Courses Offered (AY2025/2026)

This course introduces students to computational thinking as applied to problems in science, with special emphasis on their implementation with Python/Python Notebook (Jupyter). A selection of examples will be chosen to illustrate (a) fundamentals of algorithm design in computer programming (b) solution interpretation, as well as (c) analysis of the computational solutions and data visualization using state-of-the-art tools in Python. The selection will tackle different types of approaches typically used in scientific computational thinking, including deterministic, probabilistic and approximation methods. The course will also highlight scientific computational issues such as accuracy and convergence of numerical results.

What is Science? How does it work? Why does it work? Not only will this course help answer these questions, but it will also hone the skills needed to negotiate a world in the post-truth era. These skills derive from the scientific method; the characteristic of modern science that has made it without a doubt the most successful endeavour in human history. These questions and these skills will be woven within a rich history of scientific accomplishment, culminating in an understanding of the frightening challenges we face to mitigate climate change and biodiversity loss.

Machine learning (ML) is the dominant component of modern research in artificial intelligence. Although ML is largely associated with computer science and software engineering, many of its foundational techniques have historical roots in the natural and social sciences, and are commonly used in those fields. More recently, the rapid development of modern ML also has growing implications for practitioners of the arts and humanities. Using only high-school mathematics and no programming, this course will peer under the tech-centric outer hood of ML, and provide a conceptual-level introduction to the field as well as its most important techniques.

Course is intended for all CHS students interested in the way the natural sciences (physics, mathematics and chemistry) did progress through the ages, and the cultural background and impact of these developments. The main focus will not be solely on the triumphs of science: As much as looking at success stories, we will also examine cases when things went wrong and try to learn about the reasons and conditions that lead to such problematic situations. We will examine how progress depends critically not only on conditions within the scientific communities but also on wider societal, economic and cultural influences.

This course starts with an introduction to the historical perspective of astronomy. Planets then stood out as wanderers that moved among the stars. Over history, the study of planets has contributed much to science and the scientific method, and continues to do so today, illustrating the point that as we take in new discoveries, we may be forced to relook our old definitions and theories.

The development of space technology during the mid-20th century ushered in a new age of discovery in which outer space is explored for advancing scientific research, commercial use, and ensuring the future survival of humanity. This course illustrates the use of scientific method to study Solar System objects and their physical characteristics, particularly the presence of water and potential biomarkers, and the multiple considerations required in the development of technology for launching artificial satellites, space tourism, asteroid mining, deflecting a potentially hazardous asteroid, and space colonization.

Scientific description of the smallest components of matter (atoms and sub-atomic particles, light) has become known as “quantum theory”. It is one of the greatest triumphs of science: it is not a formalisation of evidence and intuition, but rather harnesses phenomena that are invisible to the naked eye and counter-intuitive. It shows how science can stand behind apparently outlandish claims, and put this knowledge to practical use. The “experimental metaphysics” aspect of quantum physics is introduced through the description of paradigmatic phenomena. Then the history and current challenges are presented, with a special focus on the emerging quantum technologies.

To early observers, Earth felt unmoving and residing at the center of the universe; the celestial objects were made of a heavenly, weightless element that naturally revolved around Earth. This course covers the history of cosmology from geocentrism and Aristotle’s physics to Einstein’s relativity and the Big Bang theory. Unsolved problems concerning the symmetry of the universe and existence of dark matter and dark energy, and philosophical questions concerning the theory of everything, origin of the universe, and existence of other universes will be addressed.

This course is intended for all CHS students interested in the application of science and scientific inquiry to a subject which is believed by most people to be far removed from science – music. The course covers the historical discovery and evolution of the musical scale systems on which all music is based, the physics and technology of musical instruments such as the modern piano, and more modern developments such as electronic music and instruments and the digitisation of music.

Medical technology is one of the most important applications of science and technology; it provides the means to protect and preserve lives in today’s world of ageing population, proliferation of chronic diseases, global pandemics and rising pollution. This course discusses the fusion of physics of biology that forms the basis of modern medical imaging and radiation therapy technology, and traces its roots from the foundational theories to its implementation in medical procedures. Students will learn how such technology is applied to disease management, as well as the modern innovations that pave the way towards the future of healthcare.

The essence of nanoscience and nanotechnology is the ability to understand and manipulate matter at atomic and molecular levels, to create artificial structures with fundamentally new atomic and molecular organizations. In this course, students will learn that crystal, electronic, optical, and magnetic structures behave differently and exhibit novel physical, chemical and biological properties when their dimensions are reduced to the range of 1–100 nanometers. The nanoworld is an exciting new realm that brings together multidisciplines. Its impact on society is expected to be as significant as the combined antibiotics, integrated circuits and polymers in the twentieth century.

This course introduces earth and planetary science in an integrated manner through the intersection of physical geography and astronomy, providing students with an understanding of Earth as a planet, alien worlds, universal processes and life beyond Earth. In particular, the students will develop an understanding of processes common to planets, with a view to understanding the potential future human exploration and colonization of the solar system. This course will also highlight the key concepts shaping planetary system science and how discoveries from different fields are changing the interdisciplinary knowledge relevant to the earth and planetary science.

Carbon emissions from energy account for over two-thirds of all global emissions and offer an avenue for mitigating climate change via a transition to clean energy. Electrifying end-use sectors and shifting electricity production towards clean sources form the basis of the decarbonised energy transition. Challenges associated with decarbonisation require an interdisciplinary approach that considers scientific and socio-environmental constraints and opportunities. This course will introduce students to the pillars, major challenges and benefits of transitioning to clean energy. Students will learn how the harnessing of clean energy technologies can be optimised to ensure rapid and fair transition to a low/zero-carbon future.

This course offers a thematic overview of the frontiers of physics, with a central focus on light due to its ubiquitous presence in the development of modern physics. It covers the classical wave description of light, from the history of its discovery to the basic mathematical notions, the speed of light and special relativity, as well as light’s impact on the development of quantum theory, highlighting some fundamental quantum processes involving one or two photons. It also explores light-based technologies and considers the historical and philosophical context of these scientific concepts, laying a solid foundation for further study in physics.

