Math Blog

5 awarded prestigious President’s Scholarship at Istana ceremony

Maths Group Tuition starting in 2014

Source: http://news.asiaone.com/news/edvantage/5-awarded-prestigious-presidents-scholarship-istana-ceremony

SINGAPORE – Five government scholarship recipients, including a missionaries’ child who grew up in Papua New Guinea and a Youth Olympic Games triathlete, have been awarded the prestigious President’s Scholarships this year, at a ceremony at the Istana on Friday evening.

Get the full story from The Straits Times.

Here is the full speech by President Tony Tan:

Deputy Prime Minister Teo Chee Hean and Mrs Teo

Minister for Education Heng Swee Keat

Excellencies

Chairman and Members of the Public Service Commission

Ladies and Gentlemen

Good evening.

Each year, the Public Service Commission awards scholarships to outstanding young men and women who want to serve Singapore and Singaporeans through a career in the Public Service. The most prestigious undergraduate scholarship awarded by the Commission is the President’s Scholarship.

It is awarded to young Singaporeans who have the integrity and commitment to work for Singapore’s continued success. To be awarded a President’s Scholarship, one must demonstrate more than just excellence in academic and non-academic pursuits. One must also show a strong ethos for public service, impeccable character, remarkable leadership and dedication towards improving the lives of Singaporeans.

2013 President’s Scholars This evening, the President’s Scholarship is awarded to five exceptional young individuals who have distinguished themselves based on their leadership capabilities and calibre, and their passion to bring the nation forward.

Continue reading at http://news.asiaone.com/news/edvantage/5-awarded-prestigious-presidents-scholarship-istana-ceremony

Challenging Binomial Question; O Level A Maths Group Tuition

Question: (Broadrick Sec Prelim Add Math Paper 1 2010, Q8b)

In the expansion of \displaystyle (x^2-\frac{1}{2x^4})^n, in descending powers of x, the seventh term is independent of x. Find the value of n and the value of this term.

Solution:

\displaystyle\begin{array}{rcl} T_{r+1}&=&{n \choose r}(x^2)^{n-r}(-\frac{1}{2}x^{-4})^r\\ &=& {n\choose r}x^{2n-2r}(-\frac{1}{2})^r (x^{-4r})\\ &=& {n\choose r}(-\frac{1}{2})^r x^{2n-6r} \end{array}

r=6 since it is the seventh term (recall T_{r+1})

2n-6r=0 (independent of x means power is 0)

2n-36=0

n=18

{18\choose 6}\times (-\frac{1}{2})^6 =290 \frac{1}{16} (Ans)

You can reach for the stars with Jaws, Braille and determination, mathematics whiz Yeo Sze Ling tells HELLEN TAN

Maths Group Tuition starting in 2014!

Source: http://ww1.math.nus.edu.sg/News%20Archive/2005,%2024%20May%20-%20Counting%20on%20her%20mind%20-%20Yeo%20Sze%20Ling.htm

Counting on her mind

1,248 words 24 May 2005 Digital Life English (c) 2005 Singapore Press Holdings Limited

You can reach for the stars with Jaws, Braille and determination, mathematics whiz Yeo Sze Ling tells HELLEN TAN

Given that multiple degrees are common today, the fact that Miss Yeo Sze Ling has two degrees in mathematics, and is working on her doctorate in the same field, is probably not news.

Until you find out that she is blind.

The 27-year-old who earned her Bachelor’s degree (Honours) and a Master’s degree from National University of Singapore (NUS) is now into research on coding mathematics theories and cryptography.

These are used in computing algorithms to protect passwords or data from being stolen when they are zipped from computer to computer.

The field is an interest she shares with John Nash Jr, a mathematical genius who won a Nobel Prize, portrayed in the Oscar-winning movie, A Beautiful Mind.

Certainly, like Nash, her achievements should mean a lot.

He was a schizophrenic who thought he was doing secret cryptography work for the American government.

She has been blind from the age of about four when glaucoma struck. Glaucoma is a condition that increases pressure within the eyeball causing sight loss.

Technology has come in handy.

On campus, she totes a laptop.

At home in a four-room HDB flat in Bishan, her desktop Compaq PC holds today’s tech staples – e-mail and MSN Messenger for exchanging notes with friends.

The Internet is her source for research as well as for online newspapers or electronic books like A Beautiful Mind.

…

Continue reading at http://ww1.math.nus.edu.sg/News%20Archive/2005,%2024%20May%20-%20Counting%20on%20her%20mind%20-%20Yeo%20Sze%20Ling.htm

Rote learning has to make way for digital literacy: Heng Swee Keat

Source: http://www.channelnewsasia.com/news/singapore/rote-learning-has-to-make/779680.html

Education Minister Heng Swee Keat has said that with information readily available, rote learning has to make way for digital literacy.

SINGAPORE: Education Minister Heng Swee Keat has said that with information readily available, rote learning has to make way for digital literacy.

Speaking at the Second International Summit of the Book on Friday, Mr Heng said there is a need to place greater emphasis on critical and inventive thinking.

Whether it is a papyrus, print or the iPad, it seems that books are here to stay.

Professor Tommy Koh, chairman of the Organising Committee of the Second International Summit of the Book, and Ambassador-at-Large, said: “I think the book will endure to the end of time.

“But the form of the book has changed and will change. The container will change, the platform on which we read the book will also change.

“My children, for example, prefer to read the book either on the computer, on the iPad, on the tablet and other electronic forms. I still prefer the printed book. But in one form or another, the book will endure. There can be no human civilisation without books.”

But the question is whether readers are able to discern truths from untruths, especially in an era that is inundated with information.

Mr Heng said: “Some fear that the technologically sophisticated books of the future will dull the mind, as we no longer bother to use our imagination to render words into sounds and images.

“They worry too that we will forget to think for ourselves after we close the book because social media offers such an array of ready-made opinions that we will just pick one off the virtual shelf rather than form our own.

“We need to place greater emphasis on critical and inventive thinking, so that we may go on to imagine and create new insights.

“At the workplace, as the information revolution transforms the nature of work, our ability to move from theory to practice, to apply learning imaginatively in different contexts, and to create new knowledge, will become increasing valuable.”

Continue reading at http://www.channelnewsasia.com/news/singapore/rote-learning-has-to-make/779680.html

PSLE could move away from aggregate scores: Lim Biow Chuan

Source: http://www.channelnewsasia.com/news/singapore/psle-could-move-away-from/777972.html

The head of the Government Parliamentary Committee (GPC) for Education, Member of Parliament Lim Biow Chuan, said that the Primary School Leaving Examination could do with less focus on aggregate scores.

SINGAPORE: The head of the Government Parliamentary Committee (GPC) for Education, Member of Parliament Lim Biow Chuan, said that the Primary School Leaving Examination (PSLE) could do with less focus on aggregate scores.

He said that this would take away the stress associated with the examination.

Education Minister Heng Swee Keat said recently that changes to the PSLE will be announced at the National Day Rally on Sunday.

It is an annual affair that sends the nation’s parents, students and teachers into a frenzy — for many in Singapore, the PSLE has become a high-stakes examination.

Roger Cheong, a parent, said: “Maybe there should not be so much emphasis on PSLE at such a young age… Maybe as a gauge, but there shouldn’t be so so much weightage on it.

The Education Ministry has acknowledged this and embarked on a year-long review sometime in 2012.

Ahead of the announcements of possible changes, some have suggested going back to basics.

Mr Lim said: “I never knew what was my PSLE score. We selected a few schools that we chose and from there, MOE would post us to those schools, based on our performance. So you don’t have to go down to those minute details as to whether you score 270 or 265 or 275.

“You get broad-based results, and from there, you are allocated schools of your choice. It may not be the exact school of your choice, but it may be a group of schools that you choose and all of them are in the same category.”

