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					<div id="intro-text" class="intro-lead-in">Master's degree in</div>
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					<div><a id="intro-btn" href="#about" class="page-scroll btn btn-xl">Why study this master?</a></div>
					<div><a id="intro-btn" href="https://www.upc.edu/en/masters/access-and-admission/pre-enrolment" target="_blank" class="btn btn-enrollment">Pre-enrolment</a></div>
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						<h2>MOTIVATION</h2>
						<p>The master's degree in Engineering Physics is oriented towards frontier engineering based on advanced education in physics. Specialist engineering fields such as nanotechnology, nanoelectronics and biomedical engineering require an
							ever-growing number of professionals who have extensive training in advanced physics and sound knowledge of quantum physics, complex system physics and device physics, which can be applied both at the nanoscopic scale and in large-scale
							facilities.</p>
						<p><a id="read-more-motivation">Read more</a></p>
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						<p><b>The master in Engineering Physics allows physicists and  interested engineers to finish off their training profile in a large number of fields within modern physics  and also broadening their scope</b><p>

						<p>The common formation offers transverse subjects on physics and advanced engineering of wide applicability in both research and industrial development applications. Furthermore, the elective subjects allow the students to complete its academic profiles with subjects complementary to their degrees: New materials, Complex systems - with applications into Biophysics -, Numerical methods and a wide offer in elective subjects from the different branches of engineering taught in UPC. This way a physicist o physics engineer can obtain a more engineering-oriented profile while an engineer can deepen into more fundamental subjects.</p>
						<p><a id="read-less-motivation">Show less</a></p>
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						<h2>A MASTER WITH PROFESSIONAL OPPORTUNITIES</h2>
						<p class="skills-p">The master's degree in Physical Engineering is associated to content with a high labor demand.</p>
						<br></br>
						<p class="skills-p">From senior researcher or technical staff, to management and management positions, going through a project, area or department, with the possibility of becoming an entrepreneur entrepreneur</p>
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							<h3 class="skills-p">Basic and applied research centres.</h3>
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							<h3 class="skills-p">Frontier engineering in the field of nanotechnology.</h3>
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						<h2>COURSES</h2>
						<p>The master program comprises 23 ECTS of common subjects, 20 ECTS of elective subjects and a master thesis of 17 ECTS. Elective subjects can be chosen among different Physics and Engineering courses.<br></br></p>
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								<h2>Common Subjects</h2>
								<p>23 ECTS</p>
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								<h2>Elective Subjects in Physics</h2>
								<p>20 ECTS</p>
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								<h2>Elective Subjects in Engineering</h2>
								<p>Max 12 ECTS</p>
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								<h2>Master Thesis</h2>
								<p>17 ECTS</p>
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								<td class="" rowspan="2">Fall semester</td>
								<td class="" style="text-align: center;"><p style="color:#397eb9; margin-bottom:0px;">Critical phenomena and complexity</p>(5 ECTS)</td>
								<td class="" style="text-align: center;"><p style="color:#397eb9; margin-bottom:0px;">Quantum Matter</p>(5 ECTS)</td>
								<td bgcolor="" style="text-align: center; "><p style="color:#397eb9; margin-bottom:0px;">Surface engineering and microdevices</p>(5 ECTS)</td>
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								<td class="" style="text-align: center; "><p style="color:#397eb9; margin-bottom:0px;">Large facilities: synchrotron and neutron sources</p><span>(5
										ECTS)</span></td>
								<td style="text-align: center;"><p style="color:#397eb9; margin-bottom:0px;">Project management</p><span>(3 ECTS)</span></td>
								<td class="" style="text-align: center;"><p style="color:#397eb9; margin-bottom:0px;">Elective subjects</p><span>(7 ECTS)</span></td>
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								<td class="" rowspan="2">Spring semester</td>
								<td class="" colspan="3" style="text-align: center;"><p style="color:#397eb9; margin-bottom:0px;">Elective subjects</p><span>(13 ECTS)</span></td>
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								<td class="" colspan="3" style="text-align: center;"><p style="color:#397eb9; margin-bottom:0px;">Master thesis
									</p><span>(17 ECTS)</span></td>
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					<h3>Duration and start date</h3>
					<p>One academic year, 60 ECTS credits.</p>
					<p>Starting September.</p>
					<h3>Fees and Grants</h3>
					<p>Approximate fees for the master’s degree, excluding academic fees and degree certificate fee, €3,200 (€5,400 for non-EU residents). </p>
					<p>The Department of Physics will offer 3 grants of 1000 € for students carrying out their master thesis in <a href="https://fisica.upc.edu/en/research/research-groups" target="_blank">research groups</a> of the Department</p>
					<p><a class="external-link" href="https://www.upc.edu/en/masters/fees-grants" target="_blank" title="">More information about fees and payment options</a>.</p>
					<h3>Timetable and delivery</h3>
					<p>Afternoons. Face-to-face.</p>
					<h3>Language of instruction</h3>
					<p>English.</p>
					<h3>Location</h3>
					<p><a href="http://maps.upc.edu/?iU=109&amp;lang=en" target="_blank">Barcelona School of Telecommunications Engineering (ETSETB)</a></p>
					<h4>Contact the master coordinator or the managing team for further information or guidance.</h4>
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					<h3>Student Profile</h3>
					<p>Holders of a degree, or students in the last year of studies of a degree, can apply for admission to the master in Engineering Physics. An official degree certificate is necessary the day of registration, in September. Please check the
						<a href="https://www.upc.edu/en/masters/access-and-admission/academic-requirements" target="_blank">general academic requirements for master's degrees at UPC-Barcelona Tech.</a><br></br>The master in Engineering Physics The master in Engineering Physics is mainly oriented to graduates in engineering physics and physicists willing to broaden their education in cutting edge engineering applications and advanced physics. Other graduates in engineering or applied
						sciences are also invited to apply.
					</p>
					<h3>Pre-enrolment is now open!</h3>
					<div style="float:left;"><a href="https://www.upc.edu/en/masters/access-and-admission/pre-enrolment" target="_blank" class="btn btn-enrolment2">Pre-enrolment</a></div>
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						<h2>Related Companies</h2>
						<p>The master in Engineering Physics, due to its standing has various agreements with many companies and  research centers. Below you will find a non-exhaustive list of companies related to the master</p>
