手拿著從同學借來的手電，到宿舍後的第一件事當然就是把電腦"settle down"－－比如檢查郵件之類的。這時我注意到桌面上放了一個黑色背包，背面寫著SIMC的字樣。好奇心驅使我打開了那個背包(用另一個說法：那個房間"是我"的話，那個背包不屬於房間的"應有設備"，就一定"是我"的了。)

裡面裝的物品也不算出乎意料之外：一個萬用插頭(當然寫著SIMC, 從插口和"腳"基本上萬能，看來不只在新加坡才能用)；一本SIMC簡介(只能用精美來形容，連各隊的學校簡介都有)；還有一個放著NUS(新加坡國立大學)的資料，最神奇的是裡面只有應用科學那邊的資科(純數啊純理化那樣都沒有)；一個印了logo的水壺，800mL，相當實用；當然還有之前訂了的SIMC T-shirt (前後都印著logo、用運動用布料做的T-shirt)。說到這裡不能不讚一下新加坡那邊的預備相當充足(這也是無可厚非的，畢竟預備了一整年)，幾乎所有要用的物品都齊全了(就差一本簿和筆？ XD)

正式活動是在Day 1開始，當中不少隊伍的航班都比較晚，於是這天晚上成為了(唯二的)自由時間。

經過一輪商議，我們最終決定了由幾位同學"帶隊"去四處遊覽一下。

遊覽的地方我就就不多說了，主要是聖淘沙(看Songs of the sea, 水柱只能令人想起Waves)，值得一提的是看來當地小吃比HK便宜：以1兌5來算的話，$1.4有杯紅豆冰或者一個格仔餅的小吃，7元在HK只夠買一串串燒啊~)

當地的紅豆冰概念跟香港的牛雜都差不多(大誤)，就是將每種配料都加點進去(當然紅豆冰會以紅豆和冰為主)，就我所看見店主先後放了紅豆、椰果、冰、菠蘿，再淋上N種醬汁(我能分辨出的就只有花奶、煉奶和可樂(對，是可樂啊啊啊)還有紅黃綠三色糖水。這樣的食物在香港我大概絕不會吃，但是在那邊我意然沒經大腦思考就整個吃掉了 OTL

另一件事是當地都有類似日O城十元店的東西。十元兌過去就是每件貨品2元，於是我就捧了二支1.5L的茶回去了。

宿舍還是老樣子，只不過不少其他隊伍也陸續到達了。我們各自離去回我們自己的房。這時最離奇的事發生了：我和幾個同學的房間都在同一棟，但去不同樓層都需要自己的卡匙，例如五樓的卡匙就不能乘電梯到六樓。其保安之嚴密，在每個樓層走廊的門口都另有一個要卡匙進入的大閘。這次有個同學按了八樓，住六樓的我卻來不及按六字，電梯自然直上八樓。我心想：八樓的話用走火通道下去就沒問題了吧？我打開防火門，卻沒有發現這是向外反鎖的門，到我跑到六樓氣喘吁吁地求救時已經太遲了。我只好跑到地下的防火門，連地下的防火門都鎖著！(說實話地下不鎖 其他樓層鎖就可以了……)還好大力拍門的我最後還是獲救。

回到宿舍要睡時已經是凌晨兩點了。我實在等不及明天的挑戰……

## Saturday 25 September 2010

## Thursday 23 September 2010

### 23-9-10

好久沒寫過一篇像樣的"日記"了……

升左上F5之後開始忙了起來(其實一直如此)，主要被Phy/Chem用了不少時間……暑假買回來的A-level Chem, Phy 書當然不會易，Stanley H.Pine的Organic Chemistry就更變態了。(最難係佢講Arometic compounds極為深入，Arometic compound之後的章節我都看不懂了……難度大概這樣：Provide an explnation for the observation that 2-aminoprydine undergoes electrophilic substitution more rapidly than pyridine and princiaplly at the 3 and 5 positions.)當然，Beyond AL的有機命名方法我也看不懂(主要係ayclclic / arometic)。不過多看幾次還是打好了基本功，DSE以至AL範圍的compounds的命名和過半反應已經記得不錯了。不過……AL有教的ozonide那本Organic chem居然沒教？！？

數理方面的確放少了時間，尤其是沒去IMO training之後。Physic和數學開學那幾份test就炒了。Maths Team的selection test已經出好，希望今次選到勁人～

