# Fizik Dersleri ve Tanımları

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### Undergraduate Courses:

101 | 102 | 111-112 | 121 | 125 | 130 | 136 | 142 | 150 | 177 | 180 | 201 | 202 | 205 | 206 | 212 | 221 | 290 | 301 | 302 | 305 | 306 | 310 | 311-312 | 325-326 | 331 | 332 | 337 | 339 | 345 | 346 | 371 | 380 | 390 | 391-392 | 401 | 402 | 407 | 408 | 410 | 411 | 412 | 421 | 422 | 442 | 443 | 445 | 446 | 447 | 448 | 449 | 452 | 456 | 458 | 462 | 466 | 472 | 480 | 481 | 482 | 483 | 484 | 485 | 486 | 487 | 488 | 489 | 490 | 48A | 48B | 48C | 48D | 48E | 48F | 480 | 48G | 48H | 48I | 48J | 48K | 48L | 48M | 48N | 48O | 48P | 48R | 48S | 48T | 48U | 48V | 48W | 48Y | 48Z | 491-492 | 493 | 494 | 495 | 496 | 497 | 498 | 499 |

### Science, Technology & Society Courses:

STS-200 | STS-230 | STS-322 | STS-323 | STS-401 | STS-410 | STS-421 | STS-440 | STS-484 | STS-485 | STS-486 | STS-487 |

### Graduate Courses:

500 | 501 | 511 | 512 | 521-522 | 525 | 531-532 | 541 | 542 | 546 | 551-552 | 553 | 554 | 555 | 556 | 561-562 | 571 | 572 | 579 | 580 | 581 | 582 | 583 | 584 | 585 | 586 | 587 | 588 | 589 | 58A | 58B | 58C | 58D | 58E | 58F | 58G | 58H | 58I | 58J | 58K | 58L | 58M | 58N | 58O | 58P | 58Q | 58R | 58S | 58T | 58U | 58V | 58Y | 590 | 591 | 592 | 593 | 594 | 595 | 596 | 597 | 598 | 599 | 611-612 | 621-622 | 625-626 | 628 | 631-632 | 641-642 | 645-646 | 648 | 651-652 | 655-656 | 661-662 | 665-666 | 675-676 | 681-682 | 683 | 684 | 685 | 686 | 687 | 688 | 689 | 68A | 68B | 68C | 68D | 68E | 68F | 68G | 68H | 68I | 68J | 68K | 68L | 68M | 68N | 68O | 68P | 68R | 68S | 68T | 68U | 68V | 68Y | 690 | 691 | 692 | 693 | 694 | 695 | 696 | 697 | 698 | 699 | 790 |

## UNDERGRADUATE COURSES

**PHYS 101 Physics I**(3+1+2) 4

(Fizik I)

Vectors, kinematics, Newton’s laws of motion, work and energy, conservation of energy, linear momentum and its conservation, rotation of rigid bodies about a fixed axis, angular momentum and its conservation. (One laboratory session every week).

(Fizik II)

Equilibrium of rigid bodies, oscillations, gravitation, fluid statics and dynamics, waves in elastic media, introduction to thermodynamics and kinetic theory, sound. (One laboratory session every week).

Prerequisite: PHYS 101.

**PHYS 111, 112 General Physics I,II** (3+1+0) 3

(Genel Fizik I,II)

General physics for students in social sciences. Basic principles of classical and modern physics.

**PHYS 121 Introductory Mechanics and Thermodynamics** (3+1+2) 4

(Mekanik ve

Termodinamige Giris)

Introduction to mechanics and thermodynamics designed for students with advanced standing, through topics such as vectorial mechanics,equilibrium of rigid bodies, rotational dynamics, oscillations, waves and thermodynamics. Not offered to students who have taken Phys 101, or Phys 102, or Phys 130.

**PHYS 125 Calculational Methods In Physics** (1+1+0) 1

(Fizikte Heaplama Yöntemleri)

Properties of elementary functions; their graphs and values at special arguments. Expansions and approximation techniques used in scientific problems. Coordinate systems; areas and volumes of basic geometrical objects.

**PHYS 130 Thermodynamics, Waves,
Optics and Modern Physics ** (3+1+2) 4

(Termodinamik

Dalgalar, Optik ve Modern Fizik)

Introduction to thermodynamics, oscillations, waves, interference and diffraction, gratings and spectra, quantization of energy and wave behaviour of particles. No cuncurrent credit with Phys 102, or Phys 121, or Phys 202.

Prerequisite: PHYS 101.

**PHYS 136 Introduction To Scientific Report Writing And Computing ** (0+0+2) 1

(Rapor Yazımı ve Hesaplamaya Giriş)

LATEX and MATLAB basics.

**PHYS 142 Basic Concepts in Modern Physics ** (1+1+0) 1

(Modern Fizikte Temel Fikirler)

Stern-Gerlach filters: probability amplitudes and probabilities for various outcomes. Compatible and incompatible observables. Resolving power and uncertainly. Filtering signals spatially (temporally) and uncertainties in resolving their wavelengths (frequencies) Uncertainty principle and the stability of hydrogen atom. Concept of simultaneity in specail relativity and applications.

**PHYS 150 Information and Entropy ** (3+1+0) 3

(Bilgi ve Entropi)

This course explores the ultimate limits to communication and computation with an emphasis on the physical nature of information and information processing. Topics include: Information and computation, digital signals, codes and compression, algorithmic information, noise, probability, error correction, reversible and irreversible operations, physics of computation, Shannon entropy. The concept of entropy applied to channel capacity and to the second law of thermodynamics, and energy and temperature of physical systems are handled using the principle of maximum entropy.

**PHYS 177 A Computational Introduction to Dynamical Systems and Probability ** (3+2+0)

(Dinamik Sistemler ve Olasılığa Hesaplamalı bir Giriş)

From Physical to Mathematical Models; Collisions of elastic and inelastic balls;

iterative function systems and fractals; mathematical features of fractals, their

visualization through simulations; simulating randomness, analyzing distributions

through histograms; random number generators and their statistical performance

analysis; simple maps with complex behaviour; (logistic map and others)

examples exhibiting chaotic behaviour; their simulation and analysis.

**PHYS 180 Exploring the Universe ** (3+1+0) 3

(Evreni tanımak)

Solar system: planets and the Sun, Milkyway. Other galaxies and the Hubble’s law. Bigbang. Inflation. The first few minutes, primordial nucleosynthesis. Cosmic Microwave Background (CMB) radiation. Life cycle of stars. Death of stars, supernovae. Brown dwarfs, white dwarfs. Neutron stars, concepts of general relativity, black holes, gamma ray bursts. Hawking radiation and evaporation of black holes. Dark matter and dark energy. The future of the universe.

**PHYS 201 Physics III** (3+1+2) 4

(Fizik III)

Charge and matter, the electric field, Gauss law, electrostatic potential,capacitance, current and resistance electromotive force and circuits, the magnetic field, Ampére’s law, Faraday’s law, inductance, magnetic properties of matter. (One laboratory session every week.)

Prerequisite:PHYS 101, PHYS 121.

(Fizik IV)

Electromagnetic oscillations, AC circuits. Maxwell’s equations,electromagnetic waves, light and its propagation, reflection, refraction, geometrical optics, interference and diffraction, gratings and spectra, polarization, the particle-like properties of electromagnetic radiation: photons, Bohr model and the spectrum of the hydrogen atom.

Prerequisite: PHYS 201.

**PHYS 205 Exploring the Cosmos I** (3+1+0) 3

(Evreni Kesfetmek I)

A survey course primarily for non-science students, with heavily visual character (slides and some videos). No calculus or science background needed. Contents of, and sizes in the cosmos. Ancient astronomy. The scientific revolution. The inner planets: Earth, Moon, Mercury, Mars, Venus. the gas giants: Jupiter, Saturn, Uranus, Neptune. Satellites and rings of the giant planets. Pluto. The asteroid belt. comets. The origin of the solar system.

**PHYS 206 Exploring the Cosmos II** (3+1+0) 3

(Evreni Kesfetmek II)

A survey course primarily for non-science students, with heavily visual character (slides and some videos). No calculus or science background needed. Contents of, and sizes in the cosmos. The Sun. Solar energy. Stellar observations. Double stars. Classification of stars. Birth and evolution of stars. Death of stars. white dwarfs, novae, supernovae, neutron stars, black holes. The Milky Way. Galaxies and the expansion of the universe. The Big Bang. Space exploration. Commercialization of space. future life in space. Space travel. SETI:Search for extraterrestrial intelligence.

**PHYS 212 Electrotechnology for Physicists ** ((1+1+0) 1

(Fizikçiler için Elektroteknoloji)

A qualitative approach to basic equipment and machinery used in electrical power applications: Electrical contacts and switching, magnetic circuits, relays and contactors, transformers, Dc generators and motors, induction and synchronous machines. Characteristics and control of electrical machinery.

**PHYS 221 Thermal Properties of Matter **(3+2+0)

3

(Maddenin Isil Özellikleri)

Elements of probability theory, Bernoulli, Poisson and Gaussian probability distributions. Random walk and diffusion. Thermal motion, molecular distribution of energy in crystals and gases, definition of temperature and the Boltzmann factor, statistical characterization of thermal equilibrium, entropy. Entropy and heat: second law of thermodynamics. Entropy of mixing. Open systems and free energy minimum principles. Applications of the equilibrium conditions: the Clausius-Clapeyron equation, Raoult’s law, Henry’s law, Osmotic pressure. Ideal gases with internal degrees of freedom. Third law of thermodynamics.

