Courses by Tristan Hübsch

Mathematical Methods II: An advanced undergraduate / introductory graduate course, sequel to Mathematical Methods I.: The main focus: solving first and second order differential equations with boundary conditions, as they appear in physics and engineering applications. Integral transforms and equations are also introduced, and the course finishes with an elementary introduction to the calculus of variation.
Electromagnetic Theory II: A graduate core course, sequel to Electromagnetic Theory I.: This course discussed the Lorentz-covariant formulation of electrodynamics, the interaction of the electromagnetic field with charged particles in motion. It then focuses on specific configurations and arrangements, involving: (1) electromagnetic waves in nonconducting media, cavities and waveguides, (2) the multipole expansion of electromagnetic fields, radiation, scattering and diffraction, and various radiative processes. The course finishes with a brief review of electrodynamic feedback and the classical models of charged particles.
Elementary Particle Physics (Univ. of Novi Sad, in Serbian): An advanced undergraduate/introductory graduate block-course.: This course introduces the concepts of fundamental physics, gives a historical sketch of the development of elementary particle physics and describes the basics of contemporary high energy physics. It covers (1) the definition of classification of “elementary particles” as currently known by experimental physics, (2) the principles of gauge invariance, (3) analysis of fundamental processes (Feynman diagrams), and (4) unification of all matter and interaction, including supersymmetry and (super)strings.
Mathematical Methods I: An advanced undergraduate / introductory graduate course.: The course began with a review of linear algebra, and vector and tensor calculus, continuing with the eigenvalue/eigenfunction problem and corresponding linear algebra. It then covers infinite series and products, complex analysis and residue calculus, and finishes with exploring Euler’s Gamma integral and its cousins as a tool to solve integrals.
Electromagnetic Theory I: A graduate core course.: A comprehensive and detailed treatment of electrostatic and magnetostatic configurations, Maxwell’s equations (and all the physics laws they encompass), and the response of dielectric and magnetic media to electromagnetic fields.
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General Physics I: An undergraduate introductory physics course (part 1).: The first of two parts of a course the aim of which is to provide a comprehensive introduction to the scientific description of Nature. This first part will cover: measurement; kinematics; forces, work and energy; harmonic motion; fluids, temperature and heat; waves and sound. Conceptual understanding rather than technical mastery is emphasized, although problem-solving skills will also be developed.
General Physics II: An undergraduate introductory physics course (part 2).: The second of two parts of a course the aim of which is to provide a comprehensive introduction to the scientific description of Nature. This second part will cover: electromagnetic forces, fields, and waves (including light and its study, optics), electric current and circuits, and an introduction to modern physics: special relativity, quantum mechanics and their applications to atomic and nuclear physics and radiation. Conceptual understanding rather than technical mastery is emphasized, although problem-solving skills will also developed.
Physics for Architects: An undergraduate introductory course.: The aim of the course, is to provide a comprehensive introduction to the scientific description of Nature. This will cover: measurement; kinematics; forces, statics, work and energy; temperature and heat; electricity; waves and sound; optics and photometry; acoustics. Conceptual understanding rather than technical mastery is emphasized, although problem-solving skills will also developed.
Physics I for Scientists & Engineers: An undergraduate core course.: The aim of the course is to introduce the students to the scientific description of Nature, including mechanics of particles, simple bodies and fluids, waves, heat and thermodynamics. Conceptual understanding rather than technical mastery is emphasized, although problem-solving skills will also developed. Prerequisites include Calculus I.
Physics II for Scientists & Engineers: An undergraduate core course.: The aim of the course, as a sequel to PHYS-013, is to introduce the students to the scientific description of Nature, including electricity, magnetism, the electromagnetic field, electronic circuits, propagation, diffraction and refraction of light and special relativity. Conceptual understanding rather than technical mastery is emphasized, although problem-solving skills will also developed. Prerequisites include Calculus I.
Intro. to Modern Physics: An introductory undergraduate course.: The aim of the course is to introduce the students to the relativistic and quantum nature of Nature. This course begins with reviewing the experimental indications of the relativistic and quantum phenomena, and then proceeds with an introduction to the methods and techniques developed to their study. Emphasis will be on conceptual understanding rather than technical mastery, although problem-solving skills will also developed. Prerequisites include a good understanding of introductory classical physics (courses PHYS 013 & 014), calculus I & II (MATH 156 & 157), and an open mind.
Physical Mechanics: An advanced undergraduate / introductory graduate course.: The aim of the course is to cover: (1) mechanics of systems of particles, (2) noninertial reference systems, (3) mechanics of rigid bodies in 2 and 3 dimensions, (4) Lagrangian mechanics, (5) dynamics of oscillating systems.
Mathematical Methods I: An advanced undergraduate / introductory graduate course.: The course began with a review of linear algebra, and vector and tensor calculus, continuing with the eigenvalue/eigenfunction problem and corresponding linear algebra. It then covers infinite series and products, complex analysis and residue calculus, and finishes with exploring Euler’s Gamma integral and its cousins as a tool to solve integrals.
