Quote: While NUS and NTU Medicine does not (officially) require H2 Maths (ie. ‘A’ level Maths), some other (overseas) Medical schools might. And not having H2 Maths might (unofficially) disadvantage your chances, even for NUS and NTU.
Therefore (assuming you intend to fight all the way for your ambition), your safest bet would be to (fight for the opportunity) to take both H2 Bio and H2 Math. The ideal Singapore JC subject combination for applying to Medicine (in any University) is :
Despite being in the Gifted Education Programme (GEP), Mr Wu is just an ordinary Singaporean. His secret to academic success is hard work and the Maths Techniques he has discovered by himself while navigating through the education system.
He would like to teach these techniques to students, hence choosing to become a full-time Mathematics tutor. Mr Wu has developed his own methods to check the answer, remember formulas (with understanding), which has helped a lot of students. Many Math questions can be checked easily, leading to the student being 100% confident of his or her answer even before the teacher marks his answer, and reducing the rates of careless mistakes.
Mr Wu’s friendly and humble nature makes him well-liked by students. Many of his students actually request for tuition by themselves! (not the parents) His students also look forward to tuition, instead of dreading tuition.
O Level E Maths and A Maths Tuition starting next year at Bishan, the best location in Central Singapore.
Timings are Monday 7-9pm, Thursday 7-9pm. Perfect for students who have CCA in the afternoon, or students who want to keep their weekends free.
Register with us now by email (mathtuition88@gmail.com). Vacancies will be allocated on a first-come-first-serve basis.
Singapore math (or Singapore maths in British English[1]) is a teaching method based on the national math curriculum used for kindergarten through sixth grade in Singapore.[2][3] It involves teaching students to learn and master fewer mathematical concepts at greater detail as well as having them learn these concepts using a three-step learning process.[2][3] The three steps are concrete, pictorial, and abstract. In the concrete step, students engage in hands-on learning experiences using concrete objects such as chips, dice, or paper clips.[4] This is followed by drawing pictorial representations of mathematical concepts. Students then solve mathematical problems in an abstract way by using numbers and symbols.[5]
The development of Singapore math began in the 1980s when the country’s Ministry of Education developed its own mathematics textbooks that focused on problem solving and heuristic model drawing.[3][6] Outside Singapore, these textbooks were adopted by several schools in the the United States (U.S.) and in other countries such as Canada, Israel, and the United Kingdom.[7][1][8] Early adopters of these textbooks in the U.S. included parents interested in homeschooling as well as a limited number of schools.[3] These textbooks became more popular since the release of scores from the Trends in International Mathematics and Science Study (TIMSS), which showed Singapore at the top of the world three times in fourth and eighth grade mathematics.[9] U.S. editions of these textbooks have since been adopted by a large number of school districts as well as charter and private schools.[3]
Madanlal Baldevraj Ghai during the city leg of his tour. Picture by Sayantan Ghosh
An army major who quit to become a mathematics teacher has embarked on a self-funded tour of the country to promote the subject.
Madanlal Baldevraj Ghai, 70, stayed in a dormitory at Howrah station to keep costs down during the three days he spent in Calcutta recently, meeting officials of the primary and secondary board and the school education department to offer suggestions on how to make the study of mathematics more interesting.
“India has produced brilliant mathematicians not just in the Vedic and medieval ages but also in modern times. Unfortunately, for quite a few years, not many students have been pursuing the subject at the higher level, which has resulted in a decline in the number of top-quality mathematicians,” the former teacher at PMN College in Rajpura, Punjab, told Metro.
“We, the elderly mathematics teachers, need to reach out to students and guardians in every corner of the country to dispel the misconception that mathematics is dry and boring,” added Ghai, who has an MPhil in the subject and is pursuing his PhD at Punjabi University, Patiala.
His 50-day tour was also prompted by the Prime Minister declaring 2012 as the year of mathematics as a tribute to Srinivasa Ramanujan, the autodidact mathematician who died in 1920 at the age of 32.
Many of the world’s most mathematically gifted teenagers come from countries with the most lucrative tutoring industries.
Figures released this week show tutoring in Asia’s powerhouses is widespread, with participation rates more than double those in Australia, though the extent to which their success is a result of a punishing study schedule is unclear.
Studying and practising Mathematics is one of the most useful things an O level student can do.
Not only are the two Maths (E Maths and A Maths) highly intertwined, studying Maths can actually help the students’ Physics too. There are some topics like Vectors and Kinematics in Physics that are also present in Mathematics.
Math is at the heart of physics. So the better your math, the better you’ll do in physics.
A good working knowledge of algebra and trigonometry is needed for Physics.
Mnemosyne with a mathematical formula. (Photo credit: Wikipedia)
TheMathist is a very unique social math note taking application. It works on every device, and is free for everyone. You can finally focus on the math, not the software.
Do I have to know TeX or similar syntax?