Mr Lim also hoped to see more places set aside for the Direct School Admission (DSA) exercise, where students apply to secondary schools based on their achievements and talents before the release of their PSLE results.

Continue reading at http://www.channelnewsasia.com/news/singapore/psle-could-move-away-from/777972.html

Sergey Brin, co-founder of Google, studied Mathematics!

Maths Group Tuition to start in 2014!

Source: http://en.wikipedia.org/wiki/Sergey_Brin

Sergey Mikhaylovich Brin (Russian: Сергей Михайлович Брин; born August 21, 1973) is an American computer scientist and Internet entrepreneur who, with Larry Page, co-founded Google, one of the most profitable Internet companies.[4] As of 2013, his personal wealth was estimated to be $22.8billion.[2] Together, Brin and Page own about 16 percent of the company.

Brin immigrated to the United States with his family from the Soviet Union at the age of six. He earned his undergraduate degree at the University of Maryland, following in his father’s and grandfather’s footsteps by studying mathematics, as well as computer science. After graduation, he moved to Stanford University to acquire a Ph.D. in computer science. There he met Larry Page, with whom he later became friends. They crammed their dormitory room with inexpensive computers and applied Brin’s data mining system to build a superior search engine. The program became popular at Stanford and they suspended their PhD studies to start up Google in a rented garage.

The Economist newspaper referred to Brin as an “Enlightenment Man“, and someone who believes that “knowledge is always good, and certainly always better than ignorance”, a philosophy that is summed up by Google’s motto “Organize the world’s information and make it universally accessible and useful”[5][6] and “Don’t be evil“.

Education in the United States

Brin attended grade school at Paint Branch Montessori School in Adelphi, Maryland, but he received further education at home; his father, a professor in the department of mathematics at the University of Maryland, encouraged him to learn mathematics and his family helped him retain his Russian-language skills. In September 1990 Brin enrolled in the University of Maryland to study computer science and mathematics, where he received his Bachelor of Science in May 1993 with honors.[14]

Sergey Brin Ted 2010.jpg

Undergraduate Study in Mathematics (NUS)

Maths Group Tuition to start in 2014!

If you are interested in Mathematics, do consider to study Mathematics at NUS!

Source: http://ww1.math.nus.edu.sg/undergrad.aspx

Quote:

Undergraduate Study in Mathematics (NUS)

Overview

The Department of Mathematics at NUS is the largest department in the Faculty of Science. We offer a wide range of modules catered to specialists contemplating careers in mathematical science research as well as to those interested in applications of advanced mathematics to science, technology and commerce. The curriculum strives to maintain a balance between mathematical rigour and applications to other disciplines.

We offer a variety of major and minor programmes, covering different areas of mathematical sciences, for students pursuing full-time undergraduate studies. Those keen in multidisciplinary studies would also find learning opportunities in special combinations such as double degree, double major and interdisciplinary programmes.

Honours graduates may further their studies with the Graduate Programme in Mathematics by Research leading to M.Sc. or Ph.D. degree, or with the M.Sc. Programme in Mathematics by Course Work.

Studying at NUS Mathematics Department

Maths Group Tuition to start in 2014!

Source: http://ww1.math.nus.edu.sg/

The history  of the Department of Mathematics at NUS traces back to 1929, when science  education began in Singapore with the opening of Raffles College with less than  five students enrolled in mathematics. Today it is one of the largest  departments in NUS, with about 70 faculty members and       teaching staff supported  by 13 administrative and IT staff.  The Department offers a wide selection  of courses (called modules) covering wide areas of mathematical sciences with  about 6,000 students enrolling in each semester. Apart from offering B.Sc.  programmes in Mathematics, Applied Mathematics and Quantitative Finance, the  Department also participates actively in major interdisciplinary programs,  including the double degree programme in Mathematics/Applied Mathematics and  Computer Science, the double major       programmes in Mathematics and Economics as  well as with other subjects, and the Computational Biology programme. Another  example of the Department’s student centric educational philosophy is the   Special Programme in Mathematics (SPM), which is specially designed for a  select group of students who have a strong passion and aptitude for  mathematics. The aim is to enable these students to build a solid foundation  for a future career in mathematical research or state-of-the-art applications  of mathematics in industry.

The  Department is ranked among the best in Asia in mathematical  research.   It offers a diverse and vibrant program in graduate  studies, in fundamental as well as applied mathematics. It promotes  interdisciplinary applications of mathematics in science, engineering and  commerce. Faculty members’ research covers all major areas of contemporary  mathematics. For more information, please see research overview, selected publications, and research     awards.

Academic grading in Singapore: How many marks to get A in Maths for PSLE, O Levels, A Levels

Maths Group Tuition

Source: http://en.wikipedia.org/wiki/Academic_grading_in_Singapore

Singapore‘s grading system in schools is differentiated by the existence of many types of institutions with different education foci and systems. The grading systems that are used at Primary, Secondary, and Junior College levels are the most fundamental to the local system used.


Overcoming Math Anxiety

Featured book:

“If you’ve ever said ‘I’m no good at numbers,’ this book can change your life.” (Gloria Steinem)

Primary 5 to 6 standard stream

  • A*: 91% and above
  • A: 75% to 90%
  • B: 60% to 74%
  • C: 50% to 59%
  • D: 35% to 49%
  • E: 20% to 34%
  • U: Below 20%

Overall grade (Secondary schools)

  • A1: 75% and above
  • A2: 70% to 74%
  • B3: 65% to 69%
  • B4: 60% to 64%
  • C5: 55% to 59%
  • C6: 50% to 54%
  • D7: 45% to 49%
  • E8: 40% to 44%
  • F9: Below 40%

The GPA table for Raffles Girls’ School and Raffles Institution (Secondary) is as below:

Grade Percentage Grade point
A+ 80-100 4.0
A 70-79 3.6
B+ 65-69 3.2
B 60-64 2.8
C+ 55-59 2.4
C 50-54 2.0
D 45-49 1.6
E 40-44 1.2
F <40 0.8

The GPA table differs from school to school, with schools like Dunman High School excluding the grades “C+” and “B+”(meaning grades 50-59 is counted a C, vice-versa) However, in other secondary schools like Hwa Chong Institution and Victoria School, there is also a system called MSG (mean subject grade) which is similar to GPA that is used.

Grade Percentage Grade point
A1 75-100 1
A2 70-74 2
B3 65-69 3
B4 60-64 4
C5 55-59 5
C6 50-54 6
D7 45-49 7
E8 40-44 8
F9 <40 9

The mean subject grade is calculated by adding the points together, then divided by the number of subjects. For example, if a student got A1 for math and B3 for English, his MSG would be (1+3)/2 = 2.

O levels grades

  • A1: 75% and above
  • A2: 70% to 74%
  • B3: 65% to 69%
  • B4: 60% to 64%
  • C5: 55% to 59%
  • C6: 50% to 54%
  • D7: 45% to 49%
  • E8: 40% to 44%
  • F9: Below 40%

The results also depends on the bell curve.

Junior college level (GCE A and AO levels)

  • A: 70% and above
  • B: 60% to 69%
  • C: 55% to 59%
  • D: 50% to 54%
  • E: 45% to 49% (passing grade)
  • S: 40% to 44% (denotes standard is at AO level only), grade N in the British A Levels.
  • U: Below 39%

Featured Mathematician of the Day: Shing-Tung Yau

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Source: http://en.wikipedia.org/wiki/Shing-Tung_Yau

Shing-Tung Yau (Chinese: 丘成桐; pinyin: Qiū Chéngtóng; Cantonese Yale: Yāu Sìngtùng; born April 4, 1949) is a Chinese-born American mathematician. He won the Fields Medal in 1982.