Mathematical Methods II: An advanced undergraduate / introductory graduate course, sequel to Mathematical Methods I.: The main focus: solving first and second order differential equations with boundary conditions, as they appear in physics and engineering applications. Integral transforms and equations are also introduced, and the course finishes with an elementary introduction to the calculus of variation.
Thermodynamics and Kinetic Theory: An advanced undergraduate / introductory graduate course.: This course introduces the classical study of thermal processes, using macroscopic, collective variables of the materials considered. The course develops following the standard introduction of the four Laws of Thermodynamics, discussing their applications en route. This is the complemented with a microscopic derivation of the phenomenological foundations of thermodynamics, based on the molecular and atomic fundamental nature of Nature.
Electromagnetic Theory I: A graduate core course.: A comprehensive and detailed treatment of electrostatic and magnetostatic configurations, Maxwell’s equations (and all the physics laws they encompass), and the response of dielectric and magnetic media to electromagnetic fields. The course includes an introduction to special theory of relativity and relativistic kinematics.
Electromagnetic Theory II: A graduate core course, sequel to Electromagnetic Theory I.: This course discussed the Lorentz-covariant formulation of electrodynamics, the interaction of the electromagnetic field with charged particles in motion. It then focuses on specific configurations and arrangements, involving: (1) electromagnetic waves in nonconducting media, cavities and waveguides, (2) the multipole expansion of electromagnetic fields, radiation, scattering and diffraction, and various radiative processes. The course finishes with a brief review of electrodynamic feedback and the classical models of charged particles.
Elementary Particle Physics (Univ. of Novi Sad, taught in Serbian): An advanced undergraduate/introductory graduate block-course.: This course introduces the concepts of fundamental physics, gives a hystorical sketch of the development of elementary particle physics and describes the basics of contemporary high energy physics. It covers (1) the definition of classification of “elementary particles” as currently known by experimental physics, (2) the principles of gauge invariance, (3) analysis of fundamental processes (Feynman diagrams), and (4) unification of all matter and interaction, including supersymmetry and (super)strings.
Fundamental Particle Physics 1: A topical graduate level course (part 1).: The aim of the course is to give a brief but uncompromising introduction to the contemporary theoretical description of the fundamental physics of elementary particles and fields. A review of the scientific methodology, practical aspects such as dimensional analysis, and the field during the XX century introduces the concepts and ideas in their historical perspective, and is followed by an introduction to Lorentz-covariant Feynman calculus. This leads to the Quark Model and the gauge theory (abelian and non-abelian) foundation of Yang-Mills theories of electromagnetic and strong interactions, including an introduction to renormalization and quantum anomalies.
Fundamental Particle Physics 2: A topical graduate level course (part 2).: This is the second part of the of the course aiming to give a brief but uncompromising introduction to the conteporary theoretical description of the fundamental physics of elementary particles and fields. After a brief review of material covered in the first part, this course will discuss the chirality of fermions and the (so-called V–A) theory of weak interactions, then its unification with electromagnetism (the Higgs mechanism) and the formulation of the Standard Model. This leads to the need to go beyond, discussing Grand-Unified Theories, general relativity and geometrization of physics, supersymmetry and finally (super)strings, ushering the Student into the fundamental physics of the 3rd millennium.
Quantum Mechanics I: A core graduate course.: The course begins with reviewing the experimental indications of the quantum nature of Nature. The study of basic general properties and simple 1-dimensional models introduces the basic ideas and prepares for the study of semiclassical and operatorial techniques in Quantum Mechanics. The study of angular momentum and spherically symmetric potentials then finishes this first part of the course in Quantum Mechanics.
Quantum Mechanics II: A graduate core course, sequel to Quantum Mechanics I.: This course continues where Quantum Mechanics I left off, discussing time-dependent perturbations, the measurement conundrum, and other developments, including the application of symmetry and quantum fields statistical mechanics.
Physical Mechanics II: A dual undergraduate/graduate (classical mechanics) course, sequel to Physical Mechanics I.: The aim of the course is to cover: (1) mechanics of systems of particles, (2) noninertial reference systems, (3) mechanics of rigid bodies in 2 and 3 dimensions, (4) Lagrangian mechanics, (5) dynamics of oscillating systems. Prerequisites: PHYS-182 or PHYS-208.
Advanced Math. Methods I: An advanced graduate course.: The aim of the course is to introduce, develop and discuss various methods of determining global characteristic properties of spaces which occur in theoretical and mathematical physics. Throughout the course, the emphasis is on the applications of these results rather than their proofs. The course is to be regarded as an statistically significant sampler rather than a definitive compendium, and students are strongly encouraged to study particular topics mentioned in the course, in detail and depth surpassing the discussions in class; this is the purpose of the term paper. Prerequisites include a good working command of “methods of mathematical physics”.