There is no need to learn TeX or save the notes as pictures, they will always be available to you as regular online documents that you can edit anywhere and anytime. We have built a revolutionary simple math editor, a lot of hours went research on this. Go ahead and give it a try!
Why should I use The Mathist?
Because it is simple and straightforward to use, a true breeze… Because you already take all your notes in digital form and save them in the cloud. Because it is fast and works on all devices. It does not require any software knowledge to start, and…
Studying Mathematics is totally different from studying Humanities, this is the reason why humanities students often don’t do well in maths. But with the right studying techniques (i.e. practising doing mathematics), humanities students can be very good at maths. Together with their creativity and good memory, humanities students have the potential to achieve the top grades in maths exams.
I have taught Pure Literature students and found that they definitely have the potential to do well in Maths once they learn the correct method of mathematical studying and thinking, and how to approach solving Maths questions.
Even if you understand every word in lecture and in the textbook, the only way to really learn mathematics is by doing mathematics. Sometimes this means doing even more than the assigned problems. (See “time committment” above.) This is how to avoid the common pitfall of “understanding everything in class but blanking out on the exams.”
I realize this isn’t welcome advice, and I admit that I haven’t always followed it myself. But in years of teaching (and 20+ years of learning) mathematics I haven’t found any shortcut.
After many days of discovering my HUGE learning curve with Minecraft, I am finally starting to feel relatively comfortable in Creative mode…I can build a house without flooding it, planted a few trees and I no longer have random blocks floating in the sky around my world! My class has been staying with me during recess to teach me how to play and I am amazed at how fast and detail-oriented they are in their designs, such as putting lava rocks under the water blocks to form a hot tub and putting glass windows in their new greenhouses. I just kept thinking that I would love for them to use this same precision and perseverance in math class.
I must have Minecraft on the brain, because I as I was planning this weekend for the upcoming week (multiplying fractions w/arrays), all of the scenarios were about planting on an acre…
Shanghai teens top international education ranking, OECD says
By Sophie Brown, CNN
December 3, 2013 — Updated 2051 GMT (0451 HKT)
(CNN) — When it comes to mathematics, reading and science, young people in Shanghai are the best in the world, according to a global education survey released Tuesday.
In all three subjects, Shanghai students demonstrated knowledge and skills equivalent to at least one additional year of schooling than their peers in countries like the United States, Germany and the United Kingdom.
In math, Shanghai had the highest score with 613 points — the equivalent of nearly three years of schooling above the average for the 34 OECDmember countries of 494, and six years above Peru which ranked last with a score of 368. The city also came top in 2009 rankings.
Singapore came second in mathematics with a score of 573, followed by Hong Kong, Taiwan, South Korea, and Macau.
U.S. lags
The United States ranked 36th, performing below the OECD average in mathematicswith 481 points, and a score indistinguishable from the average for reading and science.
Part of the reason pupils do so well in Shanghai, according to the OECD’s deputy director of education, Andreas Schleicher, is that they have the drive and confidence to fulfill their potential.
“In China and Shanghai, you have nine out of ten students telling you, ‘It depends on me. If I invest the effort, my teachers are going to help me to be successful’,” Schleicher told CNN’s On China program, which will air later this month.
I’m sure many secondary school/Junior College students have know some China scholars in your schools scoring results that are seemingly impossible to reach (90+ for H2 Maths etc.) But when asked what’s their secret to scoring so well, they said they just study & memorize the same way any other student would do before exams.
I heard from my seniors that China scholars usually study till 2 am every night, but I don’t buy into that. I think they’re just exaggerated rumors to explain their excellent grades. Some of my friends say that China’s education gave them really solid foundation, such that they can grasp concepts much faster than the rest.
Synopsis: Some have seen philosophy embedded in episodes of The Simpsons; others have detected elements of psychology and religion. Simon Singh, bestselling author of Fermat’s Last Theorem, The Code Book and The Big Bang, instead makes the compelling case that what The Simpsons’ writers are most passionate about is mathematics. He reveals how the writers have drip-fed morsels of number theory into the series over the last twenty-five years; indeed, there are so many mathematical references in The Simpsons, and in its sister program, Futurama, that they could form the basis of an entire university course. Using specific episodes as jumping off points – from ‘Bart the Genius’ to ‘Treehouse of Horror VI’ – Simon Singh brings to life the most intriguing and meaningful mathematical concepts, ranging from pi and the paradox of infinity to the origins of numbers and the most profound outstanding problems that haunt…
Minister for Education Heng Swee Keat has said parents should consider other factors apart from a school’s previous year cut-off point (COP) when helping their P6 children decide on which secondary school to choose.
Minister for Education Heng Swee Keat (Photo: MOE)
SINGAPORE: Minister for Education Heng Swee Keat has said parents should consider other factors apart from a school’s previous year cut-off point (COP) when helping their P6 children decide on which secondary school to choose.