Prerequisite: PHYS 102.

**PHYS 290 Computer Applications in Physics** (2+2+2) 3

(Fizikte Bilgisayar Uygulamalari)

The aim of this course is to give the student a knowledge about computer systems, use of peripherals and graphical user interfaces, scientific word processing (via WORD, WORD PERFECT or LATEX), tabulation, spreadsheets (via EXCEL or PARADOX), graphical presentations, application of these facilities to simple physical problems, electronic mail and information retrieval systems (Bitnet, Internet), rudiments of programming.

**PHYS 301 Classical Mechanics I** (3+2+0) 3

(Klasik Mekanik I)

Review of basic mathematical tools used in mechanics. Dynamics of particles and systems of particles, motion under a central force, conservation of energy and momentum, dynamics of rigid body motion. Introduction to the mechanics of continua. Relativistic dynamics.

Prerequisites: PHYS 102 and MATH 152.

**PHYS 302 Classical Mechanics II **(3+2+0) 3

(Klasik Mekanik II)

Review of conservation principles, oscillations in one dimension, damped forced oscillations, non-linear oscillations and introduction to classical perturbation theory. Oscillations in more than one dimension: coupled oscillations, normal modes and coordinates. Introduction to analytical mechanics. Lagrange and Hamilton’s equations, conservation principles. Small oscillations, selected applications. Canonical transformations.

Prerequisites: PHYS 301 or CE 241 and MATH 251. (Waived for double major students upon consent of the instructor)

**PHYS 305 Computerized Data Collection and Analysis**(3+0+0) 3

(Bilgisayarlı Veri Toplama ve Analizi)

Overview of a data acquisition and analysis system. Analog to digital converters. Range, unipolar and bipolar modes, multiplexing. Sample-and-hold circuits, single ended and differential inputs, computers. Software, data format and storage space, digital-to-analog converters. Sampling rates, low-pass filters, oversampling, aliasing. Maximum frequency present in a signal, digital-to-analog conversion. Transducers: Temperature, strain, force, acceleration, displacement, pressure. Isolation amplifiers, nonlinear sensors, linearization. Data manipulation: Data format; statistics; peak, through, and zero crossing detection. Data processing: Curve fitting, filters, spectral analysis, correlation, chaos.

**PHYS 306 Introduction to Metrology**(3+0+0) 3

(Ölçümbilime giriş)

Introduction and historical background. Metrology in practice: impact in modern life. Overview of the SI. Mass metrology: the kilogram. Derived units. Length: the meter. Units, symbols, dimensional analysis, Electrical units: ampère, volt, ohm. Cryogenic metrology. Uncertainties, traceability and accreditation. Temperature: kelvin, low temperatures. General terms and definitions in metrology. Time and frequency: second and hertz. Luminous intensity: candela. Chemical metrology: mole, ionizing radiation and acoustics. Metrology ın medicine. International structure and standardisation bodies. The new SI.

Prerequisites: PHYS 102 or PHYS 121 or PHYS 130, PHYS 201

**PHYS 310 Applied Metrology **(3+0+0) 3

(Uygulamalı Ölçümbilim)

Metrology culture: Metrology and global trade, the four stages of the SI, types of metrology: primary, secondary and industrial metrology; maintenance of standards; calibration. Temperature Metrology: International Temperature Scale of 1990 (ITS-90) and realisation of the kelvin; Contact Temperature measurements; thermoelectric effects. Electrical Metrology: International realisation of d.c. electrical quantities through fundamental constants of physics: the volt – Josephson junction and the Ohm – quantum Hall effect; electrical standards. Dimensional metrology: international realisation of the meter. Temporal metrology: The cesium clock; optical frequency standards; dimensional standards; artefacts (Gauge blocks, micrometers, Vernier callipers, ring gauges, dial gauges). Uncertainty calculations; uncertainty budgets; updating the international definitions : The kilogram (kg), ampere (A), mole (mol), and kelvin (K).

Prerequisites: Consent of Instructor

**PHYS 311, 312 Quantum Physics I,II** (3+2+0) 3

(Kuantum Fizigi I,II)

The aim of the course is to expose students to the basic idea of relativity, quantum physics and to the wide range of applications of these ideas. A survey of applications include the structure of atoms, molecules and nuclei, radioactivity and nuclear reactions, elementary particles, solid-state physics, astrophysics and cosmology. Emphasis on understanding physics of quantal phenomena and on order of magnitude estimates rather than formalism.

Prerequisites: PHYS 202 for PHYS 311 and PHYS 311 for PHYS 312.

**PHYS 325, 326 Mathematical Methods of Physics I,II** (3+2+0) 3

(Fizikte Matematiksel Metodlar I,II)

Vectors and matrices: linear vector spaces, gradient, divergence, curl, Gauss and Stoke’s theorems, coordinate transformations, diagonalization of matrices, eigenvalue problem. Abstract formalism of vector spaces: Green’s function and the inhomogeneous equation, perturbation theory. Function spaces and expansion in orthogonal sets. Infinite series. Ordinary differential equations: solutions in closed form, power series solutions, special functions. Functions of a complex variable, calculus of residues. Contour integration. Contour integral representations of special functions. Asymptotic methods: steepest descents, stationary phase, WKB. Integral transform. Integral equations. Partial differential equations. Calculus of variations Introduction to groups and group representations.

Prerequisites: MATH 252 for PHYS 325 and PHYS/MATH 325 for PHYS 326.

**PHYS 331 Electronics for Physicists I** (2+1+2) 3

(Fizikçiler Icin Elektronik I)

A treatment of the fundamental concepts of electronic circuits and circuit components to provide an adequate understanding of electronic techniques used in modern instrumentation and experimental physics: diode and transistor characteristics, transistor biasing and thermal stabilization. Small and large signal low frequency transistor models transistor amplifier circuits, field-effect transistors. Integrated circuits-operational amplifiers, feedback amplifiers and oscillators. Impedance matching. Large signal amplifiers, rectifiers and filters. (One laboratory session every week)

Prerequisites: PHYS 201 and EE 210 .

**PHYS 332 Electronics for Physicists II** (2+1+2) 3

(Fizikçiler Icin Elektronik II)

Continuation of PHYS 331 with emphasis on integrated circuits and the use of field-effect transistors in electronic circuit switching and digital methods: Linear and non-linear analog systems, combinational and sequential digital systems, metal-oxide semiconductor/large scale integrated (MOS/LSI) digital systems, digital to analog and analog to digital (D/A and A/D) systems.

Prerequisite: PHYS 331.

**PHYS 337 Introdution to Physical Methods in Medical Diagnosis** (3+2+0) 3

(Tipta Tani Amaciyla Kullanilan Fiziksel Yöntemler)

Fundamentals of X-rays, generation and detection of X-rays, X-ray diagnostic methods, fundamentals of acoustics, propogation, generation and detection of ultrasound, ultrasound diagnostic methods, fundamentals of radioactivity, generation and detection of nuclear emission, diagnostic methods using radiation detector probes, radiation dosimetry, biolaogical effects of ionizing and non-ionizing radiation, principles of nuclear magnetic resonance, magnetic resonance imaging, review of other physical diagnostic procedures, biological effects of high magnetic fields.

Prerequisite: PHYS 202.

**PHYS 339 Biological Aspects of Radiation Interactions ** (3+0+0) 3

This course is intended to provide a basic understanding of radiation and its interactions with biological materials. Types of radiation and energy deposition mechanisms will be discussed. A general understanding of processes leading to cellular damage due to radiation will be sought. Topics will include:

* various effects of radiation on biological systems

* basic mechanisms of cell survival

* environmental sources of radiation

* aspects of radiation protection

Level: The course is suitable for advanced-level undergraduates.

**PHYS 345 Classical Astronomy** (3+2+0) 3

(Klasik Astronomi)

Motion of the sun, moon, planets and stars as observed by the naked eye, celestial mapping and time-keeping; Kepler’s laws of planetary motion planetary physics, stellar parallax and stellar aberration, the Doppler effect, variable stars, the measuement of stellar distances, the proper motion of stars, star clusters and galaxies; gaseous nebulae and planetary nebulae; the Hertzsprung-Russell diagram and stellar evolution, red giants and white dwrarfs; novae and supernovae, pulsars and x-ray sources, neutron stars and black holes, the Big-Bang theory and the expanding universe. Cosmological questions.

Prerequisite: PHYS 202.

**PHYS 346 Introduction to Astrophysics** (3+2+0) 3

(Astrofizige Giris)

Basics of astrophsical studies, positions of stars and their proper motions, distance determination to nearby stars; brightness calculations, angular radii of stars, spectral classification of stars, equations of stellar structure, physics of stellar interiors.

Prerequisite: PHYS 202.

**PHYS 371 Modern Physics for Engineers** (3+2+0)

3

(Mühendisler Icin Modern Fizik)

Basic concepts of quantum physics. Solutions of the Schrödinger equation in one dimension: particle in a box, finite squarewell, harmonic oscillator, periodic potentials, barrier penetration. Tunneling phenomena in metal and molecules. The hydrogen atom in wave mechanics. Many-electron atoms: optical excitations and X-ray line spectra. Molecular structure: bonding mechanisms, vibrational and rotational degrees of freedom. The ammonia maser, statistical physics: electron gas, photon gas. Lasers. The specific heat of crystalline solids. Brownian motion. Thermionic emission. Elementary solid state physics: Crystal lattices and phonons, metals, semiconductors and superconducts. The Josephson junction.