This course aims to bridge the gap between ‘O’-level physics and first-year-level university physics. The course covers two branches of fundamental physics: mechanics and electricity & magnetism. Topics included in mechanics are linear motion, circular motion, Newton’s laws of motion, work and energy, conservation of energy, linear momentum, and simple harmonic motion. Topics included in electricity & magnetism are electric force, field & potential, current & resistance, DC circuits, electromagnetism and electromagnetic induction.

This course is an introduction to electromagnetics (EM) for electrical engineers. Electromagnetics is essential in all disciplines of electrical engineering. At the end of this course, students will be able to explain many physical phenomena in everyday life, such as electricity energy transmission, wave reflection/transmission, and the impact of skin depth on wave propagation. Topics covered include: static electric fields, static magnetic fields, timevarying fields, electromagnetic waves, transmission lines and antennas.

This core course for Physics majors offers a comprehensive foundation in Electricity and Magnetism, essential for advancing in Science and Engineering. Starting with vector calculus (covering gradient, divergence, curl, and the divergence and Stokes’ theorems), the course then addresses electrostatic fields, Coulomb’s law, and Poisson’s equation, including electrostatic fields in matter. Following this, students will study magnetostatic fields, Biot-Savart’s law, and Poisson’s equation, including magnetostatic fields in matter. The course progresses to time-varying electric and magnetic fields through Faraday’s and Ampère’s laws, culminating in Maxwell’s equations and electromagnetic waves in a vacuum. Knowledge from PC2032 is recommended.

This essential course for Physics majors introduces the mathematical framework underlying advanced theoretical physics. Building on H2 Mathematics, it explores the principles of classical mechanics, covering Newtonian mechanics topics like kinematics, forces, torques, and conservation laws, with applications to Kepler’s laws. Students learn about linear and angular momentum, systems of particles, and Newtonian gravity. The course introduces Lagrangian mechanics and the Euler-Lagrange equations, presenting a powerful alternative to Newtonian methods. Fluid mechanics concepts, such as fluid statics, dynamics, and Bernoulli’s equation, are also covered, providing a robust foundation for further study in mechanics and theoretical physics.

This course provides a rigorous introduction to quantum mechanics. It begins with a brief introduction to the development of quantum physics. Then it discusses topics like particle-wave duality, the Schrödinger equation, one dimensional systems like free particle, square potential well, quantum tunnelling, harmonic oscillator, and the formal description of quantum systems including Hilbert space, observables and operators, eigenfunctions, the uncertainty relations, the Dirac notation and simple two-level systems. The course ends with discussions of some stationary problems in three dimensions like particle in a box and degenerate states, the Schrödinger equation in spherical coordinates, and the hydrogen atom.

Introductory aspects of quantum physics. Two state quantum systems. The wave function and Schrodinger equation. Quantum harmonic oscillator; hydrogen atom; spherical harmonics. Atomic spectra. Scattering theory. Applications such as semiconductors, lasers, quantum dots and wires.

This essential course for Physics majors is intended for students who wish to acquire a deep understanding of systems of many particles. It considers the fundamentals of thermodynamics and statistical mechanics and is a prerequisite to advanced statistical mechanics. It covers topics such as: the laws of thermodynamics, thermodynamic functions, ideal gases, heat engines; microcanonical ensemble, canonical ensemble, Boltzmann distribution and partition function; introduction to quantum gases.

This course aims to give students the necessary mathematical skills for other physics courses. The topics to be covered include: complex numbers and hyperbolic functions; single-variable calculus; Taylor series; first order and second order ordinary differential equations; vectors and matrices; eigenvalues and eigenvectors; partial differentiation; multiple integrals; physical applications.

This course provides a comprehensive training of both experimental and data analytical skills in mechanics, electronics, magnetism, nuclear physics, semiconductors, optics and lasers. In particular, emphasis is placed on the basic measurement skills in physics experiments, familiarisation of the commonly used experimental apparatus, as well as the collection, handling, and analysis of real world data. While this module is mainly targeted at physics majors, it is also suitable for science and engineering students who are interested in a career in the industries of semiconductors, optical communications, and life sciences.

This course introduces the underlying principles and mechanisms of physics behind life sciences. It incorporates introductory concepts of physics into the phenomena associated with biological functions. The topics to be covered include: biological structures and the relation to biophysics; principles and methods of physics applied to biology; physical aspects of structure and functionalities of biomolecules, physical principles of bioenergy conversion and membrane-bound energy transduction; physical processes of bio-transport, nerves and bioelectricity. The course includes some basic biophysics experiments. It is targeted at both physics and non-physics students who already have basic knowledge in physics.

This course introduces the use of telescopes and data collection in astronomy. Students will learn how to set up and competently operate a telescope. Then students will learn how to plan and conduct astronomical observations for scientific purposes. Finally, students will learn how to process and analyse astronomical data.

This course will adopt a heuristic approach to celestial dynamics. Mathematics will be introduced only when necessary. Participants will also be enthused with the historical and philosophical development of celestial adventures discussed. Topics covered include elements of Newton and Kepler’s Laws, Planetary Orbits and Rocketry, Apollo program, Saturn V & SpaceX Boosters.

The satisfaction of understanding how rainbows are formed, how ice skaters spin, or why ocean tides roll in and out — phenomena that we have known — is one of the best motivators available for building scientific literacy. This course aims to make the physics of the world around us accessible to non-science majors. The coverage will be broad, and it includes Newtonian mechanics, fluid and heat, electricity and magnetism, waves and optics, and modern physics, with emphasis on relevance to everyday phenomena. The use of mathematics will be limited in this course and subordinated to the physical concepts being addressed.