Writing on his Facebook page, Mr Heng said it would be good for parents to have an open talk with their children to know what type of secondary school they are interested in.
…
Mr Heng, however, noted that how well a child does in school depends on how motivated he is.
So he encourages parents to carefully consider the kind of environment that will best motivate their children, and enable them to develop themselves fully in the next four to five years.
Some children, he said, are late developers and the right environment helps them thrive.
Mr Heng urged parents to think of how best they can help their children develop confidence and enjoy the space to discover his talents and passions.
Mr Wu’s O Level Certificate (with A1 for both Maths). Mr Wu sincerely wishes his students to surpass him and achieve their fullest potential.
Despite being in the Gifted Education Programme (GEP), Mr Wu is just an ordinary Singaporean. His secret to academic success is hard work and the Maths Techniques he has discovered by himself while navigating through the education system.
Directions to Bishan Tuition Centre:
A) Via BISHAN MRT (NS17/CC15)
(10 minutes by foot OR 2 bus stops from Junction 8. From J8, please take bus numbers, 52, 54 or 410 from interchange. The centre is just after Catholic High School, just beside Clover By-The-Park condominium.
Other landmarks are: the bus stop which students alight is in front of Blk 283, where Cheers minimart and Prime supermarket are.)
It’s one street away from Raffles Institution Junior College (RIJC), previously known as Raffles Junior College (RJC). It’s also very convenient for students of Catholic Junior College (CJC), Anderson Junior College (AJC), Yishun Junior College (YJC) and Innova Junior College (IJC).
Other secondary schools located near Bishan are Catholic High School, Kuo Chuan Presbyterian Secondary School, and Raffles Institution (Secondary). Schedule •Monday 7pm-9pm •Thursday 7pm-9pm
(Perfect for students who have CCA in the afternoon, or students who want to keep their weekends free.)
Math Olympiad Books are useful for GEP/DSA preparation. It is also useful for the latest type of test called Domain Tests, which is basically a subject test (Math included) for entry into top secondary schools like the Raffles / Hwa Chong family. There are different subject domains (depending on the school), ranging from General domain / Academic domain / CCA domain. A First Step to Mathematical Olympiad Problems (Mathematical Olympiad Series)
The first book is written by Professor Derek Holton. Prof Holton writes a nice column for a Math magazine, which gives out books as prizes to correct solutions.
GEP Math Olympiad Books
If you are searching for GEP Math Olympiad Books to prepare for the GEP Selection Test, you may search for Math Olympiad Books for Elementary School. Note that Math Olympiad Books for IMO (International Mathematics Olympiad) are too difficult even for a gifted 9 year old kid!
Math, Science, Reading Scores Show U.S. Schools Slipping Behind
Posted: December 10, 2010 PRINTER FRIENDLY VERSION: PDF
The United States received a stark wake-up call this week with the release of international test results showing students in other countries are surpassing American students when it comes to math, science and reading. China and Australia outperformed the U.S. in each of the three subject areas tested.
The results of a major international education assessment show that American students are lagging behind many other countries in crucial skills like reading, math and science.
“The United States came in 23rd or 24th in most subjects. We can quibble, or we can face the brutal truth that we’re being out-educated,” said U.S. Education Secretary Arne Duncan.
Test compares U.S. to other countries
The PISA tests how advanced students are in science, math and reading compared to their peers around the world.
The test, known as the Program for International Student Assessment (PISA), directly assesses how prepared teenagers are in math, science and reading compared to their peers in other countries.
The test is translated into each country’s language, and officials from the participating countries are able to review questions before students take the exam to make sure each test is fair and unbiased.
In the U.S., the participating schools and students are randomly selected. On average, about 4,500 students are tested in each of the participating countries.
China and Finland lead the way
Chinese and Finnish students scored highest on the PISA test.
Each PISA subject area is scored on a scale where 500 points is the average. The results announced this week show many countries outperforming the U.S. Here’s a sample:
Math: China 600, Germany 513, United States 487 (31st place)
Reading: China 556, Korea 539, United States 500 (17th place)
Science: China 575, Finland 554, United States 502 (23rd place)
The results of a major international education assessment show that American students are lagging behind many other countries in crucial skills like reading, math and science.
Patient and Dedicated Maths Tutor available for Maths Tuition (NUS Maths Major 1st Class Honours, Dean’s List, RI Alumni)
Past students have gone from fail to top in class! Mr Wu is a good mentor, and elder brother to two medical students (one studying in Monash University, Australia, another studying in NUS)
Despite being in the Gifted Education Programme (GEP), Mr Wu is just an ordinary Singaporean. His secret to academic success is hard work and the Maths Techniques he has discovered by himself while navigating through the education system.
