1971-08-21 — Page 15

育教俘雜食三笠張第「一个月十年李SF亨WAH KIII. YAT PO

學畢業同學

暑期進修專欄

0

新數量

智慧出版社主

(土)

Elementary Modern Mathematics

Lesson 10

Numbers

Basic operation and Tawi

報日僑

REFEREE LIBRARY

ITY HALL

六期星日一廿月八一七九一零公布十六同

文

有關函授教育問題

P

期联变十五元。 在尖沙咀正光行九八〇九八一大關 全 一九七一年九月卅日起每星期四下午六時至七時

一 在斯康共六十五元。 宇 由神志勳先生以粵語)輔以英語第1 六、六十年代世界藝術——本海岛共陈雅 |平在尖沙咀星光行九八〇九蛮八一大全開張 第 九七一年九月廿八日起每期下午八冉至九時, 一由事創先生以糖(以英出,定自己

:: 九本美術俊軒——本得共十]]

[香港函授敦育的正規化」一文中1 編號先生,六月十七日丸報登校一士學位」,未知有何根己。 關于倫敦大学校外學位及英英函伊革可,已取消侖大校外學位课程;因此最近倫大校 陳倫大校外學位考試制度(可自己 | 人生評册人數已比以前少了很多。近會有入摄

·現時英國多數工科學院,因已獲CNAA之寫

五

元。

·三樓開,全斯經費六十五元。 其麒先生以粵語主體,定第一九七一年九月廿日 inity 械花圈——本傑共十二群,出 中在尖沙咀瑞興大蔞十三樓開課,鞏期學弁卅五

IND ENGLISH PART-TIME KEI LONDON EXTERNAL, DEGREENTA WHES THE PERERUKAVAKKET

的讓丁(READING ,大多數相修照作開闊的成鹹,即讓大蔥節可敬,能滋料區位。在美國現有約五十間跑可的大餐(一,由國濟與先生、希國髗先生、陳鴻規先生以鹰, ACCREDITED UNIVERSITIES ),S利寤 牾CF以英語主席,宗自一九七一年九月廿八

門檢定函授學生而如 [ ◎大外學位制度以前主·索審查 位制的臀際的貓哭。前幾年于偏大亦已裘示决定七一年九月廿四日起每星期五下午六時英大肉核 基 熱學位的戲構」;造共熱碘的報導。 决定吸時錨續舉辦,並亦已進行調查並維校外學,湖二小時,由檗码國先生以邁語主牌,定自一 英國在網楣股女中的大學學生程度,,不再教校外部。起夏天了各班。快發很星光行大樓八〇九至八一大縮開跟1全说

六學院,本身因發育焄案關係, 【GREES)。除了上述之大型外,在英國還有工 SOCIATION)愛程。(撰述人,與高還 共由佛 大學頒鰲校外學位(EXTERNAL DE TIONAL UNIVERSITY EXTENSION AS 及屈志仁先生主牌(二)陶瓷(四章)由塔文 ,以前的畢業生,都一西安祺程。洋世可參考該條大學函授等产州NA:分只四項:(一)繪畫及雕塑、四譯)由莊先 [奇先生主講(七) 由朱忠泰先生主持

