SP1201 - Seminar Topics in AY2009/10
Please take note of the corresponding lecture group in order to bid for the correct seminar in CORS.

In Semester 1


In Semester 2

Lecture Group Seminar Title Facilitated By Day & Time Venue
SP1201B_SL1 Understanding the Fundamentals of Biotechnology Prof Hew Choy Leong, Biological Sciences Thu, 1600-1800 S9A-01-03
SP1201B_SL2 Why are studies on plant biology important? Prof Prakash Kumar, Biological Sciences Thu, 1600-1800 S9A-02-01
SP1201B_SL3 DNA- 2 Strands, 3 Men, 1 Dark Lady Prof Ding Jeak Ling, Biological Sciences Fri, 1600-1800 S9A-01-03
SP1201C_SL1 The Five S's of Molecules Prof Andy Hor, Chemistry Mon, 1600-1800 S9A-02-01
SP1201C_SL2 From Magic to a Modern Science - The Changing History of Chemistry Dr Zhao Jin, Chemistry Tue, 1600-1800 S9A-02-01
SP1201C_SL3 Idols of the Mind Dr Adrian Michael Lee, Chemistry Wed, 1600-1800 S9A-01-03
SP1201C_SL4 Learning to Fish (Molecular Science) from the Open Sea (Research Literature) Prof Andy Hor, Chemistry Wed, 1600-1800 S9A-02-01
SP1201M_SL1 Analogy and Intuition in Mathematics A/P Leong Yu Kiang, Mathematics Mon, 1600-1800 S9A-01-03
SP1201M_SL2 Appreciation of Basic Results in Mathematics Prof Koh Khee Meng, Mathematics Tue, 1600-1800 S16-04-40
SP1201M_SL3 Mathematics in Science, Technology and Society Prof Lee Seng Luan, Mathematics Wed, 1600-1800 S16-04-37
SP1201P_SL1 The Beauty of Symmetry Dr Wang Qinghai, Physics Mon, 1600-1800 S16-04-37
SP1201P_SL2 Thinking Like a Scientist Physics Wed, 1600-1800 S16-04-40
SP1201P_SL3 Are We Alone? Dr Rajesh Parwani, Physics Thu, 1600-1800 ADM SR5, USP
SP1201P_SL4 Conceptual Development of Physics Prof Oh Choo Hiap, Physics Fri, 1600-1800 S9A-02-01
SP1201S_SL1 Statistical Game Theory Dr Alex Cook, Statistics & Applied Probability Mon, 1600-1800 S16-04-40
SP1201S_SL2 Randomness in Scientific Thinking Dr Alex Cook, Statistics & Applied Probability Fri, 1600-1800 S16-04-40

The Global Impact of Biological Computing
This course is intended for freshman students who have entered the Computational Biology major degree programme. The course begins with an overview of the information requirements for the study of biodiversity, and presents a number of recent scientific articles in support of the information. A deep focus will be on the Barcode of Life project, and students will become familiar with the technology and aims of this biodiversity catalogue. Students will become familiar with the nucleic acid and protein molecules used in the Barcode of Life, and how PCR sequencing is used to read out the barcode information. Next students will learn about the challenges that plant species and bacteria present to the Barcode methodology, and some ways that these are being addressed to improve the barcode. Other technology including mass spectrometry approaches will be presented that aim to solve the problem of identifying bacteria. The course will conclude by having students consider and propose to construct a computational system that can meet the challenges these projects face as the scale of information integration grows. Students will discuss and debate the problems of making software faster when computers have reached the limits of Moore's law, and consider how biological computing must rise to the challenge.


This seminar is given by Prof Christopher W. V. Hogue who is an Associate Professor at the Department of Biological Sciences at the National University of Singapore. Chris received his Honours B.Sc. in Biochemistry from the University of Wiindsor and his Ph.D. in Biochemistry from the University of Ottawa. A self-taught software developer and architect, he did his Postdoctoral training in Bioinformatics and Computational Biology at NCBI as a Genbank Fellow. Highly cited with over 50 peer reviewed papers, he has an ongoing academic interest in wet-lab research involving the validation of protein-protein and protein-small molecule interactions. Formerly at the University of Toronto, Dr. Hogue was the Principal Investigator on Genome Canada's largest Bioinformatics research grant to date - the BIND Project. BIND is recognized as the first and most complete molecular interaction database of its kind. The intellectual property behind his research - including BIND and over a million lines of source code - was acquired by Thomson Scientific in 2007.