He would like to teach these techniques to students, hence choosing to become a full-time Mathematics tutor. Mr Wu has developed his own methods to check the answer, remember formulas (with understanding), which has helped a lot of students. Many Math questions can be checked easily, leading to the student being 100% confident of his or her answer even before the teacher marks his answer, and reducing the rates of careless mistakes.
Mr Wu’s friendly and humble nature makes him well-liked by students. Many of his students actually request for tuition by themselves! (not the parents) His students also look forward to tuition, instead of dreading tuition.
O Level E Maths and A Maths Tuition starting next year at Bishan, the best location in Central Singapore.
Timings are Monday 7-9pm, Thursday 7-9pm. Perfect for students who have CCA in the afternoon, or students who want to keep their weekends free.
Register with us now by email (mathtuition88@gmail.com). Vacancies will be allocated on a first-come-first-serve basis.
Mr Wu’s O Level Certificate (with A1 for both Maths). Mr Wu sincerely wishes his students to surpass him and achieve their fullest potential.
Despite being in the Gifted Education Programme (GEP), Mr Wu is just an ordinary Singaporean. His secret to academic success is hard work and the Maths Techniques he has discovered by himself while navigating through the education system.
Directions to Bishan Tuition Centre:
A) Via BISHAN MRT (NS17/CC15)
(10 minutes by foot OR 2 bus stops from Junction 8. From J8, please take bus numbers, 52, 54 or 410 from interchange. The centre is just after Catholic High School, just beside Clover By-The-Park condominium.
Other landmarks are: the bus stop which students alight is in front of Blk 283, where Cheers minimart and Prime supermarket are.)
It’s one street away from Raffles Institution Junior College (RIJC), previously known as Raffles Junior College (RJC). It’s also very convenient for students of Catholic Junior College (CJC), Anderson Junior College (AJC), Yishun Junior College (YJC) and Innova Junior College (IJC).
Other secondary schools located near Bishan are Catholic High School, Kuo Chuan Presbyterian Secondary School, and Raffles Institution (Secondary).
Asia-Pacific higher education is becoming a global force, but only some nations in the region have achieved or approached parity with Western Europe and North America.
The truly spectacular success story is from the Confucian zone in East Asia. Japan achieved high participation rates and research-intensive universities in the 1970s: now Hong Kong, Singapore, South Korea, Taiwan and China are following suit. Student numbers and research are growing by leaps and bounds.
…
East Asia embodies a new Confucian model of higher education. The key is the willingness of families to invest in schooling, tertiary education and extra tuition. Households are driving the growth in participation. Private investment is secured less by neoliberal ideology than an older Confucian respect for self-formation via education, within a social hierarchy “harmonised” by fierce competition for university entry.
…
China and Singapore maintain higher public funding. But the jury is still out on the extent to which these systems can foster a spirit of openness, criticism and free-wheeling creativity.
O Level Group Tuition Flyer
O Level E Maths & A Maths
Tuition at Bishan
碧山数学补习
Location: Block 230 Bishan Street 23 #B1-35 S(570230)
Schedule:
• Monday 7pm-9pm (E Maths)
• Thursday 7pm-9pm (A Maths)
Website: https://mathtuition88.com/group-tuition/
Tutor: Mr Wu
(from RI GEP, NUS Maths 1st Class Honours, Dean’s List)
Class size is limited to 8 students only! (Small Group Tuition)
Even as an MIT student, you can’t study all the time. In fact, we learn better by switching gears frequently. Here are some tips for breaking up your study time effectively.
Approach the same material in several different ways. This increases learning by using different brain pathways. Read a textbook section, aloud if possible, then review your lecture notes on the same concept. Write a one-sentence summary of a chapter or a set of questions to test your understanding. Then move on to the next textbook section.
Study in blocks of time. Generally, studying in one-hour blocks is most effective (50 minutes of study with a ten-minute break). Shorter periods can be fine for studying notes and memorizing materials, but longer periods are needed for problem-solving tasks, psets, and writing papers.
Break down large projects (papers, psets, research) into smaller tasks. The Assignment Timeline can help with this. Check off each task on your to-do list as you finish it, then take a well-earned break.
Plan regular breaks. When building a schedule for the term, srategically add several regular breaks between classes and in the evenings. Take 20-30 minutes; never work through these scheduled breaks. Our minds need an occasional rest in order to stay alert and productive, and you can look forward to a reward as you study. If your living group has a 10 pm study break, or you have a circle of friends that likes to go out for ice cream together at 7 on Wednesdays, put that on your schedule. These small, brief gatherings will become more welcome as the term intensifies.
Get up and move.Research shows that sitting for more than three hours a day can shorten your life by up to two years. At least every hour, stand up, stretch, do some yoga or jumping jacks, or take a walk, and breathe deeply.
Schedule meals to relax and unwind with friends; don’t just inhale food while tooling.
