Faculty of Physics and Applied Computer Science

Zdjęcie dekoracyjne. Fragment blatu a na nim otwarte trzy czasopisma ułożone jedno na drugim. W tle stos czasopism położonych jedno na drugim.

 

Physical sciences

The candidate is expected to answer questions from the general list and one of the specialized list of his/her choice.

1. Fundamentals of classical and relativistic mechanics:

  • Momentum conservation principle
  • Angular momentum conservation principle
  • Energy conservation principle
  • Galileo and Lorentz transformations
  • Mass-energy equivalence, examples

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 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

1. 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 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)

 3. 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
  • Nuclear methods in condensed-matter investigations
  • Synchrotron radiation – generation, properties and examples of application
  • Basic ideas of new materials: quasicrystals, fullerenes, high-temperature superconductors, conducting polymers, semiconducting nanostructures

 4. 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

5. Elements of  elementary particle interactions and detection techniques

  • Elementary particles – the Standard Model: material particles and bosons mediating the interactions. Unification of electroweak interactions.
  • Relativistic momentum, kinetic energy, total energy, relativistic effects, fourvectors formalizm and relativistic ivariants (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 & fix-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 spectr

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.

Biomedical engineering

Knowledge expected from for all candidates

The domain range of "biomedical engineering". Concepts of: biocybernetic model, simulation of biological system and examples of their application to selected problems of biology and medicine. The role of biocybernetics and biomedical engineering in progress of technology, biology and medical sciences as well as civilization achievements.

Knowledge representation methods. Concepts of incomplete and tentative knowledge. Expert systems. Inference rules in systems with rule-based representation of knowledge. Fuzzy logic, evolutionary algorithms. Biomedical engineering systems and applications for diagnostics, therapy, rehabilitation and prosthetics of various organs and body parts – examples and general design rules.

Domain range I: electronics and computers in medicine

Backgrounds of theoretical neurocybernetics, goals and methods of brain modeling, various types of artificial neural networks with applications, basics of cognition sciences. Models of biological and technical perception systems (auditory and visual systems in human), regulatory systems (the concept of homeostasis and structure of management systems), and control systems (control and coordination of motor system, control with the gamma loop, cooperation of synergic and antagonist muscles). Population models.

Computer methods for biomedical signal processing and methods for automated analysis and image recognition. Selected issues of artificial intelligence in biomedical applications.

Methods applied in biological and physiological measurements, monitoring of blood circulation, muscle stress, fetal wellbeing, brain function, visual and auditory perception. Examples of digital supportive tools for signal and image-based diagnostics. Multidimensional and multimodal signals. Computer methods for feature extraction and objects / events classification. Methods of surveillance of human in daily living activities (assisted living), ordination and particular characteristics of sensors. Sensor networks. Data security and privacy-related problems in physiological measurement and data transmission. Hospital information systems, therapy planning automatic and telematic triage. Problems of telemedicine: data secyrity and reliability, seamless data access, aspects of mobility and energetic efficiency of equipment. Brain-Computer Interfaces: paradigms and particular characteristics of BCIs.  

Domain range II: biomaterials engineering

Basic concepts and definitions: biomaterial, biocompatibility, bioactivity, medical device, implant, transplant, artificial organ, hybrid organ. The relationship between the structure, properties and manufacturing methods of different types of  biomaterials: metallic, polymeric, ceramic and composite. Classification of biomaterials by: material type (metals and alloys, ceramics, polymers, carbons, composites, hybrids) and behavior in the biological environment (biostable, degradable, resorbable). Application of metals, polymers, carbons, composites, calcium phosphate bioceramics, bioactive glasses in medicine, e.g. in surgery, orthopedics, cardiac surgery, dentistry. Surface engineering and surface modification techniques. Methods of analysis: structure, microstructure and properties of biomaterials. Biological response to the implant. Biomaterials testing in vitro and in vivo. Tissue engineering and regenerative medicine.

Domain range III: biomechanics

Basic concepts and definitions: Biomechanics and mechanobiology. Fields and directions of research in biomechanics. Structure – function relationship of tissues. Research fields in biomechanics, Division of joints due to type of movement, Biotribiology and issues related to the exploitation of joints and tissues, Bones – structure and mechanical properties, Models of mechanical properties of bones, Functions and properties of articular cartilage, Models of articular cartilage, Structure and properties of connective tissues based on tendon example, Models describing tendon properties, Structure and functions of the spine, Natural and synthetic biomaterials, Modeling of biomaterials as a viscoelastic elements, Experimental methods in tissue biomechanics (including measurements of stress, strain, displacement etc.). Basics of mechanics of tissue and other biological materials – ultimate tensile, compression, bending and torsional strength.