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School of Physical and Mathematical Sciences

2.2.2 Description of Courses


MPS811 Defence Science

AUs: 3, Prerequisites: NIL, Semester 2
This course fosters an appreciation of how fundamental sciences with its principles and approaches can be applied to the creation of advanced technologies and methodologies for national defence.


MPS812 Entrepreneurship

AUs: 3, Prerequisites: NIL, Semester 1 and 2
The course will provide the fundamental concepts of entrepreneurship and deals with entrepreneurial perspective through class discussions, case analysis and out-of-class reading. Business planning is essential to any entrepreneurial venture, whether it is to start a new business or expand an existing one. This, therefore, forms the main project for the course. However, the focus is not on the business plan itself but on the processes and tools leading to the development of the plan. The Internet and role of e-commerce in entrepreneurship and business is recognized, introduced and discussed. Similarly, the importance of technology as a source of entrepreneurial ventures will be introduced.


MPS901 Physical and Mathematical Sciences I

AUs: 3, Prerequisites: GCE ‘A’ level or H2 level Mathematics or equivalent, Special Term 1
This course prepares students for degree courses in the physical and mathematical sciences by exposing them to key topics and concepts. Students will grasp the fundamental principles of chemistry and physics, and techniques in mathematics, and be able to apply them in problem solving.


MPS902 Physical and Mathematical Sciences II

AUs: 3, Prerequisites: GCE ‘A’ level or H2 level Mathematics or equivalent, Special Term 2
This course prepares students for degree courses in the physical and mathematical sciences by exposing them to key topics and concepts. Students will grasp the fundamental principles of chemistry and physics, and techniques in mathematics, and be able to apply them in problem solving.
Note: The courses are still subject to minor revisions. Please check http://www.spms.ntu.edu.sg regularly for the latest updates.


Division of Chemistry and Biological Chemistry


CBC111 Principles of Modern Chemistry with Laboratory 1

AUs: 4, Prerequisites: GCE ‘A’ level or H2 level Chemistry or equivalent or by permission, Semester 1
This course adopts a topical approach with a strong problem-solving orientation. A series of discussions covering modern day research as well as the impact of chemistry will be used to illustrate the various fundamental concepts. To be introduced are concepts of structures and properties of atoms and molecules, bonding, periodicity, isomerism and chemical reactions, and the fundamentals of spectroscopy. Laboratory work includes both qualitative and quantitative analysis.


CBC112 Principles of Modern Chemistry with Laboratory 2

AUs: 4, Prerequisites: CBC111 or by permission, Semester 2
A continuation of CBC111, this course covers thermodynamics, the rate of chemical reactions and reaction kinetics, chemical equilibria, electrochemistry and nuclear chemistry. Laboratory work includes chemical synthesis, separation and purification processes, and qualitative and quantitative analysis.


CBC113 Basic Organic Chemistry with Laboratory

AUs: 4, Prerequisites: GCE ‘A’ level or H2 level Chemistry or equivalent or by permission, Semester 1
This course covers the chemistry, structures and reactions of the compounds of carbon and the concept of mechanism. It introduces the characteristic properties, synthesis and reactivity of alkanes, alkenes, alkynes, benzene, and other aromatic compounds, halides, alcohols, ethers, epoxides, phenols, aldehydes, ketones, carboxylic acids, amines, and their derivatives. Laboratory work involves techniques of separation and purification, organic reactions and preparation and systematic identification of compounds by the spectroscopy and physical properties.


CBC121 Biological Chemistry 1

AUs: 3, Prerequisites: GCE ‘A’ level or H2 level Chemistry or equivalent or by permission, Semester 1
Biological Chemistry 1 provides a survey of significant biomolecules and their roles in living systems and relates both their structure and reactivity to the principles of organic chemistry.


CBC122 Biological Chemistry 2

AUs: 3, Prerequisites: GCE ‘A’ level or H2 level Chemistry or equivalent or by permission, Semester 2
This course covers the reactivity of biomolecules, especially in enzymatic reactions, both qualitatively and quantitatively. The interaction of drug molecules with biological systems will be outlined based on chemical principles. The use of structural techniques for enzymology will be introduced.


CBC211 Analytical and Bioanalytical Chemistry

AUs: 3, Prerequisites: CBC111, CBC112 or by permission, Semester 2
The topics covered are sample treatment and extraction, sample preparation techniques, separation science, modern extraction techniques, chromatography, electrochemistry and electroanalytical methods. Examples from the biological systems will be used to illustrate the above concepts.


CBC212 Inorganic and Bioinorganic Chemistry

AUs: 3, Prerequisites: CBC111, CBC112 or by permission, Semester 1
This course covers coordination chemistry, nomenclature, structure and properties of transition metal complexes, stability constants and isomerism. It integrates chemical principles with biological applications with examples drawn from biochemistry, and molecular and cell biology.


CBC213 Organic and Bioorganic Chemistry

AUs: 3, Prerequisites: CBC113 or by permission, Semester 1
Topics covered include functional group transformations, disconnection approach to synthesis, synthesis and reactivity of polyfunctional organic molecules, heteroaromatic compounds, free radical reactions, pericyclic reactions, stereochemistry and reaction mechanisms. Examples from the biological systems will be used to illustrate the above concepts.


CBC214 Physical and Biophysical Chemistry 1

AUs: 3, Prerequisites: CBC111, CBC112, MAS182, PAP182 or by permission, Semester 2
This course covers properties of the Gibbs functions, chemical potential, fugacity, changes of states, phase equilibria, chemical equilibria, electrochemical equilibria, molecular reaction dynamics and potential energy surfaces, kinetics and principles of photochemistry. It integrates chemical principles with biological applications with examples drawn from biochemistry and molecular and cell biology.


CBC215 Chemistry and Biological Chemistry Laboratory 1

AUs: 2, Prerequisites: CBC111, CBC112, CBC113, CBC121, CBC122 or by permission, Semester 1
Laboratory work includes synthesis, qualitative and quantitative analysis of organic and inorganic compounds. Experiments are designed to illustrate topics covered in CBC212 and CBC213. They cover techniques of separation, organic and inorganic reactions, preparation and systematic identification of compounds by their spectroscopic and chemical properties. Examples from the biological systems will be used to illustrate the above concepts.


CBC216 Chemistry and Biological Chemistry Laboratory 2

AUs: 2, Prerequisites: CBC111, CBC112 or by permission, Semester 2
Experiments are designed to illustrate topics covered in CBC211 and CBC214. this module aims to integrate chemical principles with biological applications, with examples drawn from biochemistry and molecular and cell biology.


CBC311 Chemical Spectroscopy and Applications

AUs: 3, Prerequisites: CBC212, CBC213, CBC214 (only CBC214 for Physical Sciences students) or by permission, Semester 1
Covers structural and dynamic studies of inorganic and organic compounds by mass spectroscopy, electronic, vibrational and multi-nuclear magnetic resonance spectroscopic methods.


CBC312 Organometallic Chemistry

AUs: 3, Prerequisites: CBC212 or by permission, Semester 2
This course covers synthesis, bonding, structure, reactivity and applications of organometallic complexes.


CBC313 Organic Reaction Mechanisms and Synthesis

AUs: 3, Prerequisites: CBC213 or by permission, Semester 2
Topics covered include strategies in organic synthesis, reactivity, molecular rearrangements, reaction intermediates, enzymatic reactions and stereoelectronic effects.


CBC314 Physical and Biophysical Chemistry 2

AUs: 3, Prerequisites: CBC214 or by permission, Semester 1
This course covers the duality of matter and the Heisenberg principle, Schršdinger equation of simple systems, postulates of quantum mechanics, symmetry elements and operators, probability, order and disorder, statistical interpretation of entropy and the Boltzmann equation, Boltzmann distribution and the partition function for an ideal gas and thermodynamic functions for ideal gases. Examples from the biological systems will be used to illustrate the above concepts.


CBC315 Chemistry and Biological Chemistry Laboratory 3

AUs: 2, Prerequisites: CBC215 or by permission, Semester 2
Experiments are designed to illustrate topics covered in CBC312 and CBC313. This module aims to integrate chemical principles with biological applications, with examples drawn from biochemistry and molecular and cell biology.


CBC316 Chemistry and Biological Chemistry Laboratory 4

AUs: 2, Prerequisites: CBC216 or by permission, Semester 1
Experiments are designed to illustrate topics covered in CBC311 and CBC314. Examples from the biological systems will be used to illustrate the above concepts.


CBC 421 Advanced Analytical and Bioanalytical Techniques

AUs: 3, Prerequisite: CBC 211, CBC316 or by permission, Semester 1
Electroanalytical devices for the in situ monitoring of industrial and biological processes. Cyclic voltammetry applied to studying the kinetics and mechanisms of electron-transfer reactions in organic and inorganic systems. Chemical and biological sensors. Specialised spectroscopic methods (EPR, FTIR-microscopy, fluorescence) for quantitative analysis.


CBC422 Structural Determination

AUs: 3, Prerequisites: CBC311, CBC312 or by permission, Semester 1
Application of modern instrumentation for structural determination, variable temperature and 2-D NMR spectroscopy, X-ray diffraction, Raman and infra-red spectroscopy.


CBC423 Asymmetric Synthesis

AUs: 3, Prerequisites: CBC313 or by permission, Semester 1
This course introduces various methodologies for the control of the absolute stereochemistry of the desired product in organic syntheses. Topics include principles of asymmetric synthesis and asymmetric catalysis, and the application of chiral synthons in total synthesis.


CBC424 Current Topics in Synthetic Organic Chemistry

AUs: 3, Prerequisite: CBC 313 or CBC 952 or by permission, Semester 1 and 2
This course will introduce students to the latest developments in synthetic chemistry. Topics will be selected from the latest research literature. The course is directed towards students majoring in chemistry and related disciplines.


CBC425 Quantum Chemistry and Statistical Thermodynamics

AUs: 3, Prerequisite: CBC 314 or by permission, Semester 2
Duality of matter and the Heisenberg indeterminacy principle, Schrödinger equation of simple systems, postulates of quantum mechanics, symmetry elements and operators, probability, order and disorder, statistical interpretation of entropy and the Boltzmann equation, Boltzmann distribution and the partition function for an ideal gas and thermodynamic functions for ideal gases.


CBC426 Chemical Kinetics and Dynamics

AUs: 3, Prerequisite: CBC 314 or by permission, Semester 2
Selected topics from stratospheric ozone depletion, rate equations and their solutions, experimental determination of rate laws, microscopic view of reactivity, transition state theory, experimental measurements of rate constants, fuel cell chemistry, reactivity in solution, catalysis, diffusion, electron transfer (Marcus theory) and proton transfer.


CBC427 Current Topics in Inorganic Chemistry

AUs: 3, Prerequisite: CBC 312 or by permission, Semester 2
This course will introduce students to the latest development in inorganic chemistry. Topics will be selected from the latest research literature. The course is directed towards students majoring in chemistry and related disciplines.