Turn off your phone while studying and on when you take a break. You may think you are multitasking when you text someone while reading or doing problems, but often the reverse is true. An assignment done while texting or following tweets will likely take two or three times longer and not turn out as well.
If you tend to lose track of time while using your phone or computer, schedule fixed times for Facebook and other fun things, and set an alarm to remind you of the end of that period.
Quote: “Math, art, English, science, history, sports, music, plumbing, dancing in the rain all have one thing in common: to do it well you need to practice, practice, practice.”
Math, art, English, science, history, sports, music, plumbing, dancing in the rain all have one thing in common: to do it well you need to practice, practice, practice.
Most people think that ‘cramming’ and ‘nap osmosis’ are the best ways to study. Just cause you sit at Starbucks or the library or go to tutoring for x hours a day does not equal success. Here are some tips:
Here is a website from MIT’s Center for Excellence on how best to study: http://web.mit.edu/uaap/learning/study/breaks.html. MIT, they know what they are talking about. If you don’t know, MIT is one of the top universities on Earth- perhaps even in the universe…
“How many of our leaders and top officers who say that every school is a good school put their children in ordinary schools near their home? (Only) until they actually do so are parents going to buy (it).”
During the first panel discussion, which was attended by about 200 participants, several educators expressed hope that parents would recognise the efforts of all schools to bring out the best in students.
The neighbourhood school’s vice principal’s startling remark drew applause from those who attended the event.
A 37-year-old mother, who has a primary-school-going child and another child attending pre-school, who did not want to be named, told Yahoo Singapore she agrees with the vice-principal’s comments.
“Look at the ministers, most of them are from good schools, like SJI and Hwa Chong,” she said.
Mr Wu’s O Level Certificate (with A1 for both Maths). Mr Wu sincerely wishes his students to surpass him and achieve their fullest potential.
Despite being in the Gifted Education Programme (GEP), Mr Wu is just an ordinary Singaporean. His secret to academic success is hard work and the Maths Techniques he has discovered by himself while navigating through the education system.
Directions to Bishan Tuition Centre:
A) Via BISHAN MRT (NS17/CC15)
(10 minutes by foot OR 2 bus stops from Junction 8. From J8, please take bus numbers, 52, 54 or 410 from interchange. The centre is just after Catholic High School, just beside Clover By-The-Park condominium.
Other landmarks are: the bus stop which students alight is in front of Blk 283, where Cheers minimart and Prime supermarket are.)
It’s one street away from Raffles Institution Junior College (RIJC), previously known as Raffles Junior College (RJC). It’s also very convenient for students of Catholic Junior College (CJC), Anderson Junior College (AJC), Yishun Junior College (YJC) and Innova Junior College (IJC).
Other secondary schools located near Bishan are Catholic High School, Kuo Chuan Presbyterian Secondary School, and Raffles Institution (Secondary).
This book is the best introductory book on Topology, an upper undergraduate/graduate course taken in university. I have written a short book review on it.
Excerpt:
Book Review: Topology
Book’s Author: James R. Munkres
Title: Topology
Prentice Hall, Second Edition, 2000
It is often said that one must not judge a book by its cover. The book with a plain cover, simply titled “Topology”, is truly a rare gem and in a class of its own among Topology books.
One striking aspect of the book is that it is almost entirely self-contained. As stated in the preface, there are no formal subject matter prerequisites for studying most of the book. The author begins with a chapter on Set Theory and Logic which covers necessary concepts like DeMorgan’s laws, Countable and Uncountable Sets, and the Axiom of Choice.
The first part of the book is on General Topology. The second part of the book is on Algebraic Topology. The book covers Topological Spaces and Continuous Functions, Connectedness and Compactness, and Separation Axioms. Some other material in the book include the Tychonoff Theorem, Metrization Theorems and Paracompactness, Complete Metric Spaces and Function Spaces, and Baire Spaces and Dimension Theory.
The book defines connectedness as follows: The space is said to be connected if there does not exist a separation of . (A separation of is defined to be a pair , of disjoint nonempty open subsets of whose union is .) Other sources may define connectedness by, is connected if continuous .
Also, the proof of Urysohn’s Lemma in the book was presented slightly differently from other books as they did not use dyadic rationals to index the family of open sets. Rather, the book lets be the set of all rational numbers in the interval , and since is countable, one can use induction to define the open sets . In hindsight, the dyadic rationals approach in other sources may be more explicit and clearer.
An interesting new concept mentioned in the book is that of locally connectedness (not to be confused with locally path connectedness). A space is said to be locally connected at if for every neighborhood of , there is a connected neighborhood of contained in . If is locally connected at each of its points, it is said simply to be locally connected. For example, the subspace of is not connected, but it is locally connected. The topologists’ sine curve is connected but not locally connected.
In general, the content of the book is comprehensive. The other book, “Essential Topology”, did not cover some topics like the Urysohn Lemma, regular spaces and normal spaces.
