Overall aim: To provide a twenty-first century perspective on fundamental concepts of major areas of classical physics which are not seen (or not covered at enough depth) at the undergraduate level.

Main topics:
- Fluid Dynamics -- Module covered during the first half of the course
- Statistical Physics -- Module covered during the second half of the course

Teachers:
- Cristobal Arratia, Assistant Professor, Nordita, teaches Fluid Dynamics
- Per Moosavi, Researcher, Stockholm University, teaches Statistical Physics

This course provides a comprehensive introduction to advanced and modern topics in Electrodynamics aimed at undergraduate and master's students. The course assumes familiarity with Newtonian mechanics, but the main concepts of special relativity and vector calculus are covered initially. 

Aim: To introduce perturbative quantum field theory and some of its applications in modern physics. 

Main topics: relativistic quantum mechanics, bosonic and fermionic fields, interactions in perturbation theory, Feynman diagram methods, scattering processes and particle decay, elementary processes in quantum electrodynamics (QED).

This course provides a basic introduction to Einstein's relativity theory: Special relativity, four-vectors and tensors. General relativity, spacetime curvature, the equivalence principle, Einstein's equations, experimental tests within the solar system, gravitational waves, black holes, cosmology.

Teachers: Benjamin Knorr and Ziqi Yan, postdocs at Nordita

In the course, the student's task consists in being a mentor for participants that are upper secondary school students and university students in the project "Sprettur". Mentors' main role is to support and encourage participants in their studies and social life. As well as creating a constructive relationship with the participants, being a positive role model, and participating in events organized in Sprettur. The mentor role centers around building relationships and spending meaningful time together with the commitment to support participants. 

Sprettur is a project that supports students with an immigrant or refugee background who come from families with little or no university education. The students in this course are mentors of the participants and are paired together based on a common field of interest. Each mentor is responsible for supporting two participants. Mentors plan activities with participants and spend three hours a month (from August to May) with Sprettur’s participants, three hours a month in a study group and attend five seminars that are spread over the school year. Students submit journal entries on Canvas in November and March. Diary entries are based on reading material and students' reflections on the mentorship. Compulsory attendance in events, study groups, and seminars. The course is taught in Icelandic and English. 

Students must apply for a seat in the course. Applicants go through an interview process and 15-30 students are selected to participate. 

See the digital application form. 

More information about Sprettur can be found here: www.hi.is/sprettur  

This course provides a general overview of diverse topics in modern astrophysics. The focus of the course might vary from year to year. In this term (Fall 2021), the topic will be high-energy astrophysics.

Introduction to how numerical analysis is used to explore the properties of physical systems. Programming environment and graphical representation. The application of functional bases for solving models in quantum and statistical mechanics. Communication with Linux-clusters and remote machines. The course is taught in English or Icelandic according to the needs of the students.

Programming language: FORTRAN-2008 with OpenMP directives for parallel processing.

The course is an introduction to some basic concepts of condensed matter physics. Curriculum: Chemical bonds, crystal structure, crystal symmetry, the reciprocal lattice. Vibrational modes of crystals, phonons, specific heat, thermal conductivity. The free electron model, band structure of condensed matter, effective mass. Metals, insulators and semiconductors. The course includes three labs.

Seminar course on topics of current interest in astrophysics and cosmology.

Banach spaces and Hilbert spaces and their main properties. Duals of Banach spaces. Convolutions. The Fourier transform on LBanach spaces and Hilbert spaces and their main properties. Duals of Banach spaces. Convolutions. The Fourier transform on L 1(R). The Plancherel theorem. Equicontinuity, the Arzelà-Ascoli theorem. The Stone-Weierstrass approximation theorem. Linear operators on Hilbert spaces, in particular compact operators. The spectral theorem. The Hahn-Banach theorem. The Baire category theorem. The uniform boundedness theorem, the open mapping theorem and the closed graph theorem.

Curves, surfaces and manifolds in Euclidean space. Differentiable manifolds, vector fields and tensor fields. Hypersurfaces in Euclidean space, first and second fundamental forms, curvature, convex hypersurfaces. Inner geometry of surfaces. Riemannian manifolds, geodesics. The Gauss-Bonnet theorem for surfaces.

Overall aim: To provide an advanced perspective on fundamental concepts of thermalization, arrow of time both in classical and quantum perspective.