Yau’s work is mainly in differential geometry, especially in geometric analysis. His contributions have had an influence on both physics and mathematics and he has been active at the interface between geometry and theoretical physics. His proof of the positive energy theorem in general relativity demonstrated—sixty years after its discovery—that Einstein‘s theory is consistent and stable. His proof of the Calabi conjecture allowed physicists—using Calabi–Yau compactification—to show that string theory is a viable candidate for a unified theory of nature. Calabi–Yau manifolds are among the ‘standard toolkit’ for string theorists today.

Yau was born in Shantou, Guangdong Province, China with an ancestry in Jiaoling (also in Guangdong) in a family of eight children. When he was only a few months old, his family emigrated to Hong Kong, where they lived first in Yuen Long and then 5 years later in Shatin. When Yau was fourteen, his father Chiou Chenying, a philosophy professor, died.

After graduating from Pui Ching Middle School, he studied mathematics at the Chinese University of Hong Kong from 1966 to 1969. Yau went to the University of California, Berkeley in the fall of 1969. At the age of 22, Yau was awarded the Ph.D. degree under the supervision of Shiing-Shen Chern at Berkeley in two years. He spent a year as a member of the Institute for Advanced Study, Princeton, New Jersey, and two years at the State University of New York at Stony Brook. Then he went to Stanford University.

Since 1987, he has been at Harvard University,[1] where he has had numerous Ph.D. students. He is also involved in the activities of research institutes in Hong Kong and China. He takes an interest in the state of K-12 mathematics education in China, and his criticisms of the Chinese education system, corruption in the academic world in China, and the quality of mathematical research and education, have been widely publicized.

Shing-Tung Yau at Harvard Law School dining hall
Shing-Tung Yau at Harvard Law School dining hall (Photo credit: Wikipedia)

Stanford University Research: The most important aspect of a student’s ideal relationship with mathematics

Source: Taken from Research by Stanford, Education: EDUC115N How to Learn Math

This word cloud was generated on August 9th based on 850 responses to the prompt “Please submit a word that, in your opinion, describes the most important aspect of a student’s ideal relationship with mathematics.”

stanford maths tuition word cloud

Prime Minister Lee Hsien Loong Truly Outstanding Mathematics Student

Just to share an inspirational story about studying Mathematics, and our very own Prime Minister Lee Hsien Loong. 🙂

Source: http://www2.ims.nus.edu.sg/imprints/interviews/BelaBollobas.pdf

(page 8/8)

Interview of Professor Béla Bollobás, Professor and teacher of our Prime Minister Lee Hsien Loong

I: Interviewer Y.K. Leong

B: Professor Béla Bollobás

I: I understand that you have taught our present Prime
Minister Lee Hsien Loong.

B: I certainly taught him more than anybody else in
Cambridge. I can truthfully say that he was an exceptionally
good student. I’m not sure that this is really known in
Singapore. “Because he’s now the Prime Minister,” people
may say, “oh, you would say he was good.” No, he was truly
outstanding: he was head and shoulders above the rest of
the students. He was not only the first, but the gap between
him and the man who came second was huge.

I: I believe he did double honors in mathematics and computer science.

B: I think that he did computer science (after mathematics) mostly because his father didn’t want him to stay in pure mathematics. Loong was not only hardworking, conscientious and professional, but he was also very inventive. All the signs indicated that he would have been a world-class research mathematician. I’m sure his father never realized how exceptional Loong was. He thought Loong was very good. No, Loong was much better than that. When I tried to tell Lee Kuan Yew, “Look, your son is phenomenally good: you should encourage him to do mathematics,” then he implied that that was impossible, since as a top-flight professional mathematician Loong would leave Singapore for Princeton, Harvard or Cambridge, and that would send the wrong signal to the people in Singapore. And I have to agree that this was a very good point indeed. Now I am even more impressed by Lee Hsien Loong than I was all those years ago, and I am very proud that I taught him; he seems to be doing very well. I have come round to thinking that it was indeed good for him to go into politics; he can certainly make an awful lot of difference.

H2 Maths 2012 A Level Solution Paper 2 Q6; H2 Maths Group Tuition

6(i)

H_0: \mu=14.0 cm

H_1: \mu\neq 14.0 cm

(ii)

\bar{x}\sim N(14,\frac{3.8^2}{20})

For the null hypothesis not to be rejected,

Z_{2.5\%}<\frac{\bar{x}-14}{3.8/\sqrt{20}}<Z_{97.5\%}

-1.95996<\frac{\bar{x}-14}{3.8/\sqrt{20}}<1.95996 (use GC invNorm function!)

12.3<\bar{x}<15.7 (3 s.f.)

(iii) Since \bar{x}=15.8 is out of the set 12.3<\bar{x}<15.7, the null hypothesis would be rejected. There is sufficient evidence that the squirrels on the island do not have the same mean tail length as the species known to her.

(technique: put in words what H_1 says!)

Geometry and Abraham Lincoln; O Level Maths Tuition Group

Source: http://www.mathopenref.com/euclid.html

At age forty, Abraham Lincoln studied Euclid for training in reasoning, and as a traveling lawyer on horseback, kept a copy of Euclid’s Elements in his saddlebag.  In his biography of Lincoln, his law partner Billy Herndon tells how late at night Lincoln would lie on the floor studying Euclid’s geometry by lamplight. Lincoln’s logical speeches and some of his phrases such as “dedicated to the proposition” in the  Gettysburg address are attributed to his reading of Euclid.

Lincoln explains why he was motivated to read Euclid:

“In the course of my law reading I constantly came upon the word “demonstrate”.  I thought at first that I understood its meaning, but soon became satisfied that I did not.  I said to myself, What do I do when I demonstrate more than when I reason or prove? How does demonstration differ from any other proof?
I consulted Webster’s Dictionary. They told of ‘certain proof,’ ‘proof beyond the possibility of doubt’;  but I could form no idea of what sort of proof that was. I thought a great many things were proved beyond the possibility of doubt, without recourse to any such extraordinary process of reasoning as I understood demonstration to be.  I consulted all the dictionaries and books of reference I could find, but with no better results.  You might as well have defined blue to a blind man.
At last I said,- Lincoln, you never can make a lawyer if you do not understand what demonstrate means;  and I left my situation in Springfield, went home to my father’s house,  and stayed there till I could give any proposition in the six books of Euclid at sight.  I then found out what demonstrate means, and went back to my law studies.”
Iconic black and white photograph of Lincoln showing his head and shoulders.

NUS Top in Asia according to latest QS World University Rankings by Subject

Source: http://newshub.nus.edu.sg/headlines/1305/qs_08May13.php

Top in Asia according to latest QS World University Rankings by Subject

08 May 2013

NUS is the best-performing university in Asia in the 2013 QS World University Rankings by Subject. With 12 subjects ranked top 10, NUS has secured the 8th position among universities globally in this subject ranking.
On the results, NUS Deputy President (Academic Affairs) and Provost Professor Tan Eng Chye said: “This is a strong international recognition of NUS’ strengths in humanities and languages, engineering and technology, sciences, medicine and social sciences.”
Prof Tan noted that the rankings served as an acknowledgement of the exceptional work carried out by faculty and staff in education and research.
NUS fared well, ranking among the world’s top 10 universities for 12 subjects namely Statistics, Mathematics, Material Sciences, Pharmacy & Pharmacology, Communication & Media Studies, Geography, Politics & International Studies, Modern Languages, Computer Science & Information Systems and Engineering (mechanical, aeronautical, manufacturing, electrical & electronic, chemical).

Continue reading at: http://newshub.nus.edu.sg/headlines/1305/qs_08May13.php

The Legendre Symbol

tomcircle's avatarMath Online Tom Circle

Prove

$latex x^{2} \equiv 3411 \mod 3457 $
has no solution?