Approach
The author’s approach is generally to give a short motivation of the concept, followed by definitions and then theorems and proofs. Examples are interspersed in between the text. The motivation tends to be a little bit too short though. For instance, in other books there is some motivation of how balls can determine the metric in a metric space, leading to the concepts of “candidate balls” . This useful concept is not found in the book Topology, nor the other book Essential Topology.
One interesting explanation of the terminology “finer” and “coarser” is found in the book. The idea is that a topological space is like “a truckload full of gravel”‘ — the pebbles and all unions of collections of pebbles being the open sets. If now we smash the pebbles into smaller ones, the collection of open sets has been enlarged, and the topology, like the gravel, is said to have been made finer by the operation.
Another point to note is that the book does not use Category Theory. Personally, I would prefer the Category approach, since it can make proofs neater, and it provides additional insight to the nature of the theorem. We also note that the other book “Essential Topology”, also does not explicitly use Category Theory. But upon closer examination, the book has expressed commutative diagrams in words, which is not as clear as in diagram form.
Organization
The organization of the book is similar to most other books, except that it covers Connectedness and Compactness before the Separation Axioms. The concept of Hausdorff spaces, however, is covered way earlier, immediately after the discussion of closure and interior of a set. This enables theorems like “Every compact subspace of a Hausdorff space is closed” to be proved in the Compactness chapter.
Style
The author’s style is to combine rigor in proofs and definitions, with intuitive ideas in the examples and commentary. This makes it both a good textbook to learn from, and a good reference for proofs too.
This informal style in the commentary makes for a especially good read. For instance, a mathematical riddle is mentioned: “How is a set different from a door?” (For interested readers, the answer can be found on page 93.)
Also, there are many figures in the book, 84 sets of figures to be precise. This is rather good for a math book, and I would recommend the book to visual learners.
However, to learn Topology from this book alone may be difficult. Even though there are exercises to practice, there are no solutions and very few hints. Also, the book uses the terminology “limit point”, which can be confusing.
The book has surprisingly few typographical errors. While reading through the book, I only spotted a trivial one on page 107, where a function written as “” should be “” instead. Upon consulting an errata list, there was only one page of errors.
Conclusion
In conclusion, despite some shortcomings of the book, Topology is a great book, and if there was one Topology book that I could bring to a desert island, it would be this one.
Recently, I read this article in The Atlantic about the myth of being innately “bad at math,” and how performing well in math is generally a result of hard work, not innate skill. By all accounts, I should have known this, but it only took that one semester to break down years of confidence in my aptitude. In the article, the author notes several patterns we see that reinforce this myth. The one that resonated most with me was as follows:
“The well-prepared kids, not realizing that the B students were simply unprepared, assume that they are ‘math people,’ and work hard in the future, cementing their advantage.”
And the B students (or in my case D student), well, they assume it’s about skill level and from that point forward it’s a self-fulfilling prophecy.
My mentor convinced me to apply to business school, and when he asked why I wouldn’t apply to Wharton, I said, “too quantitative.” I was scared. But he convinced me to apply, and after a crash course in Calculus, I learned that if I worked hard enough, indeed I could have success… even when my classmates were so-called quant jocks.
For me, it worked out, but for millions of kids in our education system, the ending isn’t so happy. Instead, parents determine at a very young age that a child has or does not have math skills. And, I would argue, they — we — do the same with reading. We decide that it’s one or the other, left or right brain. Instead, we can acknowledge our kids’ struggles with a particular subject, while continuing to encourage and remind them that a consistent effort can make a tremendous difference, but it takes perseverance.
What do I wish my teacher had done? I wish he had told me that I could do everything my classmates were doing, but I lacked the preparation beforeI ever stepped foot in his classroom. If only he had instilled that confidence in me, that simple knowing that I could do better, who knows what else I might have tackled coming out of high school.
Here are some useful study tips for Mathematics. The key to acing Maths is to understand that practice is key for Mathematics!
Sincerely hope these tips help.
Please do not study Maths like studying History, Literature or Geography, the study method for Maths is totally different and opposite from studying Humanities. Reading a Maths textbook without practicing is not very helpful at all.
Once a student understands the basic theory of a certain topic (usually just one or two pages of information), he or she can move on to practicing actual questions immediately. While practicing, the student will then learn more and more knowledge and question-answering strategies for that Maths topic.
Even if you already know how to do a question, it is useful to practice it to improve on speed and accuracy.
The study strategy for Maths and Physicsare kind of similar, hence usually you will find that students who are good in Maths will also be good in Physics, and vice versa.
Students from China usually do very well in Maths exams because they understand the strategy for studying Maths (which works very well up till JC level), namely a lot of practice with understanding. The strategy is called “题海战术” in Chinese, which means “immersing oneself in a sea of questions”.
Source for diagram below: Email from JobsCentral BrightMinds
For high school math, inborn talent is much less important than hard work, preparation and self-confidence.