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								<img src="https://telecos.upc.edu/ca/shared/masters-degree-in-engineering-physics/images/logo_alba.png" alt="Synchrotron ALBA"/>
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								<div>
									<p>ALBA is a 3rd generation Synchrotron Light facility located in Cerdanyola del Vallès, (Barcelona), being the newest source in the Mediterranean area.</p><p>It is a complex of electron accelerators to produce synchrotron light, which allows the visualization of the atomic structure of matter as well as the study of its properties.</p>
									<p style="text-align:center;"><a href="https://www.cells.es/en/home?set_language=en">Synchrotron ALBA</a></p>
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								<img src="https://telecos.upc.edu/ca/shared/masters-degree-in-engineering-physics/images/logo_dexeus.jpg" alt="Hospital Universitari Dexeus - grup Quiron salud"/>
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								<div>
									<p>Dexeus University Hospital is one of the most technologically advanced centers in Spain in diagnostic facilities.</p><p>The Image Diagnostic Service of the Dexeus University Hospital offers patients all sorts of diagnostic explorations. In addition to the conventional radiological procedures (simple radiology, orthopantomography, specific radiology of trauma, proven tests), it also studies body, neuro and musculoskeletal in CT and magnetic resonance.</p>
									<p style="text-align:center;"><a href="https://www.quironsalud.es/dexeus-barcelona/ca/cartera-de-serveis/diagnostic-per-la-imatge">Hospital Universitari Dexeus - grup Quiron salud</a></p>
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								<img src="https://telecos.upc.edu/ca/shared/masters-degree-in-engineering-physics/images/logo_sefm.png" alt="Sociedad Española de Física Médica - Radiofísica hospitalaria"/>
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								<div>
									<p>Medical Physics is the application of the methods of Physics to Health Sciences, playing an important role in health care, biomedical research and prevention. It could be considered as one of the applications of Physics that has the greatest and most direct impact on people, because it has a direct impact on Health.</p><p>The medical activity in Medical Physics, as a professional activity, takes place in Spain through a health specialty called Hospital Radiophysics.</p>
									<p style="text-align:center;"><a href="https://sefm.es/radiofisica-hospitalaria/">Sociedad Española de Física Médica - Radiofísica hospitalaria</a></p>
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			<h2>Ph.D. Program</h2>
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					<p style="text-align: center;"><b>PhD studies in Computational and Applied Physics</b> provide a high level training in the fields of Computational Physics and Applied Physics, as well as supplying an appropriate background in the general
						methodologies of the scientific and
						technical research. Our aim is that future PhDs have the capacity to lead both research and technological innovation in the fields indicated above.</p>
					<p style="text-align: center;">Please visit <a target="_blank" href="https://doctorat-fcia.postgrau.upc.edu/en">the PhD in Computational and Applied Physics website</a></p>
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						<h2>ACADEMIC INFORMATION</h2>
						<p>Relevant information on the present schoolyear will be posted here. Keep in mind that the information shown below belongs to the course 18-19</p>
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									<h3>Autumm Semester Timetable 18-19</h3>
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												<p>Hours</p>
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												<p>Monday</p>
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												<p>Tuesday</p>
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												<p>Wednesday</p>
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												<p>Friday</p>
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												<p>14:00-15:00</p>
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												<p>Large facilities: synchrotron and neutron sources</p>
											</td>
											<td bgcolor="#e6eeff" class="" rowspan="2">
												<p>Critical phenomena and complexity<span style="text-align: left; text-decoration-style: initial; text-decoration-color: initial; float: none; "><span>
														</span></span></p>
											</td>
											<td bgcolor="#f2ffe6">
												<p>Physics of materials</p>
											</td>
											<td bgcolor="#ffe6ff" rowspan="2">
												<p>Quantum Matter</p>
											</td>
											<td bgcolor="#eee6ff" class="" rowspan="2">
												<p>Large facilities: synchrotron and neutron sources</p>
											</td>
										</tr>
										<tr>
											<td>
												<p>15:00-16:00</p>
												<p> </p>
											</td>
											<td bgcolor="#e6ffe6" rowspan="2">
												<p>Project management</p>
											</td>
										</tr>
										<tr>
											<td>
												<p>16:00-17:00</p>
												<p> </p>
											</td>
											<td bgcolor="#ffe6ff" rowspan="2"><p>Quantum Matter</p></td>
											<td bgcolor="#ffe6e6" roeee6ffwspan="3">
												<p>Machine learning with neural networks</p>
											</td>
											<td bgcolor="#e6eeff" class="" rowspan="2">
												<p>Critical phenomena and complexity<span style="text-align: left; text-decoration-style: initial; text-decoration-color: initial; float: none; "><span>
														</span></span></p>
											</td>
											<td bgcolor="#f2ffe6" rowspan="2">
												<p>Physics of materials</p>
											</td>
										</tr>
										<tr>
											<td>
												<p>17:00-18:00</p>
												<p> </p>
											</td>
											<td bgcolor="#e6fffa">
												<p>Numerical methods for continuum systems<span style="text-align: left; text-decoration-style: initial; text-decoration-color: initial; float: none; "><span> <br /></span></span></p>
											</td>
										</tr>
										<tr>
											<td>
												<p>18:00-19:00</p>
												<p> </p>
											</td>
											<td bgcolor="#e6fffa" rowspan="2">
												<p>Numerical methods for continuum systems<span style="text-align: left; text-decoration-style: initial; text-decoration-color: initial; float: none; "><span> </span></span></p>
											</td>
											<td bgcolor="#fff2e6" rowspan="2">
												<p>Surface engineering and microdevices</p>
											</td>
											<td bgcolor="#fff2e6" rowspan="2">
												<p>Surface engineering and microdevices</p>
											</td>
											<td rowspan="2">
												<p> </p>
											</td>
										</tr>
										<tr>
											<td>
												<p>19:00-20:00</p>
												<p> </p>
											</td>
											<td></td>
										</tr>
									</tbody>
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								<h3>Spring Semester Timetable 18-19</h3>
							</div>
							<br></br>
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								<tbody>
									<tr>
										<td>
											<p style="text-align: center; ">Hours</p>
										</td>
										<td style="text-align: center; ">
											<p>Monday</p>
										</td>
										<td style="text-align: center; ">
											<p>Tuesday</p>
										</td>
										<td style="text-align: center; ">
											<p>Wednesday</p>
										</td>
										<td style="text-align: center; ">