**PHYS 380 Introduction to Electromagnetic Radiation** (3+2+0) 3

(Elektromanyetik Isimaya Giris)

Review of Maxwell’s equations, and derivation of their differential form. Importance of continuity equation and displacement current. Derivation of EM wave equation in vacuum, simple solutions and their basic properties, including Poynting’s vector etc. Interaction f radiation with matter, physical basis of the index of refraction. Boundary conditions and simple discussion of reflection and refraction of EM waves from conductors and insulators.

Prerequisite: PHYS 202.

**PHYS 390 Computer Assisted Data Analysis in Physics** (2+1+2) 3

(Fizikte Bilgisayar Destekli Veri Analizi)

Review of program and data strucrures in a strucrured programming language. Processing large volumes of data with computers and collection of statistics. Measures of central tendency and dispersion. Moment generating functions, Poisson and Bernoilli processes and hypothesis testing. Variance analysis. Least squares, maximum likely hood, and Bayes analysis. Error analysis and propagation. Monte Carlo simulation and its applications. Case studies, laboratory exercises, and projects on the computer, supporting topics covered in lectures.

Prerequisite: Math 252 and computer literacy (Phys 290 or Cmpe 150 or consent of instructor).

**PHYS 391, 392 Physical Electronics I,II** (3+2+0) 3

(Fiziksel Elektronik I,II)

Basic principles pertaining to the operation and characteristics of electron devices: Electron ballistics and applications, electron emission (field, thermal and photoelectric.) Energy levels and energy bands. Conduction in metals and semiconductors. Electron statistics, Shottky barriers, p-n junctions and applications. Bipolar, field-effect and metal-oxide -semiconductor (MOS) transistors. Photoelectric devices. Negative resistance devices.

Prerequisites: PHYS 202 and MATH 251

**PHYS 401 Electromagnetism I** (3+2+0) 3

(Elektromagnetizma I)

Vector analysis, solution of electrostatic problems: Poissons’s and Laplace’s equations, method of images. Electrostatics in dielectric media, electrostatic energy. Electric current, magnetic field of steady current, electromagnetic induction, magnetic properties of matter, magnetic energy.

Prerequisites: MATH/PHYS 325 and PHYS 202

**PHYS 402 Electromagnetism II** (3+2+0) 3

(Elektromagnetizma II)

Maxwell’s equations, electromagnetic waves, interaction of radiation with matter: the physical origin of the refractive index, Fresnel’s equations. Multipole expansions of the radiation field: electric dipole, magnetic dipole and electric quadrupole radiation. Waveguides and cavity resonators. Theory of diffraction. Electrodynamics, special theory of relativity and transformations of the electric and magnetic fields.

Prerequisite: PHYS 401 or consent of the instructor.

**PHYS 407 Advanced Quantum Physics I** (3+2+0) 3

(Ileri Kuantum Fizigi I)

Fundamental concepts of relativity and quantum physics and their applications to the structures of single and multielectron atoms. Introduction to mathematical foundations of quantum physics. Emphasis on understanding quantal phenomena order of magnitude estimates. Cannot be taken for credit in addition to Phys 311.

Prerequisite: PHYS 202.

**PHYS 408 Advanced Quantum Physics II** (3+2+0) 3

(Ileri Kuantum Fizigi II)

Continuation of Phys 407 involving applications of relativity and quantum physics to molecules, nuclei, radioactivity and nuclear reactions, elemetary particles, condensed matter physics, astrophysics and cosmology. Cannot be taken for credit in addition to Phys 312.

Prerequisite: PHYS 407.

**PHYS 410 Quantum Mechanics** (3+2+0) 3

(Kuantum Mekanigi)

Wave packets and uncertainity relations, the Schrodinger equation, one dimensional Potentials, the Schrodinger equation in three dimensions, angular momentum, the hydrogen atom, spin angular mimentum, the elementary treatment of addition of angular momenta, the structure of atoms and molecules, first order perturbation theory.

**PHYS 411 Quantum Mechanics I** (3+2+0) 3

(Kuantum Mekanigi I)

Basic postulates of quantum mechanics. Wave and matrix mechanics. The Schrödinger equation. Orbital angular momentum. Exactly soluble bound state problems. The independent perturbation theory and applications. Spin angular momentum. Addition of angular momenta, variational methods.

Prerequisites: MATH/PHYS 325 and PHYS 311

**PHYS 412 Quantum Mechanics II** (3+2+0) 3

(Kuantum Mekanigi II)

Time dependent perturbation theory and applications. Scattering theory. Born approximation, partial waves, phase shifts and cross sections. Spin dependent scattering amplitudes. Introduction to relativistic quantum mechanics.

Prerequisite: PHYS 411 or consent of the instructor.

**PHYS 421 Statistical Mechanics** (3+2+0) 3

(Istatistik Mekanik)

Review of thermodynamics. Microcanonical, canonical and grand canonical ensembles. Classical and quantum gases. Applications.

**PHYS 422 Statistical
Mechanics and Introduction to Many Body Theory** (3+2+0) 3

(Istatistik Mekanik ve Çok Cisim Kuramina Giris)

Review and further study of the properties of quantum gases. Second quantization. Fluctuations and the fluctuation-dissipation theorem. Interacting Bose and Fermi systems. Superfluidity and super conductivity. Introduction to many body theory, Feynman and Goldstone diagrams. Selected applications in nuclear and solid-state physics.

**PHYS 442 Experimental Physics I** (2+0+4) 4

(Deneysel Fizik I)

Experiments illustrative of basic experimental techniques in modern physics such as photoelectric effect, charge to mass ratio of the electron, scattering, Cavendish torsion balance, study of counting statistics, x-ray scattering, radioctivity, quantization of atomic energy levels. Furthermore, quick review of data analysis: statistics, probability distributions, least squares method, Chi-square test.

Prerequisites: PHYS 311 or 407.

**PHYS 443 Experimental Physics II** (2+0+4) 4

(Deneysel Fizik II)

Continuation of Phys 442 Experimental Physics I. Hall effect in semiconductors, gamma-ray attenuation, laser applications, Na-doublet wavelength separation, Fabry-Perot interferometer, coherence length, diffraction of matter waves, Stefan Boltzman law and other modern physics experiments. A quick review of computers, programming, internet, vacuum techniques, particle accelerators, passage of radiation through matter and radiation safety.

Prerequisites: PHYS 442 or consent of the instructor.

**PHYS 445 Observational Astronomy** (3+0+0) 3

(Gözlemsel Astronomy)

Principles of Applications of the telescope, prism spectrometer, grating spectrograph, Michelson-Morley, Fabry-Perot interferometers in astronomy and astrophysics.

Prerequisite: PHYS 345.

**PHYS 446 Computational Astronomy** (3+2+0) 3

(Hesaplamali Astronomi)

Computational methods used in astronomy. Study of celestial charts and atlases, as well as the analysis of astronomical data, use of computer programs on these subjects.

Prerequisite: PHYS 345.

**PHYS 447 Computationa Astrophysics** (3+2+0) 3

(Hesaplamali Astrofizik)

Study of some general astrophysics package programs and observational individual source spectra.

Prerequisite: PHYS 346.

**PHYS 448 History of Astronomy** (3+2+0) 3

(Astronomi Tarihi)

History of astronomy from ancient times to the present day, astronomy in ancient Babylonia and Egypt, ancient Greek astronomy, the heliocentric theory of Aristarchus, the geocentric theory of Ptolemy, astronomy in Islam, the heliocentric theory of copernicus, the work of Tycho Brahe, Kepler, Galileo and Huygens, Newton’s laws of motion and universal gravitation, measuremant of the velocity of light by Romer, Laplace’s celestial mechanics, the beginning of astrophysics in the theories and observations of modern physics, the discoveries and theories of modern astronomy.

Prerequisite: PHYS 202.

**PHYS 449 Cosmic X=Ray Astronomy ** (3+2+0) 3

(Kozmik X Isini Astronomisi)

Galactic and extra-galactic x-ray sources. Instrumentation, X-ray emission mechanisms, and the spectra of X-ray sources.

Prerequisite: PHYS 346.

**PHYS 452 Atomic and Molecular Physics ** (3+2+0) 3

(Atom ve Molekül Fizigi)

Hydrogen atom and its spectrum. Many electron atoms. Hartree theory, Thomas-Fermi theory. Electron correlations. Interaction of atoms with static electric and magnetic fields and with electromagnetic radiation. Hyperfine structure. Exotic atoms. Rydberg atoms. Structure of molecules. Molecular spectroscopy.

Prerequisite: PHYS 411.

**PHYS 456 Modern Optics** (3+2+0) 3

(Modern Optik)

Maxwell’s equations. Plane and spherical waves. Polarization. Crystal optics, propagation of light in anisotropic media. Optical activity. Interference. Fraunhofer and Fresnel diffraction. Fourier optics.

Prerequisites: PHYS 311, PHYS 401 or PHYS 380.

**PHYS 458 Quantum Electronics** (3+2+0) 3

(Kuantum Elektronigi)

Generation, manipulation, propagation and application of coherent radiation. Fundamental processes in lasers and masers. The basic theory of interaction of electromagnetic radiation with resonant atomic transitions. Laser oscillations, Raman effect and non-linear optics. Light modulation, introduction to quantum noise theory.

Prerequisite : consent of the instructor.

**PHYS 462 Solid State Physics** (3+2+0) 3

(Kati Hal Fizigi)

Crystal structure, electron gas, band theory, electronic conductivity, semiconductors, superconductivity, magnetic properties of matter.