How do we know this? First of all, both of us have taught math for many years — as professors, teaching assistants and private tutors. Again and again, we have seen the following pattern repeat itself:
Different kids with different levels of preparation come into a math class. Some of these kids have parents who have drilled them on math from a young age, while others never had that kind of parental input.
On the first few tests, the well-prepared kids get perfect scores, while the unprepared kids get only what they could figure out by winging it — maybe 80 or 85 percent, a solid B.
The unprepared kids, not realizing that the top scorers were well-prepared, assume that genetic ability was what determined the performance differences. Deciding that they “just aren’t math people,” they don’t try hard in future classes and fall further behind.
The well-prepared kids, not realizing that the B students were simply unprepared, assume that they are “math people,” and work hard in the future, cementing their advantage.
Thus, people’s belief that math ability can’t change becomes a self-fulfilling prophecy.
…
So why do we focus on math? For one thing, math skills are increasingly important for getting good jobs these days— so believing you can’t learn math is especially self-destructive. But we also believe that math is the area where America’s “fallacy of inborn ability” is the most entrenched. Math is the great mental bogeyman of an unconfident America. If we can convince you that anyone can learn math, it should be a short step to convincing you that you can learn just about anything, if you work hard enough.
Is America more susceptible than other nations to the dangerous idea of genetic math ability? Here our evidence is only anecdotal, but we suspect that this is the case. While American fourth- and eighth-graders score quite well in international math comparisons — beating countries like Germany, the U.K. and Sweden — our high-schoolers underperform those countries by a wide margin. This suggests that Americans’ native ability is just as good as anyone’s, but that we fail to capitalize on that ability through hard work.
In response to the lackluster high school math performance, some influential voices in American education policy have suggested simply teaching less math — for example, Andrew Hacker has called for algebra to no longer be a requirement. The subtext, of course, is that large numbers of American kids are simply not born with the ability to solve for x.
We believe that this approach is disastrous and wrong. First of all, it leaves many Americans ill-prepared to compete in a global marketplace with hardworking foreigners. But even more important, it may contribute to inequality. A great deal of research has shown that technical skills in areas like software are increasingly making the difference between America’s upper middle class and its working class. While we don’t think education is a cure-all for inequality, we definitely believe that in an increasingly automated workplace, Americans who give up on math are selling themselves short.
Too many Americans go through life terrified of equations and mathematical symbols. What many of them are afraid of is “proving” themselves to be genetically inferior by failing to instantly comprehend the equations (when, of course, in reality, even a math professor would have to read closely). So they recoil from anything that looks like math, protesting: “I’m not a math person.” And so they exclude themselves from quite a few lucrative career opportunities. This has to stop.
The secret to being good at Maths (or any other subject) is to like it and enjoy it. This would make working hard and practicing Maths easier and more efficient. 2 hours can easily fly past while doing Maths if one is interested in it.
Most people think of mathematicians as solitary, working away in isolation. And, it’s true, many of them do. But Paul Erdos never followed the usual path. At the age of four, he could ask you when you were born and then calculate the number of seconds you had been alive in his head. But he didn’t learn to butter his own bread until he turned twenty. Instead, he traveled around the world, from one mathematician to the next, collaborating on an astonishing number of publications. With a simple, lyrical text and richly layered illustrations, this is a beautiful introduction to the world of math and a fascinating look at the unique character traits that made “Uncle Paul” a great man.
‘Above all, it is a cultural thing.” Professor Lianghuo Fan is reflecting on the differences he has noticed between maths education in China and Singapore, where he lived and taught for 40 years, and in Britain, where he is now based. “In China, all parents know that maths is the number one subject in schools, and they expect that in a modern society everyone must be comfortable with maths, even if that means they have to work hard at it.“That attitude is passed on to their children. But here in Britain, you can feel students’ attitude about mathematics is different. They feel all right if they say they don’t like mathematics.”
Professor Fan is not alone in highlighting this national phobia of ours about maths. The government has this week shown itself determined to tackle the problem head on with the unveiling of a new “back-to-basics” primary school maths curriculum, with a renewed emphasis on times-tables, mental arithmetic, fractions and rote learning.
Most people over 40 will see the proposals as a return to the classroom practice of their childhood – but in its introductory remarks the Department for Education claimed inspiration from Asian model that Professor Fan knows so well: “I never heard a child in China or Singapore say that they don’t like maths’,” he stresses, “without a sense of embarrassment.”
We are sitting in a café near Southampton University – where 50-year-old Professor Fan has been head of the Mathematics and Science Education Research Centre since 2010 – as we try to decide if anything lies behind the popular stereotype that Asian children are “naturally” better at maths than those in the West. It is, for example, in the core storyline of Safe, the recent Hollywood blockbuster, starring Jason Statham. An 11-year-old girl, Mei (played by Chinese-born actress Catherine Chan), is a maths prodigy who can decode number sequences at a glance – and therefore has to be protected from the baddies.
