Final Questions

21 08 2010
Hi, our final questions are reserved for the literature and maths students.
1. Did reading books beyond the five selected for our examinations in any way help with your analyzing the larger topics in the text?
2. Is it possible for a novel to be adapted into a film while withholding all the major elements of the novel?
3. How do interpretations of tragedy change with the times?
4. Are tragedies representative of the culture they were written in, or more dependent on their author’s perspective of tragedy?
5. Do autobiographies ever actually reveal the truth about a person?
6. What defines a feminist?
7. What types of feminists are usually represented in novels/plays? Are these accurate, or more representative of the society’s view of feminists during that time period?
8. How accurate are plays of novels, as compared to actual plays?
9. How does learning events from a man’s perspective change views of women?
10. How is war generally depicted in novels, and how does the male point of view change this depiction?
1. According to the Bayer’s Theorem sent, the number of event occured was only 2 (searching for probability event A occur, when event B already happened). what will happen if the number of event increased (Such as probability of event A occur, when event B and C already happened)?
2. how to use wedge product and what do you meant by vectors of more than 3 dimensions?
3. what is functional?
Have a good flight home.




Maths 16 and 17 Aug

19 08 2010

16th Aug and 17 Aug

The tour of cambridge enabled us  to look through the cambridge campus which consists of 31 colleges  and we went to at the Kings College chapel, Trinity College where (gasp) Newton used to live and St John’s College. The architecture seemed identical at first glance but as we looked at more of the intricate details on each building the differences in age shows.

John,Marie,Melvin,Mr Lim and Jonathan beside the Math Giant
Viren teaching the RJC students how to solve a question

We also realised that we  could only fully understand a subject or topic such as differentiation only after we understood its proofs . During the time given to solve a particular question or so,we had a lot of peer interaction as well which also increased our insight into the subject as we gained knowledge on how it was plausible for us to solve a particular problem or question in a variety of ways.

In the morning, we learn the theory behind Vector Calculus. In this topic, we learnt about scalar product, vector product, triple scalar product and triple vector product. We also knew that for vectors of more than 3 dimensions, we cannot do vector product but use wedge product. We were introduced to the concepts of curl and divergence which are important to understand differentiation of vectors. Can you imagine that vectors can be differentiated? Cool right? In fact they can be integrated as well.

In the afternoon, we did complex numbers. We were introduced to basic properties of complex numbers, nth roots of unity, Euler’s formula and used complex numbers to help us do differentiation and integration of complicated expressions.

17 Aug

In the morning, we were introduced to Calculus of Variations. Essentially, we realized that to determine the nature of stationary points of functions with more than 1 variable, we need to use Euler Larange Equations. To solve this equations, we need to learn integration and differential equations. We forgot much of our integration stuff so find this part a bit tough going. But the tutor was patient enough to show the steps.

In the afternoon we did some examples which were linked with themes in physics such as the study of mechanics, proving the shortest distance between two points is indeed a straight line and so on.  When we apply scientific method to the physical world, we qualify or define things, then we quantify or measure them. Therefore,it’s inevitable that  measurement of quantities  in physics involves mathematics.

We also further learned about a new concept called functionals. We all know that  functions  map from a domain of numbers to the range which is usually real numbers. However, a functional maps a function to the range of real numbers. In other words, it is a function that takes another function and returns a scalar result. It can be easily thought of as a function of a function. One mistake many people made was that they immediately thought of composite functions. But the problem is that composite functions are functions that takes the scalar results of the first function. It is not an easy concept to accept though.

We did realise that the course was very objective driven as the teachers were very focused on completing a particular topic before the lesson ended. Also,our Vector Calculus tutor Sitikantha Das even gave one to one “lessons” when individuals did not understand a particular concept or so.

Sitikantha teaching students

We did feel, however it was essential that everyone had a rough outline of the courseline as at certain times it was arduous to follow the lesson given that it was a new concept. Having a rough outline would also prompt us to read ahead and during class,it would be easier to follow the lesson.





Response to question on Bayes’ Theorem

18 08 2010

Question: What is Bayes Theorem and how to apply it to our daily life?

Bayes Theorem is the main tool in Statistics. It can be applied in the medical field like drug testing and many situations where decision making is required. For example, we were given an example in the form of a question:

Qn: Suppose that the blood test for some disease is reliable in the following sense:

  1. For people whom are infected by the disease, the blood test produces a positive result in 99.99% of cases.
  2. For people whom are not infected by the disease, the positive test result is only present in 0.02% of cases.
  3. In the general population, 1 person in 10 000 people is infected.