Advanced Math. Methods II: An advanced graduate course.: The aim of the course is to introduce, develop and discuss various methods of supersymmetry and supergravity. Throughout the course, the emphasis is on the applications of these results rather than their proofs. The course is to be regarded as an statistically significant sampler rather than a definitive compendium, and students are strongly encouraged to study particular topics mentioned in the course, in detail and depth surpassing the discussions in class; this is the purpose of the term paper. Prerequisites include a good working command of “methods of mathematical physics”.
Computational Methods: A graduate upper-core (PhD) course.: The course discusses computational algorithms used to solve scientific problems, estimates of numerical errors, presentation of the scientific background, methods and results.
Theoretical Physics I: An advanced graduate course: a “crash-course” in Quantum Field Theory.: The aim of the course is to give a brief but uncompromising introduction to Quantum Field Theory, some of the basic computational methods and techniques and to serve as a preparatory course for the second part (Theoretical Physics II), studying constrained models and supersymmetry. We begin with reviewing the necessity of passing from a quantum particle to quantum fields. The study of free spin-0 and -1/2 quantum fields will establish the basic formalism and introduce the perturbative approach to interactive field theory. This leads to a detailed study of renormalization, and a cursory inspection of so-called anomalies. Prerequisites include an excellent working knowledge of “methods of mathematical physics”, classical and quantum mechanics, electrodynamics and the general ideas of statistical physics.
Theoretical Physics II : An advanced graduate course: a “crash-course” in supersymmetry.: The aim of the course is to give a brief but uncompromising introduction to supersymmetry, both global (rigid) and local (supergravity). We begin with reviewing the motivation for considering supersymmetry, and then proceed by studying the simplest (and most often used) supersymmetric models. The first part of the course considers only global (rigid) supersymmetry, i.e.., supersymmetry in flat spacetime. The second part introduces supergravity: the fully dynamical theory of local supersymmetry which induces and generalizes gravity. Prerequisites include an excellent working knowledge of “methods of mathematical physics”, classical and quantum mechanics, electrodynamics... and quantum field theory (Theoretical Physics I).
Advanced Topics in Astrophysics II: An advanced graduate course.: The aim of the course is to give a brief but uncompromising introduction to Brane Word cosmologies, based on the background set in the optional texts listed above. As this field is currently developing, part of the course will consist of literature-search, starting with some sources provided in class. Prerequisites include a good working command of “methods of mathematical physics”.
Fundamentals of Mathematics: Introduction to algebra.: Emphasis will be on representations and operations on numbers and sets, as well as introductory concepts of basic statistical measurements, variable expressions, and first-degree equations.
Introduction to College Mathematics: An extension of Fundamental Mathematics.: Emphasis will be on representations and operations on polynomials and rational expressions. Algebraic and graphical methods of solving linear and quadratic equations will be discussed. The course will end by a brief introduction to complex numbers, radical expressions, and conical sections.
Precalculus: A precalculus course with applications to business, life and social sciences.: The course will review algebraic functions and techniques, explore analytic geometry, introduce exponential and logarithmic functions, include matrices and determinants as techniques for solving linear systems in three or more variables and emphasize real-life problems and applications.
College Algebra and Trigonometry: An undergraduate introductory course.: This course lays the foundation for the study of mathematics and its applications in science, business, economics, social science, art, and music.
Differential Equations: An undergraduate (Math-major) core course.: The course introduces and developing methods for solving various ordinary differential equations and linear systems, and discusses their applications.
Methods of Applied Math I: An advanced undergraduate, introductory graduate course.: The course began with a review of linear algebra, and vector and tensor calculus, continuing with the eigenvalue/eigenfunction problem and corresponding linear algebra. It then covers infinite series and products, complex analysis and residue calculus, and finishes with exploring Euler’s Gamma integral and its cousins as a tool to solve integrals.
Methods of Applied Math II: A graduate core course, sequel to Mathematical Methods I.: The main focus: solving first and second order differential equations with boundary conditions, as they appear in physics and engineering applications. Integral transforms and equations are also introduced, and the course finishes with an elementary introduction to the calculus of variation.
Quantitative Methods (for Masters in Business Administration): A course on business applications of linear algebra.: Applies quantitative methods to systems management (Decision Theory), and/or methods of decision-making with respect to sampling, organizing, and analyzing empirical data.
Combinatorics: A graduate upper-core course.: This course introduces some essential topics in discrete, combinatorial mathematics and samples their applications in sciences and otherwise.
Ordinary Differential Equations: A graduate core (MS) course.: The course introduces and developing methods for solving various ordinary differential equations and linear systems, and discusses their applications.
Complex Analysis II: The second part of a 2-semester course.: The course revisits the maximum and minimum modulus principles, continues with the study of meromorphic functions and analytic continuation. This leads into Conformal mapping, harmonic functions and the Picard Theorems.
QEM/NAFEO Workshop: Learning to Research.

Courses by Tristan Hübsch

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