Prerequisite: consent of the instructor.

**PHYS 466 Nuclear Physics** (3+2+0) 3

(Nükleer Fizik)

Nuclear structure: liquid drop model, simple shell model, rotational and vibrational nuclei. Natural and artificial radioactivity, alpha, beta and gamma radiation. Nuclear reactions and cross-sections. Optical model, compound nucleus reactions, direct reactions. Heavy ion reactions. Fission.

Prerequisite: PHYS 411 or PHYS 312

**PHYS 472 Elementary Particle Physics** (3+2+0) 3

(Temel Tanecikler Fizigi)

Classification of elementary particles. Particle scattering and decay. Conservation principles. Particle interactions and resonances. Parity and CP violation, quark model, unification of weak and electromagnetic interactions.

Prerequisite: PHYS 411.

**PHYS 480 Selected Topics in Physics:Fluid Mechanics** (3+0+0) 3

**PHYS 481 Selected Topics in Physics Physics of Communication** (3+0+0) 3

**PHYS 482 Selected Topics in Physics: Programming with C/C ++** (3+0+0) 3

**PHYS 483 Selected Topics in Physics: Algorithms and Data Structures in C** (3+0+0) 3

**PHYS 484 Selected Topics in Physics: Object Oriented Programs** (3+0+0) 3

**PHYS 485 Selected Topics in Physics: ** (3+0+0) 3

**PHYS 486 Selected Topics in Physics: Introduction to Quantum Computing** (3+0+0) 3

**PHYS 487 Selected Topics in Physics: Machine Learning for physicists** (3+0+0) 3

**PHYS 488 Selected Topics in Physics: Programming with C** (3+0+0) 3

**PHYS 489 Selected Topics in Physics: Symbolic Programming** (3+0+0) 3

**PHYS 490 Selected Topics in Physics: Synchrotron Radiation and its applications** (3+0+0) 3

**PHYS 48A Selected Topics in Phys: Computer Algebra and Diff. Egs.** (3+0+0) 3

**PHYS 48B Selected Topics in Phys: Wawelets** (3+0+0) 3

**PHYS 48C Selected Topics in Physics: Acoustic Field Theory ** (3+0+0) 3

**PHYS 48D Selected Topics in Physics: Operating Systems for Physicists** (3+0+0) 3

**PHYS 48E Selected Topics in Physics: Programming with Java** (3+0+0) 3

**PHYS 48F Selected Topics in Phys: Superconductivity, Superfluids, Condensates** (3+0+0) 3

**PHYS 48G Selected Topics in Phys: Nanoscience and Nanotechnology** (3+0+0) 3

**PHYS 48H Selected Topics in Phys: Theoretical Optics** (3+0+0) 3

**PHYS 48I Selected Topics in Phys: Database** (3+0+0) 3

**PHYS 48J Selected Topics in Phys: Fundamentals of Computing** (3+0+0) 3

**PHYS 48K Selected Topics in Phys: Analog Circuit Applications** (3+0+0) 3

**PHYS 48L Selected Topics in Phys: Physical Principles and Applications of Video Processing** (3+0+0) 3

**PHYS 48M Selected Topics in Phys: Biophysics** (3+0+0) 3

What’s inside cells. Molecular motion, random walks, friction and diffusion. The low Reynolds-number world, entropic forces, chemical forces and self-assembly. Cooperative transitions in macromolecules. Enzymes and molecular machines, membranes. Nerve impulses.

**PHYS 48N Selected Topics in Phys: The Physics of Medical Imaging** (3+0+0) 3

**PHYS 48O ** (3+0+0) 3

**PHYS 48P Selected Topics in Phys: Climate Physics** (3+0+0) 3

**PHYS 48R Selected Topics in Phys: Introduction to the Theory of Relarivity** (3+0+0) 3

**PHYS 48S Selected Topics in Phys: Exploring the Universe** (3+0+0) 3

Solar system: planets and the Sun. Milkyway. Other galaxies and the Hubble’s law. Bigbang. Inflation. The first few minutes, primordial nucleosynthesis. Cosmic Microwave Background (CMB) radiation. Life cycle of stars. Death of stars, supernovae. Brown dwarfs, white dwarfs. Neutron stars, concepts of general relativity, black holes, gamma ray bursts. Hawking radiaton and evaporation of black holes. Dark matter and dark energy. The fate of the universe.

Prerequisite: Phys 101 or 121, Math 101

Corequisite: Phys 102 or Phys 130

**PHYS 48T Selected Topics in Phys: A Survey of Quantum Many-Body Methods in Physics ** (3+0+0) 3

**PHYS 48U Selected Topics in Phys: Cosmology** (3+0+0) 3

**PHYS 48V Selected Topics in Phys: Physics and Modeling of Nanoscale Transistor (Online)** (3+0+0) 3

The goal of this course is to build a conceptual understanding of nanoscale transistor -the building block of electronics today and will be in the foreseeable future. The approach is to study nanoscale device physics, compare different modeling approaches and to use actual device simulations. The subjects include:

· Basic transistor physics: A barrier-controlled device model

· Traditional drift-diffusion modeling approach

· Ballistic transport

· Scattering in nanoscale transistor

· Quantum transport

· Parasitic effects: Band-to-band-tunneling and interface states

· A real world issue: Device variations

· Hands-on numerical simulation exercises: Using online device simulation tools to obtain the value of a device output parameter as a function of a device design knob.·Numbers to insights: Convert simulations results to actual device understanding

**PHYS 48W Selected Topics in Phys: Physics and Chemistry at Surfaces (Online)** (3+0+0) 3

Bulk electronic structure (Hande Toffoli, METU), Electron states at the surface (Hande Toffoli, METU), Photoelectric emission (Mehmet Erbudak, BU), Crystal structure determination (Mehmet Erbudak, BU), Atomic structure at the surface (Mehmet Erbudak, BU), Scanning techniques (Oguzhan Gürlü, ITÜ), Adsorption at the surface (Mehmet Erbudak, BU), Multimode dynamics (Daniele Toffoli, METU), Electron spectroscopy at seurfaces (Mehmet Erbudak, BU)

Prerequisites: PHYS 201, Solid state physics

**PHYS 48Y Selected Topics in Phys: Programming with Python** (3+0+0) 3

This course is aimed at students with little or no programming experience. It aims to provide students with an understanding of the role computation can play in solving wide variety of problems in science and technology. It also aims to help students, regardless of their major, to feel justifiably confident of their ability to write small programs that allow them to accomplish useful goals. The course will start with the language syntax and writing simple scripts. Then, the built-in data types and notations of Python will be explored. Object-oriented programming with Python will also be discussed.

**PHYS 48Z Selected Topics in Phys: Group Theory for Physicists** (3+0+0) 3

**PHYS 491, 492 Introduction to Research in Physics I,II** (3+2+0) 3

(Fizikte Arastirmaya Giris I,II)

Literature search for a specified research topic, preferably involving the study of relevant articles in international research journals. Attempt to make an independent experimental or theoretical contribution to the topics.

**PHYS 493 Selected Topics in Physics:VBA and Macro Programming** (3+0+0) 3

**PHYS 494 Selected Topics in Physics :Applied Fourier Analysis** (3+0+0) 3

**PHYS 495 Selected Topics in Physics: Web Technologies** (3+0+0) 3

**PHYS 496 Selected Topics in Physics: Computational Physics** (3+0+0) 3

**PHYS 497 Selected Topics in Physics: ** (3+0+0) 3

**PHYS 498 Selected Topics in Physics: Quantum Computing and Quantum Information** (3+0+0) 3

**PHYS 499 Selected Topics in Physics : Data Structures and Algorithms** (3+0+0) 3

## SCIENCE, TECHNOLOGY AND SOCIETY COURSES

**STS 200 Science and Technology as Contemporary Issues**(3+0+0) 3

(Bilim ve Teknolojinin Çagimizdaki Yeri)

A brief review of landmark in the history of science and technology. Science versus art, scientific discovery versus technical innovation, discussion of the role of mathematics in the context of science and technology. The relevance of progress in science and technology to social and economic developments. Developments such as high temperature superconductivity, artificial intelligence, genetic engineering, nuclear fusion are also to be discussed. (Not offered to science and engineering students).

**STS 230 Theory of Musical Sound ** (3+0+0) 3

(Müzikte Ses Kurami)

The physics of oscillations and wave motion. Sound, its generation and propagation, harmonics, interference, beats and combinations. Characteristics of a musical tone; notation of duration; meter. Intervals and construction of scales. Chords and harmonic progression. Characteristics of musical instruments. Introduction to musical forms.

Prerequisite: PHYS 102 and MATH 152.

**STS 322 History of Classical Physics ** (3+0+0) 3

(Klasik Fiziğin Tarihi)

Presentation of the development of important principles and interesting details of classical physics from the deepest past to the invention of radio in essentially chronological order.

**STS 323 History of Modern Physics ** (3+0+0) 3

(Modern Fiziğin Tarihi)

Presentation of the development of principles and interesting details of modern physics from the discovery of X-rays to present in essentially chronological order.

**STS 401 History of Science (up to the 18th Century)** (3+0+0) 3

(Bilim Tarihi: 18. Yüzyila Kadar)

The evolution of science in the ancient Near Eastern Civilizations; followed by a survey of Greek and Arab sciences. Scientific activity in the Renaissance, with particular attention to astronomy (Kepler, Tycho Brahe, Copernicus, Galileo). The development of mathematical analysis. The epoch-making work of Newton in Physics and Mathematics.