美術音樂課程十九項 財越它們的烈阳,大部份的台模外,中文大學院外進修部一定自一九七一年九月十五日起每星期三下午五時。

AM),赫爾(BULL).H頓(SOUTHA | SIN)、雅磁頓(WASHINGTON),芝加哥一九樓開踝,全湖學費卅五元。

得政府第一祖尼亚(CALIFORNIA J. - 威斯康辛(WISCON 日起每星期二下午七時至八時,在尖沙咀星光行

SG METER),及阿斯盟(CHICAGO)大學等,除正式程外,亦飛獅·十三中國文化——本謝用英授

十、你一、各LEEDS UNIVERSITY PRESS )。但倫大仍一)家具設計——本課程共十二牌,

考取襬大校外學何試後,才可正式得武倫大校

高至六時半在尖沙咀基光行九樓八八號

隼歷限制 【 九月初陸續開課,參加者無

- 《十四 日本現代文化——本课程共十二课,

英自稱生了。黑實話,除大校外學位的源發展完 考試或作標準,可以說異而投絕無克鋭

星生

雞也不盡不實。素英國可在共有六間正把图校, 工作,由舖世墨院以函把方式負責執行」。這報「宇

(悲慨,中文大學俊外告部4年秋装 米行 國際 ·杭州 「經已公佈,其中有關英褫音樂與共+九項,一元。

九七街和行计由,

汝撼大 學位課務,其中五間地原為係大校外會議,安、名LETH 音樂欣賞——本礙程共十二,由

(一)殴楚初階——本傑柽共計四講,由骑月七日起每垦期四下午六時至七時在尖沙咀風、 行九樓八〇九至八一六宮開課,全湖區登卅五元 ,由商依神先生以粵語主講,是自一尤七一年十

仲黃而設立的,計有倫大所辦的商科位函授學

|院 COMMERCE DEGREE BUREAU )時中在尖沙咀盡興大樓開,全面推行達牌九

,現在只径研濟學位課程:

R

O图

NATIONAL EXTEN - LEE CALL,,,, 核八〇九 六室開,全期改变卅五元*v

TBRIDGE),按單都送( METROPOLITAND:

一八二

(十七)和聲學——本课程共八強,由導演

FORD E謀文中所提及之一 趙世墨院」);及七時至九時在尖沙帕瑞興大夏十三總開,全下午五時半至七脚在尖沙咀及光行九樓入,水是 |COLLEGE);胡礼堂(WOLSEY HALL OX、 主講。定自一九七一年十二月八日起每星期三下・本先生以導師主講,定自十月十一日起包星斯

SERAPID RESULTS COLLEGE) 19‡R• .

DING ), 亦辦有面摸課銎,專爲考取該大學地

ORREKA (UNIVERSITY OF REA

4大乘爾共殛降及领悟國家西接學院外,都是商,星光行大選胡桃,全期學費六十五元 | 50 至1K黨開鷸,金熊受費卅五元。

九月八日起每星期三下午七時至九時在尘沙咀瑞

助北棹職業教育根批五月七日之颢麟士段艺一顆大夏十三橋開眼,金剡图变六十五元。

一八八六五

生

甲按限限加

九九星生入開半

七军

報修 大

又娥文中提及之「全國紙術資格評」 五行色彩。一九一世,有志人士均可報名參加,但熱性。

WEET COUNCIL FOR NATIONAL AC

ADEMIC AWARDERCNAA。責此快精麗杯 尖沙咀道光行九攢八〇九至八一六全關蹣,全期 安钜可按下列辦法横要、

學號六十五元。 七一年九月十六日起每星期四下午七時至九時在,有安格限制者除外毂名袼用正楷對

在粹院。根據CNAAA

六速為創作——本線共千11篇,手一名義抬頭,並血檻織,連同報名表格酒许九

松街,始能得CNAA學位。至於博士學位,戴上月中計變钳羅斯下午也附室九時在尖沙咀革,校外進修部收。

,由徐榕生先生以邊靜主講,自一九七一年九|龍尖沙咀彌敦 二號瑞興大厦十三書中文大學

糖乙

分鄉收

淨行付

名沙,

蒸

By

Basic Operations

we mean the four

sub- traction, multiplication and division. In car-

rules in arithmetic. They are addition,

rying out mathematical operations, we can make use of some rules and laws in order to speed up our tedious working

Taws of addition

The commutative law :

This law of addition states that the addends may be arranged in any order without changing the sum

十九

大機校龍學

行

骨

外

eg:

We can see that

For any numbers

arid

Use of Commutative Law

'Commutative law can be applded to the adding of a group of numbers, Since this: law permits us to arrange the numbers in any order, we can add the numbers group by group so that the we can get the answer morw quickly.