Legendre Symbol:

$latex \displaystyle
x^{2} \equiv a \mod p
\iff
\boxed{
\left( \frac {a}{p} \right)
= \begin{cases}
-1, & \text{if 0 solution} \\
0 , & \text{if 1 solution} \\
1, & \text{if 2 solutions} \\
\end{cases}
}
$

Hint: prove $latex \left( \frac{3411}{3457} \right) = -1$

Using the Law of Quadratic Reciprocity, without computations, we can prove there is no solution for this equation.

Solution:

1.
3411 = 3 x 3 x 379 = 9 x 379

$Latex \displaystyle
\boxed{
\left(\frac{a}{p}\right)
\left(\frac{b}{p} \right)=
\left(\frac{ab}{p}\right)
}
$

$latex \displaystyle
\left(\frac{3411}{3457} \right)=
\left(\frac{9}{3457} \right).\left(\frac{379}{3457} \right)=
\left(\frac{379}{3457} \right)
$
since
$latex \displaystyle\left(\frac{9}{3457} \right)=1 $
because 9 is a perfect square, 3457 is prime.

2. By Quadratic Reciprocity,
$latex \displaystyle
\boxed{
\text{If p or q or both are } \equiv 1 \mod 4 \implies
\left(\frac{p}{q} \right)=
\left(\frac{q}{p} \right)}
$

Since
$latex…

View original post 212 more words

Singapore matematika kuliah

Kami penuh waktu Matematika guru, Mr Wu (Citizen Singapura), memiliki pengalaman yang luas (lebih dari 7 tahun) di les matematika. Mr Wu telah mengajar matematika sejak tahun 2006.

Mr Wu adalah pasien dengan siswa, dan akan menjelaskan konsep jelas kepada mereka. Dia mendorong untuk siswa lemah, sedangkan siswa yang lebih kuat tidak akan merasa bosan karena Mr Wu akan memberikan latihan yang cukup menantang bagi mereka untuk belajar lebih banyak. Singkatnya, setiap siswa harus mengalami perbaikan setelah kuliah.

Mr Wu lulus dengan B.Sc. (First Class Honours) dengan Mayor di Matematika (National University of Singapore).

Kami sangat percaya bahwa kepribadian dan karakter guru adalah sama pentingnya dengan kualifikasi akademik. Untuk Matematika Tutor, kesabaran ketika menjelaskan kepada siswa mutlak diperlukan.

Tutor Kualifikasi:

NUS: B.Sc. (First Class Honours) dengan Mayor di Matematika, Daftar Dean (Top 5% dari seluruh Fakultas Ilmu)

A Level: Matematika (A), Fisika (A), Kimia (A), Biologi (A), General Paper (A1)

O Tingkat: (Raffles Institution)

Bahasa Inggris (A1), Gabungan Humaniora (A1), Geografi (A1), Matematika (A1), Matematika Tambahan (A1), Fisika (A1), Kimia (A1), Biologi (A1), Bahasa Cina lebih tinggi (A2)

PSLE: (Nanyang Primer) 281, Lee Hsien Loong Excellence Award

Bahasa Inggris (A *), Bahasa Cina (A *), Matematika (A *), Sains (A *), Bahasa Cina Tinggi (Distinction), Ilmu Sosial (Distinction)

Apakah dalam Program PMP dari Pratama ke tingkat sekunder.

Terdaftar dengan MOE sebagai Guru Bantuan

(Orang tua yang ingin melihat sertifikat Mr Wu silahkan email kami. Orang tua juga dapat melihat profil StarTutor Mr Wu pada http://startutor.sg/23561, dengan sertifikat diverifikasi.)

Meskipun kualifikasi akademik Mr Wu, ia tetap seorang guru yang rendah hati dan sabar. Juga, orang tua dapat yakin bahwa Mr Wu mengajar pada tingkat yang siswa dapat sepenuhnya mengerti. Untuk A Level, kami akan mencoba untuk mengajarkannya dengan cara yang jelas dan sederhana sehingga bahkan Sec 3/4 siswa dapat mengerti. Untuk O Levels, kita akan mengajarkannya sedemikian rupa sehingga bahkan Sec 1/2 siswa dapat memahami, dan sebagainya.

Mr Wu hanyalah orang biasa yang telah menguasai keterampilan dan teknik yang diperlukan untuk unggul dalam matematika di Singapura. Dia ingin mengajarkan teknik ini untuk siswa, maka memilih untuk menjadi Matematika penuh waktu guru. Mr Wu telah mengembangkan metode sendiri untuk memeriksa jawaban, mengingat rumus (dengan pemahaman), yang telah membantu banyak siswa. Banyak pertanyaan Math dapat diperiksa dengan mudah, menyebabkan siswa menjadi 100% yakin nya atau jawabannya bahkan sebelum guru menandai jawabannya, dan mengurangi tingkat kesalahan ceroboh.

Mr Wu juga kakak dari dua mahasiswa kedokteran. Adiknya sedang belajar Kedokteran di Universitas Monash, dan adiknya sedang belajar Kedokteran di Yong Loo Lin School of Medicine, NUS.

Tujuan Pengajaran:

Tujuan pengajaran adalah untuk memungkinkan siswa untuk memahami konsep-konsep dalam silabus, meningkatkan minat pada pelajaran, dan untuk menjelaskan dengan jelas metode untuk memecahkan masalah matematika. Matematika adalah subjek yang sangat kumulatif, dasar yang kuat diperlukan untuk maju ke tingkat berikutnya. Kami sangat berharap dapat membantu lebih banyak siswa membangun fondasi yang kuat di Matematika.

Untuk Matematika, kami percaya bahwa cara terbaik untuk maju adalah melalui praktek dan pemahaman. Teknik untuk memeriksa jawaban dan metode singkat untuk menjawab pertanyaan lebih cepat berguna. Ketekunan sangat penting dalam Matematika, yang penting adalah untuk tidak menyerah, dan terus mencoba!

Untuk individu Matematika kuliah, tutor dapat melakukan perjalanan ke rumah siswa.

“Didiklah anak di jalan yang patut baginya: dan ketika dia sudah tua, dia tidak akan menyimpang dari itu.”

– Amsal 22:6

Математика Групповые занятия класса, чтобы начать в следующем году, 2014 году.

Математика Групповые занятия класса, чтобы начать в следующем году, 2014 году.

Математика Обучение центр

คณิตศาสตร์ชั้นเรียนกลุ่มที่จะเริ่มต้นในปีหน้า 2014

คณิตศาสตร์ชั้นเรียนกลุ่มที่จะเริ่มต้นในปีหน้า 2014

ศูนย์คณิตศาสตร์เล่าเรียน

H2 Maths A Level 2012 Solution, Paper 2 Q5; H2 Maths Tuition

5(i)(a)

P(\text{patient has the disease and test positive})=0.001(0.995)=9.95\times 10^{-4}

P(\text{patient does not have the disease and he tests positive})=(1-0.001)(1-0.995)=4.995\times 10^{-3}

P(\text{result of the test is positive})=9.95\times 10^{-4}+4.995\times 10^{-3}=5.99\times 10^{-3}

(b)

Let A=patient has disease

Let B=result of test is positive

\displaystyle\begin{array}{rcl}P(A|B)&=&\frac{P(A\cap B)}{P(B)}\\ &=&\frac{(0.001)(0.995)}{5.99\times 10^{-3}}\\ &=&0.166 \end{array}

Note that the probability is surprisingly quite low! (This is called the False positive paradox, a statistical result where false positive tests are more probable than true positive tests, occurring when the overall population has a low incidence of a condition and the incidence rate is lower than the false positive rate. See http://en.wikipedia.org/wiki/False_positive_paradox)

(ii)

\displaystyle P(A|B)=\frac{(0.001)p}{(0.001)p+(1-0.001)(1-p)}=0.75

By GC, p=0.999666 (6 d.p.)