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Biological Machines
The world of biology is a world of machines. Nano-, micro-, and macro- machines of all sizes and types power the function of cells, tissues, and organs. This seminar is intended for students who are interested in machines-how they work and what they do. Examples will range from molecular machines, the true nano-machines, to the machinery of tissues and organs and comparisons with machines in the everyday physical world. The goal is to identify the scientific principles and key concepts that describe biological machines, the engineering design that generates force or power from a fuel or energy source, and the ways in which the machine is used in biology or elsewhere. The case-study format will provide opportunities for student and group-led discussions in addition to conventional lectures/seminars. Students must be committed to serious preparation before class and participation during class. The end-of-term paper will describe a novel biological machine. The grade will be based on preparation (20%), participation (40%), and project (40%).


Professor Matsudaira is a molecular cell biophysicist who is the Head of Biological Sciences, Director of the NUS Centre for BioImaging Sciences, and co-Director of the Research Centre of Excellence in Mechanobiology. From 1985-2008, he was at the Whitehead Institute and Massachusetts Institute of Technology where he was Professor of Biology and Bioengineering. His lab studies the biophysics of cell migration. He is devoted to teaching undergraduates and is an author of the textbook, Molecular Cell Biology. While at MIT he introduced and taught Fundamentals of Biology, Experimental Biology, and the largest freshman seminar, Introduction to Biological Engineering.

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From Toxins to Therapeutics
A number of animals use venoms to capture their prey. These venoms are a mixture of toxins which attack critical life-supporting systems including nerve transmission and blood circulation. Studies of individual toxins help us not only to understand how they assist in prey capture, but also to use them in developing new drug leads for the treatment of some of the leading causes of human death. In this module students will explore the beneficial side of animal toxins. They will find out information about how some of the life-saving drugs were designed and developed based on toxin structure through case studies in groups. They will also participate in discussions on toxin-based drugs for some of devastating diseases such as heart attack, stroke and cancer. Students will have opportunities to make individual and team oral presentations and written reports. This freshman seminar is suitable for both life science and non-life science majors


Professor Manjunatha Kini obtained his PhD in Biochemistry from the University of Mysore, India. After postdoctoral training in Kyushu University (Japan) and Virginia Commonwealth University (US), he joined NUS in 1994. He is a protein chemist by training and has been interested in structure-function relationships and mechanism of action of snake venom toxins. He is one of the most cited authors in the field of toxins. He has developed a number of therapeutic agents based on the structure of toxins. He teaches protein chemistry, protein design and engineering.

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The Biodiversity Crisis in Tropical Asia
The dire state of biodiversity in tropical Asia is the stuff of newspaper headlines, television programmes, political statements, and campaigns by green groups. This seminar looks at the Science behind these headlines and asks the questions: How big is the problem? What went wrong? and, What can we do about it? The answers to these questions - in as far as they are known - span 50,000 years of human history and implicate everyone from prehistoric hunters to developed - world consumers. They involve biological processes from the molecular to planetary scale, as well as physics, chemistry, sociology and economics. Invasive aliens have a role, as do oil palm, air pollution and climate change. Relevant examples can be found on the NUS campus and in the last strongholds of the Bornean orangutan. The seminar also aims to encourage the acquisition of general learning and research skills, including searching for information, writing short, informative summaries, giving brief oral presentations, and making use of the new Internet media.


Professor Richard Corlett obtained his BA in Natural Sciences from the University of Cambridge before doing his PhD at the Australian National University, with fieldwork in Papua New Guinea. He has since lived and worked in tropical Asia, teaching ecology at the University of Chiang Mai, at NUS, at the University of Hong Kong, and now again at NUS. Much of his research has focused on plant-animal interactions, but he has also worked on tropical biogeography, and the impacts of deforestation, invasive species and climate change. His new book on the Ecology of Tropical East Asia will be published this year. .