Climate change and global warming are currently some of the most pressing problems that the world has to address. This course aims to provide a basic introduction to the processes that are involved in climate change, based on a physics perspective. Students will learn about climate processes, solar radiation and the energy budget of the earth, as well as basic thermal and radiation physics behind the greenhouse effect and the phenomenon of global warming. The phenomena of loss of sea ice and accelerated sea level rise will also be discussed.

The solutions to the global energy crisis lie in harnessing what Mother Nature has already provided. This course aims to help students discover the scientific underpinnings of natural phenomena that can be tapped for energy production and storage. Students will learn about the physical principles behind harnessing energy from the sun, ocean, wind and atomic nuclei (nuclear energy), as well as forms of energy storage such as batteries and fuel cells. The impact of these technologies on the environment will also be discussed. All physics concepts will be taught as needed. The course is suitable for students from diverse backgrounds.

Many topics debated in nanoscience are frontier and futuristic, although some have immediate technological applications. The fundamental scientific principles of all nanotechnology applications, however, are grounded in basic physics and chemistry. This course thus aims to illustrate and discuss the physics and chemistry that are operative at the nanoscale. Students will be introduced to some fundamental principles of physics and chemistry important to the nanoscale and learn to appreciate what the world is like when things are shrunk to this scale. They will also learn about some basic physical tools that can be used to explore structures at this length scale. On completion of this course, students will learn to appreciate the linkages between the fundamental sciences and practical applications in nanotechnology.

Computing plays a crucial role in how science understands our world. It is often considered the ‘third pillar’ of science, alongside theory and experiments. This course will allow you to experience how computers can be used to solve fun and interesting problems (e.g. climate models, real-time measurements), in interdisciplinary science. You will also learn how to approach tackling complex problems by breaking them into smaller ones, noting similarities, identifying what data is essential and devising steps that will lead to a solution. We will then learn to use the Python programming language to implement some of these solutions.

This course continues from PC2130 and aims to complete basic introductions of quantum mechanics to physics oriented students. This course will mainly cover the following: angular momentum albegra, spin, identical particles, time-independent perturbation theory, variational principle, time-dependent perturbation theory, and basics of quantum scattering theory, with applications including the Zeeman effect, atomic fine structure and hyperfine structure, ground state of the helium atom, the Fermi golden rule, atom in a classical electromagetic field, stimulated and spontaneous emission, s-wave scattering.

This continuous assessment course is intended to provide training in experimental techniques and analytical skills. Experiments are based on various areas of physics such as spectroscopy, nuclear physics, laser physics, optics and electronics. Some experiments involve the use of research-grade equipment like the electron microscope, the atomic force microscope and the FTIR spectrophotometer. Project-type experiments are also available. The course is targeted at science and engineering students who have a foundation in Level 2 experimental physics.

This elective course assumes knowledge of and is a sequel to PC2131. A good command of calculus and linear algebra is desirable. It is intended for students who wish to acquire a deeper understanding of Electricity and Magnetism. It prepares students for more advanced study at the postgraduate level. This course provides a comprehensive treatment of electromagnetic fields and forces. It covers the following topics: Electrostatic fields in matter, magnetostatic fields in matter, time-varying electric and magnetic fields in matter, relativistic electrodynamics, and radiation.

PC3232 is an intermediate course in nuclear physics with an introduction to particle physics. The course begins by exploring the Standard Model, which seeks to explain the Universe in terms of fundamental particles, interactions, and symmetries. The focus then shifts to nuclear particles and nuclear phenomena, applying these foundational concepts to model and understand key topics such as stability, decay, fission, and fusion. Throughout the course, you will gain an appreciation of how the principles of quantum mechanics and relativity shape our Universe.

This course presents the basic concepts and principles of atomic and molecular physics. In particular, the course revolves around the energy level schemes of atoms and molecules which are essential to the interpretation of atomic and molecular spectra. Topics covered include the hydrogen and helium atoms, spin-orbit coupling schemes, hyperfine interaction, Lamb shift, atoms in magnetic fields, multi-electron atoms, Pauli exclusion principle, Hund’s rules, diatomic molecules, Born-Oppenheimer approximation, electronic, vibrational, rotational and rotational-vibrational spectra; The course is targeted at students who have background in quantum mechanics and want to build the foundations for studying the interactions of matter and light in modern atomic physics contexts.

This is a first course in solid state physics. It aims to lay the foundations for students seeking to major in physics as well as students studying in materials science and engineering. The lectures emphasize on the fundamental concepts of condensed matter, covering crystal structure and reciprocal lattice, crystal binding and elastic constants, crystal vibrations and thermal properties, free electron theory and physical properties of metals, electron in periodic potentials, and basic semiconductors. Simple model prediction data and the experimental data from real systems would be compared and discussed to help students develop an intuitive understanding of the subject.

The course covers fundamental solid state physics concepts (crystal structure, reciprocal lattice, free electron theory) and the physical properties of metals, electrons in periodic potentials, and basic semiconductor physics: Doping, p-n junctions, crystal defects, diffusion processes, energy bands of the nearly free electron model, tight binding approximations, Fermi surfaces and their experimental determination, optical processes, piezoelectricity, basic ideas of magnetism.

The course presents basic computational methods useful for physics and science students. The lectures cover: (1) Basic numerical methods – differentiation, integration, interpolation, root-finding and random number generators, (2) Differential equations – finite difference method, shooting method and relaxation method; applications to chaotic dynamics of a driven pendulum, one-dimensional Schrödinger equation, and fast Fourier transform, (3) Matrices – Gaussian elimination scheme for a system of linear equations, eigenvalues of Hermitian matrices; Hartree-Fock approximation, (4) Monte Carlo simulations – sampling and integration; random walk and simulation of diffusion equation, stochastic differential equation, Brownian dynamics; variational Monte Carlo simulation; Metropolis algorithm and Ising model, and (5) Finite element methods – basic concepts; applications to the Poisson equation in electrostatics.