CBC428 Advanced Bioorganic Chemistry

AUs: 3, Prerequisite: CBC 313 or by permission, Semester 1 and 2
Biomolecules, chemical ecology, chemicals used by living organisms for defense and sexual attraction, biosynthesis, structure and function of enzymes, affinity labeling reagents, mechanism inactivators, transition state analogue inhibitors and the mechanism of action of some important enzymes. Examples from the biological systems will be used to illustrate the above concepts.


CBC491 Honours Project I

AUs: 12, Prerequisites: CBC315, CBC316 or by permission, Semester 1 and 2
One semester of research activity in chemistry culminating in a presentation and a comprehensive written report (compulsory for students on track to a First Class Honours).


CBC492 Industrial Internship

AUs: 12, Prerequisites: CBC315, CBC316 or by permission, Semester 1 and 2
One semester of industrial placement in an approved chemical company or institution.


CBC493 Honours Project II

AUs: 3, Prerequisites: CBC315 or CBC316 or by permission, Semester 1 and 2
An investigative project in Chemistry and Biological Chemistry. Students who opted for CBC 491 may choose to extend their project work here and acquire more skills in communication and scientific presentation. Students who opted for industrial attachment can acquire crucial experience in academic research through this project.


CBC801 Impact of Chemistry on Society

AUs: 3, Prerequisites: NIL, Semester 2
This course discusses Chemistry in the context of selected current or potential socio-technological problems. Chemistry is central to a better understanding of our world. The issues selected, the facts and principles presented, and the habits of mind developed serve as a guide on how to live responsibly into the future.


CBC811 Forensic Science

AUs: 3, Prerequisites: NIL, Semester 1
This course provides general knowledge of forensic science, the use of chemicals and chemical technology to commit and to detect criminal offences, and the modern development of crime detection. The course covers some aspects of crime scene physical evidence, such as fingerprinting, firearms and ammunition, hair, fibres, drug identification, serology and DNA methods. This module can be studied by those without a strong scientific background.


CBC921 Molecular Modelling: Principles and Applications

AUs: 3, Prerequisites: CBC213, CBC214 or by permission, Semester 2
Introduces computational chemistry to synthetic organic chemists. Emphasis is to train students to be able to study organic chemistry related problems by using computational tools. This course is to provide an introduction to some of the techniques used in computational chemistry, and to illustrate how these techniques can be used to study organic chemical phenomena. Topics covered include building molecular structures, studying molecular properties, searching structural conformations and analyzing the thermodynamics and kinetics of organic reactions. The course will be a combination of lectures and hands-on work.


CBC922 Medicinal Chemistry

AUs: 3, Prerequisites: CBC213 or by permission, Semester 1
This course covers physicochemical principles of drug action, basic principles of drug design, the molecular basis of drug action and the structure-physicochemical activity relationship.


CBC923 Drug Discovery and Design

AUs: 3, Prerequisites: CBC121 or BS104, CBC122 or BS106, CBC212, CBC213, CBC922 or by permission, Semester 2
Basic principles of drug discovery and design, fundamental molecular basis of drug action, discussion of target discovery and “drugability”, structure-activity relationships, new design and high throughput screening methods to discover new drugs and classes of drugs.


CBC931 Industrial Chemistry

AUs: 3, Prerequisites: CBC112, CBC113 or by permission, Semester 1
This course provides an overview of the interrelations between the different branches of the modern chemical commodities industry, and of abstract concepts that are important in the manufacture of its products. Topics covered include sources of raw materials and new materials, overviews of trends in major chemical industries, principles and applications of chemical processes and unit operations in chemical industry and industrial catalysts.


CBC932 Polymer Chemistry

AUs: 3, Prerequisites: CBC113 or by permission, Semester 1
Classification of polymers, structure-property relationship, polymer technology and synthesis, stabilisation, composites, biocomposites and applications are covered under Polymer Chemistry


CBC933 Green Chemistry

AUs: 3, Prerequisites: CBC113 or by permission, Semester 2
Application of innovative technology to established industrial processes, environmentally improved routes to important products, design of new green chemicals and materials, sustainable resources, biotechnology alternatives and evaluation of environmental impact.


CBC934 Heterocyclic Chemistry

AUs: 3, Prerequisites: CBC113, CBC213 or by permission, Semester 1
This course outlines the role of heterocycles in organic, pharmaceutical and biological chemistry andexplains the methods for chemical synthesis, elaboration and use.


CBC941 Undergraduate Research Experience in Chemistry and Biological Chemistry I

AUs: 4, Prerequisites: By permission, Special Terms I and II
This vacation-long module (40 hours per week for 10 weeks) provides an opportunity to carry out research with one or more faculty members in Chemistry and Biological Chemistry.


CBC942 Undergraduate Research Experience in Chemistry and Biological Chemistry II

AUs: 4, Prerequisites: By permission, Special Terms I and II
This vacation-long module (40 hours per week for 10 weeks) provides an opportunity to carry out research with one or more faculty members in Chemistry.


CBC943 Undergraduate Research Experience in Chemistry and Biological Chemistry III

AUs: 4, Prerequisites: By permission, Special Terms I and II
This vacation-long module (40 hours per week for 10 weeks) provides an opportunity to carry out research with one or more faculty members in Chemistry.


CBC951 Materials Chemistry

AUs: 3, Prerequisites: CBC111, CBC112 or by permission, Semester 2
Covered in this course are the fundamentals of solid state chemistry, crystalline solids, crystal structure, Bragg equation, Madelung constant, lattice energy, bonding, intermolecular forces, lattice planes and surfaces, defects, solid-solid phase transition, non-crystalline solids, local order and glasses.


CBC952 Metal Mediated Reactions

AUs: 3, Prerequisites: CBC212, CBC213 or by permission, Semester 2
Applications of organometallic and transition metal complexes in major homogenous and heterogeneous catalytic reactions, reaction mechanism, selectivity, stereochemistry and activation energy are covered in this course.


CBC953 Natural Product Chemistry

AUs: 3, Prerequisites: CBC213 or by permission
The diversity of natural products and their roles in biological systems, chemistry and biosynthesis of important natural product classes such as terpenoids and steroids, fatty acids, arachidonic acid derivatives, polyketides, shikimic acid and alkaloids.


CBC961 Food Chemistry and Analysis

AUs: 3, Prerequisites: NIL, Semester 1
Structure and properties of food components (water, carbohydrates, proteins, lipids, other nutrients, food additives). The chemistry of changes occurring during processing, storage and utilization. Principles, methods and techniques of qualitative and quantitative physical, chemical and biological analyses of food and food ingredients.


CBC962 Food Microbiology and Safety Control

AUs: 3, Prerequisites: CBC112, CBC113 or by permission
Pathogenic and spoilage microorganisms in foods. Beneficial microorganisms in food systems. Influence of the food system on the growth and survival of microorganisms. Control of microorganisms.


CBC963 Food Processing and Preservation

AUs: 3, Prerequisites: CBC961, CBC962 or by permission
Characterisation of raw food material. Principles of food preservation. Principles of food processing techniques (freeze drying, high pressure, asceptic processing, extrusion etc). Packaging materials and methods. Cleaning and sanitation. Water and waste management.


CHEM1 Principles of Modern Chemistry

AUs: 4, Enrollment is limited to students who have gained entry into the scholar programme or by permission of the instructor, Semester 1
This course adopts a topical approach with a strong problem-solving orientation. A series of discussions covering modern day research as well as the impact of chemistry will be used to illustrate the various fundamental concepts. To be introduced are concepts of structures and properties of atoms and molecules, bonding, introductory thermodynamics, periodicity, isomerism and chemical reactions, the fundamentals of spectroscopy, electronic structure of atoms, periodic properties, ionic substances, covalent bonding, Lewis representations of molecules and ions, shapes of molecules, Lewis acids and bases, Bronsted acids and bases, hybridisation and resonance, an introduction to organic chemistry, the chemistry of life and Biological Chemistry.


CHEM2A Fundamental Techniques of Experimental Chemistry and Biological Chemistry

AUs: 3, Prerequisites: NIL, Semester 1
This course introduces the basic principles and techniques of synthesis and analysis, such as extraction, TLC, distillation, recrystallisation, titration, acid-base work-up, and the synthesis of organic compounds. It develops the laboratory skills and precision that are fundamental to experimental chemistry and Biological Chemistry.


CHEM2B Undergraduate Research Experience in Chemistry and Biological Chemistry

AUs: 3, Prerequisites: NIL, Semester 2
This course provides an opportunity to carry out research during the semester with one or more faculty members in Chemistry and Biological Chemistry. Students will be required to write a proposal, submit a report and give a presentation of their research. Enrollment s limited to students who have gained entry to the scholar programme or by permission of the instructor.


Division of Mathematical Sciences


MAS110 Introduction to Scientific Programming

AUs: 3, Prerequisites: GCE ‘A’ level or H2 level Mathematics or equivalent, Semester 1
This introductory course on scientific programming using Fortran and C/C++ equips students with basic programming skills, including the use of existing libraries, useful in the study of physical and mathematical sciences. It covers:

• fundamental concepts of programming
• a brief overview of scientific programming languages (Fortran, C/C++)
• basic data types, functions, classes, templates, STL (container classes, algorithms), memory management
• compilation process, use of existing C/C++/Fortran libraries
• algorithmic problem solving and design process, programme development, coding and debugging, fundamental programming constructs, data structures, recursions, simple file processing, algorithmic complexity
• case studies in physical and mathematical sciences

MAS111 Foundations of Mathematics

AUs: 3, Prerequisites: GCE ‘A’ level or H2 level Mathematics or equivalent, Semester 1
This course introduces fundamental ideas and techniques used in many different areas of mathematics.

• elementary logic, mathematical statements, quantified statements
• sets, operations on sets, Cartesian products, properties of sets
• natural numbers, integers, rational numbers, real numbers, complex numbers
• relations, equivalence relations, equivalence classes
• functions, injective and surjective functions, inverse functions, composition of functions
• mathematical proofs, mathematical induction

MAS112 Calculus I

AUs: 3, Prerequisites: GCE ‘A’ level or H2 level Mathematics or equivalent (Preclusions: Students who read MAS112 are not allowed to read MAS181 and CPE103), Semester 1
This is the first course on calculus in a sequence of four modules. The objective is to introduce basic notions of calculus and analytic geometry, including differentiation.

• real numbers, functions, their inverses and graphs
• transcendental functions: trigonometric and inverse trigonometric, logarithm and exponential, hyperbolic
• limits of functions, continuity at a point, continuity on an interval
• differentiability, derivatives of functions, chain rule, implicit differentiation, derivatives of higher order
• local maxima and local minima, Rolle’s Theorem and Mean Value Theorem, points of inflection, first-derivative and second-derivative tests, Netwon’s Method
• antidifferentiation

MAS113 Calculus II

AUs: 3, Prerequisites: MAS112 (Preclusions: Students who read MAS113 are not allowed to read MAS181 and CPE103), Semester 2
This second course in the calculus sequence studies integration and related topics.