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Electrochemical Phenomena: From Clean Energy to Pollutant Sensors
Electrochemistry first began in 16th century with the discovery of electricity and later, through applications of electricity in chemical and biological systems. For example, the connection between muscular motions and electricity by Luigi Galvani in the late 1700s; the breakdown of water into hydrogen and oxygen by Nicholson and Ritter in the 1800s, and the development of the theory on electromotive force of voltaic cell by Walther Hermann Nernst in late 1800s. Electrochemical phenomenon has also been discovered to occur commonly in nature. For example, the conversion of light energy to chemical energy through the process of photosynthesis in plants; the movement of ions into/out of cells which give rise to electrical impulses in nerve cells and the generation of high voltage for self-defense in certain animals, such as certain eels, catfish and rays. In present days, electrochemistry has been used to protect objects using electrodeposition of inert metal oxides, sensing of ultratrace amounts of pollutants in waters using electrochemical sensors and production of useful chemicals such as chlorine, aluminum and titanium. The objectives of this module are to introduce students to electrochemical phenomena in daily life and to appreciate electrochemistry within the context of present day science and technology.


Dr Toh obtained his Bachelor of Science (Hons) and carried out the Masters of Science research studies at the National University of Singapore. He subsequently further his graduate studies at the University of Southampton, U.K., working with Phil Bartlett on electrochemical biosensors. Thereafter, he continued his postdoctoral work at the California Institute of Technology with Nathan Lewis on electrochemical nanostructured materials. His general interest is electrochemistry and his current research interests are in the developments of new sensing and separation techniques using nanostructured membrane electrodes, electrode-membrane-electrode system and electroanalytical methods.

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From Magic to a Modern Science - The Changing History of Chemistry
Chemistry has the most fascinating history of all the natural sciences. It has both mystical and practical sources. This seminar aspires to provide the students with a tour through the 7000-year history of chemistry using selected highlights. The students will be divided into several groups for this seminar series. They will explore what alchemy was and how alchemists worked and how they attempted to understand the transformations of matter. They will experience how alchemy evolved from obscure origins into a modern science. Moreover the students will be encouraged to understand early experimental chemistry and learn how it has been in industry and farming throughout the ages and the role of chemistry in our society. The students will gain insight into the origin and structure of matter and how modern views of chemical bonding have been established. Finally, the new development of chemistry in 20th century will be introduced. The student will understand the chance of chemistry, its challenges to our society and environment.


Dr. Zhao Jin obtained the Bachelor degree in the department of chemistry in Liaoning University in 1992 and the Master degree in Changchun physical institute of Chinese Academy of Science in 1995. After 5-year teaching and research work, she has been granted by DAAD (German Academic Exchange Service) for the PhD work in the department of chemistry of Technische Universitaet Muenchen in Germany from 2001 to 2005. After one-year postdoctoral work, she joined NUS. Currently she is a lecturer in the department of chemistry. Her research interest is organometallic chemistry and catalysis and she has published about 30 international papers.

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Mathematics and Computer Science
The history of Computing is quite linked to mathematics. Mathematicians like Blaise Pascal and Charles Babbage constructed calculators on a mechanical basis, George Boole's work on algebras became laid the foundations of the binary logic used in computers and Alan Turing contributed to the field in many ways. Alan Turing developed together with people like Kurt Goedel and Alonzo Church the theoretical foundations of computer science; but he contributed also to the more applied part by playing a key role in supporting his country's work on cryptography. The topics of this seminar will be the mathematical foundations of computer science, for example number systems (like binary, octal, decimal and hexadecimal), Boolean algebra, formal models of computing and the famous P-NP question. For students with less mathematical background will historical topics be available as well, for example the following: Charles Babbage and his Analytical Engine; the American census of 1890, tabulating machines and the founders of the company IBM; calculating tools before the age of electronics. In the case that a student wants to propose an own topic, this is possible as well.


A/P Frank Stephan has studied computer science in Karlsruhe and received a Diploma in Computer Science in 1989. He continued his studies in mathematics and received a Doctorate of Natural Sciences in 1990. In 1999 he received from the Faculty of Mathematics of the University of Heidelberg the habilitation degree. Frank Stephan has worked in the fields of recursion theory and inductive inference since 1990 and has published about 70 research articles in journals so far. He has been working at the universities of Karlsruhe, Heidelberg, New South Wales (Sydney) before he came to Singapore to join the National University of Singapore.