One person is selected at random and found to test positive for the disease. What is the probability that the individual is actually infected?

In this example, the probability of an infection is the cornerstone of the question. As a result, we can set up the conditions:

Let B be the event that the individual is infected.

Let A be the event that the individual tests positive for the disease

In this question, Bayes Theroem can be applied as it is a direct result of conditional probability, which is basically the probability of some event A occuring, given that some event B has already occured. It is denoted by P(B|A), which reads as “the conditional probability of of B, given A”. To see the derivation of this theorem, please see the attached document.

Derivation of Bayes Theorem





The Weekend

17 08 2010

London is indeed a beautiful city. It is well known for its heritage and culture. London, a city deep in its history, has developed into a metropolis. Her famous shopping district, spanning famous locations like Oxford Street and Covent Garden, contain modern retail brands housed in the architecture of old London, showing how London has managed to conserve the old and advance the new. In Singapore, on the other hand, our old and new are kept separate as they develop separately rather than together. As such, Singapore can learn from London, by incorporating new developments into old buildings by redeveloping them to pristine conditions. Through this, tourists and even our own local people can get a glimpse of Old Singaporean architecture. It would serve as a good reminder for Singaporeans of our tumultuous past, and how we have risen from it.

With just a glance around London, we can see how proud the English are of the history. They have maintained that powerful historical feel through the old architecture that lingers even when other cities have moved forward in time. The statues of the numerous key figures in British history stand proudly, showing how England remembers those who have made her who she is today. Singapore’s array of searing skyscrapers and high-rise HDB blocks are orderly and well played, whereas the cramped London streets are dripping with reverance for the past. A departure from Singapore, where practicality is emphasized and the character of the city does not show as much. Through all of that we’ve seen in our weekend trip,  we’ve been able to see how despite London and Singapore (both cities) differ greatly not just in term of architecture but also in historical value.

Yet another differing point would be the level of freedom of speech people are given in the UK. As the bus drove past near Trafalgar square, we could see people pitching tents in the middle of a busy area in order to protest various things such as the war in afghanistan.

As we stepped into the British Museum we cannot help but feel awestruck. We were greeted by treasures from all over the world ranging from Chinese pottery, Maori relics to Eyptian Mummies.

Taking a glance through the map tells one just how vast this museum really is, artifacts from every corner of the world, pieces of stones that are millions of years old, the evolution of human technology throughout the ages. An entire room was dedicated to the history of the mechanical clock, one could literally walk around this museum for days absorbing all kinds of knowledge with no specific subject area. Everything was there from one of the earliest prints of shakespeare’s works, to the first kind of currency used and of course the famed rosetta stone that allowed academics to finally decipher the hierogylphs from ancient egyptian times.

One thing that appears saliently remarkable, is that the English are
able to keep up with the changing times (Bustling Oxford Street and beautiful Covent
Garden), yet they fall back on tradition to preserve their culture (Old Spitelfield Market,
Trafalgar Square, and countless statues of Legends like Winston Churchill and Admiral
Lord Nelson). By the mere comparative analysis between Singapore and London, it is
obvious that we Singaporeans are too pragmatic to preserve our cultures and traditions
(in fact they are on the brink of eradication). However, we’re glad to know that Singapore
is taking steps to preserve our culture (but we’re a little slow). Personally, we feel that
more funds should be channelled towards culture preservation, education, and of course,
tourism and hospitality. London is truly inspiring, and it has opened our eyes to many
historical developments that we have, till now, overlooked.

Sunday : Cruise down River Thames

Today, the group took a short cruise river cruise down river Thames. We started off first at Westminster pier, where we could see the famous battle ship Belfast, which survived both World Wars. Shortly after the departure, we passed the still constructing Shard, which will be region’s tallest building after construction is completed. Also, there were many old buildings like the parliament building could be seen on the boat.

As we continue to go down stream, we could see that the urban landscape was well planned. Many new and old buildings stood next to each other, without looking out of place. The buildings complement each other as they still reflect the busy London skyline. We also marveled at how London’s urban planners have managed to embrace both the new and old architecture. Singapore has clearly adopted this approach as seen in its plans to merry the old and new architecture of Singapore in the civic district.

 

 

Being geography students, we paid attention to the river processes while enjoying the views. While passing under the bridges, the captain commented on the rapid flow of water which was up to 6km/hr. It was later that we found out that  locks,  weirs and various other river management strategies were used to manage the flow of the river. Hence, the cruise was clearly both and educational and recreational experience we will never forget.