Prerequisite : junior or senior standing in sciences or engineering.

**STS 410 History of Science (From the 18th century to the present)** (3+0+0) 3

(Bilim Tarihi: 18. Yüzyildan Günümüze)

A survey of the growth of sciences since the Enlightenment: 18th century developments in theoretical astronomy, applied mathematics and biology. The electromagnetic theory and thermodynamics (19th c.). Development of modern physics, mathematics and biology in the 20th century. Space technology, computers and the “revolution” in electronics.

Prerequisite: junior or senior standing in sciences or engineering.

**STS 421 History of Mathematics** (3+0+0) 3

(Matematik Tarihi)

Mathematics as a deductive science in pre-classical and classical times. Developments in mathematics from 500 A.D. to 1500 A.D. in the Far East, India, Persia, Arabia and Europe. 16th century developments in algebra. The development of analytic geometry and calculus, culminating in the works of Newton and Leibnitz (17th C.). Applications of calculus in the 18th century (Euler, Lagrange, Laplace). The emergence of set theory, abstract algebra, complex analysis and mathematical logic (19th C.). 20th century developments, generalizations in mathematical structures, computers.

Prerequisite: junior or senior standing in sciences or engineering.

**STS 440 Science in Turkish Civilizations** (3+0+0) 3

(Türk Medeniyetlerinde Bilim)

A survey of the field with special emphasis on the development of science in Turkish-Islamic civilizations. Scientific activity in the Seljuk and Ottoman states. Science, scientific policies and institutions in modern Turkey.

Prerequisite: Junior or Senior standing in sciences or engineering.

**STS 484 Special Topics in Physics: History of Science and Tecnology: Perspectives on Tecnology** (3+0+0) 3

**STS 485 Special Topics in Physics: Seventeenth Century Scientific Revolution** (3+0+0) 3

**STS 486 Special Topics in Physics: Responsible Conduct of Research** (3+0+0) 3

**STS 487 Special Topics in Physics: Biomedical Ethics** (3+0+0) 3

## GRADUATE COURSES

**PHYS 500 Readings in Physics**(1+0+0) 1

(Fizikte Literatür Incelemesi)

Supervised reading and library work. Choice of material according to individual needs. Both written and oral presentations are required.

** **(3+2+0) 4

(Klasik Dinamik)

Review of principles of mechanics. Hamilton’s principle and Lagrange’s equations, conservation laws. The principle of least action. Lagrangian formalism: Central forces, rigid body motion, small oscillations. The Hamilton’s equation of motion, canonical transformations, Hamilton-Jacobi theory. Lagrange’s and Hamilton’s equations for continuous media.

**PHYS 511 Electromagnetic Theory I** (3+2+0) 4

(Elektromanyetik Teori I)

Electrostatics and magnetostatics. Time-dependent fields and Maxwell’s equations. Multipole expansion of the radiation field. The interaction of radiation with matter. Interference and diffraction. Wave guides and cavities. Electromagnetism and

relativity.

**PHYS 512 Electromagnetic Theory II** (3+2+0) 4

(Elektromanyetik Teori II)

Further elaboration on some of the topics covered in PHYS 511. Dynamics of charged particles in external electromagnetic fields. Radiation by moving charges, Lienard-Wiechert potentials. Scattering of electromagnetic waves. Cherenkov radiation, Bremsstrahlung. Vector multipole fields. Electromagnetic fluctuations. Radiation damping.

**PHYS 521,522 Mathematical Methods of Physics I,II ** (3+2+0) 4

(Fizikte Matematiksel Metodlar I,II)

Vectors and matrices, complex analysis, differential and integral equations, special functions, asymptotic methods, calculus of variations. Tensor analysis. Introduction to group theory.

**PHYS 525 Introduction to General Relativity** (3+2+0) 4

(Genel Rölativiteye Giris)

Kinematics, dynamics, and four dimensional formulation of special relativity. The equivalance principle, introduction to classical differential geometry. Einstein’s equations and simple applications, introduction to big-bang cosmology, and Inflation theories. White dwarfs, neutron stars and black holes.

**PHYS 531, 532 Quantum Mechanics I,II** (3+2+0) 4

(Kuantum Teorisi I,II)

Bound state problems. Scattering theory, symmetries. Time independent perturbation theory. Applications. Semiclassical theory of radiation. Introduction to relativistic quantum mechanics.

**PHYS 541 Statistical Mechanics I** (3+2+0) 4

(Istatistik Mekanik I)

Laws of thermodynamics and their applications. Classical kinetic theory and the Boltzmann equation. Microcanonical, canonical and grandcanonical partition functions. Ideal quantum gases. Various applications in solid-state, nuclear and astrophysics.

**PHYS 542 Statistical Mechanics II ** (3+2+0) 4

(Istatistik Mekanik II)

Cluster expansion for non-ideal classical and quantum gases, virial coefficients, phase transitions, magnetism. Ising model in two dimensions. Introduction to critical phenomena.

(Polimerler)

Molecular weight and configurations of macromolecules. Statistical thermodynamics of long-chain-molecules. Elastic and

viscoelastic deformation. Electrical and optical properties of polymers. The emphasis is on an understanding of polymer properties in terms of molecular structures.

**PHYS 551, 552 Experimental Physics I,II** (2+0+4) 4

(Deneysel Fizik I,II)

Laboratory experiments fundamental to the development of modern physics. Students are also encouraged: (i) to develop experiments of their own selection, (ii) design and build instruments by themselves with close faculty guidance.

**PHYS 553 Scientific Computation on The Unix Workstation ** (3+0+2) 4

(Unix İş İstasyonunda Bilimsel Hesaplama)

Historical survey of workstations, Unix and Linux. Setting up a Linux.Workstation. Unix fundamentals. Graphics and Visualization. GPL’d scientific applications in Linux including the TeX/LaTeX system, the GNU compiler suite, linear algebra and matrix tools, statistical packages, symbolic programming tools. Use of program libraries. Techniques for power users. Supercomputer clusters, vector and parallel computing/using GPU.

**PHYS 554 Numerical and Symbolic Computation ** (3+0+2) 4

(Sayısal ve Simgesel Hesaplama)

Typical numerical and symbolic programming systems. Use of techniques such as special function evaluation, integration, root finding, solution of linear systems, the eigenvalue problem, variational and finite element techniques, Monte Carlo methods in the framework of actual problems such as nonlinear oscillations, scattering, Fourier and spectral analysis, nonlinear data fitting, eigenvalues and eigenfunctions of Sturm-Liouville systems, integration of partial differential equations.

**PHYS 555 Numerical Methods in Chaotic Systems ** (3+0+2) 4

(Kaotik Sistemlerde Sayısal Yöntemler )

Steady state behavior of dynamical systems. Poincare maps, stability and Liapunov exponents, limit sets, stable and unstable manifolds, phase portraits, construction of bifurcation diagrams. Fractals, dimensions and their determination, the Kaplan-Yorke conjecture, the embedding theorem, attractor reconstruction methods. Weakly deterministic systems and noise reduction.

**PHYS 556 Simulation of Physical Phenomena** (3+2+0) 4

(Fiziksel Olayların Benzetimi)

Role of computer simulation in physics with emphasis on methodologies, data and error analysis, approximations, and potential pitfalls. Methods like Monte Carlo simulation, molecular dynamics, and first-principles calculations for materials.

**PHYS 561, 562 Many-Body Theory I,II** (3+2+0) 4

(Çok Cisim Teorisi I,II)

Many particle Hilbert space, creation and annihilation operators. Green functions at zero temperature. Interacting Fermi and Bose systems. Wick’s theorem and diagrammatic analysis of perturbation theory. Linear response theory. Field theory at finite temperature. Functional integrals. Applications to nuclear and condensed matter physics.

**PHYS 571 X-Ray Astronomy** (3+2+0) 4

(X-Isini Astronomisi)

Description of instruments used in detecting x-ray emission in various wavelengths. Methods of data analysis. Production mechanisms of x-ray emission. Galactic and extra-galactic x,ray sources and systems. x-ray binaries. Background radiation.

**PHYS 572 High Energy Astrophysics** (3+2+0) 4

(Yüksek Enerji Astrofiziği)

Compact objects as X-ray and gamma-ray sources : white dwarfs, neutron stars and black holes, cataclysmic variables, novae, low mass and high mass x-ray binaries, various types of isolated neutron stars. low mass and high mass stellar evolution, radiation mechanisms. supernova remnants: formation, physical processes and evolution, connection between supernova remnants and neutron stars.

**PHYS 579 Graduate Seminar** (0+1+0) Non-credit

(Lisansüstü Seminer)

The widenening of students’ perspectives and awareness of topics of interest to physics through seminars offered by faculty, guest speakers and graduate students.

**PHYS 580 Special Topics in Physics : QED** (3+0+2) 4

**PHYS 581 Special Topics in Physics Quasicrystals** (3+0+2) 4

**PHYS 582 Special Topics in Molecular and Atomic Physics II** (3+0+2) 4

**PHYS 583 Special Topics in Physics Quantum Groups** (3+0+2) 4

**PHYS 584 Special Topics in Physics Galaxy Formation** (3+0+2) 4

Galaxy formation mechanisms are discussed theoretically as well as observationally.Many samples are provided as observational aspects to the

subject.

**PHYS 585 Special Topics in Physics Nonlinear Physics** (3+0+2) 4

One Dimensional Maps. Period doubling, Intermittency and Strange Attractor

routes to chaos. Information content and fractal dimensions. Analysis of time

series. Lyapunov Exponents and their calculation. Stability Theory.