Main topics: Non-equilibrium thermodynamics, quantum thermalization, ergodicity hypothesis.

Path integral formulation of quantum field theory, anomalies, Ward identities, regularization and renormalization. Yang-mills theory, spontaneous symmetry breaking and the Higgs mechanism.

This is a reading course.

The core subject matter of this course is the evolution of the dark matter distribution from the Hot Big Bang through to the present day. We will develop methods to compute the dark matter density across time and find methods to test the results of these calculations. We will also cover elements of cosmology generally and consider methods for establishing the nature of dark matter, from observations of galaxy properties through to laboratory experiments.

The primitive equations are derived and applied on atmospheric weather systems on various scales. Geostrophic wind, gradient wind, sea breeze, thermal wind, stability and wind profile of the atmospheric boundary layer. Vertical motion. Gravity waves and Rossby waves. Introduction to quasi-geostrophic theory, vorticity equation, potential vorticity, omega-equation and geopotential tendency equation. Quasi-geostrophic theory of mountain flows.

Introduction to the scientific method. Ethics of science and within the university community.
The role of the student, advisors and external examiner. Effective and honest communications.
Conducting a literature review, using bibliographic databases and reference handling. Thesis structure, formulating research questions, writing and argumentation. How scientific writing differs from general purpose writing. Writing a MS study plan and proposal. Practical skills for presenting tables and figures, layout, fonts and colors. Presentation skills. Project management for a thesis, how to divide a large project into smaller tasks, setting a work plan and following a timeline. Life after graduate school and being employable.

Introduction to stochastic processes with main emphasis on Markov chains.

Subject matter: Hitting time, classification of states, irreducibility, period, recurrence (positive and null), transience, regeneration, coupling, stationarity, time-reversibility, coupling from the past, branching processes, queues, martingales, Brownian motion.

Many real-world systems—such as social networks, ecosystems, brain networks, and communication infrastructures—are inherently complex. These systems exhibit emergent behaviors that cannot be predicted by studying their individual components alone. The significance of studying these complex systems was highlighted by the 2021 Nobel Prize in Physics, awarded for groundbreaking research in this area.

Network science provides powerful tools for modeling and understanding complex systems, and offers data-driven approaches to uncovering their underlying structures and dynamics. This course introduces students to fundamental statistical methods with a particular focus on their application within network science. It is designed to provide a comprehensive foundation in the principles and techniques essential for network modeling, analysis, and statistical inference in complex networks.

Students will explore:

1. Network Structure – Core concepts include random networks, such as configuration models, degree distribution, centrality measures, and community structures.
2. Network Dynamics – Key dynamic processes on networks, such as diffusion, random walks, epidemic spread modeling, percolation, and branching processes.
3. Statistical Inference on Networks – Techniques for inferring structure and dynamics from networked data, covering topics like network reconstruction, community detection, and dynamic inference.

Overall aim: To provide a twenty-first century perspective on fundamental concepts of major areas of classical physics which are not seen (or not covered at enough depth) at the undergraduate level.

Main topics:
- Fluid Dynamics -- Module covered during the first half of the course
- Statistical Physics -- Module covered during the second half of the course

Teachers:
- Cristobal Arratia, Assistant Professor, Nordita, teaches Fluid Dynamics
- Per Moosavi, Researcher, Stockholm University, teaches Statistical Physics

This course provides a comprehensive introduction to advanced and modern topics in Electrodynamics aimed at undergraduate and master's students. The course assumes familiarity with Newtonian mechanics, but the main concepts of special relativity and vector calculus are covered initially. 

Aim: To introduce perturbative quantum field theory and some of its applications in modern physics. 

Main topics: relativistic quantum mechanics, bosonic and fermionic fields, interactions in perturbation theory, Feynman diagram methods, scattering processes and particle decay, elementary processes in quantum electrodynamics (QED).

This course provides a basic introduction to Einstein's relativity theory: Special relativity, four-vectors and tensors. General relativity, spacetime curvature, the equivalence principle, Einstein's equations, experimental tests within the solar system, gravitational waves, black holes, cosmology.