This course introduces fundamental aspects of fluid dynamics, with emphasis on topics relevant to atmospheric and ocean dynamics. The Navier-Stokes equations are derived from first principles. After an introduction to potential flow theory, the study of water waves is taken up to illustrate the behaviour of dispersive wave propagation and nonlinear shock forming tendency. Effects of vertical stratification and rotation on fluid flows are then discussed, and applied to the analysis of atmospheric and ocean flow phenomena. The course closes with an introduction to the theories of turbulence, with application to the atmospheric boundary layer.

This course is a first course on photonics that combines fundamentals with important applications, and is targeted at students interested in modern optical technology. The course covers planar dielectric waveguides, basics of optical fibre communication, optical properties of crystals and semiconductors, interband transitions and radiative recombination, semiconductor detectors, stimulated emission and population inversion, diode laser threshold and output power, argon and YAG lasers, Q-switching and mode-locking, electro-optics modulators and flat panel displays. The course strives to maintain succinctness in physical meaning and simplicity in approach with generous allotment of numerical examples to help in understanding the equations.

This course introduces students to astrophysics. It covers observational astronomy, celestial mechanics, and stars. Students will learn to conduct astronomical observations, analyse and interpret astronomical data, and use the principles of physics to study stars. The major topics covered in this course include celestial motions, telescopes, stellar properties, binary systems, stellar spectra, equations of stellar structure, and star formation.

The objective of this course is to establish the interconnectedness of knowledge between principles of optics and modern sciences/technologies and identify the applications in our daily life. It covers wave properties, refraction and dispersion, interference, Michelson interferometer, Fabry-Perot cavity and optical resonator, interference filter, Fraunhofer and Fresnel diffraction, resolution limit, Fourier transformation, holography; polarisation, birefringence and wave plates, light absorption and emission, lasers. This course is targeted at physics and non-physics students, who are interested in principles of modern optics.

The changes to physical properties (electronic, optical and magnetic) due to formation of structures at the nanoscale will be the main emphasis of this course. Properties differing from the bulk due either to an increase in surface area/volume ratio or quantum confinement will be studied in structures ranging from quantum wells, wires and dots to self-assembled mono-layers and heterostructure formation. The kinetics and thermodynamics driving the formation of these nanostructured surfaces and interfaces will be discussed. The course will also highlight current and potential applications of these nanoscale systems. Examples of materials systems will include metals, oxides, III-V, II-VI, CNT, SiC and SiGe systems.

This elective course assumes knowledge of and is a sequel to PC2132. A good command of calculus and linear algebra is desirable. It is intended for students who wish to acquire a deeper understanding of our Mechanical Universe. It considers the principles of relativistic, Lagrangian and Hamiltonian mechanics, and aims to establish a bridge to the principles of modern Physics. Topics covered include: dynamics with central forces, bound and unbound orbits, scattering; relativistic kinematics and dynamics of a particle, Lorentz transformations, four-dimensional notations; Lagrangian mechanics, the action principle, Euler-Lagrange equation; Hamiltonian mechanics.

This course aims to introduce the principles and approaches of physics in the area of molecular biophysics. It includes molecular complexes of biomolecules; physical and symmetrical relationships between biomolecules; physical and structural characteristics of proteins and amino acids; symmetric and statistical descriptions of nucleic acids; first law and second law of thermodynamics in biological systems; bonding and non-bonding potentials, and stabilizing interactions in biomacromolecules, and the correlation to macromolecular structures; molecular mechanics in biological systems; bio soft condensed materials, bio-membrane and biomembrane structure, principles of molecular self assembly of biomolecules. There is a lab component included in this course. This course is targeted at both physics and non-physics students who already have basic knowledge in physics and life sciences.

This course aims to give students the necessary mathematical skills for other physics courses. The topics to be covered include: vector spaces; Fourier series; Dirac delta-function; Fourier transforms; partial differential equations, separation of variables; physical applications.

The course provides hands-on experience with modern detectors, electronics, data acquisition systems, radiation sources and other nuclear physics equipment that forms the basis for the applications of nuclear physics to medical physics, radiation protection and other fields. The course will be restricted to the students in the Medical Physics minor.

The course gives an introduction to the basic physics, the biology and the applications of radiation in medical imaging and radiation therapy. After a review of basic radiation physics and the relevant radiobiology, the currently used major modes of diagnostic and interventional imaging are covered. This will be followed by a discussion of the major methods of radiation cancer therapy (by photons, protons and electrons).

This course adopts a heuristic approach to understanding the current paradigm of the first 3 minutes of the Big Bang. Mathematics will be introduced only when necessary. Participants will also be enthused with the historical and philosophical development of Space and Time discussed. Topics covered include Relativity, Quantum Physics and Cosmology.

This course provides an introduction to the scientific study of stars. It covers the physical properties of stars, the measurements of these properties, and the relevant laws of physics. It discusses the relationship among stellar physical properties as a step towards understanding star formation and stellar evolution. Some advanced topics, including variable stars, supernovae and black holes, are briefly discussed.

This course covers the structure of galaxies starting from star formation and star clusters with a strong focus on the analysis of observational data and insights from simulations. We discuss the underlying physics that give rise to the various shapes and structures that we see in galaxies, and briefly discuss the role of the supermassive black hole in the centre of many galaxies. Finally, we end off with clusters of galaxies and the large-scale structure of the universe.

Quantum phenomena based on the superposition principle and quantum entanglement have attracted significant attention in the past. Nowadays, strong efforts are being made to develop applications based on these phenomena. Such Quantum Technologies includes use cases in quantum communication and information processing, quantum enabled sensing, and quantum computations and simulations. The aim of this course is to provide the student with an overview of the applications and underlying principles. This covers a broad range of topics from quantum key distribution, over atomic clocks, inertial sensors, to early types of quantum computers.