Approximation Methods: Central Manifolds Normal Form theory and its analytic continuation. Local Bifurcation Theory. Linstedt and canonical perturbation theory. Use of numerical and symbolic programming techniques will be stressed.

**PHYS 586 Special Topics in Physics Application of Statistical Mechanics to Problems in Biology and Combinatorics** (3+0+2) 4

**PHYS 587 Special Topics in Physics Data An. in X-ray Astronomy** (3+0+2) 4

Contents:

1. X-ray detectors

a) X-rays

b) Photon interaction in detecting media

c) Compton scattering

d) Photoelectric effect

e) Statistics of the detecting medium

f) İntensity,interaction probability of photons

g) Detector efficiency

h) X-ray detector types

i) Proportional counters

j) Scintillators

k) Solid-state detectors

l) Bragg X-ray spectrometry

m) Areas of collectors for detectors

n) Detector counting statistics

o) Brief introduction to Chi-squared test

p) Observational keys

2. Statistical methods used in X-ray astronomy

a) Distrubutions

b) Permutations and combinations

c) Binomial distribution

d) Poisson distribution

e) Gaussioan (Normal) distribution

f) Lorentzian distribution

g) How to fit an experimental data

h) Maximum likelihood and Gaussian curve chi-squared test

i) Estimanting mean and errors

j) Statistical fluctuations versus Instrumental uncertainities

k) Sampling distribution of the sample variance and inference about a single

variance Sigma2

1) Correlation alaysis

m) Error estimation in X-ray astronomy

n) Parameter estimation in X-ray astronomy

3. Spectral analysis

a) The spectra of cosmic X-ray sources

b) Observational history

c) Production mechanisms of X-ray spectra

d) Thermal Bremmstrahlung

e) Cyclotron and Synchrotron radiation

f) Inverse compton scattering

g) Blackbody emission

h) Radiative recombination

i) Collisionally excited lines

j) Recombination lines

k) Fluorescence lines

l) Charge transfer

m) Cyclotron lines

n) Photoelectric absorption

o) Synchrotron self-absorption

p) Resonance line absorption

q) Free-free absorption

r) e scattering

s) Search for the signatures of radiation mechanisms

t) Conventional spectral analysis procedures

u) Direct analysis of spectral data

v) Fourier Transform deconvolution

w) Interactive techniques

4.Timing analysis

a) Fourier techniques in X-ray timin analysis

b) FT

c) Discrete FT

d) FFT

e) Continuous FT

f) Power spectrum

g) Power spectral statistics

h) Probabilty distribution of noise power

i) Detection level of a signal over a background noise

j) Dead time

k) İntrinsic noise

l) How to handle the power spectrum of any arbitrary signal

m) Ficker noises

**PHYS 588 Special Topics in Physics Mathematical Methods in Classical Mechanics** (3+0+2) 4

**PHYS 589 Special Topics in Physics Quantum Electronics** (3+0+2) 4

**PHYS 58A Special Topics in Physics Computer Algebra and Diff. Egs.** (3+0+2) 4

In Physics and Engineering differential equations commonly serve as the basis for mathematical models and their solutions describe real processes and phenomena. Suppose you have to solve a differential equation. You may look up textbooks and reference books for solution methods appropriate for your equation. If that does not help, you have to leave the problem unsolved, with the uneasy feeling that there might be a method you are unaware of, and the question of whether the solution to your equation can be given in terms of known functions will still be open. Sophus Lie discovered that symmetry is the key to solving differential equations. He invented the theory of Lie groups when studying symmetries of differential equations and applied it for constructing exact solutions of these equations. The aim of this course is to teach the theory of Lie symmetry groups and algebras and, based on it, powerful methods of integration of ordinary andpartial differential equations. In many cases, practical implementation of these methods by hands might be a hard problem involving huge calculations. The unique feature of this course, that presently has no analogues in teaching this subject all over the world, is an extensive use of computer algebra systems (programs of symbolic calculations), mainly Reduce 3.8. Students will learn how to find symmetries and conservation laws (integrals of motion), possessed by mathematical models based on differential equations, by using powerful computer software and how to apply them for obtaining solutions of these equations. We will use the textbook by Hans Stephani: “Differential equations: their solution using symmetries”, 1989, Cambridge University Press, that have the advantage that the exposition is most close to the original Lie’s work, so that many results cannot be found in other available monographs on the subject. As an important supplement to this book, almost all the examples and problems given there will be solved using the computer software.

**PHYS 58B Special Topics in Physics: Particle Accelerator Physics I** (3+0+2) 4

Linear Accelerators, Circular Accelerators, Charged Particles in lectromagnetic Field, Linear Beam Dynamics, Periodic Focusing Systems, Perturbations in Beam Dynamics, Charged Particle Acceleration, Synchrotron Radiation, Particle Beam Parameters, Beam Life Time, Collective Phenomena, Beam Emittance and Lattice Design.

**PHYS 58C Special Topics in Physics: Fundamentals of Atmospheric Modeling** (3+0+2) 4

This course is aimed towards graduate or advanced undergraduate students inthe physics and possibly in environmental sciences. Topics will include:

Brief history of meteorological sciences Atmospheric structure, composition, and thermodynamics The continuity and thermodynamic energy equations The momentum equation in Cartesian and spherical coordinates Vertical-coordinate conversions

Numerical solutions to partial differential equations Finite-differencing the equations of atmospheric dynamics Boundary-layer and surface processes 3 hours per week (WWW 123)

**PHYS 58D Special Topics in Physics:Operating System for Phys.** (3+0+2) 4

The open source movement and Linux, Linux Distributions, Installation of Linux, GPL’d Scientific software including graphical user interfaces, development using Fortran and C under Linux, gnuplot, octave/scilab, maxima and other scientific applications of Linux not covered elsewhere. Basics of Operating Systems: Shell Scripting, Computer System Structures, Operating-System Structures. Processes. Kernel compilation, Commands that manipulate processes (fork, exec, wait) Process Synchronization Critical sections, Deadlocks.

**PHYS 58E Special Topics in Physics: Spintronics** (3+0+2) 4

“Few subjects in science are more difficult to understand than magnetism” –Encyclopedia Britannica There is an increasing demand for scientists and engineers with skills in magnetism because of the growing number of technological applications utilizing this phenomenon. Spintronics is a unique field which crosses traditional disciplinary boundaries between solid state physics, materials science and electrical engineering. The utilization of a purely quantum mechanical property, the electron spin is undoubtedly going to uncover a great potential for applications beyond imagination, in addition to the existing spin- based technologies of magnetic recording, magnetic sensors, magnetic resonance imaging to count a few. The aim of this course is to provide the students with a sound understanding of magnetic phenomena and leading device applications

TOPICS:

• Basic Concepts and Units of Magnetism

• Introduction to Experimental Techniques- Generating and Measuring Magnetic Fields

• Magnetic Properties of Solids- Diamagnetism, Paramagnetism, Ferromagnetism,

• Antiferromagnetism and Ferrimagnetism

• Magnetic Anisotropy : shape, magnetocrystalline, magnetostriction

• Domains and Magnetization Process- Stoner Wohlfarth Hysteresis

• Magnetization Dynamics- Ferromagnetic Resonance, EPR and NMR

• Magnetic Thin Films and Nanomagnetism- Superparamagnetism and Induced Anisotropy

• Hard and Soft Magnetic Materials

• Magnetotransport – Giant Magnetoresistance, Tunneling Magnetoresistance, Spin Transfer Torque

• Magnetic Recording – Hard Drives, Magnetic Random Access Memory

• Magneto Optics- Kerr Effect, Faraday Effect and magneto-optical recording

• Magnetic Semiconductors and Spin Electronics, Spin Hall Effect

• Magnetic Properties of Superconductor

**PHYS 58F Special Topics in Physics:Geometry and Topology of Gauge Theory** (3+0+2) 4

**PHYS 58G Special Topics in Physics: Non-Equilibrium Statistical Mechanics** (3+0+2) 4

This course will survey current problems and approaches to non-equilibrium statistical mechanics. The focus will be on processes such as aggregation, fragmentation, coarsening and basic transport. The following topics will be covered in detail: diffusion, basic kinetic theory, exclusion processes, aggregation and fragmentation, population dynamics and complex networks.

**PHYS 58H Special Topics in Physics: Mathematical Methods ın Physics I** (3+0+2) 4

Current field theory problems require some acquintance with techniques of analysis and geometry, and geometric analysis. The aim of the course is to introduce students to this vast subject.

Sources: I. Chavel “Eigenvalues in Riemannian Geometry”

E. B. Davies “Heat kernels and spectral theory”

A. Grigoryan “Heat kernels and analysis on manifolds”

1) Basic results of operators, self-adjointness, compactness, spectral theorem for self-adjoint operators.

2) Review of Riemannian geometry, geodesics, Laplacian, geodesic coordinates, embeddings, extrinsic and intrinsic geometry.

3) Sobolev spaces, inequalities. Heat kernels. Bounds on heat kernels. Applications to some singular problems in physics.

**PHYS 58I Special Topics in Physics: Analysis for Scientists and Engineers** (3+0+2) 4

**PHYS 58J Special Topics in Physics: Fundamentals of Computing** (3+0+2) 4

**PHYS 58K Special Topics in Physics: The Physics of Traffic** (3+0+2) 4

Historical overview, three-phase traffic theory. Empirical spatiotemporal congested traffic patterns, microscopic three-phase traffic theory. Engineering applications.