10

10

= 14

(-3)

(-5) (-3)+(-5

+(-5) + ( −5 }}

-10)

Associative Law of Addition

The Associative law of addition states 'that the addends can be grouped in any com-

bination without changing the sum

IEYIF 中學同學暑期進修專欄 臺英文書院Ì碼

新數學進修

(五)

BRUSH-UP YOUR MODERN MATH. (5)-

Mappings

Lecture Definition

Let A, B be any two sets, then a mapping F of Ainto B is a correcpondence between A and B. which assigns to each element x of A, one and only one element y of B, called the image of x under F.

Notation:

or

→ E(X)

A, Bare respectively called the domain, and. range of f.

Note that for given be B, there may not exist a e A such that b f(a), or there may exist. more than one ae A satisfying this condition. Examples 1: fi

set of all people

BA

B-set

set of all integers,

if xG A. then f(x) is the age of

g+R—>R___\R = set of all rea.

numbers

Hg(x)new

Theorem: 2 mappings f t A→Band

equal if and only if A = and f(x) = g(x) for all xe

D are

Mapping of finite sèts If A = {a a,*••*mi

is a finite set, and B is any set the mapping F:A. B can be represented by symbo

قة

f(a,) f(az)

2,

An injective (respectively

surjective,

bijective) mapping is called an injection (respectively surjection, bijection)

Bijective mappings are particularly...

Important; TEF: A→B is bijective, it means that for each ye B, there is a unique element xeA such that f(x) = y. Therefore, we can define a mapping B→A, called the inverse of f, by the rule: if yes let f(y)

where x.is the element of A such that f(x) = y. f+ is defined only when fis bijective: :It is easy to see that fis itself bdjective and that (f-1)' =2.

Example: The mappingg

where g(x)

is injective because if e

R

then x

R→R

It is not surjective because if y is any negative. number or zero, there is no real such; that ex = y. But if ht where: h(x) = e" and R = set of all positive

real number.

his both surjective and injective. ice. h is bijective

Therefore, there is an inverse mapping

rtR, and this is given by the rule

if yent then h (y) = log y

Compet

Let

of mappings

A, B, C be any se B→C.

mapping gOF AC called the product of and g can now be defined such that

go f(a) = g( f(a) } for every até A. diagrammatically,

gof

eg.

(4+

Therefore (3 + 4)+ 7

(5 + 3)+ ( −

+(3

Aence, : (5 + 3)+

that for any numbers the following: law holds

dan Bac

14.

3+ (-5))

and:

That is

we can add up the first two numbers first on We can add up the last two numbers

It makes no difference in the sum

9. if A

3} B = {ab}, then

(do)is the mapping of A into B defined by

F(1)

==D, IL) - a. If A and B are both finite with order m, respectively. Then, there are n. different mappings f

into B.

For we can choose, as the iman of each

x of A; any one of the n elements of B; this gives n x nxn

xnnn possibilities.

{1,2,3} into B

The 2 = 8 mappings of A =

{a,b} are

(2 2 3), (1 2 3), (3 8 3), (1 2 3), (223),

a a

(2) ( ) ( ) (品) ()

Definition A mapping f

(a) injective (or f is a

B is said

be

mapping from

A into B)iff, for all a, a A:

{f(a) = f(a})、

- surjective (or f is a mapping from A onto B) 1FF F(A) = B, ie. iff, for every bЄB there exist some as A such that f(a) Bijective

(or fds a one-one mapping from A onto B) iff f is both injective and surjective

Similarly,

Then holgof) A

where ho(gof}(x) = h({gof)(x)) = h{g(f(x))

Further (hog)of is also defined

and hofgof) = (hog)of

Diagrammatically

ho(gof) =(hag)o!

Identity mappings:.

Definition; Let A be any set, the identity

mapping on A is the mapping i

defined by: if x∈ A, i(x)

Clearly, in ds bijective; and IF FA

B, then foi

and ipoe bijective then fo

and

P

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