H2 Maths 2012 A Level Paper 2 Q4 Solution; H2 Maths Tuition

(i)

1 Jan 2001 –> $100

1 Feb 2001 —> $110

1 Mar 2001 –> $120

Notice that this is an AP with a=100 ; d=10

\displaystyle\begin{array}{rcl}S_n&=&\frac{n}{2}(2a+(n-1)d)\\ &=&\frac{n}{2}(200+10(n-1))>5000 \end{array}

\frac{n}{2}(200+10(n-1))-5000>0

From GC, n>23.5

n=24 (months)

This is inclusive of 1 Jan 2001!!!

Thus, 1 Jan 2001 + 23 months —> 1 Dec 2002

(ii)

1 Jan 2001 –> 100

end of Jan 2001 –> 1.005(100)

1 Feb 2001 –> 1.005(100)+100

end of Feb 2001 –> 1.005[1.005(100)+100]=1.005^2 (100)+1.005(100)

From the pattern, we can see that

\displaystyle\begin{array}{rcl}S_n&=&1.005^n(100)+1.005^{n-1}(100)+\cdots+1.005(100)\\ &=&\frac{a(r^n-1)}{r-1}\\ &=&\frac{1.005(100)[1.005^n-1]}{1.005-1}\\ &=&\frac{100.5(1.005^n-1)}{0.005}\\ &=&20100(1.005^n-1) \end{array}

$5000-$100=$4900

20100(1.005^n-1)>4900

20100(1.005^n-1)-4900>0

From GC, n>43.7

So n=44 months (inclusive of Jan 2001 !!!)

1 Jan 2001+36 months —> 1 Jan 2004

1 Jan 2004+7 months —> 1 Aug 2004

Then on 1 Sep 2004, Mr B will deposit another $100, making the amount greater than $5000.

Hence, answer is 1 Sep 2004.

(iii)

Let the interest rate be x %.

Note that from Jan 2001 to Nov 2003 is 35 months. (Jan 2001 to Dec 2001 is 12 months, Jan 2002 to Dec 2002 is 12 months, Jan 2003 to Nov 2003 is 11 months :))

$5000-$100=$4900

Modifying our formula in part ii, we get

\displaystyle S_n=\frac{(1+x/100)(100)[(1+x/100)^n-1]}{(1+x/100)-1}=4900

Setting n=35 and using GC, we get

x=1.80

Hence, the interest rate is 1.80%.

A Level H2 Maths 2012 Paper 2 Q3 Solution; H2 Maths Tuition

A Level H2 Maths 2012 Paper 2 Q3 Solution

(i)

cubic graph maths tuition

(The graph above is drawn using the Geogebra software 🙂 )

(ii)

x^3+x^2-2x-4=4

x^3+x^2-2x-8=0

By GC, x=2

By long division, x^3+x^2-2x-8=(x-2)(x^2+3x+4)

The discriminant of x^2+3x+4 is

D=b^2-4ac=3^2-4(1)(4)=-7<0

Hence, there are no other real solutions (proven).

(iii) x+3=2

x=-1

(iv)

cubic absolute graph maths tuition

(v)

|x^3+x^2-2x-4|=4

x^3+x^2-2x-4=4 or x^3+x^2-2x-4=-4

x^3+x^2-2x-8=0 or x^3+x^2-2x=0

x^3+x^2-2x-8=0 \implies x=2 (from part ii)

x^3+x^2-2x=x(x^2+x-2)=x(x-1)(x+2)=0

x=0,1,-2

In summary, the roots are -2,0,1,2

List of JCs in Singapore; H2 Maths Tuition

Source: http://en.wikipedia.org/wiki/List_of_schools_in_Singapore#Junior_Colleges_.28JC.29

Junior Colleges (JC)

These offer two-year courses leading to the GCE A-level examination.

Code Zone College Name Established Address Type Special Programmes
English Chinese Abb.
0705 North Anderson Junior College 安德逊初级学院 AJC 1984 4500 Ang Mo Kio Avenue 6 Government
7001 West Anglo-Chinese School (Independent) IB World School 英华中学 (自主) ACS(I)-IBDP 2004 (IBDP) 121 Dover Road Independent IP, MEP
0803 West Anglo-Chinese Junior College 英华初级学院 ACJC 1977 25 Dover Close East Government-Aided MEP, DEP(TSD), LEP (EL)
0802 South Catholic Junior College 公教初级学院 CJC 1975 129 Whitley Road Government-Aided LEP (EL)
3101 East Dunman High School 德明政府中学 DHS 2005 – IP 10 Tanjong Rhu Road Autonomous IP, MEP, BSP, LEP (CL), AEP
0806 Central Hwa Chong Institution 华侨中学 HCI 1974 661 Bukit Timah Road Independent IP, HP, LEP (CL), AEP, BSP
0713 North Innova Junior College 星烁初级学院 IJC 2005 21 Champions Way Government LEP (ML)
0703 West Jurong Junior College 裕廊初级学院 JJC 1981 800 Corporation Road Government LEP (CL)
0712 East Meridian Junior College 美廉初级学院 MJC 2003 21 Pasir Ris Street 71 Government
0908 West Millennia Institute 励仁高级中学 MI 2004 60 Bukit Batok West Avenue 8 Government DTP
0805 North Nanyang Junior College 南洋初级学院 NYJC 1978 128 Serangoon Avenue 3 Government-Aided LEP (CL), AEP
0712 Central National Junior College 国家初级学院 NJC 1969 37 Hillcrest Road Government IP, HP, AEP, MEP, STaR
7801 West NUS High School of Mathematics and Science 新加坡国立大学附属数理中学 NUSHS 2005 20 Clementi Ave 1 Independent IP, DIP
0711 West Pioneer Junior College 先驱初级学院 PJC 1999 21 Teck Whye Walk Government
0704 South Raffles Institution 莱佛士初级学院 RI 1826 10 Bishan Street 21 Independent IP, HP, LEP (JL), LEP (EL), MEP, TSD
3103 West River Valley High School 立化中学 RVHS 1956 2006 – IP 6 Boon Lay Avenue Autonomous IP, BSP
0710 North Serangoon Junior College 实龙岗初级学院 SRJC 1988 1033 Upper Serangoon Road Government
0804 South Saint Andrew’s Junior College 圣安德烈初级学院 SAJC 1978 55 Potong Pasir Avenue 1 Government-Aided
0709 East Tampines Junior College 淡滨尼初级学院 TPJC 1986 2 Tampines Avenue 9 Government LEP (ML), TSD
0702 East Temasek Junior College 淡马锡初级学院 TJC 1977 22 Bedok South Road Government IP, HP, LEP (CL), MEP
0706 East Victoria Junior College 维多利亚初级学院 VJC 1984 20 Marine Vista Government IP, HP, TSD, NAV
0708 North Yishun Junior College 义顺初级学院 YJC 1986 3 Yishun Ring Road Government

Centralised Institutes (CI)

The only centralised institute is Millennia Institute (MI), which offers a three-year course leading to the GCE A-level examination in arts, science, and commerce.[3]