另一方面，我亦要下好決心讀好以下幾個field (？

1. Calculus (pure math) ，覺得自己基本功做不好

2. Co-geom(China AL) ，就算DSE唔考都要學好佢

3. Abstract Algebra -- M. Artin的那本Algebra還有陶哲軒的實分析

4. E&M 不知怎的，AL的EM睇極唔明

再講下業餘興趣……

Osu! - 已經做好被作弊佬爆上黎搶overall #1的準備，同時刷25000PC去做全破achievements，自己現在map > play

CG - 努力練習中，目標係CW33/34出現

同人寫作 - 沒空 (逃

另外自己也開始試下玩vocaloid了？！？

升左上F5之後開始忙了起來(其實一直如此)，主要被Phy/Chem用了不少時間……暑假買回來的A-level Chem, Phy 書當然不會易，Stanley H.Pine的Organic Chemistry就更變態了。(最難係佢講Arometic compounds極為深入，Arometic compound之後的章節我都看不懂了……難度大概這樣：Provide an explnation for the observation that 2-aminoprydine undergoes electrophilic substitution more rapidly than pyridine and princiaplly at the 3 and 5 positions.)當然，Beyond AL的有機命名方法我也看不懂(主要係ayclclic / arometic)。不過多看幾次還是打好了基本功，DSE以至AL範圍的compounds的命名和過半反應已經記得不錯了。不過……AL有教的ozonide那本Organic chem居然沒教？！？

數理方面的確放少了時間，尤其是沒去IMO training之後。Physic和數學開學那幾份test就炒了。Maths Team的selection test已經出好，希望今次選到勁人～

另一方面，我亦要下好決心讀好以下幾個field (？

1. Calculus (pure math) ，覺得自己基本功做不好

2. Co-geom(China AL) ，就算DSE唔考都要學好佢

3. Abstract Algebra -- M. Artin的那本Algebra還有陶哲軒的實分析

4. E&M 不知怎的，AL的EM睇極唔明

再講下業餘興趣……

Osu! - 已經做好被作弊佬爆上黎搶overall #1的準備，同時刷25000PC去做全破achievements，自己現在map > play

CG - 努力練習中，目標係CW33/34出現

同人寫作 - 沒空 (逃

另外自己也開始試下玩vocaloid了？！？

## Tuesday 21 September 2010

### A rough answer about variations

Question 1: rather easy...

i)yes since x=+/- sqrt (k) y, no matter it's positive or negative it can be written in forms of x=cy.

ii)yes for the same reason.

iii)no except x=y (bonus for x=y) since log x = k log y, x=y^k.

iv, v)By contradiction, i.e., when x=cy, f(x)=kf(y), f(cy)=kf(y) is

b)So far I can only find three characteristics:

1)fixed point 0: f(0)=kf(0).

2)Strictly increasing: k^nf(y)=f(c^n)y

3)Everywhere differentiable: Proof left for readers.

For geometrical approach the obvious way is "parametic equations".

Question 2: hard

a)It must be multivariate functions.

b,c) They can be

d)They can be non-partial variations as long as the degree of the function is unique.

e,f)Kept open.

i)yes since x=+/- sqrt (k) y, no matter it's positive or negative it can be written in forms of x=cy.

ii)yes for the same reason.

iii)no except x=y (bonus for x=y) since log x = k log y, x=y^k.

iv, v)By contradiction, i.e., when x=cy, f(x)=kf(y), f(cy)=kf(y) is

*solvable*(Bonus for solvable) i.e., unique numbers of x,y is obtainable so x,y is no longer a variables.b)So far I can only find three characteristics:

1)fixed point 0: f(0)=kf(0).

2)Strictly increasing: k^nf(y)=f(c^n)y

3)Everywhere differentiable: Proof left for readers.

For geometrical approach the obvious way is "parametic equations".

Question 2: hard

a)It must be multivariate functions.

b,c) They can be

*non-partial variations*since the comoponent of the product has the same nature.d)They can be non-partial variations as long as the degree of the function is unique.

e,f)Kept open.