											<p>Thursday</p>
										</td>
										<td>
											<p style="text-align: center; ">Friday</p>
										</td>
									</tr>
									<tr>
										<td>
											<p>14:00-15:00</p>
										</td>
										<td bgcolor="#eee6ff" class="" rowspan="3"><p>Atomic and molecular physics</p></td>
										<td bgcolor="#ffe6ff" rowspan="3"><p>Molecular and soft condensed matter</p></td>
										<td bgcolor="#e6eeff" rowspan="3">
											<p>Complexity in biological systems</p>
										</td>
										<td bgcolor="#f2ffe6" rowspan="3">
											<p>Stochastic methods</p>
											<p>for optimization and simulation</p>
										</td>
										<td bgcolor="#eee6ff" rowspan="3"><p>Atomic and molecular physics</p></td>
									</tr>
									<tr>
										<td>
											<p>15:00-16:00</p>
										</td>
									</tr>
									<tr>
										<td>
											<p>16:00-17:00</p>
										</td>
									</tr>
									<tr>
										<td>
											<p>17:00-18:00</p>
										</td>
										<td bgcolor="#fff2e6" rowspan="3">
											<p>Computational astrophysics</p>
										</td>
										<td bgcolor="#f2ffe6" rowspan="3">
											<p>Stochastic methods</p>
											<p>for optimization and simulation</p>
										</td>
										<td bgcolor="#ffe6ff" rowspan="3"><p>Molecular and soft condensed matter</p></td>
										<td bgcolor="#fff2e6" rowspan="3">
											<p>Computational astrophysics</p>
										</td>
										<td bgcolor="#e6eeff" rowspan="3">
											<p>Complexity in biological systems</p>
										</td>
									</tr>
									<tr>
										<td>
											<p>18:00-19:00</p>
										</td>
									</tr>
									<tr>
										<td>
											<p>19:00-20:00</p>
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					<h3>Academic Calendar</h3>
					<p>The Academic year consists in 2 semesters, for a more detailed information check the following PDF<p>
							<div><a href="https://engineeringphysics.masters.upc.edu/en/shared/calendari_lectiu_mef_18-19_v2.pdf" target="_blank" class="btn btn-enrolment2">Academic Calendar 18/19</a></div>
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					<h3>Information about Master Degree Theses</h3>
					<p>The organization, enrolment procedures and evaluation of the MEF Master Theses are governed by the following regulations<p>
							<div><a href="https://engineeringphysics.masters.upc.edu/en/Academic/Normativa_master_TFM_ang_v1.pdf" target="_blank" class="btn btn-enrolment2">Master Degree Theses regulations</a></div>
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						<h2>Contact Us</h2>
						<p>The master in Engineering Physics is offered at the <a target="_blank" href="https://telecos.upc.edu">Escola Tècnica Superior d'enginyeria de Telecomunicació de Barcelona (ETSETB)</a>, member of <a target="_blank" href="https://upc.edu">Universitat Politècnica de Catalunya - BarcelonaTech (UPC)</a>.<br></br>It is located on Campus Nord <a target="_blank" href="https://www.google.es/maps/place/Escola+T%C3%A8cnica+Superior+d'Enginyeria+de+Telecomunicaci%C3%B3+de+Barcelona+(ETSETB)+-+UPC/@41.3885012,2.1099008,17z/data=!3m1!4b1!4m5!3m4!1s0x12a49856d0c02eaf:0x6bdb5654e2465736!8m2!3d41.3885012!4d2.1120948">See location in Google maps.</a></p>
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					<p style="margin-bottom: 0px;"><b>Academic coordination:</b></p><p>Prof. Jordi Boronat <a href="mailto:jordi.boronat@upc.edu">jordi.boronat@upc.edu</a></p>
					<p style="margin-bottom: 0px;"><b>Administrative coordinator:</b></p><p>Alicia Sanchez-Nabau <a href="mailto:alicia.sanchez.nabau@upc.edu">alicia.sanchez.nabau@upc.edu</a></p>
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					<p style="margin-bottom: 0px;"><b>Secretary:</b></p><p>93 405 4174 <b>/</b> 93 401 6772 <b>/</b> 93 401 5966 <b>/</b> 93 401 6750 <a href="mailto:secretaria@etsetb.upc.edu">secretaria@etsetb.upc.edu</a></p>
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					<p>Common subjects will be scheduled in the first semester (autumm).</p>
					<p>Below there is the list with all the common subjects students must enroll: </p>
					<ul>
						<li><a class="my-popover" data-placement="top" data-html="true" data-trigger="focus" id="pop-critical" href="#" data-toggle="popover">Critical phenomena and complexity</a> (5 ECTS)</li>
						<li><a class="my-popover" data-placement="top" data-html="true" data-trigger="focus" id="pop-quantum" href="#" data-toggle="popover">Quantum Matter</a> (5 ECTS)</li>
						<li><a class="my-popover" data-placement="top" data-html="true" data-trigger="focus" id="pop-surface" href="#" data-toggle="popover">Surface engineering and microdevices</a> (5 ECTS)</li>
						<li><a class="my-popover" data-placement="top" data-html="true" data-trigger="focus" id="pop-large" href="#" data-toggle="popover">Large facilities: synchrotron and neutron sources</a> (5 ECTS)</li>
						<li><a class="my-popover" data-placement="top" data-html="true" data-trigger="focus" id="pop-project" href="#" data-toggle="popover">Project management</a> (3 ECTS)</li>
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					<p>Elective subjects in Physics are broadly grouped in three main areas:</p>
					<ul>
						<li>Physics of matter and materials
							<ul>
								<li><a class="my-popover" data-placement="top" data-html="true" data-trigger="focus" id="pop-molecular" href="#" data-toggle="popover">Molecular and soft condensed matter</a> (4 ECTS)</li>
								<li><a class="my-popover" data-placement="top" data-html="true" data-trigger="focus" id="pop-atomic" href="#" data-toggle="popover">Atomic and molecular physics</a> (4 ECTS)</li>
								<li><a class="my-popover" data-placement="top" data-html="true" data-trigger="focus" id="pop-materials" href="#" data-toggle="popover">Physics of materials</a> (4 ECTS)</li>
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						<li>Complex systems
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								<li><a class="my-popover" data-placement="top" data-html="true" data-trigger="focus" id="pop-complexity" href="#" data-toggle="popover">Complexity in biological systems</a> (4 ECTS)</li>
								<li><a class="my-popover" data-placement="top" data-html="true" data-trigger="focus" id="pop-machine" href="#" data-toggle="popover">Machine learning with neural networks</a> (4 ECTS)</li>
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						<li>Numerical methods in physics and engineering
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								<li><a class="my-popover" data-placement="top" data-html="true" data-trigger="focus" id="pop-numerical" href="#" data-toggle="popover">Numerical methods for continuum systems</a> (4 ECTS)</li>
								<li><a class="my-popover" data-placement="top" data-html="true" data-trigger="focus" id="pop-stochastic" href="#" data-toggle="popover">Stochastic methods for optimization and simulation</a> (4
									ECTS)</li>
								<li><a class="my-popover" data-placement="top" data-html="true" data-trigger="focus" id="pop-computational" href="#" data-toggle="popover">Computational astrophysics</a> (4 ECTS)</li>
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					<p>Elective subjects in Engineering up to 12 ECTS can be chosen from the offer of all masters offered by UPC. <br></br>The following list is indicative but not exhaustive:</p>
					<ul>
						<li>Fundamentals of Nuclear Engineering and radiologic protection (<a class="external-link" href="https://nuclearengineering.masters.upc.edu/en" target="_blank" title="">Master in nuclear engineering</a>)</li>