This course introduces students to the science and practice of numerical weather prediction (NWP) and climate modelling, with emphasis on the numerical methods for solving the system of governing equations. The major topics covered include: 1. Basic equations governing the dynamics and thermodynamics of the atmospheric and oceanic processes. Modes of atmospheric motions and the filtering approximations. 2. Solution of parabolic, elliptic and hyperbolic equations. Finite-difference, finite-volume, spectral numerical methods. Linear and nonlinear computational instability. Students will develop codes for solving 2-D shallow water systems. 3. Parameterisation of subgrid scale processes. 4. Data assimilation. 5. Atmospheric predictability and ensemble forecasting.

This course provides an overview of the fundamental dynamical and physical processes important in meteorology and oceanography, explaining how their interactions and feedbacks contribute to the complex, nonlinear weather/climate system. Students will emerge with an understanding of the fundamental atmospheric and oceanic processes e.g. surface heating, convection, radiation, friction, etc. and how their interactions with the water cycle leads to much of the weather we see on earth.

This is the fourth course of an interdisciplinary program covering nature at different scales from ‘Atoms to Molecules, ‘The Cells’, ‘The Earth’ and ‘The Universe’. This course traces the developments in theoretical and observational cosmology, starting from Newtonian cosmology, Hubble’s observations, the Big Bang, formation of stars and black holes to recent ideas in the origin and fate of the Universe.

This course exposes senior students to nanoscience research and nanotechnology-based industry. This is done through a series of weekly seminars by principal investigators and industrial experts in the field, laboratory and industrial visits, and by completion of nanosynthesis/nanocharacterization-related mini projects. The course culminates in an intensive one-week study tour to Japan, organised in collaboration with La Trobe University and Tokyo University.

Quantum technology is a field of physics and engineering which exploits quantum phenomena, such as entanglement, superposition and tunneling, for advanced applications, including quantum computing, quantum key distribution, quantum metrology, and information processing. This is a fast emerging field with strong industry potential. In this course, students will be equipped with essential knowledge in the physics and technology of a wide range of quantum devices, including quantum detectors, quantum light sources, quantum number generators, quantum sensors, and quantum computers. Students will also learn skills in the characterization of these devices, including data analysis and interpretation of quantum behavior.

This third undergraduate module in quantum mechanics starts with a recap of the main contents covered by lower-level quantum mechanics courses, in particular time-independent and time-dependent perturbation theory, with more depth. Matlab is introduced to implement the discrete variable representation to solve time-independent Schrodinger equations, and the Split-Operator technique to solve time-dependent Schrodinger equations, with necessary coding from the stratch. This module also covers a number of frontiers topics, including adiabatic theorem, adiabatic control, shortcuts to adiabaticity, geometric phases, density matrix, reduced density matrix, quantum measurement models, quantum master equations, spin-boson model, decoherence, and dynamical decoupling.

Computation is playing an increasingly important role in materials discovery. This course introduces the basic concepts and provides an overview of methods in modern computational condensed matter physics. Major topics to be covered include a brief review on empirical and semi-empirical approaches in electronic structure calculation, density functional theory, methods for solving the Kohn-Sham equation, applications to different types of materials, modelling effects of external fields and transport property. The course is suitable for upper level undergraduate and graduate students who are interested in computer modelling and simulation in condensed matter physics and materials science.

This course introduces students to elements of the physics of crystalline solids. Topics covered include: energy bands of the nearly free electron model, tight binding method, Fermi surfaces and their experimental determination, plasmons, polaritons and polarons, optical processes and excitons. We will also cover superconductivity, dielectrics and ferroelectrics, diamagnetism, paramagnetism, ferromagnetism and antiferromagnetism, and magnetic resonance. This course is targeted at physics majors, and is useful for science and engineering students who already have background knowledge of solid state physics on par with PC3235 Solid State Physics I.

This course presents the fundamentals of statistical mechanics. Starting with the classical and quantum postulates, the three ensembles of Gibbs are derived. The statistical interpretation of thermodynamics then follows. The thermodynamic quantities are obtained in terms of the number of states, partition and grand partition functions. Applications to independent electron systems, with and without magnetic field, and Bose-Einstein condensation are given. The course ends with a brief introduction to phase transitions. This course is targeted at physics students with at least one year of thermal physics.

The objective of this course is to provide students with a background to the important developments in atomic physics over the last 30 years that have now become standard techniques utilized in many laboratories around the world. The lectures provide a detailed description of the interaction of atoms with electromagnetic fields and applies this analysis to a number of applications such as laser spectroscopy, laser cooling, and magnetic and optical trapping. The course will provide students with a comprehensive background to the tools of modern atomic physics.

This is an introductory course on the fundamental constituents of matter and their basic interactions; important concepts and principles, recent important experiments, underlying theoretical tools and calculation techniques in elementary particles physics will be expounded. The topics covered are: basic properties of elementary particles and the standard model, relativistic kinematics; symmetries: isospin and SU(3), quark model; parity and CP violation; Feynman diagrams and rules; quantum electrodynamics; cross sections and lifetimes: deep inelastic scattering; and introductory gauge theories and unified models. This course is mainly targeted at physics majors.

This course is an introduction to the quantum description of the electromagnetic fields at optical frequencies. Students will learn how to construct quantum models of common experiments in quantum optics. Topics include the quantisation of the electromagnetic fields, common quantum optical states, quantum models of linear optics and loss, common optical measurements, interferometers, squeezing, and the generation of entangled photons via spontaneous parametric down conversion. Important applications of quantum optics are discussed, including the use of squeezed light in interferometers for gravitational-wave detection and the use of entangled photons in experimental tests of quantum mechanics.

This course provides an introduction to the theory of general relativity. The topics covered are: general tensor analysis, the Riemann tensor, the gravitational field equation, the Schwarzschild solution, experimental tests of general relativity, black holes, and Friedmann-Robertson-Walker models of the expanding universe. While this course is mainly targeted at physics majors, it is also suitable for science students with a strong mathematical foundation.