Teachers: Benjamin Knorr and Ziqi Yan, postdocs at Nordita

In the course, the student's task consists in being a mentor for participants that are upper secondary school students and university students in the project "Sprettur". Mentors' main role is to support and encourage participants in their studies and social life. As well as creating a constructive relationship with the participants, being a positive role model, and participating in events organized in Sprettur. The mentor role centers around building relationships and spending meaningful time together with the commitment to support participants. 

Sprettur is a project that supports students with an immigrant or refugee background who come from families with little or no university education. The students in this course are mentors of the participants and are paired together based on a common field of interest. Each mentor is responsible for supporting two participants. Mentors plan activities with participants and spend three hours a month (from August to May) with Sprettur’s participants, three hours a month in a study group and attend five seminars that are spread over the school year. Students submit journal entries on Canvas in November and March. Diary entries are based on reading material and students' reflections on the mentorship. Compulsory attendance in events, study groups, and seminars. The course is taught in Icelandic and English. 

Students must apply for a seat in the course. Applicants go through an interview process and 15-30 students are selected to participate. 

See the digital application form. 

More information about Sprettur can be found here: www.hi.is/sprettur  

This course provides a general overview of diverse topics in modern astrophysics. The focus of the course might vary from year to year. In this term (Fall 2021), the topic will be high-energy astrophysics.

Introduction to how numerical analysis is used to explore the properties of physical systems. Programming environment and graphical representation. The application of functional bases for solving models in quantum and statistical mechanics. Communication with Linux-clusters and remote machines. The course is taught in English or Icelandic according to the needs of the students.

Programming language: FORTRAN-2008 with OpenMP directives for parallel processing.

The course is an introduction to some basic concepts of condensed matter physics. Curriculum: Chemical bonds, crystal structure, crystal symmetry, the reciprocal lattice. Vibrational modes of crystals, phonons, specific heat, thermal conductivity. The free electron model, band structure of condensed matter, effective mass. Metals, insulators and semiconductors. The course includes three labs.

Seminar course on topics of current interest in astrophysics and cosmology.

Banach spaces and Hilbert spaces and their main properties. Duals of Banach spaces. Convolutions. The Fourier transform on LBanach spaces and Hilbert spaces and their main properties. Duals of Banach spaces. Convolutions. The Fourier transform on L 1(R). The Plancherel theorem. Equicontinuity, the Arzelà-Ascoli theorem. The Stone-Weierstrass approximation theorem. Linear operators on Hilbert spaces, in particular compact operators. The spectral theorem. The Hahn-Banach theorem. The Baire category theorem. The uniform boundedness theorem, the open mapping theorem and the closed graph theorem.

Curves, surfaces and manifolds in Euclidean space. Differentiable manifolds, vector fields and tensor fields. Hypersurfaces in Euclidean space, first and second fundamental forms, curvature, convex hypersurfaces. Inner geometry of surfaces. Riemannian manifolds, geodesics. The Gauss-Bonnet theorem for surfaces.

Overall aim: To provide an advanced perspective on fundamental concepts of thermalization, arrow of time both in classical and quantum perspective.

Main topics: Non-equilibrium thermodynamics, quantum thermalization, ergodicity hypothesis.

Path integral formulation of quantum field theory, anomalies, Ward identities, regularization and renormalization. Yang-mills theory, spontaneous symmetry breaking and the Higgs mechanism.

This is a reading course.

The core subject matter of this course is the evolution of the dark matter distribution from the Hot Big Bang through to the present day. We will develop methods to compute the dark matter density across time and find methods to test the results of these calculations. We will also cover elements of cosmology generally and consider methods for establishing the nature of dark matter, from observations of galaxy properties through to laboratory experiments.

The primitive equations are derived and applied on atmospheric weather systems on various scales. Geostrophic wind, gradient wind, sea breeze, thermal wind, stability and wind profile of the atmospheric boundary layer. Vertical motion. Gravity waves and Rossby waves. Introduction to quasi-geostrophic theory, vorticity equation, potential vorticity, omega-equation and geopotential tendency equation. Quasi-geostrophic theory of mountain flows.

Introduction to the scientific method. Ethics of science and within the university community.
The role of the student, advisors and external examiner. Effective and honest communications.
Conducting a literature review, using bibliographic databases and reference handling. Thesis structure, formulating research questions, writing and argumentation. How scientific writing differs from general purpose writing. Writing a MS study plan and proposal. Practical skills for presenting tables and figures, layout, fonts and colors. Presentation skills. Project management for a thesis, how to divide a large project into smaller tasks, setting a work plan and following a timeline. Life after graduate school and being employable.