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Analogy and Intuition in Mathematics
The development of mathematical concepts and theories is often influenced by an intuition acquired from physical experience and by analogy with various areas of scientific and mathematical knowledge. Analogy is a powerful force in preparing, if not predicting, new concepts while an experience-based intuition can sometimes be an obstacle. The objective of this seminar module is to present case studies of the creative role of analogy in mathematics and of the ground-breaking importance of "counter-intuition" in modern mathematics. A wealth of examples of both can be ground in geometry, number theory, analysis, algebra, logic, set theory and theoretical computer science. Students of this module are expected to source for relevant material in books, journals and even the internet under the guidance of the lecturer. The emphasis, however, will be on the spirit of the mathematical enterprise rather than on the technical mastery. To illustrate the use of analogy and intuition in problem solving, some elementary problems will be posed in class for attempt and discussion. In view of the intellectual maturity and some minimal technical (mathematical) knowledge that will be needed to understand, analyze and present the material, students of this module should have completed at least ONE mathematics modules.


A/P Leong Yu Kiang is an Associate Professorial Fellow at the Department of Mathematics. He obtained his B Sc (Hons) in 1969 from the University of Singapore and his Ph D (in group theory) in 1972 from the Australian National University. He has been teaching at the University of Singapore and National University of Singapore since 1972. He was Chairman of the Department’s Curriculum Committee from 1995 to 2003 and an Academic Advisor to the Open University Degree Programmes (conducted by the Singapore Institute of Management) from 1993 to 2005. He has held offices of the Singapore Mathematical Society from 1974 to 1998 as Committee Member, Editor, Honorary Secretary and Vice-President. He was editor of the Institute for Mathematical Sciences newsletter “Imprints” from 2003 to 2005.

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Is Computer Science Science?
This seminar seeks to help the freshmen to gain a fundamental understanding of Computer Science and a broader perspective of how it relates to other sciences. The major topics include the similarity and differences between Computer Science and the traditional sciences (Physics, Biology, Mathematics, etc.), the objective and methodology in Science, and the scientific aspects of computation (hardware, software, systems, etc.).


Prof Y.C. Tay received his B.Sc. degree from the University of Singapore and Ph.D. degree from Harvard University. He is a professor in the Departments of Mathematics and Computer Science. He has spent sabbaticals at Princeton University, Massachusetts Institute of Technology, Cambridge University, Microsoft Corporation and Intel Research. He has multiple teaching awards. His main research interest is performance modeling of computer systems.

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The Physics of Time
Everyone knows what time is, yet when pressed to explain what it really is, few would be able to give a satisfactory scientific answer. The purpose of this Freshman Seminar is to introduce freshmen to the modern ideas and physical theories regarding time, and to enable them to distinguish scientific fact from science fiction. Amongst the questions that would be dicussed are: What is time? How do we measure time? What is the theory of relativity? What are the arrows of time? Is time travel possible? What are the possible paradoxes involving time travel?

 


A/P Edward Teo received his Ph.D. from the University of Cambridge in 1994. He joined NUS in 1997, and is presently an Associate Professor in the Department of Physics, carrying out research into black holes.

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Matter and Interaction
What is matter? Since the times of Aristotle and Democritus, scientists and natural philosophers have wondered what makes up the stars, the world, and its inhabitants. Subsequent realization by Dalton, Bohr, and others that the universe is made of atoms served only to complicate the issue. What are atoms? Is there anything inside of them? How do they interact with each other? The answers to these questions are not simple but there are many things that we do understand. In this course, we will review the history of the study of matter, discuss the constituents of matter, and examine how atoms, molecules, and the smallest elementary particles interact with each other up close and at vast distances.


Dr Goldman is currently a lecturer at the Physics Department.

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Statistics as an Integral Part of Science and Society
The goal of this seminar will be to introduce students to the role that statistics plays in scientific research as well as in understanding society. The focus will be on introducing students to real-world problems - from various fields of science as well as society in general - for which statistics reasoning is an important component and to show how statistical thinking can help in finding solutions. Instruction will be provided on several commonly used statistical methods but the focus will be on linking the statistics with the underlying scientitic or societal problem. Emphasis will be placed on self-evaluation of statistical reasoning, interpretation of results, and the development of statistical judgement.

 


Dr Lim joined NUS in 1998 after completing his PhD in Statistics at Stanford University. He is currently Deputy Head (Academic) of the Department of Statistics and Applied Probability. His research areas are in mathematical finance and financial statistics; he is particularly interested in optimal stopping and stochastic control problems in finance.