						<li>Energy technology (<a class="external-link" href="https://engquim.masters.upc.edu/en" target="_blank" title="">Master in chemical engineering</a>)</li>
						<li>Renewable energy technology (<a class="external-link" href="https://energia.masters.upc.edu/en" target="_blank" title="">Master in energy engineering</a>)</li>
						<li>Particle accelerators engineering (<a class="external-link" href="https://muei.etseib.masters.upc.edu/en/general-information" target="_blank" title="">Màster Universitari en Enginyeria Industrial</a>)</li>
						<li>Introduction to photonics, optics and lasers (<a class="external-link" href="http://photonics.masters.upc.edu/en" target="_blank" title="">Master of photonics</a>)</li>
						<li>Quantum optics (<a class="external-link" href="http://photonics.masters.upc.edu/en" target="_blank" title="">Master of photonics</a>)</li>
						<li>Telecommunication systems (<a class="internal-link" href="http://etsetb.upc.edu/ca/estudis/masters/masters-degree-in-telecommunications-engineering-met" target="_blank" title="">Master's degree in Telecommunications Engineering</a>)</li>
						<li>Communication networks (<a class="internal-link" href="http://etsetb.upc.edu/ca/estudis/masters/masters-degree-in-telecommunications-engineering-met" target="_blank" title="">Master's degree in Telecommunications Engineering</a>)</li>
						<li>Microwaves and antennas (<a class="internal-link" href="http://etsetb.upc.edu/ca/estudis/masters/masters-degree-in-telecommunications-engineering-met" target="_blank" title="">Master's degree in Telecommunications Engineering</a>)</li>
						<li>Introduction to computer vision (<a class="internal-link" href="http://etsetb.upc.edu/ca/estudis/masters/masters-degree-in-telecommunications-engineering-met" target="_blank" title="">Master's degree in Telecommunications Engineering</a>)</li>
						<li>Continuous optimization (<a class="external-link" href="https://mesioupcub.masters.upc.edu/en/pathways/Operations%20Research%20%28IO%29" target="_blank" title="">Master in optimization and operations research</a>)</li>
						<li>Linear multivariate control systems (<a class="external-link" href="https://mar.masters.upc.edu/en" target="_blank" title="">Master's in automatic control and robotics</a>)</li>
						<li>Data mining (<a class="external-link" href="https://www.talent.upc.edu/ing/professionals/presentacio/codi/200800/big-data-management-technologies-analytics/" target="_blank" title="">Master in big data management and analytics</a>)</li>
						<li>Computational vision (<a class="external-link" href="https://www.fib.upc.edu/en/studies/masters/master-artificial-intelligence" target="_blank" title="">Master in artificial intelligence</a>) </li>
						<li>Mathematical models in biology (<a class="external-link" href="https://mamme.masters.upc.edu/es" target="_blank" title="">Master in advanced mathematics and mathematical engineering</a>)</li>
						<li>Biomaterials (<a class="external-link" href="https://materials.masters.upc.edu/en" target="_blank" title="">Master in materials science and engineering</a>)</li>
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					<p>The master thesis can be performed in a research group of UPC, in a research institute or in a company, either in Catalunya or abroad.</p>
					<p>To facilitate the development of the master thesis outside UPC some of the elective subjects will be taught in the first semester and other will be taught in the first two months of the second semester.</p>
					<p>Institutions offering Masters Thesis:</p>
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						<li>ALBA Sincrotró</li>
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			<h2>Syllabus</h2>
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				<li><b>Critical phenomena</b></li>
				<ul>
					<li>Mean Field</li>
					<li>Scaling and renormalization group</li>
					<li>Kinetic Ising models</li>
					<li>Continuum models</li>
					<li>Growth Models</li>
					<li>Percolation</li>
				</ul>
				<li><b>Dynamical Systems</b></li>
				<ul>
					<li>Flows and maps</li>
					<li>Normal Forms</li>
					<li>Stability; Bifurcations</li>
					<li>Intermittency; Chaos</li>
					<li>Pattern formation</li>
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				<li><b>Stochastic Processes</b></li>
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					<li>Markov processes</li>
					<li>Master equations</li>
					<li>Stochastic differential equations</li>
					<li>Fokker-Planck equations</li>
					<li>Relaxation and First-passage times</li>
				</ul>
				<li><b>Introduction to complex networks</b></li>
				<ul>
					<li>Small-world networks</li>
					<li>Scale-free networks</li>
					<li>Characterization of networks</li>
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			<h2>Syllabus</h2>
			<ol>
				<li><b>Approximate methods in Quantum Mechanics.</b></li>
				<ul>
					<li>Description of the problem. Mathematical formulation.</li>
					<li>Solution of the problem using variational methods. Time-independent perturbation theory approach.</li>
				</ul>
				<li><b>Introduction to Scattering theory in Quantum Mechanics.</b></li>
				<ul>
					<li>Formulation of the problem, differential cross section and Lipmann-Schwinger equation. T-matrix, Born approximation and partial wave expansions. Low-energy scattering.</li>
				</ul>
				<li><b>The many-body problem in Quantum Mechanics.</b></li>
				<ul>
					<li>Bose and Fermi statistics, wave functions and simmetries.</li>
					<li>Second quantization: creation and anihilation operators. Operators and observables in second quantization.</li>
					<li>Hartree-Fock approximation, Gross-Pitaevskii equation and the Bogoliubov approximation.</li>
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				<li><b>Magnetic systems</b></li>
				<ul>
					<li>Polarized and unpolarized free Systems.</li>
					<li>Ferromagnetic states. Single-particle excitations and particle-hole pairs. Magnons. Superconductivity and Cooper pairs. Introduction to BCS theory.</li>
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				<li><b>Lattice systems: Bose- and Fermi-Hubbapop-contentrd models.</b></li>
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			<h2>Syllabus</h2>
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				<li><b>Physical Chemistry of surfaces</b></li>
				<ul>
					<li>Introduction to surfaces</li>
					<li>Structure of surfaces</li>
					<li>Solid-liquid and solid-gas interphases</li>
					<li>Characterization techniques</li>
					<li>Applications in sensors and catalysis</li>
					<li>Functionalization of nano- and microreactors</li>
				</ul>
				<li><b>Mechanics and Fluid mechanics at micron scale</b></li>
				<ul>
					<li>Introduction to micromechanic and microfluidic behavior.</li>
					<li>Biosensor structure</li>
					<li>Design and simulation of the biosensor fluidic behavior</li>
					<li>Design and simulation of the biosensor mechanic behavior</li>
					<li>Case studies in bioengineering and comunications.</li>
				</ul>
				<li><b>MEMS microdevices applied to communication circuits</b></li>
				<ul>
					<li>Introduction to MEMS micro-devices. Materials and structures.</li>
					<li>Ohmic- and capacitive-contact micro-switches.</li>
					<li>MEMS micro-switch electromagnetic simulation</li>
					<li>Application of MEMS micro-switches to reconfigurable communication circuits.</li>
					<li>Circuit simulation.</li>
					<li>Experimental characterization of MEMS micro-switches.</li>
				</ul>
			</ol>
		</div>
	</div>