Introduction to stochastic processes with main emphasis on Markov chains.

Subject matter: Hitting time, classification of states, irreducibility, period, recurrence (positive and null), transience, regeneration, coupling, stationarity, time-reversibility, coupling from the past, branching processes, queues, martingales, Brownian motion.

Many real-world systems—such as social networks, ecosystems, brain networks, and communication infrastructures—are inherently complex. These systems exhibit emergent behaviors that cannot be predicted by studying their individual components alone. The significance of studying these complex systems was highlighted by the 2021 Nobel Prize in Physics, awarded for groundbreaking research in this area.

Network science provides powerful tools for modeling and understanding complex systems, and offers data-driven approaches to uncovering their underlying structures and dynamics. This course introduces students to fundamental statistical methods with a particular focus on their application within network science. It is designed to provide a comprehensive foundation in the principles and techniques essential for network modeling, analysis, and statistical inference in complex networks.

Students will explore:

1. Network Structure – Core concepts include random networks, such as configuration models, degree distribution, centrality measures, and community structures.
2. Network Dynamics – Key dynamic processes on networks, such as diffusion, random walks, epidemic spread modeling, percolation, and branching processes.
3. Statistical Inference on Networks – Techniques for inferring structure and dynamics from networked data, covering topics like network reconstruction, community detection, and dynamic inference.

Overall aim: To provide a twenty-first century perspective on fundamental concepts of major areas of classical physics which are not seen (or not covered at enough depth) at the undergraduate level.

Main topics:
- Fluid Dynamics -- Module covered during the first half of the course
- Statistical Physics -- Module covered during the second half of the course

Teachers:
- Cristobal Arratia, Assistant Professor, Nordita, teaches Fluid Dynamics
- Per Moosavi, Researcher, Stockholm University, teaches Statistical Physics

This course provides a comprehensive introduction to advanced and modern topics in Electrodynamics aimed at undergraduate and master's students. The course assumes familiarity with Newtonian mechanics, but the main concepts of special relativity and vector calculus are covered initially. 

Aim: To introduce perturbative quantum field theory and some of its applications in modern physics. 

Main topics: relativistic quantum mechanics, bosonic and fermionic fields, interactions in perturbation theory, Feynman diagram methods, scattering processes and particle decay, elementary processes in quantum electrodynamics (QED).

This course provides a basic introduction to Einstein's relativity theory: Special relativity, four-vectors and tensors. General relativity, spacetime curvature, the equivalence principle, Einstein's equations, experimental tests within the solar system, gravitational waves, black holes, cosmology.

Teachers: Benjamin Knorr and Ziqi Yan, postdocs at Nordita

In the course, the student's task consists in being a mentor for participants that are upper secondary school students and university students in the project "Sprettur". Mentors' main role is to support and encourage participants in their studies and social life. As well as creating a constructive relationship with the participants, being a positive role model, and participating in events organized in Sprettur. The mentor role centers around building relationships and spending meaningful time together with the commitment to support participants. 

Sprettur is a project that supports students with an immigrant or refugee background who come from families with little or no university education. The students in this course are mentors of the participants and are paired together based on a common field of interest. Each mentor is responsible for supporting two participants. Mentors plan activities with participants and spend three hours a month (from August to May) with Sprettur’s participants, three hours a month in a study group and attend five seminars that are spread over the school year. Students submit journal entries on Canvas in November and March. Diary entries are based on reading material and students' reflections on the mentorship. Compulsory attendance in events, study groups, and seminars. The course is taught in Icelandic and English. 

Students must apply for a seat in the course. Applicants go through an interview process and 15-30 students are selected to participate. 

See the digital application form. 

More information about Sprettur can be found here: www.hi.is/sprettur  

This course provides a general overview of diverse topics in modern astrophysics. The focus of the course might vary from year to year. In this term (Fall 2021), the topic will be high-energy astrophysics.

Introduction to how numerical analysis is used to explore the properties of physical systems. Programming environment and graphical representation. The application of functional bases for solving models in quantum and statistical mechanics. Communication with Linux-clusters and remote machines. The course is taught in English or Icelandic according to the needs of the students.

Programming language: FORTRAN-2008 with OpenMP directives for parallel processing.