Starting with an introduction to the nuclear physics of stars and the processes of nucleosynthesis, following a brief introduction to nuclear physics. nucleosynthesis via quiescent burning, and the processes that lead to the production of heavy (A>60) elements are covered. The endstages (brown dwarfs, white dwarfs, neutron stars and black holes) are discussed in detail. In the second part of the course, large structures in the universe, are discussed, including star clusters, galaxy structure, and galaxy clustering. The course ends with a discussion of the cosmological scale structure of the universe. This course is a continuation of PC3246 Astrophysics I.

The scope of the course embraces the basic principles of thin-film deposition techniques such as chemical vapor deposition and physical vapor deposition as well as their applications in the microelectronics industry. The basic principles include vacuum technology, gas kinetics, adsorption, surface diffusion and nucleation. These are the fundamental features which determine the film growth and the ultimate film properties. Common thin-film characterization methods which measure film composition and structure as well as mechanical and electrical properties are also covered. This course is for senior physics students with an interest in pursuing a career in industry.

Remote sensing is the acquisition of information about a target from a distance, in particular from satellites, aircrafts, and drones. This course equips students with knowledge to understand, and model, satellite orbital dynamics and global positioning, radiometry, multi-spectral and hyper-spectral imaging of atmosphere, land, and ocean. Students will also learn skills in data processing of real-life satellite images through project work, including the application of radiometric, terrain and atmospheric corrections. The course will also leverage on access to Singapore’s Centre for Remote Imaging, Sensing and Processing.

This course aims to introduce students to solid-state devices, which are fundamental components in modern electronics. The topics covered include: introduction to semiconductors, charge carrier concentrations, drift of carriers in electric and magnetic fields, diffusion and recombination of excess carriers, p-n junction physics, junction diodes, tunnel diodes, photodiodes, solar cells, light emitting diodes, bipolar junction transistors, metal-semiconductor contacts, metal-insulator-semiconductor interfaces, basic MOSFET.

This course covers the principles of statistics in relation to biophysics and bio soft materials. It focuses on: modeling of biomacromolecular structure and statistical complexities; molecular mechanics of biomolecules; statistical models for structural transitions in biopolymers, statistical physical description of structural transitions in macromolecules, simulation of macromolecular structure, structural transitions in polypeptides and proteins; coil-helix transitions; prediction of protein secondary and tertiary structures; statistics of structural transitions in polynucleotides and DNA; modeling of non-regular structures of biomacromolecules. This course is targeted at both physics and non-physics students who already have basic knowledge in physics, thermodynamics and molecular biology.

This course introduces important mathematical methods for the solution of a variety of mathematical problems in physics. The following topics are covered: functions of a complex variable, singularities and residues, contour integration; transformations in physics, symmetries and group theory, discrete groups, group representations and their applications in physics; tensor analysis, application to classical mechanics, electrodynamics, and relativity.

This is a new course which aims to highlight the relevance and importance of physics in many aspects of technology. It aims to serve as the overview course to expose the students to a few key technological development when Physics plays a vital role. This course will be conducted by our own lecturers. The selected topics will be current and directly relevant to the potential career options that the MSc students will be considering. Discussion of each topic shall cover the basic physics principles leading to the state of the art development in the technology. The duration on each topic can last from 2 weeks to 3 weeks. Examples of the topics include energy and batteries, solar energy systems, quantum technologies, computer modelling in Physics, sensor devices, communication systems, microelectronics, advanced functional materials, biophysical instruments, etc.

This course covers a series of lecture clusters/seminars in industrial physics co-taught by our lecturers and our industrial partners and collaborators. Students will be exposed to the multiple-faceted career options that a physicist can choose in the industry. Our industrial partners will provide an overview of a certain industry sector and share their experience on the role a physicist plays in this sector. Our partners shall also emphasize the important skillsets to learn in order to be well-prepared for the career chosen. The range of industrial sectors shall cover Semiconductors, Engineering, Material Science, IT, Data Sciences, Energy Sector etc.

This is a required course for all research Masters and PhD students admitted from AY2004/2005. The main purpose of this course is to help graduate students to improve their presentation skills and to participate in scientific seminars/exchanges in a professional manner. The activities of this course include giving presentations during the lecture hours and attending seminars organised by the Department. Students are also required to write summaries of some departmental seminars attended. The grade of this course will be “Satisfactory/Unsatisfactory” based on student’s talk presentations, participation of seminars and the summary writing.

This course is an introduction to advanced topics in quantum mechanics. Topics include relativistic quantum mechanics and the Dirac equation, identical particles and second quantization, and the path-integral formulation of quantum mechanics.

This course presents an introduction to phase transitions and fluctuations. For phase transitions, the course starts with the treatment of Landau and mean field. Exact Ising model results are then discussed. Critical exponents are introduced and their relations obtained using the scaling hypothesis and Kadanoff’s scheme. Real space renormalization is then used to show how the critical exponents can be calculated. For fluctuations, Langevin, Fokker-Planck equations will be used. Time dependence and fluctuation dissipation theorem then follow. Brownian motion will be used as an example. This course is targeted at physics graduate students with at least one year of statistical mechanics.

This course aims to give graduate students additional training in the foundations of solid state physics and is intended to prepare them for research work and other graduate coursework courses. Topics to be covered include: translational symmetry and Bloch’s theorem, rotational symmetry and group representation, electron-electron interaction and Hartree-Fock equations, APW, OPW, pseudopotential and LCAO schemes of energy band calculations, Boltzmann equation and thermoelectric phenomena, optical properties of semiconductors, insulators and metals, origin of ferromagnetism, models of Heisenberg, Stoner and Hubbard, Kondo effect. Students are expected to read from a range of recommended and reference texts, and will be given an opportunity to present their reading as part of the regular lessons.

Spintronics is the study of the intrinsic spin of the electron and its application in spin-logic and devices, spin-polarized injection devices, and storage media. This is important for a variety of current and emerging applications in magnetic memories. This course equips students with essential knowledge of magnetism, and exchange interactions in solids; half metals, and dilute magnetic semiconductors; spin injection, transport and detection; and magnetic nanostructures, and their applications in: GMR read-write heads, MRAM, spinFET, spin-torque oscillators.