	<div id="popover-content-large" class="hide">
		<div class="pop-content">
			<h2>Syllabus</h2>
			<ol>
				<li><b>Sources of Synchrotron and neutron radiation.</b></li>
				<ul>
					<li> Continuous and pulsed sources.</li>
				</ul>
				<li><b>Safety in large facilities.</b></li>
				<li><b>Design of main devices in Sinchrotron and neutron sources:</b></li>
				<ul>
					<li>focusing of photons and neutrons</li>
					<li>dispersion and detection</li>
				</ul>
				<li><b>Design and use of special sample environments:</b></li>
				<ul>
					<li>High pressure</li>
					<li>high and low temperature</li>
					<li>magnetic fields.</li>
				</ul>
				<li><b>Experimenal techniques available in large facilities.</b></li>
				<ul>
					<li> Complementarity between experimental techniques</li>
				</ul>
				<li><b>Generation, storage and analysis of large facilities:</b></li>
				<ul>
					<li>Experimental data</li>
				</ul>
			</ol>
		</div>
	</div>

	<div id="popover-content-project" class="hide">
		<div class="pop-content">
			<h2>Syllabus</h2>
			<ol>
				<li>Project planning.</li>
				<li>Planning methods based on critical path.</li>
				<li>Precedence analysis, PERT and GANTT chart.</li>
				<li>Time and cost estimation.</li>
				<li>Risk identification and mitigation plans.</li>
				<li>Stakeholders communication management.</li>
				<li>Project execution management: earned value.</li>
				<li>Project closure: success criteria and lessons learned.</li>
			</ol>
		</div>
	</div>