The course is an introduction to some basic concepts of condensed matter physics. Curriculum: Chemical bonds, crystal structure, crystal symmetry, the reciprocal lattice. Vibrational modes of crystals, phonons, specific heat, thermal conductivity. The free electron model, band structure of condensed matter, effective mass. Metals, insulators and semiconductors. The course includes three labs.

Seminar course on topics of current interest in astrophysics and cosmology.

Banach spaces and Hilbert spaces and their main properties. Duals of Banach spaces. Convolutions. The Fourier transform on LBanach spaces and Hilbert spaces and their main properties. Duals of Banach spaces. Convolutions. The Fourier transform on L 1(R). The Plancherel theorem. Equicontinuity, the Arzelà-Ascoli theorem. The Stone-Weierstrass approximation theorem. Linear operators on Hilbert spaces, in particular compact operators. The spectral theorem. The Hahn-Banach theorem. The Baire category theorem. The uniform boundedness theorem, the open mapping theorem and the closed graph theorem.

Curves, surfaces and manifolds in Euclidean space. Differentiable manifolds, vector fields and tensor fields. Hypersurfaces in Euclidean space, first and second fundamental forms, curvature, convex hypersurfaces. Inner geometry of surfaces. Riemannian manifolds, geodesics. The Gauss-Bonnet theorem for surfaces.

Overall aim: To provide an advanced perspective on fundamental concepts of thermalization, arrow of time both in classical and quantum perspective.

Main topics: Non-equilibrium thermodynamics, quantum thermalization, ergodicity hypothesis.

Path integral formulation of quantum field theory, anomalies, Ward identities, regularization and renormalization. Yang-mills theory, spontaneous symmetry breaking and the Higgs mechanism.

This is a reading course.

The core subject matter of this course is the evolution of the dark matter distribution from the Hot Big Bang through to the present day. We will develop methods to compute the dark matter density across time and find methods to test the results of these calculations. We will also cover elements of cosmology generally and consider methods for establishing the nature of dark matter, from observations of galaxy properties through to laboratory experiments.

The primitive equations are derived and applied on atmospheric weather systems on various scales. Geostrophic wind, gradient wind, sea breeze, thermal wind, stability and wind profile of the atmospheric boundary layer. Vertical motion. Gravity waves and Rossby waves. Introduction to quasi-geostrophic theory, vorticity equation, potential vorticity, omega-equation and geopotential tendency equation. Quasi-geostrophic theory of mountain flows.

Introduction to the scientific method. Ethics of science and within the university community.
The role of the student, advisors and external examiner. Effective and honest communications.
Conducting a literature review, using bibliographic databases and reference handling. Thesis structure, formulating research questions, writing and argumentation. How scientific writing differs from general purpose writing. Writing a MS study plan and proposal. Practical skills for presenting tables and figures, layout, fonts and colors. Presentation skills. Project management for a thesis, how to divide a large project into smaller tasks, setting a work plan and following a timeline. Life after graduate school and being employable.

Introduction to stochastic processes with main emphasis on Markov chains.

Subject matter: Hitting time, classification of states, irreducibility, period, recurrence (positive and null), transience, regeneration, coupling, stationarity, time-reversibility, coupling from the past, branching processes, queues, martingales, Brownian motion.

Many real-world systems—such as social networks, ecosystems, brain networks, and communication infrastructures—are inherently complex. These systems exhibit emergent behaviors that cannot be predicted by studying their individual components alone. The significance of studying these complex systems was highlighted by the 2021 Nobel Prize in Physics, awarded for groundbreaking research in this area.

Network science provides powerful tools for modeling and understanding complex systems, and offers data-driven approaches to uncovering their underlying structures and dynamics. This course introduces students to fundamental statistical methods with a particular focus on their application within network science. It is designed to provide a comprehensive foundation in the principles and techniques essential for network modeling, analysis, and statistical inference in complex networks.

Students will explore:

1. Network Structure – Core concepts include random networks, such as configuration models, degree distribution, centrality measures, and community structures.
2. Network Dynamics – Key dynamic processes on networks, such as diffusion, random walks, epidemic spread modeling, percolation, and branching processes.
3. Statistical Inference on Networks – Techniques for inferring structure and dynamics from networked data, covering topics like network reconstruction, community detection, and dynamic inference.