• indefinite and definite integrals, mean value theorem for integrals, fundamental theorems of calculus, area of plane regions
• parametric equations, polar coordinates
• volumes of solids, length of arcs, other applications of the definite integral
• techniques of integration
• elementary differential equations

MAS114 Linear Algebra I

AUs: 4 , Prerequisites: GCE ‘A’ level or H2 level Mathematics or equivalent (Preclusions: Students who read MAS114 are not allowed to read MAS183, EE2007 and CPE103), Semester 2
This first of two courses on linear algebra introduces basic notions in linear algebra that are often used in other areas of mathematics and applications.

• Systems of linear equations, Gaussian elimination
• Matrices, inverses, determinants
• Vectors, dot product, cross product
• Vector spaces, subspaces, linear independence, basis, dimension, row and column spaces, rank

MAS181 Calculus for the Sciences I

AUs: 3, Prerequisites: GCE ‘A’ level or H2 level Mathematics or equivalent (Preclusions: Students who read MAS181 are not allowed to read MAS112, MAS113 and CPE103), Semester 1
This first of two courses on calculus equips students in the sciences with a basic working knowledge of calculus. Applications and computer-based learning are also included.

• functions and graphs, real numbers
• differentiation of functions of one variable, derivative as rate of change, chain rule, implicit functions, inverse functions
• local maxima and minima
• indefinite and definite integrals, applications of integration
• methods of integration
• fundamental theorem of calculus

MAS182 Calculus for the Sciences II

AUs: 3, Prerequisites: MAS181 or equivalent (Preclusions: Students who read MAS182 are not allowed to read MAS113, MAS211 and CPE103), Semester 2
} This second course on calculus equips students in the sciences with knowledge of further topics in this useful tool for modern science and engineering.

• differential equations — first-order and second-order linear differential equations
• techniques of solving differential equations, applications
• series and power series
• Taylor’s series
• Fourier series

MAS183 Linear Algebra and Multivariable Calculus

AUs: 4, Prerequisites: MAS181 or equivalent (Preclusions: Students who read MAS183 are not allowed to read MAS114, MAS212, MAS213 and CPE103), Semester 2
This course introduces techniques in linear algebra and multivariable calculus which are useful in applications. Applications and computer-based learning areincluded.

• systems of linear equations
• matrices, determinants
• vectors in 2- and 3-dimensional Euclidean spaces
• vector spaces, linear independence, basis, dimension
• linear transformations
• Eigenvectors and eigenvalues
• calculus of functions of several variables, aprtial derivatives, constrained and unconstrained optimisation, applications
• curl(f), gradient(f), div(f), and Jacobian(f) and write them in Cartesian, cylindrical and spherical coordinates.
• multidimensional integration, Green’s theorem, divergence theorem, Stokes’ theorem

MAS211 Calculus III

AUs: 3, Prerequisites: MAS113 (Preclusions: Students who read MAS211 are not allowed to read MAS182 and CPE103), Semester 1
This third course in the calculus sequence explores further topics in one-variable calculus such as sequences and series, as well as rudiments of multi-variable calculus.

• indeterminate forms, improper integrals
• Taylor’s formula
• sequences, monotonic and bounded sequences
• infinite series, tests for convergence and divergence, alternating series, absolute and conditional convergence
• power series, differentiation and integration of power series, Taylor series, binomial series, Fourier series
• vector-valued functions and parametric equations, calculus of vector-valued functions, solid analytic geometry

MAS212 Calculus IV

AUs: 3, Prerequisites: MAS113 (Preclusions: Students who read MAS212 are not allowed to read MAS183), Semester 2
This last of four courses in the calculus sequence introduces multi-variable calculus.

• functions of more than one variable, limits, continuity, partial derivatives, differentiability and total differential, chain rule
• directional derivatives, gradients, Lagrange multipliers
• double integrals, area of a surface, triple integrals
• line integrals, Green’s Theorem, surface integrals, Gauss’ divergence theorem, Stokes’ Theorem

MAS213 Linear Algebra II

AUs: 3, Prerequisites: MAS114 (Preclusions: Students who read MAS213 are not allowed to read MAS183), Semester 1
This second of two courses on linear algebra focuseson topics such as eigenvalues and canonical forms.

• linear transformations, kernels and images
• inner products, inner product spaces, orthonormal sets, Gram-Schmidt process
• Eigenvectors and eigenvalues, diagonalisation, applications
• symmetric and Hermitian matrices
• quadratic forms, bilinear forms
• • Jordan Normal Form and other canonical forms

MAS215 Probability and Statistics I

AUs: 4, Prerequisites: {MAS112 and MAS113} or {MAS181 and MAS182} (Preclusions: Students who read MAS215 are not allowed to read CPE103), Semester 1
This course focuses on probability theory, with the view of probability distributions as models for phenomena with statistical regularity.

• discrete distributions (binomial, hypergeometric and Poisson)
• continuous distributions (normal, exponential) and densities
• random variables, expectation, independence, conditional probability
• introduction to the law of large numbers and the central limit theorem

MAS281 Complex Methods for the Sciences

AUs: 3, Prerequisites: MAS182, MAS183 (Preclusions: Students who read MAS281 are not allowed to read MAS312), Semester 1
Some tools in complex methods and special functions that are commonly used in the sciences are introduced in this course.

• complex numbers, Argand diagrams, modulus and arguments, De Moivre’s theorem
• functions of a complex variable, elementary examples, Cauchy-Riemann equations
• contour integrals, Cauchy’s theorem and Cauchy’s integral formula
• Taylor series, Laurent series, zeros, poles and essential singularities, residues
• Fourier transform, inversion, convolution, Parseval’s theorem, delta function, applications
• elementary partial differential equations, methods of separation
• brief introduction to special functions, e.g., gamma function, beta function, Bessel’s function, Legendre’s function

MAS311 Real Analysis I

AUs: 4, Prerequisites: MAS112, MAS113, MAS211, Semester 1
This first course in real analysis – the rigorous investigation of calculus -- emphasisesrigour and proofs.

• basic properties of real numbers, supremum and infimum, completeness axiom
• limits and convergence of sequences, subsequences, Bolzano-Weierstrass theorem, Cauchy sequences
• limits of functions, continuity, intermediate value theorem, extreme-value theorem
• differentiability, derivatives, chain rule, Rolle’s theorem, mean value theorem, inverse functions, Taylor’s theorem, Lagrange’s form of the remainder

MAS312 Complex Analysis

AUs: 4, Prerequisites: MAS211, MAS212 (Preclusions: Students who read MAS312 are not allowed to read MAS281), Semester 1
This course is an introduction to the theory of complex variables, whichis useful in many branches of pure and applied mathematics.

• Analytic functions of one complex variable, Cauchy-Riemann equations
• Contour integrals, Cauchy’s theorem and Cauchy’s integral formula, maximum modulus theorem, Liouville’s theorem, fundamental theorem of algrebra, Morera’s theorem
• Taylor series, Laurent series, singularities of analytic functions
• Residue theorem, calculus of residues
• Fourier transforms, inversion formula, convolution, Parseval’s formula
• Applications

MAS313 Abstract Algebra I

AUs: 3, Prerequisites: MAS111, MAS213, MAS214, Semester 2
This first course on modern algebra introduces basic algebraic structures such as groups, rings and fields.

• Groups, subgroups, cyclic groups, groups of permutations, Cosets, Lagrange’s Theorem, homomorphism, factor groups
• Rings and fields, ideals, integral domains, quotient fields, rings of polynomials, factorisation of polynomials over a field

MAS314 Numerical Analysis I

AUs: 3, Prerequisites: { MAS114 and MAS213 } or { MAS181 and MAS183 }, Semester 2
This first course on the theory and applications of numerical approximation techniques equips students with a number of commonly used numerical algorithms, knowledge, experience in writing a program from an algorithm, and skill in performing numerical computations using MATLAB.

• Basics on computational errors, basic numerical methods for solutions of systems of linear equations, iterative methods for systems of linear equations, polynomial interpolation, numerical integration, numerical solutions of nonlinear equations, implementation of algorithms using MATLAB

MAS315 Probability and Statistics II

AUs: 4, Prerequisites: MAS215 (Preclusions: Students who read MAS315 are not allowed to read CPE103), Semester 2
This course introduces modern statistical concepts and procedures derived from a mathematical framework.

• Statistical inference, decision theory, point and interval estimation, tests of hypotheses, Neyman-Pearson lemma
• Bayesian analysis, maximum likelihood, large sample theory

MAS316 Regression Analysis

AUs: 4, Prerequisites: MAS215, MAS315, Semester 1
The object of study in this course is regression analysis – one of the most widely used statistical techniques. The course also covers:

• multiple linear regression, nonlinear regression, analysis of residuals and model selection
• One-way and two-way factorial experiments, and random and fixed effects models

MAS317 Data Analysis with Computer

AUs: 3, Prerequisites: MAS215, Semester 2
This course on the use of statistical computer packages focuses on MINITAB, SAS and R. It covers pseudorandom number generation, generating discrete and continuous random variables, data access, transformations, estimation, testing hypotheses, ANOVA, resampling methods and simulations


MAS321 Ordinary Differential Equations

AUs: 4, Prerequisites: MAS212, Semester 1
This course provides methods and techniques to solve typical ordinary differential equations, introduces the fundamental theory of ODEs, and develops methods to analyze given equations.

• first-order equations, exact equations, integrating factors, separable equations, linear homogenous and non-homogenous equations, variation of parameters, Principle of superposition
• second-order equations, Wronskian, Abel’s formula, variation of parameters, exact equations, adjoint and self-adjoint equations, Lagrange and Green’s identities, Sturm’s comparison and separation theorems
• first-order linear systems, Wronskian, Abel’s formula, variation of parameters, systems with constant coefficients
• first-order nonlinear equations, initial value problem
• use of ODE in simple modelling problems

MAS323 Number Theory

AUs: 4, Prerequisites: MAS214, Semester 1
This course introduces basic number theory – a topic that epitomises the beauty and elegance of pure mathematics – and its modern applications. The course covers:

• A review of modular arithmetic, Chinese remainder theorem, Fermat’s little theorem, Wilson’s theorem
• number-theoretic functions: T, •, Euler’s •-function, Mšbius inversion formula, applications to cryptography
• primitive roots, indices
• Legendre’s symbols, quadratic reciprocity law
• continued fractions, Pell’s equations
• primality tests and factorisation of integers, RSA cryptosystem

MAS324 Graph Theory

AUs: 4, Prerequisites: MAS214, MAS215, Semester 1
This course provides an introduction to working with the most accessible discrete structures, i.e., graphs.