## Monday 20 September 2010

### Drafts of answers to the "question of applied maths" Part 2

My answer: As mentioned in (a) the main prupose of score is to compare, one of the example will be the examinations and tests. (1+1) Since "result" shows an integrated review of the process, and different results can't be directly compared, score instead of results shows "how good does it performed" instead of "how can it perform". Moreover not just only the overall results are quantificated, "advantages" and "disadvantages" of performance is quantificated. As a result, extra infromation from the score is obtained through the process. (5)

The most important factor that decides f is the reversibility of the performance. (1) For example, scores in a competition or examination is not reversable but scores in a game is reversable through Save and Load Method. (1)

First we consider the case that "the process is not reversable".

It means that only one results will be put into f(x). (1) The output of f(x) is directly put into comparason. Assume all factor (elements of input set) is

When the process is reversable, we have to consider one more factor: the overall score is counted as sum of each play or best play among the many trials. (2)

Case 1: The process is reversable, but only the best one is counted. (e.g. sports, musical game)

In this case the "final score obtained" will be man{f(x1), f(x2)...f(xn)}.

Assume the score that can be obtained by a player with his

When number of plays is infinite-ly high, it is expected the the score obtained will be S. And within a finite number of plays, a trend that tends to S is also expected. As result, the

For example, the exercise brings improvements on the performance at the rate of (x^1/2), f can be a quardratic function so that the overall exercise is directly proportional to the score obtained.

Another exmaple is the musical game, when a broken combo is completed, the scores multiplies geometrically. However the probabilty of complete one more broken combo is much smaller than the original performance, which is approximately "quadratic effort" to get "quardratic score". (2)

Case 2: The process is reversable, and there's another column as the "overall score" of score obtained for each process.

In this case, the final score will be Σf(xi).

As long as the score obtained is

However in reality we can't play an infinite number of the process, which enable us to find the equilibrium between number of plays and quality of plays. (2)

Case i: Quality >> Quantity

In this case we assume that quantity is negligible when compared to quality. A tiny change in quality will lead to an irretrievable change in total score. That is, f(x)>>f(x-Δx) or even f(x)>>kf(x-Δx).

However "quality" can be improved in terms of "quantity". i.e., through lots of exercise the quality can be improved. This surely violates the irretrievability of quality. Therefore the improvement of quality through quantity can't be directly shown in the score obtained, the only solution to f is that, the final score is the

Case ii: Quality > Quantity

In this case quality is important than quantity where the difference can be offsets by more plays. Considering the improvement of quality by increasing quantity f can be (growth rate of quality by quantity)(growth rate of quality).

For the case Quality =< Quantity it's similar to case ii.

When Quality is much less important than Quantity, where 2min(f)>max(f). It's quite obvious that whenever max(f) > min (f), there exist m>n such that m min(f) < n max (f). Then we can conclude that min (f) = max (f), i.e., f is a constant. When the score shows somehow like "play count", quality is not important at all. (8)

d)Now extend the co-domain of the process into an n-space vector. Give examples that how f process and affect the coming decision of controlling invariate x. Discuss the feasibility to put a continous movement of controller (reality player) in the computer / processor, and after a strict process (i.e., f(x) is fixed), to give the expected results. (Hint: Chaos Theory may be involved.) (43M)

I'm afraid that I can't really answer this one since this is far mor difficult. However we can surely answer no to the second half of the question provided that random decision is made by processor. If random decision is made, the "score" obtained after a certain process (f) must differs between a more preferred result and a less one. As a result the difference in cabability cause different decision in later stage of the play.

Last part of the question : Paper-scissor-stone is a very simple game that paper < scissor < stone < paper. We can see that there's no stright order between the three signs. Inversely the "win rate" can't reflect which of the signs were used most.

i)Show that when your opponent plays perfectly random, you chance to win is 1/3. (8M)

ii)Show the relationship between inversability of score and information and the inordered nature of the process. (12M)

iii)Account the possibility to create a mathematical tool towards cyclic inequalities system (i.e., a>b>c>a or more variables, not the inequalities involving cyclic functions) to process such scores. (30M)

part d,e is kept open...

The most important factor that decides f is the reversibility of the performance. (1) For example, scores in a competition or examination is not reversable but scores in a game is reversable through Save and Load Method. (1)

First we consider the case that "the process is not reversable".