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DNA Strands - 2 Strands, 3 Men, 1 Dark Lady
The discovery of the DNA structure - the molecule that encodes our genetic inheritance was such a major scientific breakthrough that the statement, "This structure has novel features which are of considerable biological interest" of Watson & Crick in the Nature April 1953 publication, may be one of science's most famous understatements. This module takes a glimpse into the archives of ~100 years of dedicated works of chemists, biochemists, physicists, microbiologists and X-ray crystallographers leading to the illumination of the DNA structure. The seminars will illustrate how this discovery has impacted our world, from the home, to agriculture, to biomedical industry and beyond. After more than 50 years of the Nobel Prize award to the 3 men in 1962, many voices have argued about the controversy behind the Nobel nomination. We will consider the crucial moments, timings, meetings of minds, territorial strife, competitions, collaborations /betrayal, and missed recognition. Topics may include: (1) hands-on DNA model building (structure reveals function); (2) 100 years of research - people behind the structure; (3) advances of techniques along the road to discovery; (4) importance of literature survey; 'connecting the dots'; keen observation; the language of science. Students will learn how to survive the transition from being taught to self-learning.

 


Prof Ding Jeak Ling obtained her PhD in Biochemistry/Molecular Biology from the Royal Postgraduate Medical School, University of London. Her research is on host-pathogen interaction and innate immunity (first line of defense), particularly on how pathogen-recognition receptors interact with each other during the acute phase infection, to alarm and send signals into the host cells of the imminent infection-inflammation (ref: http://www.dbs.nus.edu.sg/staff/djl.htm) . She teaches biochemistry, molecular biology and biotechnology.

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Understanding the Fundamentals of Biotechnology
The emergence and success of the biotechnology industry depends on major scientific breakthroughs in biology. The module will focus on four of the most important discoveries in biology, and to examine the sciences behind these discoveries, and their contribution and impact to the industry. Specifically, we will study (1) the discovery of DNA double helix as the foundation of modern biology (2) the discovery of restriction enzymes for the advent of recombinant DNA technology (3), the complete sequencing of human genome as the basis for molecular medicine and (4) the development of cloning and embryonic stem cells for modern regenerative medicine.

 


Prof. Hew received his PhD at the University of British Columbia and postdoctoral trainings at Yale and University of Toronto. He was earlier a professor at University of Toronto and the Research Institute, Hospital for Sick Children, Toronto. From 1999- 2008, he was the Head, Department of Biological Sciences, at NUS. Prof. Hew is a biochemist interested in the structure and function of proteins, gene regulation and control mechanisms, marine biology and biotechnology applications. His research laboratory has studied the biology of fish antifreeze proteins, their adaptation mechanisms as well as applications in agriculture and the cryo-related industries; the development of transgenic fish; and the structural and functional genomics of viral pathogens important in the aquaculture industry.

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Why are studies on plant biology important?
Why should we study plants? The combined annual global production of food grains including, rice, wheat, corn, barley and soybean, reaches astronomical quantities. Production of milled rice alone was about 417 million tons in 2006/07, which would be equivalent to over $400 billion at an average price of $1000 per ton. Besides being the primary source of food and oxygen for all animals, including human beings, plants share numerous basic biological processes with animals. Many of the molecular genetic processes underlying cell division and development in animals can be traced to parallel processes occurring in plants, which had evolved much earlier than animals. This module will explore the similarities and differences in some of the major biological processes such as signal transduction and cell division in plant and animal systems. Students will explore these basic developmental events and how such information can be used for improving productivity of agricultural crops. Discussions will also cover the use of plants (including genetically modified crops) as sources of food, fuel and other commercial products.

 


Professor Prakash Kumar is a plant developmental biologist who earned his PhD degree from the Department of Biological Sciences, University of Calgary, Canada. He joined NUS in 1989 and during the last 20 years he has been working on plant developmental biology research with focus on tissue culture, molecular biology and biotechnology. A recent discovery from his lab is currently being explored as a method to enhance yield of crops such as rice. He is well recognized by his peers internationally and he has been appointed as an Editor of several international scientific journals in his research expertise.