Questions from Singapore

14 08 2010

Hi there,

glad to hear your activities are doing so well in Cambridge.

Below are some questions posted by your classmates to you.

How is the studying environment in cambridge different as compared to Singapore?

Some of the topics in Reach Cambridge are also covered in the H2 Geography syllabus. How are these topics different? Are they useful and relevant for future usage in H2 Geography?

What is Bayes Theorem and how to apply it to our daily life?

regards.

Singapore





Math Days 2 & 3

13 08 2010

Lessons were interesting as usual, as the days go on, the defining characteristics of teaching/learning at Cambridge become more obvious. We learnt about Combinatorics and Probability Theory. We did not know that Bayes Theorem is so important until the lecturer pointed out the applications in daily life.

Proving, such as when the birthday problem was raised, everyone knew of the high probability involved but when asked how to prove it no one knew. Venn diagrams versus algebraic proofs. They made us question every fundamental intuitive reason. It’s not simply listening to the teacher and memorizing the formulas given, it’s understanding and proving every step of the way, making sure that you take nothing as given.

Questions are harder, distinct and different. So understanding is a requirement, not just memory. They’re more conceptually demanding than practice demanding, even though that runs against what most people think maths is. Lessons really required thorough understanding that would allow manipulation and application.

Shows how math is applied in real life, for example when probability is used to estimate the accuracy of tests for diseases or to approximate the number of infected people during an epidemic.

This phrase was frequently used: “ have a think about that “ More refined thought processes and encourages thought about everything other than memory work. Understand the topic rather than know. We initially had a pre-conceived notion that math requires a lot of practice. Now we know it is not just practice, but with understanding.

A change in setting, to really spark interest that is conducive for studying. This is shown in the astronomy lesson where we sat inside a dome instead of a usual lecture theatre.

Resources available and easily accessible from the library at cambridge. All our learning needs can be fulfilled by books or other objects without the need for a teacher. While a teacher does make work easier, being able to work independently helps when teacher’s are unavailable or unable to help.

We have to copy slides, rather than having it printed for us. Copying rather than just looking, helps with remembering what we are taught

Longer periods, 3 hours straight going through everything without leaving anything hanging

The dynamics of a subject. What we learn may not be true for long, so we are encouraged to question more and learn more. And look up more updated news pertinent to the area of expertise.

Suggestions for improvements:

It’s easier to start a lesson with an overview.

Give a piece of the summary to help with recapping.





Best Wishes from Singapore

8 08 2010

Good luck in Cambridge, gain knowledge and experience, make new friends while strengthing old ones, and stay healthy!

- wishes from Singapore





Day 0

31 07 2010

The fact that we were on our way to THE Cambridge University took a little while to sink in. The sudden outburst of euphoria as we were walking through the gate to board the plane screaming ” WE’RE GOING TO CAMBRIDGE! “. Randomly grabbing each other while walking to Trinity Hall, where we now reside, and going ” Omg we’re in the UK. “

Departure hall T3,  an entire division of friends and families swarmed us.  As we posed for the following shot, camera flashes went off in all directions. Felt good. So THANK YOU ALL FOR MAKING US FEEL LIKE ROCK STARS!

The flight was thankfully uneventful ( Or sadly depending on how you look at it. Flying 14 hours on economy is hell after the first few hours ). At one point in time, to fight the leg cramps plaguing our entire deck, we ran to the back of the plane and started playing cards!

"No we're not queuing up for the lavatories"

Arrival saw renewed enthusiasm in everyone,  until we got on the bus and traveled for 2 hours through an undulating landscape which looked pretty much like this throughout the entire ride

And as these large expanses of flat ground provide about as much entertainment as the morning announcements, we all slept!

Until…

The Jerwood library!

We finally arrived at Cambridge! Not much else to say here we gaped in awe at the beautiful architecture and clicked the capture button on our cameras at everything we saw.

Our dormitories

Taken from the entrance of Trinity Hall

For more pictures to gape at add the reach cambridge people on facebook or flickr. I’m sure there will be hundreds more for anyone to peruse at their leisure.

We spent the rest of the day exploring the city area, dodging in and out of small alleys, inching our way through the crowd at the marketplace to get some ostrich burgers ( yes that’s right ostrich, they’re amazing ) and getting completely lost!

After that, we got a quick tour around the city and Downing college, another constituent college of Cambridge University.

And that pretty much concludes Day 0!  Departure, flight, arrival. There will be more updates, photos and backlogged homework to come as we begin our first academic day tomorrow! Signing off, from a dimly lit room, a cold breeze flowing in through the open window.








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