• review of introductory graph theory from MAS214
• connectivity and matchings, Hall’s theorem, Menger’s theorem, Network flows
• paths and cycles, complete subgraphs and Turán’s theorem, Erdšs-Stone theorem
• graph colouring, four-colour theorem
• Ramsey theory
• probabilistic methods in graph theory
• use of software to solve graph-theoretic problems

MAS326 Basic Optimisation

AUs: 4, Prerequisites: MAS213 or MAS183, Semester 2
This basic course in optimisation and operations research covers:

• introduction of Optimisation models: objective and constraints, convex sets and functions, polyhedron and extreme points
• introduction to LP: solving 2-variable LP via graphical methods; simplex method; dual LP and sensitivity analysis
• Karush-Kuhn-Tucker optimality conditions, optimal solution via optimality conditions, Duality theory
• Network Optimisation: Shortest path, maximum flow, minimum cost flow, assignment problem, transportation problem, network simplex method

MAS328 Stochastic Processes

AUs: 4, Prerequisites: MAS215, Semester 1
This course introduces modeling dependence and covers:

• Discrete-time Markov chains, examples of discrete-time Markov chains, classification of states, irreducibility, periodicity, first passage times, recurrence and transience, convergence theorems and stationary distributions
• Random walk, Poisson processes

MAS331 Undergraduate Research Experience in Mathematical Sciences I

AUs: 4, Prerequisites: Approval by Division, Special Terms I and II
This research-based course will see students work on a specific topic under the supervision of a faculty member.


MAS332 Undergraduate Research Experience in Mathematical Sciences II

AUs: 4, Prerequisites: MAS331, Approval by Division, Special Terms I and II
This research-based course will see students work on a specific topic under the supervision of a faculty member.


MAS371 Mathematical Foundations of Game Theory

AUs: 4, Prerequisites: MAS215, Semester 2
This course provides an introduction to game theory, studying basic concepts, models and solutions of games and their applications.

• Games of normal form and extensive form, applications in economics, relations between game theory and decision making
• Games of complete information: static games with finite or infinite strategy spaces, Nash equilibrium of pure and mixed strategy, dynamic games, backward induction solutions, information sets, subgame-perfect equilibrium, finitely and infinitely repeated games
• Games of incomplete information: Bayesian equilibrium, first price sealed auction, second price sealed auction, and other auctions, dynamic Bayesian games, perfect Bayesian equilibrium, signaling games
• Cooperative games: bargaining theory, cores of n-person cooperative games, the Shapley value and its applications in voting, cost sharing, etc

MAS421 Real Analysis II

AUs: 4, Prerequisites: MAS212, MAS311, Semester 2
A continuation of MAS311, this course investigatesfurther topics in real analysis with rigour.

• Riemann integral, integrability, fundamental theorem of calculus, improper integrals
• convergent series, absolute convergence, tests of convergence
• sequence and series of functions, uniform convergence
• power series, radius of convergence, local uniform convergence of power series

MAS422 Real Analysis III

AUs: 4, Prerequisites: MAS311, MAS421
This is a continuation of MAS 421 where further topics in real analysis are investigated with rigour.

• Normed space R n, Lipschitz mappings, Bolzano-Weierstrass theorem in R n, open and closed sets, sequences, Cauchy sequences, completeness, continuity of functions, compactness, Heine-Borel Theorem, Bolzano-Weierstrass Theorem, connectedness.
• Introduction to metric spaces, limits, continuity, balls, neighbourhoods, open and closed sets, completeness, compactness, space of continuous functions, contraction mapping principle, Arzela-Ascoli Theorem, Weierstrass Approximation Theorem.

MAS423 Partial Differential Equations

AUs: 4, Prerequisites: MAS311, MAS321 (MAS421 is useful but not essential), Semester 2
This introductory course on partial differential equations outlines their basic properties andthe techniques to solve the equations.

• first-order equations, Quasi-linear equations, general first-order equation for a function of two variables, Cauchy problem
• wave equation, wave equation in two independent variables, Cauchy problem for hyperbolic equations in two independent variables
• heat equation, the weak maximum principle for parabolic equations, Cauchy problem for heat equation, regularity of solutions to heat equation
• Laplace equation, Green’s formulas, harmonic functions, maximum principle for Laplace equation, Dirichlet problem, Green’s function and Poisson’s formula

MAS425 Abstract Algebra II

AUs: 4, Prerequisites: MAS213, MAS313
Further topics in groups, rings and fields are discussed in this course.

• Sylow’s Theorems, Abelian groups
• Homomorphisms of rings, factor rings, prime and maximal ideals
• unique factorization domains, Euclidean domains, principal ideal domains
• modules, submodules, homomorphisms, quotient modules, modules over principal ideal domains

MAS426 Galois Theory

AUs: 4, Prerequisites: MAS313, MAS425
This course deals with the theory of fields, culminating in Galois theory, the most famous of whose application is the proof that the general quintic equation with rational coefficients cannot be solved by radicals.

• Field extensions, algebraic extensions, geometric constructions. Finite fields. Automorphisms of fields, splitting fields, normal and separable extensions, Galois extensions, Galois groups. Galois correspondence
• Solution of equations by radicals, insolvability of the quintic equation. Fundamental Theorem of Algebra.

MAS427 Set Theory and Logic

AUs: 4, Prerequisites: MAS111, MAS214
This course introduces the notions of validity and provability in formal logic, the concepts of ordinals and cardinals as well as some formal set theory.

• Partially-ordered sets, well-orderings and order-types, induction and recursion on ordinals, ordinal arithmetic, cardinals, cardinal arithmetic
• Axiom of choice and its equivalences
• Axiom of determinacy
• Propositional calculus
• Truth tables, validity and contradictions
• Predicate calculus with equality
• Completeness and compactness theorems
• Löwenheim-Skolem theorem

MAS431 Combinatorics

AUs: 4, Prerequisites: MAS211, MAS213, MAS214

• The purpose of this course is to study some topics in combinatorics and their connections with other branches of mathematics and theoretical computer science
• Recursions and generating functions. Partitions and tableaux. Designs, Latin squares, combinatorial designs and projective geometries. Extremal combinatorics, asymptotic analysis

MAS432 Coding Theory

AUs: 4, Prerequisites: MAS213, MAS214, Semester 2
This course introduces basic notions in the theory of error-correcting codes, which is used in data storage and telecommunication.

• error detection, correction and decoding, Hamming distance
• basic facts on finite fields
• linear codes, Hamming weight, generator and parity-check matrices, encoding, decoding
• bounds, Hamming codes, Golay codes, perfect codes, MDS codes
• construction of codes, Reed-Muller codes
• cyclic codes, generator polynomials, BCH codes, Reed- Solomon codes
• computer implementation of efficient coding and decoding

MAS433 Cryptography

AUs: 4, Prerequisites: MAS214, MAS313 , Semester 1
This course is an introduction to some basic issues in cryptography, especially the underlying mathematical concepts. Classical ciphers, cryptanalysis, linear complexity. Data Encryption Standard. RSA cryptosystem, primality testing and factorization of integers. Discrete logarithms. Signatures, Digital Signature Standard.


MAS434 Topics in Mathematics of Information and Communication

AUs: 4, Subject to approval by the Head of Division, Semester 2
This course introduces specialized advanced topics related to information theory, coding theory and cryptography. The choice of the topic depends on the instructor.


MAS436 Topology

AUs: 4, Prerequisites: MAS311 and MAS421, Semester 1
This course introduces the notions of metric and topological spaces.

• metric spaces, limits, continuity, balls, neighbourhoods, open and closed sets
• topology, metric topologies, convergence, Hausdorff spaces, homeomorphisms, topological and non-topological properties, subspace, quotient and product topologies
• connectedness, components, path-connectedness
• compactness, sequential compactness
• contraction mapping theorem

MAS437 Algebraic Topology

AUs: 4, Prerequisite: MAS313, MAS421 (MAS436 is useful but not essential)
Basic ideas in algebraic topology will be introduced in this course.

• Simplicial complexes, subdivisions, simplicial approximation theorem, classification of surfaces
• Fundamental groups, homotopy of continuous functions and homotopy equivalence, change of base point, van Kampen’s theorem
• Euler characteristic, Lefschetz fixed point theorem
• Covering spaces and covering maps
• Homology

MAS438 Differential Geometry

AUs: 4, Prerequisite: MAS311 and MAS421 (MAS422 and MAS436 is useful but not essential)
This introduction to differential geometry, with curves and surfaces in the Euclidean 3 dimensional space as the focus, covers:

• metrics, lie brackets, connections, curvature and torsion of curves, the Frenet-Serret equations, Gaussian and mean curvature of surfaces, geodesics, isometries and Gauss’s Theorem Egregium, tensors
• Gauss-Bonnet theorem

MAS441 Numerical Analysis II

AUs: 4, Prerequisite: MAS314, MAS321 (MAS423 is useful but not essential) , Semester 1
This course is to provide numerical solutions of differential equations using finite difference methods and to understand the implementation of the numerical computations using computer software packages such as MATLAB.

• Finite difference formulae
• Consistency of difference schemes, finite difference methods for ordinary differential equations
• Classification of second-order partial differential equations
• First and second order characteristics
• Matrix method and von Neumann method for stability analysis
• Lax's equivalence theorem for convergence
• Method of characteristics
• Application to heat equation, wave equation and Poisson’s equation

MAS442 Mathematical Tools of Image and Signal Processing

AUs: 4, Prerequisite: MAS311, MAS441 (MAS421 and MAS422 are useful but not essential)
This course is to provide the necessary mathematical tools for image and signal processing

• Fourier transform, Window Fourier transform, Fourier series, discrete Fourier transform and discrete Window Fourier transform, orthonormal basis and tight frames
• Splines, approximation by splines. Refinable functions, subdivision scheme
• Multiresolution analysis, orthonormal wavelets, spline tight frame wavelets, discrete wavelet transform, analysis and synthesis algorithms

MAS443 Topics in Scientific Computing

AUs: 4, Prerequisite: Approval by the Division of Mathematical Sciences
This course is to introduce specialized advanced topics in scientific computation and continuous applied mathematics. The choice of the topic depends on the instructor.


MAS445 Deterministic Methods in OR

AUs: 4, Prerequisite: MAS212 and MAS326
This course introduces some deterministic methods commonly used in operations search and covers:

• unconstrained optimization: one dimensional search, gradient method, Newton-Raphson method
• constrained optimization: feasible direction methods, penalty/barrier function methods, modern interior point methods for convex programming
• discrete optimization: formulations, cutting plane methods, branch-and-bound methods, Lagrangian relaxation, dynamic programming approach

MAS446 Probabilistic Methods in OR

AUs: 4, Prerequisites: MAS215 and MAS326, Semester 1
This course introduces some useful probabilistic methods commonly used in operations research and statistics.

• Queuing: basic models, performance analysis, simulation of queuing systems
• Stochastic optimization: Stochastic programming, modelling and algorithms, Markov decision process, stochastic approximation

MAS447 Logistics and Supply Chain Management

AUs: 4, Prerequisites: MAS215 and MAS326
This course focuses on issues which arise in the integrated design and management of the entire logistics network.

• Overview of supply chains – components of a supply chain, material and information flow, supplier-retailer-customer interaction, e-business
• Inventory and materials management - Economic order quantity model, Lot sizing models, models with uncertain demands, MRP/JIT
• Facility location and transportation - single-source capacitated facility location, vehicle routing problems with equal, unequal demands and time-window constraints.

MAS451 Time Series Analysis

AUs: 4, Prerequisite: MAS215, MAS315 and MAS316, Semester 2
This course introduces time series models used in economics, engineering and finance, and covers:

• trend fitting, autoregressive and moving average models, spectral analysis
• seasonality, forecasting and estimation
• use of computer package to analyze real data sets

MAS452 Multivariate Analysis

AUs: 4, Prerequisite: MAS215, MAS315 and MAS316, Semester 2
This course focuses on the standard methods of multivariate statistical analysis.