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Idols of the Mind
Is there a universal set of rules for discovering and testing scientific hypotheses? Since the birth of modern science, many thinkers have wrestled with this fundamental question of scientific practice. Can we approach a natural phenomenon with a tabula rasa as envisioned in the philosophy of Bacon or do the idols of the mind predetermine the hypotheses that we might test? Indeed what role does chance play in scientific discovery? For that matter, what is science and what are its limits? This seminar will investigate many questions which are philosophical in nature within the context of many of the great ideas that permeate our current worldview from evolution and DNA to relativity and quantum theory. Reading this seminar, the student will gain insights not only into the way scientists think and work, but also an understanding of how many of the great ideas of science came into being. Students will develop an appreciation of the status of scientific theories and their relationship to observational data, the extent to which scientific theories rest on improvable paradigms, and the nature of scientific explanations.
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Learning to Fish (Molecular Science) from the Open Sea (Research Literature)
We live in a molecular era when molecular science and technology is the focus of many contemporary research areas such as environment, energy, chemical biology, electronics and chemical processes. Yet, how many of us fully understand what "molecular science" entails? What does it mean? What does it include? Where are the boundaries? How are they applied? So what, if we knew little about it? In this series of seminars, we shall analyse the nature and impact of this field. We approach this not from the basic textbooks, but from the other end of the reference -"Hot-from-the-oven" open scientific literature. We shall focus on the trunk that shapes the molecular science, i.e. molecules. The class will identify representative systems from the research literature, start from the top, and trace back to its root. We call this "molecular journey". In this journey, we examine the concepts that have evolved over the years as well as the inventors of the "classic molecules", and the legacy that they left behind.

 


Andy Hor is Professor of Chemistry in NUS. He has published over 230 international papers in molecular assembly, heterometallic syntheses and catalysis. He won the University Educator Award in 2001, Faculty Outstanding Scientist Award in 2007, and an accolade of teaching excellence awards. He is a synthetic chemist whose team single-mindedly makes molecules, examines their structures and explores their functions. His research doctrine is simple -if it is not exciting, it is not worth doing. His teaching principle is guided by the five C's -Creativity, Commitment, Communication, Common sense, and, Chemistry! He was an Imperial College (B.Sc.(Hon) and Oxford (D.Phil.) graduate, who had carried out his postdoctoral research in Yale before he joined NUS.

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The Five S's of Molecules
We live in a molecular world, when many current science subjects seem to gravitate towards molecules. Examples are plentiful, such as "Molecular Biology", "Molecular Genetics", "Molecular Electronics", "Molecular Medicine", "Molecular Informatics", "Molecular Engineering", "Molecular Pharmacology", "Molecular Ecology", "Molecular Machines"... etc. In the "Science of Molecules" viz. "Chemistry", the focus is on molecular design, molecular structure, molecular synthesis, molecular activity and molecular function. The function depends on the activity, which in turn is governed by the design and structure. Chemical synthesis is generally guided by good structural design. Molecular structures therefore are the fundamentals in molecular science. In this seminar series, we shall discuss with the class the underlying principles of chemical structures, with specific focus on the interrelationship among the five S's of molecules -Science, Structure, Stability, Symmetry, and, Space. The mode of teaching and learning focuses on group learning, interaction, independent enquiry, project work, molecular models, and public presentations. Writing and presentations are essential elements in this freshmen seminar.

 


Andy Hor is Professor of Chemistry in NUS. He has published over 230 international papers in molecular assembly, heterometallic syntheses and catalysis. He won the University Educator Award in 2001, Faculty Outstanding Scientist Award in 2007, and an accolade of teaching excellence awards. He is a synthetic chemist whose team single-mindedly makes molecules, examines their structures and explores their functions. His research doctrine is simple -if it is not exciting, it is not worth doing. His teaching principle is guided by the five C's -Creativity, Commitment, Communication, Common sense, and, Chemistry! He was an Imperial College (B.Sc.(Hon) and Oxford (D.Phil.) graduate, who had carried out his postdoctoral research in Yale before he joined NUS.

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Appreciation of Basic Results in Mathematics
Mathematical results are crystallizations of the collective wisdom of mankind and have their historical backgrounds, significances, impacts and applications. This seminar module provides a platform for freshmen to discuss these aspects of some selected mathematical results and principles. Amongst the topics that would be discussed are:

- Prime numbers and the Fundamental Theorem of Arithmetic
- Complex numbers and the Fundamental Theorem of Algebra
- Fibonacci sequence
- Golden section
- Catalan numbers
- Euler's formula v - e + f = 2 and Pick's Theorem
- The Pigeonhole Principle
- Mathematical Induction
- The identity eip = -1
- Inequalities, arithmetic mean, geometric mean and harmonic mean
- Modular arithmetic, congruence and Fermat's Little Theorem
- Counting Principles and Binomial coefficients
- The Fundamental Theorem of Calculus
- L'Hopital's Rule