List of Secondary Schools in Singapore; A Maths Tuition

Source: http://en.wikipedia.org/wiki/List_of_secondary_schools_in_Singapore

Mainstream schools

Name Type School code Area[2] Notes Website
Admiralty Secondary School Government 3072 Woodlands [1]
Ahmad Ibrahim Secondary School Government 3021 Yishun [2]
Anderson Secondary School Government, Autonomous 3001 Ang Mo Kio [3]
Anglican High School Government-aided, Autonomous, SAP Bedok
Anglo-Chinese School (Barker Road) Government-aided Novena
Anglo-Chinese School (Independent) Independent, IP Dover Offers the IB certificate
Ang Mo Kio Secondary School Government 3026 Ang Mo Kio
Assumption English School Government-aided Bukit Panjang
Balestier Hill Secondary School Government Novena
Bartley Secondary School Government 3002 Toa Payoh
Beatty Secondary School Government 3003 Toa Payoh
Bedok Green Secondary School Government Bedok
Bedok North Secondary School Government Bedok
Bedok South Secondary School Government Bedok
Bedok Town Secondary School Government Bedok
Bedok View Secondary School Government Bedok
Bendemeer Secondary School Government Kallang
Bishan Park Secondary School Government Bishan
Boon Lay Secondary School Government Jurong West
Bowen Secondary School Government Hougang
Broadrick Secondary School Government Geylang
Bukit Batok Secondary School Government Bukit Batok
Bukit Merah Secondary School Government Bukit Merah
Bukit Panjang Govt. High School Government, Autonomous Chua Chu Kang
Bukit View Secondary School Government Bukit Batok
Catholic High School Government-aided, Autonomous, SAP, IP Bishan
Canberra Secondary School Government Sembawang
Cedar Girls’ Secondary School Government, Autonomous 3004 Toa Payoh
Changkat Changi Secondary School Government Tampines
Chestnut Drive Secondary School Government Bukit Panjang
CHIJ Katong Convent Government-aided, Autonomous Marine Parade
CHIJ Secondary (Toa Payoh) Government-aided, Autonomous 7004 Toa Payoh
CHIJ St. Joseph’s Convent Government-aided Sengkang
CHIJ St. Nicholas Girls’ School Government-aided, Autonomous, SAP Ang Mo Kio
CHIJ St. Theresa’s Convent Government-aided Bukit Merah
Chong Boon Secondary School Government Ang Mo Kio
Chua Chu Kang Secondary School Government Chua Chu Kang
Church Secondary School Government-aided
Chung Cheng High School (Main) Government-aided, Autonomous, SAP Marine Parade
Chung Cheng High School (Yishun) Government-aided Yishun
Clementi Town Secondary School Government Clementi
Clementi Woods Secondary School Government Clementi
Commonwealth Secondary School Government, Autonomous Jurong East
Compassvale Secondary School Government Sengkang
Coral Secondary School Government Pasir Ris
Crescent Girls’ School Government, Autonomous Bukit Merah
Damai Secondary School Government Bedok
Deyi Secondary School Government Ang Mo Kio
Dunearn Secondary School Government Bukit Batok
Dunman High School Government, Autonomous, IP, SAP Kallang
Dunman Secondary School Government, Autonomous Tampines
East Spring Secondary School Government Tampines
East View Secondary School Government Tampines
Edgefield Secondary School Government Punggol
Evergreen Secondary School Government Woodlands
Fairfield Methodist Secondary School Government-aided, Autonomous Queenstown
Fajar Secondary School Government Bukit Panjang
First Toa Payoh Secondary School Government 3208 Toa Payoh
Fuchun Secondary School Government Woodlands
Fuhua Secondary School Government Jurong West
Gan Eng Seng School Government Bukit Merah
Geylang Methodist School (Secondary) Government-aided Geylang
Greendale Secondary School Government Punggol
Greenridge Secondary School Government Bukit Panjang
Greenview Secondary School Government Pasir Ris
Guangyang Secondary School Government Bishan
Hai Sing Catholic School Government-aided Pasir Ris
Henderson Secondary School Government Bukit Merah
Hillgrove Secondary School Government Bukit Batok
Holy Innocents’ High School Government-aided Hougang
Hong Kah Secondary School Government Jurong West
Hougang Secondary School Government Hougang
Hua Yi Secondary School Government Jurong West
Hwa Chong Institution Independent, IP, SAP Bukit Timah
Junyuan Secondary School Government Tampines
Jurong Secondary School Government Jurong West
Jurong West Secondary School Government Jurong West
Jurongville Secondary School Government Jurong East
Juying Secondary School Government Jurong West
Kent Ridge Secondary School Government Clementi
Kranji Secondary School Government Chua Chu Kang
Kuo Chuan Presbyterian Secondary School Government-aided Bishan
Loyang Secondary School Government Pasir Ris
MacPherson Secondary School Government Geylang
Manjusri Secondary School Government-aided Geylang
Maris Stella High School Government-aided, Autonomous, SAP 7111 Toa Payoh
Marsiling Secondary School Government Woodlands
Mayflower Secondary School Government Ang Mo Kio
Methodist Girls’ School (Secondary) Independent Bukit Timah
Montfort Secondary School Government-aided Hougang
Nan Chiau High School Government-aided, SAP Sengkang
Nan Hua High School Government, Autonomous, SAP Clementi
Nanyang Girls’ High School Independent, IP, SAP Bukit Timah Affiliated to Hwa Chong Institution
National Junior College Government, IP Bukit Timah
Naval Base Secondary School Government Yishun
New Town Secondary School Government Queenstown
Ngee Ann Secondary School Government-aided, Autonomous Tampines
Northlight School Independent
North View Secondary School Government Yishun
North Vista Secondary School Government Sengkang
Northbrooks Secondary School Government Yishun
Northland Secondary School Government Yishun
NUS High School of Mathematics and Science Independent, IP, Specialised Offers the NUS High School Diploma
Orchid Park Secondary School Government Yishun
Outram Secondary School Government Central
Pasir Ris Crest Secondary School Government Pasir Ris
Pasir Ris Secondary School Government
Paya Lebar Methodist Girls’ School (Secondary) Government-aided, Autonomous Hougang
Pei Hwa Secondary School Government Sengkang
Peicai Secondary School Government Serangoon
Peirce Secondary School Government Bishan
Ping Yi Secondary School Government Bedok
Pioneer Secondary School Government 3062 Jurong West
Presbyterian High School Government-aided Ang Mo Kio
Punggol Secondary School Government Punggol
Queenstown Secondary School Government Queenstown
Queensway Secondary School Government Queenstown
Raffles Girls’ School (Secondary) Independent, IP Central Affiliated to Raffles Institution
Raffles Institution Independent, IP Bishan
Regent Secondary School Government Chua Chu Kang
Riverside Secondary School Government Woodlands
River Valley High School Government, Autonomous, IP, SAP Jurong West
St. Andrew’s Secondary School Government-aided 7015 Toa Payoh
St. Patrick’s School Government-aided Bedok
School of Science and Technology, Singapore Independent, Specialised Clementi
School of the Arts, Singapore Independent, Specialised Offers the IB certificate
Sembawang Secondary School Government Sembawang
Seng Kang Secondary School Government Sengkang
Serangoon Garden Secondary School Government Serangoon
Serangoon Secondary School Government Hougang
Shuqun Secondary School Government Jurong East
Si Ling Secondary School Government Woodlands
Siglap Secondary School Government Pasir Ris
Singapore Chinese Girls’ School Independent Novena
Singapore Sports School Independent, Specialised
Springfield Secondary School Government Tampines
St. Anthony’s Canossian Secondary School Government-aided, Autonomous Bedok
St. Gabriel’s Secondary School Government-aided Serangoon
St. Hilda’s Secondary School Government-aided, Autonomous Tampines
St. Margaret’s Secondary School Government-aided, Autonomous Bukit Timah
St. Joseph’s Institution Independent Novena
Swiss Cottage Secondary School Government Bukit Batok
Tampines Secondary School Government Tampines
Tanglin Secondary School Government Clementi
Tanjong Katong Girls’ School Government, Autonomous Marine Parade
Tanjong Katong Secondary School Government, Autonomous Marine Parade
Teck Whye Secondary School Government Chua Chu Kang
Temasek Academy Government, IP Affiliated to Temasek Junior College
Temasek Secondary School Government, Autonomous Bedok
Unity Secondary School Government Chua Chu Kang
Victoria Junior College Government, IP
Victoria School Government, Autonomous
West Spring Secondary School Government Bukit Panjang
Westwood Secondary School Government Jurong West
Whitley Secondary School Government Bishan
Woodgrove Secondary School Government Woodlands
Woodlands Ring Secondary School Government Woodlands
Woodlands Secondary School Government Woodlands
Xinmin Secondary School Government, Autonomous Hougang
Yio Chu Kang Secondary School Government Ang Mo Kio
Yishun Secondary School Government Yishun
Yishun Town Secondary School Government, Autonomous Yishun
Yuan Ching Secondary School Government Jurong West
Yuhua Secondary School Government Jurong West
Yusof Ishak Secondary School Government Bukit Batok
Yuying Secondary School Government-aided Hougang
Zhenghua Secondary School Government Bukit Panjang
Zhonghua Secondary School Government, Autonomous Serangoon