It means that only one results will be put into f(x). (1) The output of f(x) is directly put into comparason. Assume all factor (elements of input set) is

*partially proportional*to the score obtained. As a result, when one of the factor goes to the "good" side (is*expected*to make an increase in score), it must be strictly increasing. As a result, "assessment quality" is nearly equivlent to the score obtained. (3)When the process is reversable, we have to consider one more factor: the overall score is counted as sum of each play or best play among the many trials. (2)

Case 1: The process is reversable, but only the best one is counted. (e.g. sports, musical game)

In this case the "final score obtained" will be man{f(x1), f(x2)...f(xn)}.

Assume the score that can be obtained by a player with his

*best*performance or*highest obtainable*score be f(k)=S.When number of plays is infinite-ly high, it is expected the the score obtained will be S. And within a finite number of plays, a trend that tends to S is also expected. As result, the

*growth rate*of the score shows the importance of repeated exercise on the process.(2)For example, the exercise brings improvements on the performance at the rate of (x^1/2), f can be a quardratic function so that the overall exercise is directly proportional to the score obtained.

Another exmaple is the musical game, when a broken combo is completed, the scores multiplies geometrically. However the probabilty of complete one more broken combo is much smaller than the original performance, which is approximately "quadratic effort" to get "quardratic score". (2)

Case 2: The process is reversable, and there's another column as the "overall score" of score obtained for each process.

In this case, the final score will be Σf(xi).

As long as the score obtained is

*positive and is bounded*, to a certain extent an infinite number of play is far important than score obtained in each process. (1)However in reality we can't play an infinite number of the process, which enable us to find the equilibrium between number of plays and quality of plays. (2)

Case i: Quality >> Quantity

In this case we assume that quantity is negligible when compared to quality. A tiny change in quality will lead to an irretrievable change in total score. That is, f(x)>>f(x-Δx) or even f(x)>>kf(x-Δx).

However "quality" can be improved in terms of "quantity". i.e., through lots of exercise the quality can be improved. This surely violates the irretrievability of quality. Therefore the improvement of quality through quantity can't be directly shown in the score obtained, the only solution to f is that, the final score is the

*mean*of the previous score. For example, a win rate of 70% in 1000 plays is much better than 60% in 10000 plays. (Of course, when quantity is not large enough comparason in this case is meaningless under disturbances of small chaos.)Case ii: Quality > Quantity

In this case quality is important than quantity where the difference can be offsets by more plays. Considering the improvement of quality by increasing quantity f can be (growth rate of quality by quantity)(growth rate of quality).

For the case Quality =< Quantity it's similar to case ii.

When Quality is much less important than Quantity, where 2min(f)>max(f). It's quite obvious that whenever max(f) > min (f), there exist m>n such that m min(f) < n max (f). Then we can conclude that min (f) = max (f), i.e., f is a constant. When the score shows somehow like "play count", quality is not important at all. (8)

d)Now extend the co-domain of the process into an n-space vector. Give examples that how f process and affect the coming decision of controlling invariate x. Discuss the feasibility to put a continous movement of controller (reality player) in the computer / processor, and after a strict process (i.e., f(x) is fixed), to give the expected results. (Hint: Chaos Theory may be involved.) (43M)

I'm afraid that I can't really answer this one since this is far mor difficult. However we can surely answer no to the second half of the question provided that random decision is made by processor. If random decision is made, the "score" obtained after a certain process (f) must differs between a more preferred result and a less one. As a result the difference in cabability cause different decision in later stage of the play.

Last part of the question : Paper-scissor-stone is a very simple game that paper < scissor < stone < paper. We can see that there's no stright order between the three signs. Inversely the "win rate" can't reflect which of the signs were used most.

i)Show that when your opponent plays perfectly random, you chance to win is 1/3. (8M)

ii)Show the relationship between inversability of score and information and the inordered nature of the process. (12M)

iii)Account the possibility to create a mathematical tool towards cyclic inequalities system (i.e., a>b>c>a or more variables, not the inequalities involving cyclic functions) to process such scores. (30M)

part d,e is kept open...