 


Koh Khee Meng is Professor at the Department of Mathematics. He obtained his PhD from the University of Manitoba in Canada in 1971. Among several other significant appointments, Professor Koh was the chairman of the Singapore International Mathematical Olympiad Committee (1991-93), a council member of the Institute of Combinatorics and Its Applications (International) (1995-97) and the president of the Singapore Mathematical Society (1996-98). He has also won numerous Teaching Awards from the Faculty of Science, NUS. Professor Koh specializes in Combinatorics and Graph Theory and has had many papers published in international scientific journals. He is co-author of the books: Principles and Techniques in Combinatorics, College Mathematics Volumes 1 & 2, Counting, Counting (Supplementary Notes and Solutions Manual), Chromatic Polynomials and Chromaticity of Graphs, Introduction to Graph Theory-H3 Mathematics and Introduction to Graph Theory-H3 Mathematics (Solutions Manual).

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Mathematics in Science, Technology and Society
Mathematics is the best known but least understood subject. It plays a fundamental role in the development of science, technology and society but it has received little commercial recognition and is often perceived as not useful in life. The seminar will expose students to various views about the nature of mathematics, the enterprise called mathematics and the role of mathematics in modern science, technology and society. Students will also learn a high-level mathematical software such as Maple or Mathematica and use them in conjunction with mathematics for modelling, computation and visualization of specific applications in modern science and technology. The mathematics will include, but not confine to, fast Fourier transform, scale-space representation, discrete wavelet transform, Bezier and B-spline curves and surfaces. The mathematics will be mostly algorithmic and discrete in the beginning and will be introduced gently at a level suitable to the students’ background, which may be different for different students.

 


Prof S. L. Lee obtained a Ph.D. degree in Mathematics from the University of Alberta, Canada, in 1974 under a Canadian Commonwealth Scholarship. He was a receipient of several research grants, including a French CNRS fellowship (1980), a U.K. NSERC research grant (1986) and an NSTB (former A*STAR) grant (1995) for his research in spline functions, wavelets and approximation. His research interests also include applications to information processing and geometric modeling. He was a winner of the Singapore National Science Award in 1998.

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Are We Alone?
How did life originate on Earth? What are its building blocks? What physical conditions are necessary for life? Are these conditions and building blocks common elsewhere in the universe? How likely is it for complex and intelligent life to evolve even if simple life-forms develop elsewhere? Is it necessary for potential life elsewhere to be based on a similar biochemistry to that on earth? How then would one detect and recognize life elsewhere? How would we communicate with potential intelligent life elsewhere in the universe? Why have not been contacted so far, or have we?

Based on readings, discussions, presentations and project work, the students will explore these questions that have fascinated not just the laymen but an increasing number of scientists working in the interdisciplinary field of Astrobiology.

 


The website for the seminar series is : http://staff.science.nus.edu.sg/~parwani/origins/originsindex.html

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Thinking Like a Scientist
This seminar will provide an introduction to the basic philosophy and methodology underlying all good scientific endeavours. We start with an exploration of our own thinking, observing if our thinking can be improved. Next we look at science developments across the ages and explore how the personalities and beliefs of individual scientists influence the development of new knowledge. Students are encouraged to identify, analyze and to present, scientific thinking found in current news, periodicals, films and television. Students will be challenged to practice scientific methodology by launching into small group projects where they can apply the basic steps of Observation-Hypothesis-Testing in real world situations. Ultimately, the goal of this seminar is for students to develop thinking skills and habits of thought that are the hallmarks of good scientists.

 


Dr Roland Su obtained both BSc and PhD in Physics from University of Bristol (UK). He joined NUS in 1999, and became Director of the Education programme for Gifted Youth (NUS-EPGY) in 2001. From 2000-2004 he was concurrently the Science coordinator for the MOE SM2 scholarship programme, a bridging programme for talented youth from China. Between 2004-2005, he was the Assistant Principal of the NUS High School of Mathematics and Science, pioneering the setting up of programmes for idetifying and nuturing gifted youths. Currently, Dr Su teaches undergraduate Physics and is the Associate Dean (Study Abroad Programmes) at the Science Dean's Office.