• Distribution theory: multivariate normal distribution, Hotelling’s T2 and Wishart distributions, inference on the mean and covariance, principal components and canonical correlation, factor analysis, discrimination and classification

MAS453 Data Mining

AUs: 4, Prerequisite: MAS215, MAS315, MAS316 and MAS317, Semester 1
This course gives an overall view of modern statistical techniques for analyzing large data sets. Neural networks, support vector machines, classification trees and boosting.


MAS454 Sampling and Survey

AUs: 4, Prerequisite: MAS215 and MAS315, Semester 1
This course is an introduction to sampling and the design of sample surveys.

• ratio and regression estimators under simple random sampling, separate and combined estimators for stratified random sampling
• systematic sampling and its relationship with stratified and cluster sampling
• further aspects of stratified sampling, clustered sampling with clusters of unequal sizes
• subsampling; multi-stage sampling
• complex sample designs

MAS455 Clinical Trials

AUs: 4, Prerequisite: MAS215 and MAS315, Semester 2
This course provides an introduction to the design and analysis of clinical trials with an emphasis on the statistical aspects. Phases of clinical trials, objections and endpoints, the study cohort, controls, randomization and binding, sample size determination, treatment allocation, monitoring trial progress: complient effects. Ethical issues, quality of life assessment, data analysis involving multiple treatment groups and endpoints, stratification and subgroup analysis, intent to treat analysis, analysis of compliance data, surrogate endpoints, multi-centre trials and good practice versus misconduct.


MAS456 Survival Analysis

AUs: 4, Prerequisites: MAS 215 and MAS 315, Semester 1
This course focuses on the standard methods of survival data analysis and covers: Examples of survival data analysis, types of censoring, parametric survival distributions (exponential, Weibull, lognormal), nonparametric methods, Kaplan-Meier estimator, tests of hypotheses, graphical methods of survival distribution fitting, goodness of fit tests.


MAS461 Special Topics in Mathematics

AUs: 4, Prerequisite: Approval by the Division of Mathematical Sciences
Some advanced topics in theoretical mathematics not normally covered in the regular courses may be offered.


MAS462 Special Topics in Applied Mathematics

AUs: 4, Prerequisite: Approval by the Division of Mathematical Sciences
Some advanced topics in applied mathematics not normally covered in the regular courses may be offered.


MAS463 Special Topics in Statistics

AUs: 4, Prerequisite: Approval by the Division of Mathematical Sciences
Some advanced topics in statistics not normally covered in the regular courses may be offered.


MAS464 Supervised Independent Study I

AUs: 4, Subject to approval by the Head of Division, Semester 1 and 2
In this course, the student will do independent reading on a topic under the supervision of a faculty member.


MAS465 Supervised Independent Study II

AUs: 4, Prerequisite: MAS464, Subject to approval by the Head of Division, Semester 1 and 2
In this course, the student will do independent reading on a topic under the supervision of a faculty member.


MAS471 Computational Economics

AUs: 4, Prerequisites: MAS214, Semester 1
The course aims to teach students about the basic notions in Game Theory and their computational issues. Further, the course will give a comprehensive study on mechanism design and auction theory, with a focus on designing protocols with different economic properties.

• Introduction to the background of Game Theory
• Introduction to the basics of the Theory of Computation
• Computation of equilibria (Nash equilibrium, market equilibrium, Walrasian equilibrium etc.)
• Algorithmic Mechanism Design
• Auction Theory (Vickrey auction, combinatorial auctions, digital-goods auctions, sponsored search auctions)
• Profit maximization
• Cost sharing mechanisms

MAS491 Honours project

AUs: 8, Prerequisite: Subject to approval by the Head of Division (Preclusions: Students who
read MAS492 are not allowed to read MAS491), Semester 1 and 2
This is a semester-long research course on an advanced topic leading to an Honours thesis under the supervision of a faculty member.


MAS492 Industrial internship (Pass/ Fail option only)

AUs: 8, Prerequisite: Subject to approval by the Head of Division (Preclusions: Students who read MAS491 are not allowed to read MAS492), Special Terms I and II
This course provides practical working experience and workplace exposure through a short-term job placement.


MAS801 It’s a discreetly discrete world: Mathematics in real-life applications

AUs: 3, Prerequisites: GCE ‘AO’ level or H1 level Mathematics or equivalent, Semester 1
Error-detecting and error-correcting codes – detecting and correcting errors in data: basic modular arithmetic used in the design of such codes, basic issues in theory and applications, well-known examples, real-life applications such as NRIC numbers, ISBN, CD, telecommunications, etc. Cryptography – ensuring security of information: basic issues and use in applications such as electronic transactions and communication, Euclidean algorithm, congruences, Chinese Remainder Theorem, the RSA cryptosystem. Travelling Salesman Problem – finding optimal routes: basic concepts in graph theory and linear programming, simplex algorithm, relationship to applications, e.g., wiring a chip, scheduling airline crews. P vs NP – understanding computational complexity: complexity classes, NP-complete problems and links with other applications such as the RSA cryptosystem and the Travelling Salesman Problem. Google – search for information on the Web: basic concepts in graph theory, probability and linear algebra, especially eigenvalues, underlying the Google search engine.


MAS802 Tackling the Odds: Inside Statistics

AUs: 3, Prerequisites: GCE ‘AO’ level or H1 level Mathematics or equivalent, Semester 1
The course provides an overview of statistics and its applications in other disciplines. In particular, this course provide students with the understanding of statistics methodology and necessary skills of evaluating statistical studies that they may encounter in some other courses, future career, or even their everyday lives. Topics includes overview of statistics; measurement; visual displays; data descriptions; probability and risk; correlation and causality; statistical methodologies; statistical modeling.


MATH1A Calculus of One Variable

AUs: 4, Prerequisites: GCE ‘A’ level or H2 level Mathematics or equivalent, Semester 1
This is an intensive introduction to calculus of one variable and (plane) analytic geometry for Science and Engineering scholars. Limits. Continutity of real valued functions, intermediate Value Theorem. Differentiability of functions from R to R, chain rule, critical points, Rolle’s Theorem and Mean Value Theorem. Inverse functions and derivatives of inverse functions. Integrability and integrals. Fundamental theorems of Calculus. Trigonometric, logarithm and exponential functions. Techniques of integration. Taylor’s formula. Infinite sequences. Infinite series. Power series and radius of convergence.


MATH1C Linear Algebra and Differential Equations

AUs: 4, Prerequisite: GCE ‘A’ level or H2 level Mathematics or equivalent, Semester 1
This is an intensive introduction to basics of sets, linear algebra and ODEs for Science and Engineering scholars. Sets, operations on sets, properties of sets. Systems of linear equations, Gaussian elimination. Matrices, inverses, determinants. Vector spaces, subspaces, linear independence, basis, dimension, row and column spaces, rank. Linear transformations, kernels and images. Eigenvectors and eigenvalues. First-order ordinary differential equations (ODEs). Second-order ODEs, oscillation and damping, series solutions of ODEs.


MTH110 Introduction to Scientific Programming

AUs: 3, Prerequisites: A or H2 Level Mathematics or equivalent, Semester 1
This is an introductory course on scientific programming using Fortran and C/C++, intended primarily for students in physical and mathematical sciences. The objective is to equip the students with basic programming skills, including the use of existing libraries, useful in the study of physical and mathematical sciences. Fundamental concepts of programming. Brief overview of scientific programming languages (Fortran, C/C++). Basic data types, functions, classes, templates, STL (container classes, algorithms), memory management. Compilation process, use of existing C/C++/Fortran libraries. Algorithmic problem solving and design process, program development, coding and debugging, fundamental programming constructs, data structures, recursions, simple file processing, algorithmic complexity. Case studies in physical and mathematical sciences.


MTH111 Foundations of Mathematics

AUs: 4, Prerequisites: A or H2 Level Mathematics or equivalent, Semester 1
- Elementary logic, mathematical statements, quantified statements
- Sets, operations on sets, Cartesian products, properties of sets
- Natural numbers, integers, rational numbers, real numbers, complex numbers
- Relations, equivalence relations, equivalence classes
- Functions, injective and surjective functions, inverse functions, composition of functions
- Division algorithm, greatest common divisor, Euclidean algorithm, fundamental theorem of arithmetic, modulo arithmetic


MTH112 Calculus I

AUs: 4, Prerequisites: A or H2 Level Mathematics or equivalent, Semester 1
Real numbers, functions, their inverses and graphs. Transcendental functions: trigonometric and inverse trigonometric, logarithm and exponential, hyperbolic. Limits of functions, continuity at a point, continuity on an interval. Differentiability, derivatives of functions, chain rule, implicit differentiation, derivatives of higher order. Local maxima and local minima, Rolle's Theorem and Mean Value Theorem, points of inflection, first-derivative and second-derivative tests, L'Hospital's Rule. Antidifferentiation. Indefinite integrals, substitution rule, integration by parts.


MTH114 Linear Algebra I

AUs: 4, Prerequisites: A or H2 Level Mathematics or equivalent, Semester 1
This is the first of two courses on linear algebra. The main objective is to introduce basic notions in linear algebra that are often used in other areas of mathematics and applications. Systems of linear equations, Matrices and their inverses, Determinants, Vector spaces, subspaces, Linear independence, bases, dimension, Row and column spaces, rank of a matrix, Linear transformations.


MTH115 Linear Algebra II

AUs: 4, Prerequisites: MTH114, Semester 2
Linear transformations, kernels and images. Inner products, inner product spaces, orthonormal sets, Gram-Schmidt process. Eigenvectors and eigenvalues, diagonalization, applications. Symmetric and Hermitian matrices. Quadratic forms, bilinear forms. Jordan normal form and other canonical forms.


MTH116 Discrete Mathematics

AUs: 3, Prerequisites: A or H2 Level Mathematics, Semester 2
- Counting, permutations and combinations, binomial theorem
- Recurrence relations
- Graphs, paths and circuits, isomorphisms – trees, spanning trees
- Graph algorithms (e.g. shortest path, maximum flow) and their computational complexity, big-o notation


MTH313 Knots and Surfaces: Introduction to Topology

AUs: 4, Prerequisites: MAS212 and MAS213, or MTH211 and MTH212. Semester 1
The topics covered include a selection of the following. Continuous functions. Surfaces. Euler characteristic. Maps and graphs. Vector fields on surfaces. Fundamental group of a surface. Knots.


MTH911 Advanced Investigations in Calculus I


AUs: 1, Approval by the Head of Division , may only be taken concurrently with MTH112, Semester 1
This course supplements MTH112, presenting challenging calculus problems to nurture the potential of students who wish to be stretched.


MTH912 Advanced Investigations in Calculus II

AUs: 1, Approval by Division of Mathematical Sciences, may only be read concurrently with MTH113, Semester 2
This course supplements MTH113, presenting challenging calculus problems to nurture the potential of students who wish to be stretched.