## Sunday 19 September 2010

### Drafts of answers to the "question of applied maths" Part 1

due to horribly long answer (over 1000 wds), I decided to present

part a,b: marking scheme provided

"score given" by another person

a)Define the term "score" in different perspectives. (15M)

Expected answer:

-Another expression of "result"; simplified and quantificated - with explaination, each 2+3M

My answer:

Score is defined as the integrated expression of a results after a certain process.(2 - "another expression") Results can be expressed in many forms in terms of visibility or sound (2 - Ex of another expression), but score is a rather simplied version of a results (2 - "simplicity"), which is presented with a number or a rank (set). (3 - Ex of simplicity)

At the same time one of the important difference between results and score comes from the compatability of scores. (2 - "quantification") Under the same system and process, scores are comparable while comparason is not so obvious as score (1 - Ex of another expression) .We can say that score is the quantification of results, with the help of ordered field (most probably real number) we can compare much more easily. (3 - Ex of quantification)

b)b)Consider the following cases, select an appropiate function f(x), state its domain and co-domain as well as the brief explaination to the process f. You may select f as a overall score (insert x and directly takes f(x) as the score) and f as a partial score (f as a partial score, while the total score is equal to sum of f(x_i).)

i)Score = hits within a period of time

ii)RPG game final results

iii)Rhythm game, score from each hits is proportional to the combo and inversely proportional to the time offsets error. (12M)

Expected answer : explaination (1) + PS/OS (1) + domain (1) + co-domain (1)

My answer:

i)

f(x)=x, since ability is strictly equivlent to the hitting speed. (1)

Obviously this is OS, or PS = 1, also f: N→N. (1+2)

ii)

f: N^n →N, each number in the n-space vector divided by the corresponding growth factor and take their absolute value or mean. (2)

The idea comes from the limited growth chance. It's also a OS system, PS can't exist in this case. (1+1)

iii)

g = sum of f and f = x^2/e where x is the current combo and e as a measurement of error, it's obviously an PS system. (1)

f: N^2→Q, g: Q→Q, if integer function is considered than g: Q→N. (2)

This calculation alogarithm is obvious to sum up points from each hits to get an overall score. (1)

c)With reference to your answer in (a), state the nature of score and what can score show. Furthermore discuss, with examples, the compatability of score and its meaning, i.e., the growth factor / f'(x) VS the number of plays, cumulative scores, etc. (30M)

Expected answer:

Nature and meaning of score (8M) - Comparason

Compatability (22M) - Reversibility of scores (e.g. S/L, replay) VS play count VS Play performance

*my*answer (not*model*answer) into 2 parts.part a,b: marking scheme provided

"score given" by another person

a)Define the term "score" in different perspectives. (15M)

Expected answer:

-Another expression of "result"; simplified and quantificated - with explaination, each 2+3M

My answer:

Score is defined as the integrated expression of a results after a certain process.(2 - "another expression") Results can be expressed in many forms in terms of visibility or sound (2 - Ex of another expression), but score is a rather simplied version of a results (2 - "simplicity"), which is presented with a number or a rank (set). (3 - Ex of simplicity)

At the same time one of the important difference between results and score comes from the compatability of scores. (2 - "quantification") Under the same system and process, scores are comparable while comparason is not so obvious as score (1 - Ex of another expression) .We can say that score is the quantification of results, with the help of ordered field (most probably real number) we can compare much more easily. (3 - Ex of quantification)

b)b)Consider the following cases, select an appropiate function f(x), state its domain and co-domain as well as the brief explaination to the process f. You may select f as a overall score (insert x and directly takes f(x) as the score) and f as a partial score (f as a partial score, while the total score is equal to sum of f(x_i).)

i)Score = hits within a period of time

ii)RPG game final results

iii)Rhythm game, score from each hits is proportional to the combo and inversely proportional to the time offsets error. (12M)

Expected answer : explaination (1) + PS/OS (1) + domain (1) + co-domain (1)

My answer:

i)

f(x)=x, since ability is strictly equivlent to the hitting speed. (1)

Obviously this is OS, or PS = 1, also f: N→N. (1+2)

ii)

f: N^n →N, each number in the n-space vector divided by the corresponding growth factor and take their absolute value or mean. (2)

The idea comes from the limited growth chance. It's also a OS system, PS can't exist in this case. (1+1)

iii)

g = sum of f and f = x^2/e where x is the current combo and e as a measurement of error, it's obviously an PS system. (1)

f: N^2→Q, g: Q→Q, if integer function is considered than g: Q→N. (2)

This calculation alogarithm is obvious to sum up points from each hits to get an overall score. (1)

c)With reference to your answer in (a), state the nature of score and what can score show. Furthermore discuss, with examples, the compatability of score and its meaning, i.e., the growth factor / f'(x) VS the number of plays, cumulative scores, etc. (30M)

