scalar potential
- Magnetic field, Vector potential of magnetic field
- Electric charge in magnetic field (examples of applications)
- Electromagnetic wave equation
- Plane and spherical waves
- Interference and diffraction
3. Thermodynamics and statistical physics
- Maxwell distribution
- Boltzmann distribution
- Temperature
- I principle of thermodynamics
- Entropy and II principle of thermodynamics
4. Experimental and theoretical foundations of quantum mechanics
- Black-body radiation
- Photoelectric effect
- Compton effect
- Atomic spectral lines
- Electron diffraction on crystal (Davisson-Germer experiment)
- Stern-Gerlach experiment, electron spin
- Postulates of quantum mechanics
- Wave function
- Uncertainty principle
5. Structure and properties of matter
- Atom and its structure
- Chemical bonds
- Electron band structure of solids
- Electrical conductivity of metals, semiconductors and insulators
- Superconductivity
- Magnetism of solids
- Crystal structure
. Fundamentals of biophysics
- Synchrotron radiation – generation, properties and examples of applications in biological studies
- Methods in surface science (for example: AES – Auger electron spectroscopy, XPS – X-ray photoelectron spectroscopy, SIMS – secondary ion mass spectrometry)
- Spectroscopic methods in biological and medical investigations (for example: EPR,
- NMR, Mössbauer spectroscopy, Infrared and Raman spectroscopy)
- Microscopies of high resolution (electron microscopy, STM – scanning tunneling microscopy, AFM – atomic force microscopy, confocal microscopy)
- Biological membranes – their structure and properties
- Proteins and enzymatic reactions
- Radiative and non-radiative energy transfer (Jabłoński diagram, Förster resonance energy transfer (FRET), Dexter energy transfer)
- Electron transfer in biological systems (temperature dependent and temperature independent – tunneling)
2. Fundamentals of medical physics
- Quantities used in dosimetry and radiation protection (physical quantities, dosimetric quantities, dose equivalents)
- Interaction of ionizing radiation with biological matter
- Physical principles of medical imaging techniques (X-ray, CT, MRI, SPECT, PET, ultrasound)
- Quality control in medical diagnostics
- Physical principles of radiotherapy and hadron therapy; elements of clinical dosimetry
- Properties of mechanical and electromagnetic waves and their applications in medicine
- Spectroscopic methods in the analysis of biological materials
- Nanomaterials and their applications in biomedicine
3. Fundamentals of nuclear physics
- Elementary particles – the standard model
- Evolution of the Universe (in particular: creation of elements)
- Properties of atomic nuclei and the methods of their investigation
- Nuclear forces, binding energy, models of atomic nucleus
- Radioactive transformations of atomic nuclei
- Natural radioactivity of rocks, waters and air
- Accelerators of charged particles
- Nuclear reactions (in particular: fission and fusion of nuclei)
- Interaction of charged particles, gamma radiation and neutrons with matter
- Detection of charge particles, gamma radiation and neutrons
- Neutron sources
- Applications of nuclear isotopes (chosen examples)
4. Fundamentals of solid state physics:
- Crystallography – basic definitions
- Free-electron model
- Interatomic bonds in solids
- X-ray diffraction
- Phonons
- Electron band-structure
- Semiconductors
- Magnetic properties of matter
- Superconductivity
- Applications of NMR and Mössbauer Spectroscopy in Solid State Physics
- Synchrotron radiation – generation, properties and examples of application
- Basic ideas of new materials: quasicrystals, fullerenes, high-temperature superconductors, conducting polymers, semiconducting nanostructures
5. Fundamentals of theoretical and computational physics
- Postulates of quantum mechanics – illustrated by examples
- Physical interpretation of wave function
- Quantum stationary states
- Electron spin: experiment and theory
- Quantum statistics: : bosons and fermions
- Pauli exclusion principle
- Exchange Interaction
- Laplace and Poisson equations and physical processes described by these equations
- Diffusion equation and physical processes described by this equation
- Simple finite-difference methods of solving equations of classical dynamics
- Physical and numerical foundations of classical molecular dynamics
- The method of simulated annealing
- Monte Carlo methods in numerical integration
6. Elements of elementary particle interactions and detection techniques
- Elementary particles – the Standard Model: matter particles and bosons mediating the interactions. Unification of electroweak interactions.
- Relativistic momentum, kinetic energy, total energy, relativistic effects, four-vectors formalizm and relativistic invariants (e.g. CMS)
- Feynman diagram formalism
- Electromagnetic processes (photoeffect, Compton effect, pair production, total cross section)
- Strong interactions (inelastic scattering)
- Accelerators of charged particles (colliders & fixed-target, linear & circular)
- Bethe-Bloch formula
- Elementary principles in particle detection, spectrometry, tracking and calorimetry.
- Fundamental concepts of collider experiments – on the example of LHC experiments (ATLAS, CMS, ALICE, LHCb)
- The working principles of radiation detectors (gaseous detector, scintillation counter, semiconductor detector, photomultiplier)
- Principles of operation of basic semiconductor devices: p-n junction, bipolar transistor, MOS transistor
- Basic principles of signal processing (signal processing in spectrometer, filtering, ENC)
Information and communication technology
- Algorithmics - definition of the algorithm, time and space complexity, classes of complexity, examples of algorithms differ in complexity classes. Asymptotic notations, running time estimation. Sorting algorithms, BFS and DFS algorithm, a minimal spanning tree of a graph, the shortest path problem and algorithms. The concept of a data structure. Different types of data structures, i.e., single-linked and double-linked lists, hash tables, binary search trees (BST), red-black trees, representations of a directed/undirected graph, and their pros and cons
- Programming languages – procedural, object-oriented, and functional languages. Popular control structures/phrases: if, for, while, do, return, break, new, delete, super, etc. Their meaning and use. The overall structure of a program providing in object-oriented and functional languages. Effective use of data structures in various programming languages. Object-oriented programming - concepts of inheritance, polymorphism, and projection. Throwing and handling exceptions.
- Parallel processing - the concept of a thread and a process. The idea of shared memory, mutual exclusion, thread, and processes synchronization. Synchronization errors, deadlock, and livelock issues. Models of concurrent systems: dining philosophers' problem, readers and writers, producers and consumers, etc. Synchronization mechanisms: semaphore, monitor, and CAS (compare-and-swap) mechanism. Their meaning and implementations in the contemporary programming languages.
- Formal languages - Chomsky's taxonomy of formal languages and automata corresponding to these languages. Turing machine as a computation model. Classes of computability: NP, NP-complete, NP-hard, and others. Examples of problems belonging to these classes. Halting problem. The relationship between formal languages and programming languages.
- Databases - types of databases. The architecture of a relational database: tables, relations, keys, indexes, views, component procedures, etc. Basics of SQL, types of queries, and their syntax. Database normalization, normal forms. Effective use of databases. Integration of programming languages and DBs.
- Software engineering - requirements engineering, product engineering. Acquisition and analysis of requirements. Models of the software development process. Structural software analysis and modeling. ERD, DFD, STD, FHD diagrams. Object-oriented design (OOD) and analysis (OOA). The concept of object, class, method, message, pattern, encapsulation, interface. UML language - basic diagrams. Software quality - evaluation methods, software metrics, quality management in the software development process.
- General IT knowledge - computer architecture and design. Problems and challenges of AI, Turing test vs. the Chinese room idea. Computer-aided decision-making. The idea of heuristics. Examples of heuristic algorithms. Binary arithmetic. Basics of formal logic and discrete mathematics. Examples of computer applications.