MTH913 Advanced Investigations in Linear Algebra I

AUs: 1, Approval by Division of Mathematical Sciences, may only be read concurrently with MTH114, Semester 1
This course supplements MTH114, presenting challenging problems in linear algebra to nurture the potential of students who wish to be stretched.


MTH914 Advanced Investigations in Linear Algebra II

AUs: 1, Approval by Division of Mathematical Sciences, may only be taken concurrently with MTH115, Semester 1 and 2
This course supplements MTH115, presenting challenging problems in linear algebra to nurture the potential of students who wish to be stretched.


MTH915 Advanced Investigations in Discrete Mathematics

AUs: 1, Approval by Division of Mathematical Sciences, may only be read concurrently with MTH116, Semester 2
This course supplements MTH214, presenting challenging problems in elementary discrete mathematics and number theory to nurture the potential of students who wish to be stretched.


MTH921 Advanced Investigations in Calculus III

AUs: 1, Approval by Division of Mathematical Sciences, may only be taken concurrently with MTH211, Semester 1
This course supplements MTH211, presenting challenging calculus problems to nurture the potential of students who wish to be stretched.


MTH941 Mathematical Problem-Solving

AUs: 2, Approval by the Division of Mathematical Sciences, may be required to sit for a qualifying test, Semester 2
Rather than studying theory or specialized techniques for solving specific mathematical problems, this seminar-style course leads students to think creatively, acquire exposition skills and develop their problem-solving skills through the solution of challenging mathematical problems from calculus, linear algebra, algebra, differential equations, probability and discrete mathematics.


Division of Physics and Applied Physics


PAP111 Mechanics and Relativity

AUs: 4, Prerequisites: Physics and Mathematics at A or H2 level, or equivalent. Not available to students who have taken/are taking PAP181, Semester 1
This course introduces fundamental concepts of mechanics and relativity. Static mechanics - force and equilibrium, pressure, moments, work and potential Linear motions
- Newton’s first and second laws, kinetic energy, linear momentum, frames of reference, rockets, collision Special relativity - Michelson-Morley experiment, Einstein’s postulates, Lorentz transformation, time and causality, world-lines and space-time, Doppler effect, momentum and energy Force fields - gravity, concept of field, conservative fields, Gauss’ law, superposition Rotational motion - centrifugal and Coriolis forces, angular speed and momentum, moment of inertia, parallel and perpendicular axes theorems, kinetic energy, gyroscope, orbits and Kepler’s law


PAP112 Fields and Oscillations

AUs: 4, Prerequisites: Physics and Mathematics at A or H2 level, or equivalent. Not available to students who have taken/are taking PAP182, Semester 2
This course introduces basic notions of fields and oscillatory behaviour. Simple harmonic motion - time-dependence, angular frequency and phase, mass on a spring, relative phases, coupled oscillations and normal modes, phasor diagrams, representations in complex plane, damped oscillations and energy decay Electromagnetic field - Coulamb’s law, electric field and potential, Gauss’ law and capacitance, moving charges, magnetic flux density and Ampere’s law, flux in circuits, Faraday’s law and magnetostatic energy, JJ Thompson’s experiment Electrical circuits - voltage, current and resistance, Kirchoff’s laws, exponential decay in circuits Oscillations in circuits - LC circuits and relative phases, complex current and voltage, complex impedance, electrical resonance, filter and bandwidth, mechanical impedance.


PAP113 Optics and Waves

AUs: 4, Prerequisites: Physics and Mathematics at A or H2 level, or equivalent. Semester 2
This course studies the behaviour and properties of optical and particle waves. Waves, interference and optics - waves on a string, 1-D wave equation and solution; 3-D running waves and wave-vector; superposition; electromagnetic waves; phase and group velocity, boundary conditions, reflection and transmission coefficients, refractive index, Brewster angle, wave attenuation; Huygen’s principle, Young’s slit and diffraction grating; reflection and refraction; lens formulae; real and virtual images; telescope Wave-particle duality-photoelectric effect; photons, energy and momentum; Compton scattering; de Broglie waves; Davisson-Germer experiment; electron microscope, Schrodinger’s equation.


PAP118 Physics Laboratory Ia

AUs: 2, Prerequisites: Physics at A or H2 level or equivalent. Semester 1
This course will train students in basic experimental physics that include topics in mechanics, basic optics and thermal physics. The laboratory sessions are designed to provide an active learning experience where key concepts can be better appreciated. Students will also learn about data acquisition, error analysis, error distribution and fitting procedures.


PAP119 Physics Laboratory Ib

AUs: 2, Prerequisites: Physics at A or H2 level or equivalent. Semester 2
This course will train students in basic experimental physics that include topics in electricity and magnetism, circuits, optics and wave phenomena. The laboratory sessions are designed to provide an active learning experience where key concepts can be better appreciated.


PAP181 Fundamentals of Physics 1

AUs: 3, Prerequisites: Mathematics at A or H2 level, or equivalent. Not available to students who have taken/are taking PAP111 and PAP113, Semester 1
Fundamentals of physics covering (a) mechanics, (b) wave motion, and (c) thermodynamics, with examples of practical applications to biomedical sciences, engineering sciences and other fields. Students learn about the principles of the physical world from which scientific and engineering applications are built upon. At a general level, students learn how to read scientific material effectively, identify fundamental concepts, reason through scientific questions, and solve quantitative problems.


PAP182 Fundamentals of Physics 2

AUs: 3, Prerequisites: PAP181. Not available to students who have taken/are taking PAP112 and PAP113, Semester 2
Fundamentals of physics covering (a) electricity and magnetism, (b) optics, and (c) modern physics, with examples of practical applications to biomedical sciences, engineering sciences and other fields. Students learn about the principles of the physical world from which scientifi c and engineering applications are built upon. At a general level, students learn how to read scientific material effectively, identify fundamental concepts, reason through scientific questions, and solve quantitative problems.


PAP211 Quantum Mechanics I

AUs: 4, Prerequisites: PAP113, Semester 1
This course introduces the basic ideas of quantisation in the physical world. Planck formula - black-body radiation and thermal equilibrium; ultraviolet catastrophe; quantisation and Planck spectrum; Stefan-Boltzmann law. Bohr atom - Balmer formula; postulates of Bohr’s model in hydrogen atom; quantisation of angular momentum; quantum jumps; limitations of Bohr’s model. Schrodinger wave equation - double slit experiment and Heisenberg’s uncertainty; Schrodinger equation; stationary states; interpretation of wave function; solution for particle in 1-D infinite square well and general features of solutions; correspondence principle. Solutions to Schrodinger’s equation - qualitative solutions; finite depth potential well; quantum mechanical tunnelling; radioactive a-decay; ammonia molecule; tunnel diode; scanning tunnelling microscope; angular momentum and rotational spectra of diatomic molecules; quantum harmonic oscillator and vibration of diatomic molecules.


PAP212 Electromagnetism

AUs: 4, Prerequisites: PAP112, MAS182, Semester 2
This course introduces key concepts in electromagnetism. Electric dipole moment, polarisation and displacement, multipole expansion. Laplace’s and Poisson’s equations; uniqueness theorem; method of images, electrostatic energy. Magnetic dipole moment, magnetic field and flux, magneticscalar and vector potentials; magnetisation and magneticmedia, permeability and susceptibility; properties of B and H; boundary conditions. Equation of continuity, Maxwell equations and relativistic invariance; Electromagnetic wave equation, electromagnetic spectrum, magnetic and electric energy densities, Poynting flux, momentum flux, radiation pressure, polarisation.


PAP213 Thermal Physics

AUs: 4, Prerequisites: PAP111, Semester 1
This course introduces the laws and key concepts of thermodynamics. Thermodynamic equilibrium, functions of state, equations of state. Zeroth law. Perfect gases and absolute zero. First law of thermodynamics. Work, heat and internal energy. Adiabatic, reversible and irreversible changes. Heat engines, efficiency and Carnot cycles. Clausius’ theorem and Second law of thermodynamics. Fundamental equation of thermodynamics. Phase changes and latent heat. Enthalpy, Helmholtz free energy and Gibb’s energy. Maxwell relations. Reciprocity theorem. Third law of thermodynamics. Kinetic theory - Maxwell distribution of velocities; pressure and effusion; mean free path; thermal conductivity and viscosity. Heat transport - conduction, radiation and convection as transport mechanisms; heat flux and heat diffusion equation; steady-state and initial-value problems; sinusoidally varying surface temperatures.


PAP218 Physics Lab IIa

AUs: 2, Prerequisites: PAP118, Semester 1
This course trains students in experimental physics and covers a wide variety of topics including quantum physics, physical optics and lasers, and electronics.


PAP219 Physics Lab IIb

AUs: 2, Prerequisites: PAP119, Semester 2
This course trains students in experimental physics and covers a wide variety of topics including electromagnetism, thermal physics, and solid state and materials physics.


PAP221 Classical Mechanics

AUs: 4, Prerequisites: PAP111 and MAS183, Semester 1
This course discusses the key ideas and principles in classical mechanics. Rigid body rotation: inertia tensor, principal axes of inertia, precession. Lagrangian mechanics: calculus of variations, action integral, Hamilton’s principle of least action, generalised coordinates, momenta and forces, Hamilton’s equations, canonical transformations, Liouville’s theorem. Symmetries and conservation laws. Examples of applications: simple harmonic oscillator; planetary motion; charged particle in electromagnetic field; Lagrangian derivation of the fluid equations of motion.


PAP231 Physical Optics

AUs: 3, Prerequisites: PAP113, Semester 2
This course establishes the basic principles of physical optics which form the foundation for many modern sciences and technologies. Wave properties, refraction and dispersion, interference, Michelson interferometer, Fraunhofer and Fresnel diffraction, resolution limit, Fourier transformation, holography; polarisation, birefringence and wave plates, Fabry-Perot etalons, optical coatings, and zone plates.


PAP232 Introduction to Solids

AUs: 3, Prerequisites: PAP113, Semester 1
This course introduces the structure of solids and the quantisation of atomic and electronic motion in a periodic solid. Crystal symmetry - lattice, basis, unit cell, Miller indices, lattice planes and spacing; reciprocal lattice and Brillouin zones. Bragg and Laue diffraction, structure factor, atomic form factor; neutron and X-ray diffraction; powder and single crystal diffraction. Nomral mode dispersion for linear atomic chains; acoustic and optic modes; Born von Karman boundary conditions; density of states; lattice quantisation and phonons; Einstein and Debye models of heat capacity. Free electron theory, density of states, Fermi energy, Fermi surface.


PAP261 Introduction to Lasers

AUs: 3, Prerequisites: PAP113, Semester 2
This course serves as an introduction to lasers and their working principles. Quantum transitions in atoms, stimulated emission and amplification, rate equations, saturation, feedback, coherent optical oscillation, laser resonators, and various types of lasers.


PAP311 Quantum Mechanics II

AUs: 4, Prerequisites: PAP211, MAS281, Semester 2
This course introduces the framework and basic tenets of quantum mechanics.