Expected answer:

Nature and meaning of score (8M) - Comparason

Compatability (22M) - Reversibility of scores (e.g. S/L, replay) VS play count VS Play performance

## Wednesday 15 September 2010

### Question on variations

F.4,5 level? yeah~

Question 1 direct variations

a)For each of the following conditions, does it imply that x is directly proportional to y? Assume x,y are real.

i)x^2 varies directly to y^2. (4M)

ii)x^3 varies directly to y^2. (4M)

iii)log x varies directly to log y. (5M + 1 Bonus)

iv)tan x varies directly to tan y. (5M + 2 Bonus)

v)sin x varies directly to cos y. (5M + 2 Bonus)

b)In a more general way, when does x proportional to y if f(x) varies to f(y) is given? Explain your answer in terms of:

i)Algebrical method (11M)

ii)Geometry apporach (15M)

Question 2 partial variations

a)State the nature of functions that is used in partial variations. (3M)

b)If the function is

c)If the function is

d)If the function is

e)If f'(x) is directly proportional to f'(y) where f is a polynomial, find the corresponding types of variation between x and y. (7M)

f)For the relationship x=f(y,z), where f is a polyomial, find the relationship between x and (δf/δy+δf/δz). (13M)

Full marks: 100 Time limits : 75 minutes or 1.5 hour

Question 1 direct variations

a)For each of the following conditions, does it imply that x is directly proportional to y? Assume x,y are real.

i)x^2 varies directly to y^2. (4M)

ii)x^3 varies directly to y^2. (4M)

iii)log x varies directly to log y. (5M + 1 Bonus)

iv)tan x varies directly to tan y. (5M + 2 Bonus)

v)sin x varies directly to cos y. (5M + 2 Bonus)

b)In a more general way, when does x proportional to y if f(x) varies to f(y) is given? Explain your answer in terms of:

i)Algebrical method (11M)

ii)Geometry apporach (15M)

Question 2 partial variations

a)State the nature of functions that is used in partial variations. (3M)

b)If the function is

*symmetrical*, what's its special properties? Explain. (6M + 1 Bonus)c)If the function is

*cyclic*, what's its special properties? Explain. (8M + 1 Bonus)d)If the function is

*alternative*, what's its special properties? Explain. (6M + 1 Bonus)e)If f'(x) is directly proportional to f'(y) where f is a polynomial, find the corresponding types of variation between x and y. (7M)

f)For the relationship x=f(y,z), where f is a polyomial, find the relationship between x and (δf/δy+δf/δz). (13M)

Full marks: 100 Time limits : 75 minutes or 1.5 hour

## Saturday 11 September 2010

### Question on Applied Maths

Pure mathematics is a strict science that "approximation" is pointless in most of the proof, and some approximation tools like big O notation (O(f(x))) is bonded to give an accurate limits on the behavior of a function.

However, we can see that approximation in the field of physics and mathsmatics is just powerful, like the formula E=mc^2, is done by approximation. The following question is quite interesting in the sense that it is approximation does give a general view of the whole problem:

a)Define the term "score" in different perspectives. (15M)

b)Consider the following cases, select an appropiate function f(x), state its domain and co-domain as well as the brief explaination to the process f. You may select f as a overall score (insert x and directly takes f(x) as the score) and f as a partial score (f as a partial score, while the total score is equal to sum of f(x_i).)

i)Score = hits within a period of time

ii)RPG game final results

iii)Rhythm game, score from each hits is proportional to the combo and inversely proportional to the time offsets error. (12M)

c)With reference to your answer in (a), state the nature of score and what can score show. Furthermore discuss, with examples, the compatability of score and its meaning, i.e., the growth factor / f'(x) VS the number of plays, cumulative scores, etc. (30M)

d)Now extend the co-domain of the process into an n-space vector. Give examples that how f process and affect the coming decision of controlling invariate x. Discuss the feasibility to put a continous movement of controller (reality player) in the computer / processor, and after a strict process (i.e., f(x) is fixed), to give the expected results. (Hint: Chaos Theory may be involved.) (43M)

If possible I will present my answer (does not means that it is model answer) for part a,b,c.