This course covers advanced mathematical methods for obtaining approximate analytical solutions to physical problems. It is designed to help graduate students build the skills necessary to analyse equations, integrals, and series that they encounter in their research. Topics include local analysis of differential equations, asymptotic expansion of integrals, and summation of series.

This course provides an introduction to surface physics for graduate and year-4 undergraduate students major in physics, chemistry and materials science and engineering. It covers the properties of solid surfaces, experimental techniques and applications. The topics include the importance of surfaces in science & technology, surface crystallography and topography, surface energy and stress, surface electronic properties (surface states, work function, band bending and Fermi level pining at semiconductor surface/interface, magnetism), surface phonon and plasmon, adsorption, desorption and reaction on surfaces. The applications of basic surface science knowledge in semiconductor technology, materials growth and processing, heterogeneous catalysis, nanoscience and thin film technology will be demonstrated. Experimental techniques, such as XPS, UPS, AES, LEED, STM, AFM, SIMS, EELS, TPD and vacuum technology, will be addressed with examples and applications. To take this course, students should have a basic knowledge of quantum physics, thermodynamics and solid state physics.

This is a course on quantum field theory aimed at students who have had some exposure to relativistic quantum mechanics. The topics covered are: canonical quantization and the path-integral formulation of quantum field theory, Feynman rules for scalar, spinor, and vector fields, regularization and renormalization, and the renormalization group.

The course aims to provide a comprehensive understanding on the principles of nonlinear optics. The course is targeted at postgraduate students who have acquired a background in optics, and who are involved in optics-related studies and research. The course presents the principles of nonlinear optics and photonics devices, which includes: nonlinear optical susceptibility, wave propagation in nonlinear media; sum and difference frequency generation, parametric amplification and oscillation, photonic crystals; phase conjugation, optical-induced birefringence, self-focusing, nonlinear optical absorption, photonic devices; ultrafast laser.

This advanced course presents the fundamentals of classical electrodynamics in much depth. It covers the following topics: Maxwell’s equations to define conservations laws for energy and momentum, properties of electromagnetic waves, light scattering from interfaces, the concept of optical dispersion, and investigate how waves propagate in bounded structures such as waveguides and transmission lines. In depth investigations of radiation by moving charges, special relativity from Maxwell’s equations such as relativistic length contraction, and covariant formulation of E&M. An understand of applications ranging satellites to fiber optics to transmon qubit would be related to E&M. A good mathematical foundation is required.

This course provides an introduction to the physics of nanostructures. Students taking this course will be introduced methods of fabrication and characterization of nanostructured materials and nanodevices, common types of nanostructures, their properties and applications. More importantly, the underlying physics of the intricate properties and functions of nanostructures will be discussed. The course starts with a brief review of relevant topics of quantum mechanics and solid state physics in reduced dimensions. Common techniques for nanostructure fabrication and characterization are introduced next. Transport in low-dimensional systems, optoelectronics of nanostructures, nanotubes and nanowires, clusters and nanocrystallites are discussed. Finally, magnetic nanostructures, and molecular electronics (optional), will be covered. This course is designed for postgraduate students who are interested in nanoscience and nanotechnology research and applications. Understanding the physics of nanostructures will allow the students to better appreciate the interesting properties and their tunability of nanostructures, understand the operating principles of nanodevices, and to design and optimize nanostructures for different applications.

This course discusses the molecules in cells and the physics behind their functions. At the core is the understanding of biomolecular conformations, structural stability and interactions under physical constraints such as force, geometry and temperature, by theory and state-of-art experimental technologies. Besides homework and quiz, projects are an important component of assignments. Multiple projects are provided for students to choose, which may involve numerical/Monte Carlo simulation of biomolecular conformations, analysis of experimental data, or investigation of the DNA micromechanics by analyzing DNA conformations. This course is targeted at students who have a basic knowledge in general physics and thermodynamics.

The ability to setup high-quality experiments and measurements is fundamental to innovation in many areas of sciences and engineering, including materials and devices. Therefore a good understanding of, and practical training, in experimental physics techniques is essential to a lot of research and development work in both academia and industry. This course equips students with the essential knowledge and practical skills in a broad range of modern experimental physics techniques, including: mechanical design and materials selection; vacuum technology, cyostats, and thin-film deposition techniques; Gaussian beam laser optics; photodetectors; stepper motors and piezoelectric actuators; feedback and control loops; techniques in analog, digital and pulse signal processing; weak-signal detection and lock-in amplifiers; fast-signal detection and transmission lines. The practical skills will be taught in laboratory classes, which are part of this course.

Covers computational techniques for the solution of problems arising in physics and engineering, with an emphasis on molecular simulation and modelling. Topics will be from the text, “Numerical Recipes”, Press et al, supplemented with examples in materials and condensed matter physics. This course insures that graduate students intending to do research in computational physics will have sufficient background in computational methods and programming experience.

This course introduces from an experimentalists point of view to the modern world of ultracold quantum gases that so much changed atomic physics in the past two decades. The lectures present the basic experimental methods of laser cooling, magnetic and optical trapping, and evaporative cooling that produce matter near absolute zero temperature. We then discuss basic effects like Bose-Einstein condensation and Pauli pressure. Further, selected research examples are presented that give insight to some of the many close relations between quantum matter designed in many labs worldwide and other physical systems found in the range of quantum information science, condensed matter physics, metrology, nuclear physics, and astronomy. Solid background in quantum mechanics, atomic physics, and statistical mechanics is desired.

This course will introduce a phenomenological description of superconducting materials and their applications to modern technologies. For this, the course will cover bulk and thin-film superconducting materials and introduce the Josephson junction, which is the basis of many superconducting devices. From this, we will introduce the main parameters that are relevant to the design of modern superconducting devices, namely resonators, qubits, SQUIDs and photodetectors. Finally, we will cover how the choice of materials and geometry influences the functioning of these devices.