• Wave mechanics - probability interpretation of interference; wave-functions, wave packets and momentum representation
• Schrodinger equation - operators; eigenfunctions and eigenvalues; solutions for free particle and barrier
• Bound states - zero-point energy; orthogonality and normalisation; expansion in basis states; expectation values; harmonic oscillator; 3D box and separation of variables
• Operator methods - Dirac notation; postulates of quantum mechanics; observables and operators; probability of measurement outcomes; orthogonality and completeness; degeneracy; discrete and continuous spectra; operator commutations and observables; generalised uncertainty relations; ladder operators; time-dependence; Ehrenfest’s theorem; time evolution operator
• Angular momentum - operators, eigenvalues and eigenstates; parity, rotational invariance and conservation; hydrogen atom; quantum numbers
• Spin and identical particles - Stern-Gerlach experiment; symmetry and multiparticle states; fermions and bosons; exchange operator; Pauli exclusion; helium atom

PAP319 Physics Lab IIIa

AUs: 4, Prerequisites: PAP218, Semester 2
This course provides advanced training in experimental physics covering a wide variety of topics: quantum physics, electrodynamics, atomic physics and spectroscopy, solid state physics, fluid mechanics, semiconductor physics, photonics, biophysics and thin film growth.


PAP321 Statistical Mechanics

AUs: 4, Prerequisites: PAP213, Semester 2
This course introduces the postulates and key ideas in statistical mechanics, with applications to classical and quantal gases.

• Basic postulates, macrostates and microstates, distinguishable and indistinguishable particles, distribution functions
• Temperature, entropy and the probability of system configuration occurring, Boltzmann relation, canonical ensemble and partition function
• Gibb’s entropy; Third law of thermodynamics; information theory; irreversible processes and arrow of time
• Density of states; heat capacity in black body radiation
• Ideal classical gas, Maxwell-Boltzmann distribution, rotational and vibrational heat
• Free electron gas, Fermi energy and distribution function, Pauli paramagnetism
• Electronic contribution to heat capacity
• Phonons as normal modes, contribution to heat capacity, Debye approximation; phonon gas, thermal conductivity of insulators
• Mean description of phase transitions - Weiss model of ferromagnetism, order-disorder transition

PAP339 Physics Laboratory IIIb

AUs: 2, Prerequisites: PAP219, Semester 2
This course provides advanced training in experimental physics and covers a wide variety of topics: quantum physics, electrodynamics, atomic physics and spectroscopy, solid state physics, fluid mechanics, semiconductor physics, photonics, biophysics and thin film growth.


PAP341 Atomic Physics

AUs: 4, Prerequisites: PAP211, Semester 2
This course discusses the origins of atomic spectra and shows the application of quantum mechanics in describing the interaction between electron and nuclei in atoms.

• Hydrogen atom - central potential approximation, radial wavefunction, quantum numbers, energy levels and degeneracy; electron spin and total angular momentum; spin-orbit coupling and fine structure; Zeeman splitting
• Helium atom - Coulomb repulsion and exchange; singlet-triplet splitting
• Electronic configuration and periodic table; alkali metals; residual electrostatic interaction; LS-coupling scheme; Hund’s rules; hyperfine structure and isotope shift
• Selection rules for electric dipole interaction
• Zeeman and Stark effects
• Inner shell transitions and x-ray spectra
• Doppler broadening in laser spectroscopy

PAP342 Solid State Physics I

AUs: 4, Prerequisites: PAP211 and PAP232, Semester 2
This course discusses the electronic and magnetic properties of solids.

• Metals - conductivity and heat capacity; density of states at Fermi level; nearly free electron model and band gaps
• Distinction between metals, semiconductors, and insulators
• Semiconductors - direct and indirect band gap (Si, Ge, GeAS); optical absorption, effective mass and holes; carrier concentration, law of mass action; impurity donors and acceptors; mobility and Hall effect; band gap measurements
• Magnetic susceptibility, Larmor diamagnetism, paramagnetism, and Curie’s law; Pauli paramagnetism; magnetic ordering (ferromagnetism and antiferromagnetism) and Weiss molecular field theory; Curie-Weiss susceptibility

PAP352 Chaotic Dynamical Systems

AUs: 4, Prerequisites: PAP221, Semester 2
This course introduces the ideas of determinism and randomness in the physical world.

• Introduction to phase plane, critical points and characterisation (hyperbolic/elliptic) - free and damped oscillators, prey-predator models
• Simple extensions to three-dimensional phase space and beyond, e.g. rotation of rigid bodis, the Lorenz system
• Integrable and non-integrable systems, Poincar¨
• return maps
• Discrete dynamics - 1D and 2D maps; fixed points and stability; period doubling - shift map, logistic map
• Breakdown of order and chaos; sensitivity to initial conditions (“butterfly effect”) and Lyapunov exponents; limit to predictability; strange attractors and fractal dimension -Kepler problem, H¨•non-Heiles system
• Stable and unstable manifolds, homoclinic and heteroclinic tangle, lobes and turnstile transport, particle motion in 2D incompressible fluid

PAP353 Fluid Mechanics

AUs: 4, Prerequisites: PAP212 and PAP221, Semester 1
This course introduces the laws governing fluid motion.

• Paschal’s theorem, Bernoulli equation, Euler’s equation, Navier-Stokes equation, vorticity and divergence
• Compressible and incompressible fluids, flow around objects, potential flow; viscosity, Reynolds number; laminar flow and turbulence; Kolmogorov scaling
• Sound waves, shock fronts, Rankine-Hugoniot relations
• Hydrostatic balance, shallow-water equations, surface waves; conservation of potential vorticity

PAP361 Semiconductor Processing

AUs: 3, Prerequisites: PAP232 or PAP233, Semester 1
This course discusses the basic principles underlying the fabrication of semiconductor devices and material processing techniques in semiconductor industry.

• Si based device fabrication - ion implantation, diffusion, oxidation, epitaxy, thin film deposition, material and device characterisation, lithography, etching and cleaning
• Processing and characterisation of photonic and nano-structured devices

PAP362 Photonics

AUs: 4, Prerequisites: PAP211, PAP231, Semester 1
This course introduces key concepts in optical, optoelectronics and optical communication technologies. Waveguides optics, fiber optics, crystal optics, interaction between photons and semiconductors, semiconductor light sources and detectors, liquid crystal optics, and flat panel displays


PAP363 Biophysics

AUs: 3, Prerequisites: PAP232, Semester 2
This course serves as an introduction to “How physics approaches living matter”. Biophysics is an extremely rich but little structured field. This makes it impossible to introduce Biophysics as an entity. We therefore aim for a limited set of areas where physical concepts and instruments have been successfully employed to biology. During the course the student will become acquainted with experimental techniques to study biological processes and physical models to describe the dynamics at the relevant biological scales of mass, time, and velocity.


PAP364 Biophysics II

AUs: 3, Prerequisites: PAP213 or PAP363, Semester 2
In this course a consistent theoretical framework is developed which describes hierarchically organized soft biological matter. The course starts with modeling the building blocks, namely polymers, their configuration, and elastic properties. Then a physical language for two-and three-dimensional networks is developed which introduces viscoelastic cell rheology. Next, we will discuss in this course bio-membranes, their self-assembly, and the mechanical properties, e.g. line tension, membrane undulations, and the important compression resistance. In the second part of the Biophysics 2, the cell as a whole is focused on. We start with energetic considerations of thin shells, the interaction between membranes, and we will develop a simple model for cell adhesion. The last part of the course deals with the very important aspects of dynamic filaments for cellular movement, in motor proteins, and for force-sensing.


PAP441 Quantum Mechanics III

AUs: 4, Prerequisites: PAP311, Semester 1 and 2
This course discusses quantum interactions between matter and electromagnetic fields.
Time-independent perturbation theory - non-degenerate and degenerate. Variational method, ground state energy and eigenfunction. Born-Oppenheimer approximation.
Hamiltonian in an electromagnetic field, vector potential, phase and Aharanov-Bohm effect. Dirac equation, spin, gyromagnetic ratio and antiparticles. Zeeman and Landau levels.
Transitions - two-state system, Rabi oscillations, Larmor precession, magnetic resonance; time-dependent perturbation theory, Fermi’s golden rule, scattering and Born approximation; radiative transition transitions; electric dipole approximation, quantised electromagnetic field.
Quantum information - quantum cryptography, entanglement and teleportation; quantum computing.


PAP442 Solid State Physics II

AUs: 4, Prerequisites: PAP342, Semester 1
This course introduces advanced concepts in solid state physics with particular attention to theoretical approaches.

• Theories and models; approaches to many-body problem; collective phenomena
• Structure and bonding - order and disordered; types of bonding and structure; electrons in periodic potential, Bloch theorem; tight-binding; 1D chain and polymer; band structure of real materials; optical transition and photoemission
• Interactions - effective medium approximation for electron-electron interaction; Hartree-Fock theory; exchange and correlation energy; electron fluid and screening; exclusion principle and quasiparticles
• Transport and scattering - crystal momentum; neutron scattering; electron-phonon scattering; optical conductivity; Drude theory, plasmons; transport in electric and magnetic fields; quantisation of orbits, cyclotron resonance; de Haas-van Alphen effect; Fermi surfaces; magnetoresistance oscillation; quantum Hall effect
• Semiconductors - thermal equilibrium of quasiparticles; field effect transistor; pn junctions, LED; exciton, heterostrutures, quantum well, semiconductor laser
• Magnetism - origin moments and interactions, ferromagnetism; itinerant magnetism, Stoner model; strongly interacting systems, Mott insulator

PAP443 Surfaces and Interfaces

AUs: 3, Prerequisites: PAP342, Semester 1
This course discusses the key concepts in surface and interface science with a special focus on electronic structure.Surface energy and thermodynamics; electronic structure; phase transition; elementary excitations; physisorption and chemisorption; energy transfer.Schottky barrier and band offsets in semiconductors; band engineering.Analytical techniques include scanning tunneling microscopy; electron diffraction methods; photoemission, ballistic electron emission microscopy


PAP444 Nanoscale Physics

AUs: 3, Prerequisites: PAP311, Semester 2
This course introduces the physical and transport properties in nanoscale systems.
Electron gas in 2D and multilayer systems.
Quantum transport in 1D; magnetotunneling; quantum capacitance and conductance.
Quantum dots and artificial atoms; eigenenergies and eigenstates; single particle conductance; Coulomb blockade; Kondo effect; Aharanov-Bohm effect.
Quantum computation – electrons and quasi-electrons as qubits; state preparation, manipulation, entanglement and measurement; Rabi oscillations and single-spin detection.
Some methods for quantum dot and nanostructure growth will be discussed.


PAP451 Statistical Mechanics II

AUs: 4, Prerequisites: PAP321, Semester 2
This course introduces the theoretical framework of statistical mechanics and applications to novel physical systems. Principle of equal equilibrium probability; Boltzmann and Gibbs entropy; configurational entropy and defects. Microcanonical, canonical and grand canonical ensembles; harmonic oscillator and paramagnetic salt; negative temperature. Fluctuations in energy, particle number and volume; critical opalescence. Classical and quantum systems - indistinguishability; equipartition theorem; grand partition function, Fermi-Dirac and Bose-Einstein statistics; quantum to classical crossover; chemical equilibrium and Langmuir isotherm. Ideal Bose gas and Bose-Einstein condensation; quantum liquids; black-body radiation; phonons and Debye model; ideal fermi gas; normal modes and elementary excitations. Classical liquids - radial distribution function, internal energy and equation of state; virial expansion.