	<div id="popover-content-molecular" class="hide">
		<div class="pop-content">
			<div class="row">
				<div class="col-sm-6">
					<img style="max-width:100%; max-height: 100%;" src="https://engineeringphysics.masters.upc.edu/en/images/real_time_crystallization_supercooled_liquid_antiepileptic_drug.png" title="Optical microscopy images of the crystallization, as observed in real time, of the supercooled liquid state of an antiepileptic drug (stiripentol)" />
				</div>
				<div class="col-sm-6">
					<img style="max-width:100%; max-height: 100%; margin-top: 2.5%;" src="https://engineeringphysics.masters.upc.edu/en/Courses/elective-subjects-in-physics/spherulites_nylon4_7.png" title="Polarized light microscopy image of a semicrystalline spherulite of the polymer Nylon 4,7 taken using a first order red plate to determine the sign of the birrefringence" />
				</div>
			</div>
			<h2>Syllabus</h2>
			<ol>
				<li><b>Basics of condensed matter</b></li>
				<ul>
					<li>Microscopic constituents and effective interactions; condensed phases: normal and supercritical fluids, crystals, glasses, mesophases; classification and examples of transitions (first order, continuous, glassy); van der Waals theory and
						isomorphic states; miscibility and binary systems</li>
					<li>Molecular disorder and dynamics; linear response theory, dielectric and mechanical spectroscopy, other experimental methods (thermodynamic and optical probes, scattering)</li>
				</ul>
				<li><b>Single-component systems</b></li>
				<ul>
					<li>Small-molecule condensed phases; crystallization kinetics &amp; polymorphism; structural glasses, ultrastable &amp; aged glasses; orientationally disordered solids &amp; plastic crystals; primary &amp; secondary relaxations; charge
						conduction in molecular solids and liquids</li>
					<li>Amorphous &amp; semicrystalline linear homopolymers; ideal chain statistics and entanglement effects, entropic forces, Rouse modes and reptation; viscoelasticity, glass transition, and crystallization of linear polymers; branched polymers,
						gelation and rubber elasticity, affine network model for elastomers; conjugated and conductive polymers</li>
					<li>Thermotropic liquid crystals (nematic, smectic, columnar) and liquid crystal polymers; optical properties and applications</li>
				</ul>
				<li><b>Multicomponent and aqueous systems</b></li>
				<ul>
					<li>Polymer solutions: non-ideal chains, theta-solutions, hydrogels, swelling phenomena; superhydrophobic/hydrophilic, superolephobic, superamphiphilic, and self-healing polymer coatings; biopolymers, helix-coil and coil-globule transitions</li>
					<li>Self-assembly in condensed matter: specific and non-specific interactions; block copolymers; colloidal systems (glasses, crystals, gels), surfactant-water systems, biomembranes, lyotropic liquid crystals, emulsions; semiflexible polymers
						&amp; cytoskeleton</li>
				</ul>
			</ol>
		</div>
	</div>