This course will introduce modern theoretical concepts and methods of quantum many-body physics. It will cover tensor networks, a graphical framework for manipulating and classifying quantum many-body states based on quantum entanglement. It will discuss bounds on quantum information propagation, and how they constrain the behavior of correlation functions of phases of matter. It will also introduce quantum circuit models as testbeds to probe collective dynamical phenomena like thermalization and emergence of random matrix theory. This course is relevant for understanding and describing the novel physical regimes realized by emerging quantum simulator and quantum computational technologies.

The course provides an introduction to quantum information and quantum computation. In addition to physics majors, the course addresses students with a good background in discrete mathematics or computer science.The following topics will be covered: (1) Introduction: a brief review of basic notions of information science (Shannon entropy, channel capacity) and of basic quantum kinematics with emphasis on the description of multi-qubit systems and their discrete dynamics. (2) Quantum information: Entanglement and its numerical measures, separability of multi-partite states, quantum channels, standard protocols for quantum cryptography and entanglement purification, physical implementations. And (3) Quantum computation: single-qubit gates, two-qubit gates and their physical realization in optical networks, ion traps, quantum dots, Universality theorem, quantum networks and their design, simple quantum algorithms (Jozsa-Deutsch decision algorithm, Grover search algorithm, Shor factorization algorithm). The course is tightly integrated with IBM quantum computer hands-on experience via IBM Q Experience cloud services. Students will learn fundamentals of Qiskit, a modern and rapidly developing quantum computer programming language, by directly implementing concepts learnt in the classroom.

Functional electronic devices are an essential part of modern technology, and they are used in a wide range of applications, including communication systems, computers, medical devices, and consumer electronics. In this course, we will discuss the working principles of a variety of functional electronic devices, such as transistors, diodes, and different photodetectors. We will focus on the physical concepts behind their work and how those devices can be built and/or improved using novel artificial materials such as van der Waals heterostructures and 2D materials.

This course will present a unified look at the basic branches of physics (classical mechanics, quantum mechanics, electrodynamics, thermodynamics and statistical physics) from the perspective of variational principles, which offer compact statements of the fundamental laws and are also an important tool for designing models and finding approximate solutions.

In the age of big scientific data, Bayesian statistical methods and machine-learning techniques are becoming a vital part of the modern scientist’s toolkit. This course provides a graduate-level introduction to the two related fields, with equal emphasis on both. Key topics for the first part include: fundamentals of probability and inference, hierarchical modelling, model validation and comparison, and Monte Carlo methods; for the second part, they include: classification and regression, kernel methods, variational methods, and neural networks. The course will be largely theoretically oriented, with the occasional computational component.

Much of our real world data are manifestations or measurements of their underlying complex interactions. Hence, modelling and analysis of the underlying complex systems can reveal understandings and predictions that complement black-box machine learning tools. This course will cover the basic concepts and tools in analysing complex systems and simulation models, and more importantly why and when we need such white-box tools derived from statistical physics. Certain key concepts in complexity science will be intrudcued. It will also provide hands-on experience with system analysis and imulation modelling in Python.

This course covers the physical principles behind a wide variety of nano/micromachines and active matters involving these small energy-consuming building blocks. Specifically, the course covers molecular motors, nano/micro-robots, microswimmers, related active matters, and applications (e.g., actuation, precise control, chemistry, biotechnology, precision medicine, etc.). This course aims at a unified physical understanding, mainly based on stochastic thermodynamics, fluid dynamics at low Reynolds numbers, and active soft matter theories. The course focuses on artificial systems but also touches biological counterparts. Advanced design and fabrication methods like DNA nanotechnology will be discussed too.

In this course, the physics behind a wide spectrum of modern sensors is covered, capturing basic properties like temperature, distance, forces, pressure, magnetic fields, and light that are relevant in everyday applications, as well as more advanced sensors for acceleration and rotation that became commonplace in mobile devices for orientation and navigation. Furthermore, advanced sensing techniques used in microbalances, particle detection and advanced optical and acoustic sensing techniques will be discussed.

This module introduces advanced mathematical methods that are essential in many areas of theoretical physics. The topics covered are: differentiable manifolds, curved manifolds, tangent and dual spaces, calculus of differential forms, Stokes’ theorem, and applications to electromagnetic theory; symmetries of manifolds, Lie derivatives, Lie groups and algebras, their representations and physical applications. The module is targeted at students who wish to study theoretical physics.

This course introduces the basic building blocks for the theory of quantum measurements. With this detailed knowledge, a rigorous discussion of measurement models, the von Neumann model in particular, error-disturbance relations, incompatibility of measurements, and sequential measurements becomes possible. During the introduction of these concepts, the students will also acquire knowledge in operational quantum theory as well as become fluent in the mathematical framework of Hilbert space quantum mechanics.

After this course, the students will master and be knowledgeable in the mathematics and operational meaning of the basic concepts of quantum measurements. This knowledge will make them able to understand key quantum physical concepts like uncertainty and error and disturbance in measurements.

The Course covers many important topics in modern quantum information theory, including error correction and fault tolerance, quantum algorithms, entanglement and communication theory, as well as nonlocality and quantum cryptography.

This Course will equip the students with an interest in theoretical aspects of quantum information with the basic tools and concepts required to do research in the field.

The Course introduces contemporary physical hardware systems that form the basis for processing quantum information with actual devices. An overview will be presented in several lecturers, and specialized topics covered in small seminar-style presentations by students.

The Course should equip students from a broad background with a basic understanding of the working mechanism of various physical approaches at an overview level and inform about relevant strengths and challenges for the specific systems.

In this course, basic electronic techniques related to quantum technologies are introduced at a level that allows students to analyze, design, build and modify electronics encountered in experimental work on quantum technologies. It covers basic circuit design, with a focus on techniques related to typical signal conditioning and processing tasks encountered in experiments and application engineering involving quantum systems like single photon detection and generation, atom and ion traps, laser spectroscopy, optical modulators and some radio-frequency techniques to drive atomic transitions, and electronic techniques at cryogenic temperatures.