Japanese Math Professor Excellent Optical Illusionist

Source: http://www.youtube.com/watch?v=Wx4yi5m8IfI

Uploaded on Mar  8, 2011

Japanese mathematics professor Kokichi Sugihara spends much of his time in a world where up is down and three dimensions are really only two. Professor Sugihara is one of the world’s leading exponents of optical illusion, a mathematical art-form that he says could have application in the real world.
For more news and videos visit ☛ http://ntd.tv Follow us on Twitter ☛ http://twitter.com/NTDTelevision Add us on Facebook ☛ http://on.fb.me/s5KV2C
Three sloped ramps are aligned along three of the four sides of a square. Each ramp appears to be sloped in the same direction but when a marble is placed at one end of the ramp it seems to defy gravity.
It’s called an “anti-gravity slide”. Only when the the entire structure is turned 180 degrees, is the illusion revealed.
Japanese mathematics professor Kokichi Sugihara from the Meiji Institute near Tokyo, has made a career of creating optical illusions. He’s devised and built more than a hundred of them, like this one called “Perches and a Ring”.
[Kokichi Sugihara, Meiji University Professor]: “Among these models, there are those which are reproductions of optical illusions, and others that seem like normal models, but when you add movement to them, they show movement that should be impossible in real life. This is done by using the same trick, and I call them ‘impossible motions’.”
Professor Sugihara’s “impossible motions” have been recognized around the world. He won first prize in an international competition last year with this one, called “Magnet-Like Slopes”.
Sugihara says the success of his illusions is tied to human perception. Because humans have the capacity to perceive two-dimensional objects as being three-dimensional, they can be fooled into believing that something “impossible” is taking place during the course of the illusion.
For Sugiraha the illusions aren’t just for amusement. He says they have real world application. For example, he says misjudgments made by drivers on steeply curved roads could be mitigated by changing their perceptions of the immediate environment.
[Kokichi Sugihara, Meiji University Professor]: “If we can find how drivers misjudge an incline, we would be able to construct roads where these incidents are less likely to happen. In other cases, we could also reorganize the surrounding environment so that drivers could more easily see the difference between an ascending and descending road, and it could lead to reducing traffic jams.”
Sugihara says says his dream is to create playground amusements – even buildings with his models. More immediately though he has plans for an “impossible object exhibition”, a venue to demonstrate that seeing really is believing.

Youngest NUS graduates for 2012 – 08Jul2012

Source: http://www.youtube.com/watch?v=q-53rIy7RGg

Published on Jul  9, 2012

SINGAPORE – Douglas Tan was only seven years old when he discovered a knack for solving mathematical problems, tackling sums meant for the upper primary and secondary levels.
He went on to join the Gifted Programme in Rosyth Primary School and, in 2006, enrolled in the National University of Singapore High School of Math and Science (NUSHS). At 15, he was offered a place at the National University of Singapore (NUS) Faculty of Science to study mathematics.
Tomorrow, the 19-year-old will be this year’s youngest graduate at NUS, receiving his Mathematics degree with a First Class Honours. This puts him almost six years ahead of those his age.
Douglas, who is currently serving his National Service (NS), said the thought of going to prestigious universities overseas never occurred to him. “I was just happy doing what I was doing – solving math problems,” he said.
In every class he took, Douglas was the youngest but it was neither “awkward nor tough to fit in”, he said. In fact, his age was a good conversation starter and his classmates, who were typically three to five years older, would take care of him.
Seeing that he could complete his degree before he entered NS, Douglas took on three modules a semester and completed the four-year course in just two and a half years.
The longest he had ever spent on a math problem was 10 hours over a few days. “I’m a perfectionist. When I do a problem, I try to do it with 100 per cent,” he noted.
Douglas aspires to be a mathematician and is looking into a Masters degree but he has yet to decide if he wants to do it here or overseas.
Another young outstanding graduate this year is 20-year-old Carmen Cheh, who received her degree in Computer Science last Friday with a First Class Honours and was on the dean’s list every academic year of the four-year course.
Offered a place at the NUS School of Computing after three and a half years in NUSHS, Carmen was then the youngest undergraduate of the programme at 16.
She was introduced to computer science and concept programming at 11 by her father, a doctor who also challenged her to solve puzzles he created. Her inability to solve them spurred her interest in the subject.
Carmen, who is from Perak in Malaysia, said she decided to study for her degree in Singapore as she wanted to study in a country she felt “comfortable” in. At the same time, she was awarded an ASEAN scholarship to study in the Republic.
Next month, Carmen will begin her doctoral programme in Computer Science with a research assistantship at the University of Illinois at Urbana-Champaign.
The youngest ever to enrol into the NUS undergraduate programme is Abigail Sin, who entered the Yong Siew Toh Conservatory of Music at 14. She graduated in 2010 at age 18 with First Class Honours. She also received the Lee Kuan Yew gold medal.
This week, NUS celebrates the graduation of 9,913 students, its largest cohort in six years.
http://www.todayonline.com/Singapore/EDC120709-­0000039/Theyre-ahead-of-the-class

The Singapore Math

tomcircle's avatarMath Online Tom Circle

The famous Singapore Math for children in primary schools is based on  visual models.

The Singapore Ministry of Education has published a new 2013 Math syllabus for primary and secondary schools, which will roll out in examinations within 4 to 6 years. Todate only Primary 1 and Secondary 1 Math syllabuses are published here:

http://www.moe.gov.sg/education/syllabuses/sciences

View original post

Algebra vs Singapore Math

tomcircle's avatarMath Online Tom Circle

Who wins?

This comic video illustrates Singapore Math’s Arithmetics Polya-style problem solving process vs Algebra’s mechanical method.

The problem is as follow:
R is 3 times older than S two years ago. From now 2 years later, their total age is 32. How old is R now ?

See my previous blog (search “Monkey”) the Nobel Physicist Paul Dirac’s problem “The Monkeys and Coconuts“, 3 methods are used: 2 adanced modern math (by Sequence, eigenvector & eigenvalue), and the easiest & intuitive method (by Singapore Modelling Math). High-school Algebra method is impossible, if not cumbersome, to solve the Monkey problem !

View original post

St Gabriel’s Secondary School Mathematics Syllabus

Source: https://sites.google.com/a/moe.edu.sg/st-gabriel-s-secondary-school-maths-dept/syllabuses

For more information on the various Mathematics syllabuses, please click on the links provided at

“I hear, I forget. I see, I remember. I do, I understand.” (Chinese proverb that was a favorite of Moore’s. Quoted in Halmos, P.R. (1985) I want to be a mathematician: an automathography. Springer-Verlag: 258)

“I hear, I forget. I see, I remember. I do, I understand.” (Chinese proverb that was a favorite of Moore’s. Quoted in Halmos, P.R. (1985) I want to be a mathematician: an automathography. Springer-Verlag: 258)

The Moore method is a deductive manner of instruction used in advanced mathematics courses. It is named after Robert Lee Moore, a famous topologist who first used a stronger version of the method at the University of Pennsylvania when he began teaching there in 1911.