	<div id="popover-content-atomic" class="hide">
		<div class="pop-content">
			<h2>Syllabus</h2>
			<ol>
				<li>Introduction: the hydrogen atom</li>
				<li>Interaction between atoms and external fields (static and oscillatory)</li>
				<li>Fine and hyperfine structure. Selection rules</li>
				<li>Symmetries of the wave function</li>
				<li>Many-electron atoms. Thomas-Fermi model, and Hartree-Fock method</li>
				<li>Understanding the periodic table of elements</li>
				<li>Molecular structure and degrees of freedom</li>
				<li>Advanced spectroscopic techniques: infra-red, Raman, and nuclear magnetic resonance</li>
				<li>Laser cooling, manipulation and detection of ultracold dilute quantum gases</li>
			</ol>
		</div>
	</div>

	<div id="popover-content-materials" class="hide">
		<div class="pop-content">
			<h2>Syllabus</h2>
			<ol>
				<li><b>Mechanical properties of materials</b></li>
				<ul>
					<li>Elasticity and related properties</li>
					<li> Non-linear mechanical properties</li>
					<li>Thermal expansion and isothermal compressibility</li>
				</ul>
				<li><b>Dielectric and optical properties of materials</b></li>
				<ul>
					<li>Polarization and polarization mechanisms</li>
					<li>Ferroelectricity</li>
					<li>Pyroelectricity</li>
					<li>Piezoelectricity</li>
					<li>Dielectric response to variable frequency electric fields</li>
					<li>Optical response of materials</li>
				</ul>
				<li><b>Magnetic properties of materials</b></li>
				<ul>
					<li>Diamagnetism</li>
					<li>Paramagnetism</li>
					<li>Ferromagnetism</li>
					<li>Other types of magnetism: ferrimagnetism, antiferromagnetism and non-collinear ferromagnetism</li>
				</ul>
				<li><b>Ferroic and multiferroic materials</b></li>
				<ul>
					<li>Ferroic transitions</li>
					<li>Multiferroic coupling: Magnetoelasticity and magnetoelectricity</li>
					<li>Applications</li>
				</ul>
			</ol>

		</div>
	</div>

	<div id="popover-content-complexity" class="hide">
		<div class="pop-content">
			<div class="row align-center">
				<div class="col-sm-2"></div>
				<div class="col-sm-8">
					<img style="max-width:100%; max-height:100%;" src="https://engineeringphysics.masters.upc.edu/en/Courses/elective-subjects-in-physics/320pxMetabolic_Metro_Map.svg.png" alt="" class="image-inline" title="" />
				</div>
				<div class="col-sm-2"></div>
			</div>
			<h2>Syllabus</h2>
			<ol>
				<li><b>Biological networks</b></li>
				<ul>
					<li>Examples in systems biology (metabolic networks, interactome, regulatory and signalling networks)</li>
					<li>Biological neural networks</li>
					<li>Networks in ecology and epidemiology</li>
				</ul>
				<li><b>Complex spatio-temporal dynamics in biology</b></li>
				<ul>
					<li>Oscillations, excitability, bistability</li>
					<li>Synchronization in biological systems: neural networks</li>
					<li>Spatio-temporal chaos: cardiac fibrillation</li>
				</ul>
				<li><b>Complex biosignal analysis</b></li>
				<ul>
					<li>Deterministic and stochastic signals</li>
					<li>Statistical properties</li>
					<li>Nonlinear time series analysis</li>
				</ul>
				<li><b>Self-organization in biological systems</b></li>
				<ul>
					<li>Morphogenesis</li>
					<li>Self-assembly (protein folding, membrane formation)</li>
					<li>Growth processes (chemotaxis, tumour growth)</li>
				</ul>
				<li><b>Collective motion and active matter</b></li>
				<ul>
					<li>Flocking, swarming and herd behaviour</li>
					<li>Cell migration</li>
				</ul>
			</ol>
		</div>
	</div>

	<div id="popover-content-machine" class="hide">
		<div class="pop-content">
			<h2>Syllabus</h2>
			<ol>
				<li><b>Introduction to Machine Learning</b></li>
				<ul>
					<li>Fundamental problem of Machine Learning</li>
					<li>Description of the inherent complexity of the problem</li>
					<li>General approximations to the solution.</li>
				</ul>
				<li><b>Classical models of Neural Networks</b></li>
				<ul>
					<li>Hopfield model</li>
					<li>Recurrent Boltzmann Machines (BM) and Restricted Boltzmann Machines (RBM)</li>
					<li>Learning with BM and RBM: gradient descent, Contrastive Divergence and variations</li>
					<li>Single-layer Perceptrons (SLP): lineal regression, logistic regression, Rosenblat perceptron</li>
					<li>Multi-layer Perceptrons (MLP)</li>
					<li>Learning with MLP: Back-propagation</li>
					<li>Convolutional Neural Networks (CNN): model, link with MLP and learning</li>
				</ul>
				<li><b>Deep Learning: link with classical models and modern learning techniques</b></li>
			</ol>