**PHYS 58L Special Topics in Physics: Climate Physics** (3+0+2) 4

An advanced survey of the climate system for science majors, origins of solar radiation, energy budget of the earth, atmosphere and oceans, clouds and aerosols, radiative transfer, the Greenhouse gases and Greenhouse effect, climate system stability, sensitivity and change, introduction to climate models and future predictions, climate politics.

**PHYS 58M Special Topics in Physics:The Physics of Medical Imaging** (3+0+2) 4

**PHYS 58N ** (3+0+2) 4

**PHYS 58O Special Topics in Physics: Mathematical Methods in Physics II** (3+0+2) 4

This course will focus in finer aspects of Riemannian geometry and its use in physical problems.

Subjects to be covered:

1) differential forms, exterior multiplication, d-operator.

2) Integration on manifolds

3) Covariant derivative on a Riemannian space

4) Isometric embeddings

5) Connections on submanifolds

6) Geodesics

7) Hopf-Rinow theorem

8 ) Exponential map, cut-locus, geodesic flow

9) Curvature tensor, Ricci tensor, scalar curvature, sectional curvature

10) Jacobi fields

11) Riemannian submersions and curvature

12) Gauss lemma, conjugate points

13) Myers theorem, Cartan-Hadamard theorem

14) Curvature and volume, volume estimates

15) Laplace operator and basic results on its spectrum

16) Spectrum of spheres

17) Bounds on eigenvalues

18) Isoperimetric inequality

19) Singular Quantum problems on manifolds

Suggested references: A) Boothby “An introduction to differentiable manifolds and

Riemannian geometry”

B)Gallot, Hulin and Lafontaine “Riemannian Geometry”

**PHYS 58P Special Topics in Physics:: Particle Physics** (3+0+2) 4

**PHYS 58R Special Topics in Physics: Special Relativity** (3+0+2) 4

**PHYS 58S Special Topics in Physics:: Simulations in Physics** (3+0+2) 4

**PHYS 58T Special topics in Physics: Complex Systems and Dynamics** (3+0+2) 4

This course is aimed towards graduate or advanced undergraduate students in the sciences, engineering and economics. We will show how key concepts in statistical mechanics, such as – critical phenomena

– diffusion and brownian motion

– mean field theories and master equations

can be used to analyze a series of real-world problems ranging from epidemic spreading, internet search engines to social networks. Physics students will benefit from exposure to how basic concepts of statistical physics are applied to areas outside of physics, while non-physics students will be introduced to ideas and concepts from physics and their application in various other subject areas including their own. Ability to program is strongly recommended (Matlab, C, Fortran, Perl, or any other language).

There will be computer assignments and term projects. 3 hours per week (1 day)

Syllabus:

1. Networks and Graphs

2. Random Network Models

– Generating Functions

– Relation to Partition Functions,

Stat. Mech. of Networks

3. Dynamical Processes: theory and simulation

– Master Equations – Mean Field Theory

4. Phase transitions on complex networks

– Percolation Theory

– Critical Phenomena on Networks

5. Walking and Searching on networks

– Brownian Motion/Diffusion

– Application: The Google PageRank

algorithm and web search engines

6. Epidemic Spreading on Networks

– SIS, SIR models applications the cases of

asian influenza and H1N1 (swine flu)

7. Social Networks and Collective Behavior

– Clustering and Communities, communitu overlap and detection

– Applications: Friendship networks such as facebook,

Science Citation Networks (who cites whom)

8. Traffic on complex networks

– transport on networks, the IATA airport network

– an introduction to weighted networks

– connections with epidemics spreading

– Application: commuter patterns

9. (Optional) Networks in Economics

– Online Auction systems

Main Text: (will be followed loosely)

- Dynamical Processes on Complex Networks by Alain Barrat, Alessandro Vespignani,

Marc Barthelemy, Cambridge U. Press

Supplementary Books:

- Evolution and Structure of the Internet: A Statistical Physics Approach by

Romualdo Pastor-Satorras, Alessandro Vespignani, Cambridge U. Press

- Evolution of Networks : From Biological Nets to the Internet and WWW by

S. N. Dorogovtsev, Jose Fernando Mendes, J. F. F. Mendes, Oxford U. Press

- Diffusion and Reactions in Fractals and Disordered Systems by

Daniel Ben-Avraham, Shlomo Havlin

- Research Articles by MEJ Newman, Vespignani, Barrat and others.

**PHYS 58U Special topics in Physics: Cosmology** (3+0+2) 4

**PHYS 58Q Special Topics in Physics: Path Integral Methods in Quantum Physics** (3+0+2) 4

**PHYS 58V Special topics in Physics: Simulation Techniques for Accelerator Systems** (3+0+2) 4

The course covers the basics of simulation techniques of accelerator systems. After a review of particle acceleration mechanisms, various simulation programs that are considered to be standard in modern accelerator physics are introduced. The students are expected to explore and design a accelerator system based on simulation of cavities and the magnet system.

**PHYS 58Y Special topics in Physics: Simulation Techniques for Linacs** (3+0+2) 4

This is a continuation of PHYS58V. The students are expected to focus on the design and simulation of linear accelerators and provide full simulation of a new design. More complex structures such as radio-frequency quadrupoles are also introduced.

**PHYS 590 Special Topics in Physics: Accretion Mechanisms** (3+0+2) 4

In this course the various accretion mechanisms are discussed including the

question/answer of what physical media are the casue of accretion.

Course also includes the ”accretion disks” which is one of the most

imported problems in astrophysics.

**PHYS 591 Special Topics in Physics: Symmetries in differential equations II** (3+0+2) 4

**PHYS 592 Special Topics in Physics: Optoelectronics** (3+0+2) 4

**PHYS 593 Special Topics in Physics: Quantum Optics** (3+0+2) 4

**PHYS 594 Special Topics in Physics: Modelling of Physical Phenomena** (3+0+2) 4

**PHYS 595 Special Topics in Physics: Integrable Systems** (3+0+2) 4

**PHYS 596 Special Topics in Physics: Intro. to String Theory** (3+0+2) 4

**PHYS 597 Special Topics in Physics: Group Theory Methods in Differential Equations** (3+0+2) 4

**PHYS 598 Special Topics in Physics: Molecular and Atomic Physics I** (3+0+2) 4

**PHYS 599 Special Topics in Physics: Computational Fluid Mechanics** (3+0+2) 4

**PHYS 611,612 Relativistic Quantum Mechanics I,II** (3+2+0) 4

(Relativistik Kuantum Mekanigi I,II)

Review of special relativity and four vectors. Klein-Gordon and Dirac equations, and their solutions. Hole theory, interactions and relativistic perturbation theory. Symmetry properties. Applications involving electromagnetic and weak interactions.

**PHYS 621,622 Group Theory for Physicists I,II** (3+2+0) 4

(Fizikçiler Icin Grup Teorisi I,II)

Intensive study of those aspects of group theory which are of greatest importance in physical applications. Definitions and introductory concepts, representations, finite groups, continuous groups: lie groups and Lie algebras. Examples: SU (2), SL (2,C), SU (3). Lie algebras and root spaces, Cartan’s classifications, Dynkin diagrams, real forms, contractions and expansions. Graded Lie groups. Selected applications to high-energy, nuclear, solid-state, crystal, molecular and atomic physics.

**PHYS 625,626 General Relativity and Gravitation I,II** (3+2+0) 4

(Genel Relativite ve Gravitasyon I,II)

Review of special relativity; modern differential geometry; the foundations of general relativity. Einstein field equations, gravitational collapse. Relativistic stars, black holes, singularities and singularity theorems, gravitational radiation, cosmology.

**PHYS 628 Geometric Approach to Mechanics** (3+0+2) 4

(Mekaniğe Geometrik Yaklaşım)

Review of Hamiltonian Mechanics. Introductory concepts from differential geometry: manifolds, vector fields, tensors and forms, exterior derivative and Lie derivative. Symplectic manifolds and Hamiltonian mechanics. Lie groups and group actions on manifolds. Coadjoint orbits as examples of symplectic manifolds. Momentum map construction. Poisson manifolds. Some applications to integrable systems.

**PHYS 631,632 Atomic and Molecular Physics I,II** (3+2+0) 4

(Atom ve Molekül Fizigi I,II)

Theory of spectroscopy in the optical and microwave region. Mean field and electron correlations. Angular momentum through use of Racah formalism. One-electron and many-electron atoms. Atoms in crystal lattices; the Stark and Zeeman effects, highly excited atoms in strong fields. Multiphoton processes, laser spectroscopy. Molecular structure. Atomic and molecular

collisions. Properties of macromolecules.

**PHYS 641,642 Solid State Physics I,II** (3+2+0) 4

(Kati Hal Fizigi I,II)

Periodic structure and symmetry of crystals, lattice dynamics, phonons, electron gas, Fermi surfaces, electrical and thermal conductivity, semiconductors and insulators, magnetic phenomena in solids, band structure.

**PHYS 645,646 Quantum Optics and Electronics I,II** (3+2+0) 4

(Kuantum Optigi ve Elektronigi)

Non-linear optics: harmonic generation, stimulated Brillouin and Raman scattering, mode locking of lasers. Quantum theory of lasers and of the interaction of radiation and atoms. Coupling of radiation to atoms, quantum noise.

**PHYS 648 Integrated and Fiber Optics** (3+2+0) 4

(Entegre ve Fiber Optigi)

Propagation of waves in dielectric thin films and cylindrical guides. Bitlimitation rate due to material dispersion and ultimoding. Step index and graded index fibers. Switching and modulation by integrated optics techniques.