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Conceptual Development of Physics
The theme of this module is on the conceptual development of physics. Several topics will be discussed e.g. (i) Conceptual development of the fundamental constituents of matter from the Greek atomists (Leucippus and Democritus) to the current M-theory. [Reference: The Elegant Universe by Brian Greene, W W Norton & Company (1999)] (ii) Conceptual development of quantum theory [Reference: The Fabric of the Cosmos by Brian Greene (2003)] (iii) Conceptual development of relativity [Reference: Albert Einstein: Opportunity and Perception by C N Yang, International Journal of Modern Physics A (Jan 2006)] (iv) Physical laws and symmetries in physics (v) Gauge field and its historical development. Core issues of physics.

 


Prof Oh Choo Hiap is a Physicist whose research interests are in High Energy Physics, Yang-Mills gauge field theories, Quantum Algebra, Yang-Baxter equations and Quantum Information Science.

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The Beauty of Symmetry
Symmetry can be observed everywhere, from our daily life to the Nobel-prize-winning research work. The purpose of this Freshman Seminar is to introduce freshman to the modern concepts of symmetry and to help them to identify and to apply ideas of symmetry in their scientific training. Amongst the questions that would be discussed are: What is symmetry? How to define symmetry precisely? How to categorize symmetry? What are applications of symmetries in various perspectives: mathematics, humanities, and sciences? What is broken symmetry and its application?

 


Dr. WANG Qinghai was born in China. He received his B.Sc. and M.Sc. from the University of Science and Technology of China and his PhD in Physics from Washington University in St. Louis (USA). Before joining NUS, he worked as a postdoctoral fellow in the University of Connecticut (USA).

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Randomness in Scientific Thinking
The purpose of this seminar is to introduce students to the roles of randomness in scientific thinking. Some of the topics covered include the following: 
1. Is probability intuitive? A class exercises will be conducted where students are asked to generate sequences of real and fake random coin tosses and are asked to develop tests to detect the difference.
2. What is the role of randomization in the design of scientific experiments (for instance, why are patients randomly assigned to treatments in a medical trial)? We recreate a famous incident in which a tea time conversation led to a statistician conducting an experiment to test whether someone could distinguish whether milk had been added first or last to a cup of tea.
3. How has statistical thinking been used and abused in the history of IQ testing?
4. In the analysis of environmental problems like global warming scientific models are often used which are deterministic (roughly speaking, such models predict a definite output for a given input). A statistical model on the other hand gives predictions in the form of probabilities of different possible outcomes. How can the deep physical understanding embedded in the deterministic models be reconciled with statistical approaches to quantifying uncertainty and risk, and why is quantifying uncertainty important?
5. How can fake random numbers generated on a computer by non-random rules sometimes do complicated calculations that aren’t easily done by other means?
6. Why is statistical thinking so crucial in modern scientific enquiries in which massive databases of mostly uninteresting information are being searched for interesting features (in astronomy, genetics and market research for example)?

 


Dr Alex Cook is a statistician whose research area is in modelling and inference for infectious diseases and ecology. Before joining NUS in 2008, Cook was a visiting scholar in the department of plant sciences, University of Cambridge, and a research associate in the department of actuarial mathematics and statistics at Heriot-Watt University, Scotland. He did his PhD at Biomathematics and Statistics Scotland.

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Statistical Game Theory
Uncertainty pervades all aspects of our lives. Decisions must often be made in the face of uncertainty. Examples range in importance from the personal---whether to take your umbrella with you in the morning---to the societal---how to deploy prophylaxis in an emerging infectious disease outbreak---when in advance it is not known if it will rain or the extent of the epidemic. It is natural to want to make the best choices possible, but reliance on intuition alone does not always lead to the best course of action. This seminar series will introduce a framework for optimal decision making, namely statistical game (or decision) theory. You will learn the basics of decision theory via a plethora of applications, spanning games of chance, finance, public health and evolution, as well as classic, bewildering examples such as the Monty Hall and Prisoner's Dilemma “paradoxes”. The seminar series requires you to be able to do basic maths, extending occasionally to integration; some knowledge of statistics would be useful but not essential: the little statistical theory needed for the course will be covered in class. You will, however, need to enjoy problem solving.

 


Dr Alex Cook is a statistician whose research area is in modelling and inference for infectious diseases and ecology. Before joining NUS in 2008, Cook was a visiting scholar in the department of plant sciences, University of Cambridge, and a research associate in the department of actuarial mathematics and statistics at Heriot-Watt University, Scotland. He did his PhD at Biomathematics and Statistics Scotland.

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