		</div>
	</div>

	<div id="popover-content-numerical" class="hide">
		<div class="pop-content">
			<p style="text-align:center;"><img src="https://engineeringphysics.masters.upc.edu/en/images/JSU_convection_in_sphere.png/@@images/ef12edd9-520b-492b-9f4c-07d20983291c.png" alt="" title="
			The image shows a spiraling columnar pattern of thermal convection of
			a rotating fluid sphere at the onset of convection. The contours plots of
			the kinetic energy on radial, equatorial and meridional sections, indicated
			with dashed lines, show how the convective structures of a high azimuthal
			wave number align with the axis of rotation and spiral in the sense of the
			rotation" /></p>
			<h2>Syllabus</h2>
			<ol>
				<li>Introducción. Métodos de discretización del continuo: diferencias finitas, elementos y volúmenes finitos, métodos espectrales y métodos sin malla o de partículas</li>
				<li> Formulaciones débiles, variacionales, de Galerkin, de Petrov-Galerkin, de colocación, etc. de diferentes problemas de la Física (Termodinámica, Elasticidad, Mecánica de Fluidos, Electromagnetismo, Mecánica Cuántica, etc.)</li>
				<li>El método de los elementos finitos. Aproximación lagrangiana a trozos. Tipología de elementos finitos. Elementos nodales y modales. Elementos isoparamétricos. Errores de interpolación y convergencias h, p i hp</li>
				<li>Implementación del método de elementos finitos. Mallado de dominios. Ensamblaje de matrices. Fórmulas de cuadratura. Estimación del error de las soluciones. Ejemplos de aplicación en Matlab/Octave o Python</li>
				<li>Complementos de álgebra lineal numérica. Almacenamiento matricial. Técnicas para sistemas lineales y problemas de valores propios para problemas de dimensión elevada.</li>
				<li>Librerías de elementos finitos. Introducción a FeniCS-Python</li>
				<li>Integración temporal. Métodos de semi-discretización, de líneas, de splitting, etc. Dificutades en problemas de tipo advección-diffusión</li>
				<li>Introducción a los métodos de volúmenes finitos y de Galerkin discontinuos. Aplicaciones</li>
				<li>Métodos de orden alto. Elementos espectrales. Integración temporal de orden alto.</li>
			</ol>
		</div>
	</div>

	<div id="popover-content-stochastic" class="hide">
		<div class="pop-content">

			<p style="text-align:center;"><img src="https://engineeringphysics.masters.upc.edu/en/Courses/elective-subjects-in-physics/image1.jpeg" alt="" class="image-inline" title="Stanisław Ulam, inventor of the Monte-Carlo method" /></p>
			<h2>Syllabus</h2>
			<ol>
				<li>Monte Carlo integration: distribution functions and their sampling. Crude Monte Carlo and rejection methods. Improving efficiency: variance reduction methods. Multidimensional integrals and Metropolis sampling.</li>
				<li>Monte Carlo methods for the study of many-particle systems: discrete systems (Ising), continuous systems in different statistical collectivities. Finite-size scaling. Advanced Monte Carlo methods.</li>
				<li>Stochastic optimization: simulated annealing and genetic algorithms.</li>
				<li>Dynamic Monte Carlo: randowm walks and the diffusion equation. Fokker-Planck and Langevin methods. Brownian dynamics.</li>
				<li>Application of Monte Carlo methods to quantum systems. Wave functions for bosons and fermions. Variational Monte Carlo. Diffusion Monte Carlo. Path integral Monte Carlo for the study at finite temperature.</li>
			</ol>

		</div>
	</div>

	<div id="popover-content-computational" class="hide">
		<div class="pop-content">

			<div id="parent-fieldname-text">
				<p style="text-align:center;"><img style="max-width:300px;" src="https://engineeringphysics.masters.upc.edu/en/Courses/elective-subjects-in-physics/fig1_20a.jpg" title="Distribution of 28Si in the &quot;cellular problem&quot;, showing the onset of Kelvin–Helmholtz
                     hydrodynamic instabilities" /></a></p>
				<h2>Syllabus</h2>
				<ol>
					<li><b>Finite difference methods applied to stellar evolution</b></li>
					<ul>
						<li>Finite difference approximations</li>
						<li>Von Neumann stability criterion</li>
						<li>Initial values and boundary conditions</li>
						<li>Explicit vs. Implicit methods</li>
						<li>Lagrangian and Eulerian formalisms</li>
						<li>Nuclear reaction networks. Adaptive networks</li>
						<li>Relativistic hydrodynamics</li>
					</ul>
					<li><b>Smoothed-Particle Hydrodynamics</b></li>
					<ul>
						<li>Fluid dynamics interpolation schemes</li>
						<li>Eulerian SPH equations</li>
						<li>Variable resolution in space and time</li>
						<li>Lagrangian SPH equations</li>
						<li>Applications of the Eulerian equations</li>
						<li>Heat conduction and mass diffusion</li>
						<li>Viscosity</li>
						<li>Application to shocks and rarefaction problems</li>
						<li>Astrophysical applications</li>
						<li>Other applications</li>
						<li>SPH in special and general relativity</li>
						<li>Future developments</li>
					</ul>
					<li><b>Astrophysical applications of Monte Carlo and classification methods</b></li>
					<ul>
						<li>Overview of basic concepts</li>
						<li>Simple applications of the Monte Carlo methods</li>
						<li>Classification methods: data analysis</li>
						<li>Examples of classification</li>
					</ul>
				</ol>


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