**PHYS 651, 652 Nuclear Physics I, II** (3+2+0) 4

(Nükleer Fizik)

Review of nuclear properties. Fermi gas model, nuclear matter. Independent particle model and the nuclear shell model, the Hartree-Fock method, RPA. Models of nuclear collective motion: rotations, vibrations and giant resonances. Nuclear pairing theory. Electromagnetic and weak interactions of nuclei:

electron scattering, beta decay, muon capture.

Nuclear reactions:

optical model, direct reactions, compound nuclear reactions, statistical properties of spectra.

Heavy ion collisions and fission.

**PHYS 655, 656 High-Energy Nuclear Physics I, II ** (3+2+0) 4

(Yüksek Enerji Nükleer Fizigi I, II)

Studies of nuclear structure using high-energy probes. Elastic and inelastic scattering of high energy electrons, nucleons, mesons, photo-disintegration. Isobars and nuclear structure. Distribution of charge, matter and magnetization in nuclei. Mesonic atoms. Presentations of topics of current interest.

**PHYS 661, 662 Particle Physics I, II** (3+2+0) 4

(Parçacik Fizigi I, II)

Phenomenology of particle properties and interactions stressing experimental results. Conservation laws. Accelerators, particle detectors and techniques. Strong interactions, quark model predictions. Electromagnetic interactions, Dirac-Feynman theory. Weak interactions, V-A theory, non-conservation of parity. Gauge field theories, Weinberg-Salam theory of electroweak interactions, color-gauge groups and recent models.

**PHYS 665, 666 Field Theory I, II** (3+2+0) 4

(Alan Teorisi I,II)

Classical field theory, canonical quantization. Dirac field. Interacting fields, perturbation

theory. S-matrix and the LSZ formalism. Feynman graphs. Functional methods, non-perturbative properties. Renormalization. Calculations in quantum electrodynamics.

**PHYS 675, 676 Phase Transitions and Critical Phenomena I, II** (3+2+0) 4

(Faz Degisimleri ve Kritik Olaylar I, II)

Physical ideas and current techniques used in the study of critical phenomena in statistical mechanics and field theory. Landau theory of phase transitions, critical indices, scaling and universality, renormalization group, duality transformations, lattice gauge theory.

**PHYS 681, 682 Graduate Seminar in Physics I,II** (3+0+0) 3

(Lisansüstü Fizik Semineri I,II)

Study of selected advanced topics under the supervision of one or more faculty members. Both written and oral presentations are required.

**PHYS 683 Special Topics in Physics Topics in 2 dimensional Field Theories** (3+0+2) 4

**PHYS 684 Special Topics in Physics Selected Topics in Astrophysics I** (3+0+2) 4

**PHYS 685 Special Topics in Physics Characterization techniques in solid state physics I** (3+0+2) 4

**PHYS 686 Special Topics in Physics Selected Topics in Astrophysics II** (3+0+2) 4

“Time series” data analysis of isolated neutron stars through XmmNewton, Chandra and Suzaku Satellites. Data Reduction techniques, Application of various time series Methods, Fast Fourier Transform Apllication to these data, and the discussion of applied methods and the results.

**PHYS 687 Special Topics in Physics Cataclysmic Variables** (3+0+2) 4

**PHYS 688 Special Topics in Physics Introduction to Supersymmetry and Supergravity** (3+0+2) 4

**PHYS 689 Special Topics in Physics Advanced Topics in Physical Electronics I** (3+0+2) 4

**PHYS 68A Special Topics in Physics** (3+0+2) 4

**PHYS 68B Special Topics in Physics: Topics in Gauge Theories** (3+0+2) 4

**PHYS 68C Special Topics in Physics Sep.Top.in High Energy Physics** (3+0+2) 4

**PHYS 68D Special Topics in Physics: Sep.Top.in Monte Carlo packages for event generation and detector simulation.** (3+0+2) 4

**PHYS 68E Special Topics in Physics : Introduction to Loop Quantum Gravity** (3+0+2) 4

**PHYS 68F Special Topics in Physics : Experimental Methods in (HEP) Hİgh Energy Physics** (3+0+2) 4

**PHYS 68G Special Topics in Physics : Photonics I** (3+0+2) 4

Optical principles and phenomena are introduced. Topics include electromagnetic theory of light, interference, diffraction, polarization, photon optics, principles of laser, Gaussian beam optics, semiconductor optics, semiconductor photonic devices, and holography.

**PHYS 68H Special Topics in Physics : Physics of Electronic Devices** (3+0+2) 4

**PHYS 68I Special Topics in Physics : Physics of Electronic Devices II** (3+0+2) 4

**PHYS 68J Special Topics in Physics: Calorimetry in CMS** (3+0+2) 4

**PHYS 68K Special Topics in Physics: Ultrafast Photonics** (3+0+2) 4

Pico/femtosecond techniques. Standing wave and travelling wave resonators.

Active and passive modelocking schemes. Saturable gain and loss. Nonlinear

optical effects for enhanced modelocking. Application examples and measurement

techniques associated with ultrashort laser pulses.

**PHYS 68L Special Topics in Physics: Atmospheric and Oceanic Fluid Dynamics** (3+0+2) 4

Equations of motion, shallow water systems, vorticity and potential vorticity, simple equations for ocean and atmosphere, barotropic and baroclinic instability, theory of incompressible turbulance, turbulent diffusion and eddy transport.

**PHYS 68M Special Topics in Physics: General circulation modelling** (3+0+2) 4

Basic equations of general circulation models, spectral method on a sphere, vertical discretization, time integration, standard experiments of AGCMs

**PHYS 68N Special Topics in Physics: Advanced Computations in Physics** (3+0+2) 4

This course aims to give the student a thorough grounding in the main computational techniques used in modern physics. The following topics will be covered in an advanced level: Computational linear algebra, numerical integration, numerical solution of ODE, root finding, minimization-maximization of generalized functions, modeling of data, interpolation-extrapolation in multi-dimensions, Monte Carlo and other simulation methods.

**PHYS 68O Special Topics in Physics: Atmospheric and Oceanic Fluid Dynamics II** (3+0+2) 4

Overturning circulation, planetary waves and the stratosphere, wind driven gyres, wind and buoyancy driven ocean circulation.

Possible book:

Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-scale Circulation (Hardcover) by Geoffrey K. Vallis

**PHYS 68P Special Topics in Physics: Physics of Regional Climate Modeling** (3+0+2) 4

Radiation scheme, land surface model, planetary boundary layer scheme, convective precipitation schemes, large-scale precipitation scheme, ocean flux parameterization, pressure gradient scheme, lake model, aerosols and dust

Possible books:

Atmospheric Circulation Dynamics and Circulation Models (Springer Praxis Books / Environmental Sciences) by Masaki Satoh RegCM Version 3.1, User’s Guide by ICTP.

**PHYS 68R Special Topics in Physics: Jordan-Brans-Dicke Theories of Gravity** (3+0+2) 4

Main aim of this course is to discover Jordan-Brans-Dicke (JBD) scalar-tensor theory of gravitation as a prototype of all other scalar-tensor theories of gravitation. To do so, firstly, required tools will be introduced from general relativity such as elements os relativistic mechanics, variational methods, energy momentum tensor and structure of field equations.

All above tools will be aimed to be given with the motivation of understanding JBD theory well in the sense that how its field equations are derived and what kind of cosmological applications can JBD have?

**PHYS 68S Special Topics in Physics: Beam Physics** (3+0+2) 4

**PHYS 68T Special Topics in Physics: Multivariate Analysis Methods in High Energy Physics** (3+0+2) 4

**PHYS 68U Special Topics in Physics: Spintronics** (3+0+2) 4

**PHYS 68V Special Topics in Phys Quantum field theory in curved space-time** (3+0+2) 4

Review of QFT in Minkowski space, basics of QFT in curved space-time (non-uniquness of vacuum, Bogolubov transformations, simple particle creation effects in time dependent backgrounds etc.), Green functions, stress-tensor renormalization (adiabatic and point splitting regularizations etc.), conformal anomalies, applications to cosmology (Robertson-Walker spaces, generation of cosmological perturbations during inflation, particle creation effects in reheating etc.), Hawking radiation.

**PHYS 68Y Special Topics in Physics: Spectral Methods in Physics** (3+0+2) 4

**PHYS 690 M.S.
Thesis**

(Yüksek Lisans Tezi)

**PHYS 691 Special Topics in Physics Symplectic Geometry** (3+0+2) 4

**PHYS 692 Special Topics in Physics Kaluza Klein Theory** (3+0+2) 4

**PHYS 693 Special Topics in Physics Linac Structures and Longitudinal Beam Dynamics** (3+0+2) 4

**PHYS 694 Special Topics in Physics Quantum Chromodynamics and weak Interactions** (3+0+2) 4

**PHYS 694 Special Topics in Physics Selected Topics in Mathematical Physics** (3+0+2) 4

**PHYS 695 Special Topics in Physics: Supersymmetric Gauge Theories** (3+0+2) 4

**PHYS 696 Special Topics in Physics** (3+0+2) 4

**PHYS 697 Special Topics in Physics: Advanced physical electronics II** (3+0+2) 4

**PHYS 698 Special Topics in Physics: Stochastic Methods in Physics** (3+0+2) 4

(Yönlendirilmis Arastirmalar)

Research in Physics, by arrangement with members of the faculty, guidance of doctoral students towards the preparation and presentation of a research proposal.