PAP452 Atmospheric Physics

AUs: 4, Prerequisites: PAP213, PAP353
This course introduces the atmosphere as a fluid system and discusses the physics that underlie weather and climate. Basic properties of the atmosphere; temperature structure, potential temperature and entropy. Hydrostatic balance and geopotential. Pressure coordinates. Radiative balance of the Earth; radiative transfer; ozone-layer; greenhouse effect. Fluid dynamics on a rotating planet; geostrophic flow; cyclones & anticyclones; thermal-wind balance. Conservation of angular momentum, Hadley circulation. Global wind circulation. Static stability and Brunt-Vassala frequency; gravity waves; Rossby waves. Thermal convection; adiabatic lapse rate; moist adiabat; radiative-convective equilibrium. Antarctic ozone hole; global warming and climate change.


PAP453 Quantum Theory

AUs: 4, Prerequisites: MAS 281, PAP 311
This course introduces the mathematical foundation of quantum mechanics and discusses the philosophical implications.
Vector spaces and basis vectors. Scalar products and norms. Hilbert spaces, Dirac notation. Linear operators, adjoint and Hermitian operators, projection operators. Eigenvectors, eigenvalues and the spectral theorem. Functions of an operator. General formalism of quantum theory. Density matrices and mixed states. Contrast with the state space of classical physics. Compatible and incompatible quantities. Symmetries and conserved quantities. Unitary operators. Stones’s theorem; Wigner’s theorem. Canonical commutation relations. Uncertainty relations; the Schwarz lemma. Conceptual issues in quantum theory: probability, quantum entanglement, measurement. Schrodinger’s cat. Kochen-Specher theorem. Quantum logic. Bell inequalities.


PAP454 Nuclear Physics

AUs: 3, Prerequisites: PAP311, Semester 1
This course provides a basic understanding of the structure of nuclei and their properties. Properties of nuclei: radii, masses, abundances, binding energies, spins and EM moments. Nuclear structure: deuteron, nucleon-nucleon scattering in terms of an exchange force. Nuclear models: the semi-empirical mass formula, the Fermi gas model, the shell model, liquid drop model with vibrational and rotational excitations, collective structure. Energy balances and spin/parity selection rules of alpha, beta and gamma decay processes. Measurement of nuclear lifetimes, applications of nuclear physics including fusion and fission processes Nucleosynthesis.


PAP455 Computational Physics

AUs: 3, Prerequisites: PAP311 and PAP342, Semester 1
This course introduces computational methods and tools to solving physical problems. Introduction to computational methods and tools. Programming Concepts. Errors and Uncertainties in Computations; Numerical solutions of differential equations in one variable. Approximation of functions. Variational Principle and Minimisation; spectral analysis, Monte Carlo simulations, Symbolic computing; High-performance computing. Applications to physical problems, molecular dynamics. Electronic structure of atoms, Hartree-Fock approximation and Density Functional Theory. Maxwell’s Equations in Matter and ionised gases. Physics with MAPLE/MATLAB.


PAP456 Electrodynamics

AUs: 4, Prerequisites: PAP212, Semester 2
This course introduces electrodynamics at a more advanced level.

• Electromagnetism in the framework of special relativity.
• Electromagnetic radiation from a moving point charge as well as a system of moving charges.
• Electromagnetic scattering.

PAP461 Semiconductor and Device Physics

AUs: 4, Prerequisites: {PAP211, PAP232} or PAP342
This course aims to introduce solid state devices that signify modern technologies and Hi-Tech industries. Electronic band structures of semiconductors, electronic properties of defects, 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, light emitting diodes, bipolar junction transistors, junction field effect transistors (JFET), metal-semiconductor contacts metal-insulator-semiconductor interfaces, basic MOSFET.


PAP462 Quantum Electronics

AUs: 4, Prerequisites: PAP311 and PAP362, Semester 2
This course aims to provide students with a solid foundation of photonics and optical technology. Gaussian beam optics, resonator optics, lasers, photon optics, statistical optics, semiclassical and quantum models on interaction between photons and atoms, electro-optics, nonlinear optics, and acousto-optics, generation of short and ultrafast laser pulses.


PAP463 Soft Condensed Matter Physics

AUs: 4, Prerequisites: PAP311, PAP342
This course provides an introduction to soft-condensed matter physics. Atomic and molecular forces. Hard-core repulsion. Polymers. Elasticity of DNA. Correlations in the fluctuations of solvent molecules; diffusion in fluids , electrostatics in solution. Poisson-Boltzmann theory. Electrophoresis; liquid interfaces and droplets. Lipid bilayers and vesicles.; membrane fluctuations, cell mechanics; Colloids. Liquid crystal phases. Random aggregation and fractals; hydrodynamics of an isotropic fluid: the Navier-Stokes equation. The Reynolds number; laminar flow. Viscoelasticity; Experimental methods - dynamic light scattering, s elf-assembling processes, f luorescence correlation spectroscopy, measuring interactions with laser tweezers and tracking experiments.


PAP491 Final Year Project

AUs: 10, Prerequisites: 12 AUs of PAP3XX courses, Semester 1 and 2
The student will undertake a project over two semesters, supervised by a faculty member. He/she will be required to produce a thesis report and prepare for seminar presentations. Assessment will be through a thesis report, viva and seminar presentation.


PAP493 Industrial Internship I

AUs: 4, Prerequisites: PAP111, PAP112, PAP113, PAP118, PAP119, PAP211, PAP212, PAP213, PAP218, PAP219 or by permission, Special Term II and II
10 weeks of industrial placement in an approved company or institution.


PAP493 Industrial Internship II

AUs: 10, Prerequisites: PAP111, PAP112, PAP113, PAP118, PAP119, PAP211, PAP212, PAP213, PAP218, PAP219, PAP311 or by permission, Semester 1 and 2
One semester of industrial placement in an approved company or institution.


PAP801 Environmental Physics

AUs: 3, Prerequisites: Physics at GCE ‘O’ level or H1 level
This course provides a broad appreciation of the physical factors that govern the environment. Physics of the atmosphere, wind and oceans; thermodynamics of the weather and solar energy; greenhouse effect and global warming.  Modeling of pollution diffusion and dispersion.  Remote sensing and detection methods. hydrology, planetary science, and field programmes.


PAP802 Physics of Sports

AUs: 3, Prerequisites: Physics at GCE ‘O’ level or H1 level, Semester 2
This course introduces the physical principles that govern human locomotion and sporting incidents.

• Human locomotion - running, jumping, swimming. Biomechanics of skating ¨C jumping (projectile motion) and rotating (angular momentum), rink conditions and boot
• Soccer - kicking, fl ight (air flow and resistance, Magnus effect)
• Baseball - throwing (spin, curve and air flow), hitting (sweet spots)
• Miscellaneous - golf and golf balls, sky diving

PAP921 Electronics for the Experimentalist

AUs: 3, Prerequisites: PAP112
This course introduces basic concepts and applications of electronic elements and circuits. Elements in analog and digital electronics will be discussed. Tools for circuit design and board layout will be introduced. Additionally an overview of typical circuits for scientific instrumentation for data acquisition and signal processing will be given. The lab sessions are an integral part in this course and focus on hands-on experiments with the goal to realize prototypes of given circuits. During their project work students have to design and realize an electronic device capable of managing a given task. By doing this project work, students will gain experience in actual electronics construction and can apply this experience to their scientific environment.


PAP929 Undergraduate Research Project I

AUs: 3, Prerequisites: Division approval, Special Terms I and II
This course introduces research work in physics that is suitable for second-year undergraduate students. The content will be determined by project supervisors.


PAP931 Thin Film Technology

AUs: 3, Prerequisites: PAP232
This course focuses on the principles of thin-film deposition techniques as well as the underlying physical principles governing the thin film growth. This programme will be supplemented with examples and applications that reflect the frontiers of modern science and technology, e.g. fabrication of semiconductor films/devices, growth of nano-structure films and materials. Growth techniques - chemical vapour deposition, physical vapour deposition, pulsed laser deposition, and electron beam epitaxy. Basic principles that determine film growth mode and quality - gas kinetics, adsorption, surface diffusion and nucleation. Thin film characterization techniques - x-ray diffraction, SEM, TEM, AFM, etc.


PAP939 Undergraduate Research Project II

AUs: 3, Prerequisites: Division approval, Special Terms I and II
This course introduces research work in physics that is suitable for third year undergraduate students. The content will be determined by project supervisors.


PHYS1A Mechanics

AUs: 4, Prerequisites: Physics at A or H2 level or by approval, Semester 1
This course introduces fundamental concepts of Newtonian mechanics. Linear motion; vectors; trajectories; Newton’s laws; forces; non-inertial frames; work and energy; energy conservation; momentum. Rotational motion: rigid rotations; angular momentum; gyroscopes. Harmonic motion. Resonance. Fluid mechanics. Gravity; Kepler’s laws and orbits; law of ellipses.


PHYS1B Electromagnetism

AUs: 4, Prerequisites: Physics at A or H2 level or by approval, Semester 2
This course introduces the concepts of electricity and magnetism and couples electromagnetic theory with relativity. Principles of relativity; time dilation and length contraction; spacetime diagrams; Lorentz transformations; energy-momentum; force and mass; mass and energy. Electric fields; Gauss’ law; electric potential; divergence and curl. Conductors; electric currents; conduction; dc circuits. Fields of moving charges; force on moving charges; general relativity. Magnetic field; vector potential; magnetostatics; fields in motion; Hall effect. Faraday’s law; induction; ac circuits; complex impedance; applications of Faraday’s law. Maxwell’s equations; electromagnetic waves. Electric dipoles; dielectrics; electric fields in matter. Magnetic dipoles; magnetic materials; ferromagnetism; accelerating charges; superconductivity


PHYS1C Waves and Quantum Mechanics

AUs: 4, Prerequisites: Physics at A or H2 level or by approval, Semester 2
This course introduces the basic ideas of waves and quantisation in the physical world and provides the framework and basic tenets of quantum mechanics. Harmonic and coupled oscillators; normal modes. Wave equation; Fourier analysis; travelling waves; dispersion; impedance; reflection and transmission; diffraction and interference. De Broglie waves; Schrodinger equation; position and momentum; energy and time. Simple 1-D potentials; harmonic oscillator. Observables and operators; angular momentum. Hydrogen atom. Identical particles. Atoms.


PHYS1P Physics Laboratory 1

AUs: 3, Prerequisites: Physics at A or H2 level or by approval, Semester 1
Students will undertake basic experimental physics. The laboratory sessions are designed to provide an active learning experience where key concepts can be better appreciated. Students will also learn about data acquisition, error analysis, error distribution and fitting procedures. Experiments include topics in mechanics, basic optics, thermal physics, electricity and magnetism, circuits, optics, wave and quantum phenomena.