However, we can see that approximation in the field of physics and mathsmatics is just powerful, like the formula E=mc^2, is done by approximation. The following question is quite interesting in the sense that it is approximation does give a general view of the whole problem:

a)Define the term "score" in different perspectives. (15M)

b)Consider the following cases, select an appropiate function f(x), state its domain and co-domain as well as the brief explaination to the process f. You may select f as a overall score (insert x and directly takes f(x) as the score) and f as a partial score (f as a partial score, while the total score is equal to sum of f(x_i).)

i)Score = hits within a period of time

ii)RPG game final results

iii)Rhythm game, score from each hits is proportional to the combo and inversely proportional to the time offsets error. (12M)

c)With reference to your answer in (a), state the nature of score and what can score show. Furthermore discuss, with examples, the compatability of score and its meaning, i.e., the growth factor / f'(x) VS the number of plays, cumulative scores, etc. (30M)

d)Now extend the co-domain of the process into an n-space vector. Give examples that how f process and affect the coming decision of controlling invariate x. Discuss the feasibility to put a continous movement of controller (reality player) in the computer / processor, and after a strict process (i.e., f(x) is fixed), to give the expected results. (Hint: Chaos Theory may be involved.) (43M)

If possible I will present my answer (does not means that it is model answer) for part a,b,c.

### Proposed Notes List

Mathematics

-Tricks on quadratic graphs and polynomials

-Trigonometry transformation

-Algebra of M2

Physics

-Gravitation

-Gas (Gas Laws, Ideal Gas Law, Kinetic Theory)

-Wave

-Electromagnetics

Chemistry

-Redox and electrolysis

-Chemistry of carbon compounds

-Introduction to physical chemistry (if it is taught)

Economics

-Efficiency and Equity

-National Income and Price level

-Money and Trade

That list is tough enough...

-Tricks on quadratic graphs and polynomials

-Trigonometry transformation

-Algebra of M2

Physics

-Gravitation

-Gas (Gas Laws, Ideal Gas Law, Kinetic Theory)

-Wave

-Electromagnetics

Chemistry

-Redox and electrolysis

-Chemistry of carbon compounds

-Introduction to physical chemistry (if it is taught)

Economics

-Efficiency and Equity

-National Income and Price level

-Money and Trade

That list is tough enough...

## Friday 10 September 2010

### 偽．SIMC回憶錄1.2

Day 0 12:00, SG

機上的四小時完全是在紙堆中渡過。我不停翻讀著那份要命的筆記……還有那一本忍不了手買下的的經濟學概論。所幸的是機上有午餐時間，我也不至於專住了好幾個小時。

降落新加坡後，第一件事……居然是去廁所(XD)～在此之前我一直認為新加坡在那種管治下不論是文化或是教養方面都有一定質素，可是這一下正好推翻了我的想法。

明明是一個機場的廁所，裡面跟香港的公廁沒兩樣，實在慘不忍睹。

至底這是個區有金玉其外而敗絮其中，還是表裡如一的城市？

這個問題成為了我此行的另一個目的。

辦完手續後當然就是正式進入新加坡了……沒想到另一個驚喜正在等候我們。

*_*

一個月前當我們接到比賽的簡介時，單張上寫著的是由新加坡國立大學附中所舉辦的比賽，當時我就想：「有沒有搞錯啊～一間學校辦的比賽認授性本來就不足，何來『國際』？」於是當時就抱著玩玩去的心態報名去了。

甫踏進接機大堂，陣陣鎂光燈向我們閃爍著，我第一個反應便是「咦，狗仔隊拍錯目標了？我又長得不帥～」於是抬頭一看，赫然發現幾個當地的同學拿著「xxx school welcome to Singapore!~」的橫幅！

嘖，錢不少呢。

相機閃夠了後我們自然走了出來，三位年紀跟我們相若前來自我介紹，一共是兩男一女－－為了不公開名字，我們即管把男同學稱為A,B，女同學稱為C吧。在一番談話中我們得知他們會負責領隊的角色，在這幾天跟著我們。

在談話中實在不難理解他們被挑選成為student leader的原因：在旅遊巴裡面沒有冷場，除了是因為有英文和普通話這兩種共通語言外，還因為那三個同學的熱情和健談。旅遊巴經過所見到的景點，從雙子塔到法院大樓他們都沒有放過。有了建築特色這種兩地的共通點，各人很快就能融入大家的對話當中。