Source: http://en.wikipedia.org/wiki/Moore_method

Information about Mathematics Department Courses (Nanyang JC)

Source: http://nanyangjc.org/index.php/staff/organisation-chart/mathematics-department/

H1 Mathematics

H1 Mathematics provides a foundation in mathematics for students who intend to enrol in university courses such as business, economics and social sciences. The syllabus aims to develop mathematical thinking and problem solving skills in students. A major focus of the syllabus will be the understanding and application of basic concepts and techniques of statistics. This will equip students with the skills to analyse and interpret data, and to make informed decisions. The use of graphic calculator is expected.

H2 Mathematics

H2 Mathematics prepares students adequately for university courses including mathematics, physics and engineering, where more mathematics content is required. The syllabus aims to develop mathematical thinking and problem solving skills in students. Students will learn to analyse, formulate and solve different types of problems. They will also learn to work with data and perform statistical analyses. The use of graphic calculator is expected.

This subject assumes the knowledge of O-Level Additional Mathematics.

Continue reading at http://nanyangjc.org/index.php/staff/organisation-chart/mathematics-department/

Carl Friedrich Gauss

Source: http://en.wikipedia.org/wiki/Carl_Friedrich_Gauss

Johann Carl Friedrich Gauss (/ɡaʊs/; German: Gauß, pronounced [ɡaʊs] ( listen); Latin: Carolus Fridericus Gauss) (30 April 1777 – 23 February 1855) was a German mathematician and physical scientist who contributed significantly to many fields, including number theory, algebra, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics.

Sometimes referred to as the Princeps mathematicorum[1] (Latin, “the Prince of Mathematicians” or “the foremost of mathematicians”) and “greatest mathematician since antiquity“, Gauss had a remarkable influence in many fields of mathematics and science and is ranked as one of history’s most influential mathematicians.[2]

Carl Friedrich Gauss.jpg

Continue reading at http://en.wikipedia.org/wiki/Carl_Friedrich_Gauss

अगले साल शुरू करने के लिए गणित समूह ट्यूशन क्लास, 2014.

अगले साल शुरू करने के लिए गणित समूह ट्यूशन क्लास, 2014.
गणित शिक्षण केंद्र

Gotthold Eisenstein (Mathematician)

Gotthold Eisenstein (Mathematician)

*Not Einstein!

Ferdinand Gotthold Max Eisenstein (16 April 1823 – 11 October 1852) was a German mathematician. He specialized in number theory and analysis, and proved several results that eluded even Gauss. Like Galois and Abel before him, Eisenstein died before the age of 30. He was born and died in Berlin, Prussia.

Gauss … in conversation once remarked that, there had been only three epoch-making mathematicians: Archimedes, Newton, and Eisenstein.

Source: http://en.wikipedia.org/wiki/Gotthold_Eisenstein

Gotthold Eisenstein.jpeg

Number Theory Notes – Art of Problem Solving

Source: http://www.artofproblemsolving.com/Resources/Papers/SatoNT.pdf

Excellent notes on Olympiad Number Theory!

Preface:

This set of notes on number theory was originally written in 1995 for students

at the IMO level. It covers the basic background material that an IMO

student should be familiar with. This text is meant to be a reference, and

not a replacement but rather a supplement to a number theory textbook;

several are given at the back. Proofs are given when appropriate, or when

they illustrate some insight or important idea. The problems are culled from

various sources, many from actual contests and olympiads, and in general

are very difficult. The author welcomes any corrections or suggestions.

 

Khan Academy

tomcircle's avatarMath Online Tom Circle

I find Khan Linear Algebra video excellent. The founder / teacher Sal Khan has the genius to explain this not-so-easy topic in modular videos steps by steps, from 2-dimensional vectors to 3-dimensional, working with you by hand to compute eigenvalues and eigenvectors, and show you what they mean in graphic views.

If you are taking Linear Algebra course in university, or revising it, just go through all the Khan’s short (5-20 mins) videos on Linear Algebra here:

In 138 lessons sequence:

http://theopenacademy.com/content/linear-algebra-khan-academy

or random revision:

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Advice to Students

Source: http://www.math.union.edu/~dpvc/courses/advice/welcome.html

Advice to Students:

Over the years, I have collected some information that I hope will help  students, particularly beginning math students, to improve their study  and learning habits.  An important part of what you learn at college is  how to learn, so that you can carry that on for the rest of your  life.  Find out what works for you and what doesn’t.

These observations are centered around first-year calculus courses, so not  everything may apply to you, but even more advanced students can benefit  from some of them.

As you develop your own learning habits, please think carefully about the  following topics:

Continue reading at http://www.math.union.edu/~dpvc/courses/advice/welcome.html

Singapore Maths Tuition Class

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Student Advice: Comments on Perseverance

Source: http://www.math.union.edu/~dpvc/courses/advice/perseverance.html

Comments on Perseverance:

One source of confusion for students when they reach college and begin to  do college-level mathematics is this:  in high school, it is usually pretty  apparent what formula or technique needs to be applied, as much of the  material in high school is computational or procedural.  In college,  however, mathematics becomes more conceptual, and it is much harder to  know what to do when you first start a problem.  As a consequence of this,  many students give up on a problem too early.

If you don’t immediately know how to attack a problem, this doesn’t mean you  are stupid,

If you already know how to do it, it’s not  really a problem.

or that you don’t understand what’s going on; that’s just how  real problems work.  After all, if you already know how to do it, it’s not  really a problem, is it?  You should expect to be confused at first.   There’s no way you can know ahead of time how to solve every problem that  you will face in life.  You’re only hope, and therefore your goal as a  student, is to get experience with working through hard problems on your  own.  That way, you will continue to be able to do so once you leave  college.

One of the first steps in this is to realize that not knowing how, and the  frustration that accompanies that, is part of the process.  Then you have  to start to figure out the questions that you can ask to help you to break  down the problem, so that you can figure out how it really works.  What’s  really important in it?  What is the central concept?  What roles do the  definitions play?  How is this related to other things I know?

Continue reading at http://www.math.union.edu/~dpvc/courses/advice/perseverance.html

Relationship-Mapping-Inverse (RMI)

tomcircle's avatarMath Online Tom Circle

Relationship-Mapping-Inverse (RMI)
(invented by Prof Xu Lizhi 徐利治 中国数学家 http://baike.baidu.com/view/6383.htm)

Find Z = a*b

By RMI Technique:
Let f Homomorphism: f(a*b) = f(a)+f(b)

Let f = log
log: R+ –> R
=> log (a*b) = log a + log b

1. Calculate log a (=X), log b (=Y)
2. X+Y = log (a*b)
3. Find Inverse log (a*b)
4. ANSWER: Z = a*b

Prove:

$latex \sqrt{2}^{\sqrt{2}^{\sqrt{2}}}= 2$

1. Take f = log for Mapping:
$latex \log\sqrt{2}^{\sqrt{2}^{\sqrt{2}}} $
$latex = \sqrt{2}\log\sqrt{2}^{\sqrt{2}}$
$latex = \sqrt{2}\sqrt{2}\log\sqrt{2} $
$latex = 2\log\sqrt{2} $
$latex = \log (\sqrt{2})^2 $
$latex = \log 2$

2. Inverse of log (bijective):
$latex \log \sqrt{2}^{\sqrt{2}^{\sqrt{2}}}= \log 2$
$latex \sqrt{2}^{\sqrt{2}^{\sqrt{2}}}= 2$

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