Honours Sessions


01.015 SHARP Honours Session Term 1

Computational Statistics

Week 2 to 4
Instructor: Dr Keegan Kang
 
Description:
The three-week SHARP course will be on computational statistics, and will comprise a theoretical and computational component. The theoretical component consists of a brief review of A-Level statistics, before moving onto variance reduction techniques and an introduction to Monte Carlo methods. The practical component involves using Matlab, understanding (some) limitations of scripting languages, plotting basic graphs to compare certain quantities of interest, and (how to) critique them as well - amidst the backdrop of the theoretical portion. Lecture notes and code will be provided.
Students are to download and install Matlab before the first class - instructions will be provided in the lecture notes.
 
Assessment:
Assessment will be based on homework (done in pairs) and exam.

Brief outline of topics covered: (subject to slight changes)
Class 1: (half theory, half Matlab)

  • Introduction
  • Review of A-Level statistics
  • Difference between theoretical / empirical expectation and variance and why it is important
  • Examples of some of these differences used in practical situations

Class 2: (mostly Matlab)

  • Limitations of Matlab (and other programming languages) ; numerical plots, experiments
  • Vectorization, more examples of plotting / visualizing data

Class 3: (mostly theory with the use of Matlab to verify)

  • Maximum likelihood estimation
  • Monte Carlo integration
  • Variance reduction techniques
  • Brief spiel on research
Nonlinear Systems and Chaos

Week 4 to 5
Instructor: Prof Ricky Ang
 
Description:
Students will learn about important concepts of nonlinear dynamics and Chaos focused on its applications to science and engineering.

  • Week 4: Linear stability analysis, Different types of Bifurcations
  • Week 5: Extension from 1 dimensional (1D) to 2D systems
  • Week 6: Lorentz equation, Chaos, Strange attractors
Group Project

Week 6 to 12
Group Project


01.016 SHARP Honours Session Term 2

Organic Chemistry

Week 1 to 3
Instructor: Dr Tan Mei Xuan

Description:
Students will learn about stereochemistry and isomerism of organic molecules, structure determination methods such as Nuclear Magnetic Spectroscopy (NMR), and strategies for total synthesis.

Primer on Lasers, Fiberoptics and applications

Week 4 to 6
Instructor: Dr Massimiliano Colla

Description:

  • Why the interest in lasers
  • Unique properties of lasers
  • How such properties originate
  • Operation of a simple laser
  • Other issues and problems
  • Types of lasers
  • Basics of Fiberoptics
  • Future developments
Experimental Project

Week 8 to 13

Experimental Project: Topics offered will be centred around at least one of the following disciplines: Biology, Chemistry and Physics


01.017 SHARP Honours Session Term 3

Statistical Physics

Week 1 to 3
Instructor: Associate Prof Dario Poletti
 
Description:
Students will embark on a journey from microscopic to macroscopic which will allow them to gain a deeper insight into thermodynamics. The students will also learn that the tools and approaches used can give insights outside of the realm of physics as, for example, in information theory and in finance.

Mathematical Modelling of Physical and Complex Systems

Week 4 to 5
Instructor: Assistant Prof Ang Yee Sin
 
Description:
In this module, we will introduce the mathematical models and the numerical methods for simulating physical and complex systems. Based on the semiclassical carrier statistics introduced in previous module, models of electron transport, conduction and emission process in solid and solid/vacuum interface will be introduced. The mathematical description of complex biological systems (e.g. population growth, cancer cell dynamics and epidemic spread) based on differential equations and compartmental models will also be covered. The students are expected to be able to construct simplistic mathematical models to describe simple dynamical systems upon the completion of this module. 

Group Project

Week 6 to 12 
Group Project

Special Programmes & Scholarships