新加坡的面積比香港小，車程不到半小時，我們便到達了以後五天的住宿地方。當旅遊巴在宿舍外圍繞圈時，我還以為是豪宅之類的建築，但竟然只是大學宿舍－－那是山上劃出來的一塊不少的區域，上面矗立了十餘座約十樓高的建築物，外面看起來由落地玻璃砌出來大樓，實在很難想像成永遠和鬼故的大學宿舍扯在一起。

宿舍房間的感覺截然不同，說白了就是一種實而不華的設計：一張床、書桌、景觀還不錯的窗口和浴室；整個房間漆上柔和的淡黃色－－宿舍，本該如此。

(待續)

*嘛, 我懶了...很多東西都沒寫出來呢

機上的四小時完全是在紙堆中渡過。我不停翻讀著那份要命的筆記……還有那一本忍不了手買下的的經濟學概論。所幸的是機上有午餐時間，我也不至於專住了好幾個小時。

降落新加坡後，第一件事……居然是去廁所(XD)～在此之前我一直認為新加坡在那種管治下不論是文化或是教養方面都有一定質素，可是這一下正好推翻了我的想法。

明明是一個機場的廁所，裡面跟香港的公廁沒兩樣，實在慘不忍睹。

至底這是個區有金玉其外而敗絮其中，還是表裡如一的城市？

這個問題成為了我此行的另一個目的。

辦完手續後當然就是正式進入新加坡了……沒想到另一個驚喜正在等候我們。

*_*

一個月前當我們接到比賽的簡介時，單張上寫著的是由新加坡國立大學附中所舉辦的比賽，當時我就想：「有沒有搞錯啊～一間學校辦的比賽認授性本來就不足，何來『國際』？」於是當時就抱著玩玩去的心態報名去了。

甫踏進接機大堂，陣陣鎂光燈向我們閃爍著，我第一個反應便是「咦，狗仔隊拍錯目標了？我又長得不帥～」於是抬頭一看，赫然發現幾個當地的同學拿著「xxx school welcome to Singapore!~」的橫幅！

嘖，錢不少呢。

相機閃夠了後我們自然走了出來，三位年紀跟我們相若前來自我介紹，一共是兩男一女－－為了不公開名字，我們即管把男同學稱為A,B，女同學稱為C吧。在一番談話中我們得知他們會負責領隊的角色，在這幾天跟著我們。

在談話中實在不難理解他們被挑選成為student leader的原因：在旅遊巴裡面沒有冷場，除了是因為有英文和普通話這兩種共通語言外，還因為那三個同學的熱情和健談。旅遊巴經過所見到的景點，從雙子塔到法院大樓他們都沒有放過。有了建築特色這種兩地的共通點，各人很快就能融入大家的對話當中。

新加坡的面積比香港小，車程不到半小時，我們便到達了以後五天的住宿地方。當旅遊巴在宿舍外圍繞圈時，我還以為是豪宅之類的建築，但竟然只是大學宿舍－－那是山上劃出來的一塊不少的區域，上面矗立了十餘座約十樓高的建築物，外面看起來由落地玻璃砌出來大樓，實在很難想像成永遠和鬼故的大學宿舍扯在一起。

宿舍房間的感覺截然不同，說白了就是一種實而不華的設計：一張床、書桌、景觀還不錯的窗口和浴室；整個房間漆上柔和的淡黃色－－宿舍，本該如此。

(待續)

*嘛, 我懶了...很多東西都沒寫出來呢

## Tuesday 7 September 2010

### 06-09-10

開學變得更忙了……

整理一下"今年無論如也要完成"的文章列表:

1)筆記； 理化經濟最好還有數學

Progress: Chem : 10% Other 0%

2)SIMC回憶錄+SIMC problem analysis PART II

Progress: 5% (1.2 50%)

3)Pilot

Progress: unknown (2.2 50%)

4)Youtube vid, CG 整理 (optional)

就這樣 ._<

Osu!繼續保overall#1, 集中衝modding, 25000PC.

以上.

整理一下"今年無論如也要完成"的文章列表:

1)筆記； 理化經濟最好還有數學

Progress: Chem : 10% Other 0%

2)SIMC回憶錄+SIMC problem analysis PART II

Progress: 5% (1.2 50%)

3)Pilot

Progress: unknown (2.2 50%)

4)Youtube vid, CG 整理 (optional)

就這樣 ._<

Osu!繼續保overall#1, 集中衝modding, 25000PC.

以上.

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