Additional Mathematics is kind of important, if your child is intending to pursue any studies related to Mathematics in university. Business, Accounting, Economics, and of course Engineering and Physics are examples of courses requiring some Mathematics.
AIMS
The syllabus is intended to prepare students adequately for A Level H2 Mathematics and
H3 Mathematics, where a strong foundation in algebraic manipulation skills and mathematical reasoning skills are required.
The O Level Additional Mathematics syllabus assumes knowledge of O Level Mathematics.
The general aims of the mathematics syllabuses are to enable students to:
• acquire the necessary mathematical concepts and skills for continuous learning in mathematics and related disciplines, and for applications to the real world
• develop the necessary process skills for the acquisition and application of mathematical concepts and skills
• develop the mathematical thinking and problem solving skills and apply these skills to formulate and solve problems
• recognise and use connections among mathematical ideas, and between mathematics and other disciplines
• develop positive attitudes towards mathematics
• make effective use of a variety of mathematical tools (including information and
communication technology tools) in the learning and application of mathematics
• produce imaginative and creative work arising from mathematical ideas
• develop the abilities to reason logically, to communicate mathematically, and to learn cooperatively and independently
Hi, I am an ex-GEP student, who wish to share some tips about what books to read to prepare for GEP, or even for kids who are already in GEP. I strongly believe that IQ is not static, i.e. it is possible to increase IQ (to a certain extent of course) by reading books. (The Einstein Factor: A Proven New Method for Increasing Your Intelligence contains research that shows that IQ can be increased.)
The GEP test has 3 main sections: Logic, Math, English. This article will introduce books suitable for preparing for these 3 main sections.
Kids nowadays love electronic devices. However iPhone / iPad have too many games and thus are not ideal for educational purposes. The ideal electronic device is Amazon Kindle Ebook reader. Read more with Amazon!
WWW.QOO10.SG
I used to read a book by Mensa when I was a kid (just for interest, not for preparing for any tests), and found it to be interesting and challenging. The exact book is probably out of print already, but here are some bestsellers by Mensa on Amazon. Hope the recommendations are helpful! This list is not exhaustive, you may purchase other books you find on Amazon, they are equally likely to be as helpful.
GEP Logic Books
(Click on the image links to go to the Amazon.com page for more details)
These books are really helpful for the “Logic” part of the GEP selection test, which is not taught anywhere in the MOE syllabus and hence one of the most challenging to prepare for.
GEP Logic Sample Question
The above Logic Books are highly recommended by Amazon (4/5 stars and above)!
The following Puzzle Adventure books are also very useful for developing logical thinking and also English. Not to mention they are really fun to read for children. I have personally read the “2nd Puzzle Adventure Omnibus” book many times and enjoyed it very much. These kinds of books train both Logic and English skills.
Another good choice of books are encyclopedias. Although Encyclopedias like Britannica are almost extinct thanks to the internet, it is good to have a children’s Encyclopedia like The New Children’s Encyclopedia to have an all-round knowledge of the world and science.
Finally, you can check out the list of Recommended Math Books, which contains books useful for Math students.
Tips on How to Get Into GEP:
Based on my experience as a student, getting into GEP requires knowing and possessing skills more advanced than the age group. I.e., at the age of 9 (Primary 3), the student who gets into GEP is probably already at the level of Primary 4 and above in terms of Math and English. True genius is neither necessary nor sufficient to get into GEP, and it is not true that GEP students are smarter than others. There is a famous IMO World Number 1 in Singapore who wasn’t from the GEP. IMO (International Math Olympiad) is definitely harder than GEP Math. One can read this book 104 Number Theory Problems: From the Training of the USA IMO Team to get an idea of the IMO (International Math Olympiad).
To be honest, it is probably currently harder to get into GEP now than in the past (1990s). During my time, a Primary 6 student who knows the Gauss trick for adding a sum of an arithmetic progression (1+2+3+…+99+100) is really at the top of his/her cohort. During the 2000 PSLE, this question came out and few people could solve it. Nowadays (2015), an average Primary 3 student would know and be familiar with this technique. Hence the bar is set much higher nowadays. Math Olympiad is the way to go to get one’s Math skills honed at the highest level.
Singapore (and Asian in general) students are very academically smart. Even the average Singapore student is likely to be 2 to 3 years ahead of their American/UK/Australian counterparts in terms of Math and Science. And to get in the GEP, it is common sense that one has to perform better than the average Singapore student in the GEP selection test at least. Hence, it is not an easy task. However, one weakness of Singaporean students is that they are not a big fan of reading, to the extent that even Borders bookstore (and others) can close down in Singapore. Hence, if your child even read a few extra books you have an advantage over the rest. Check out this book by Moshe Kai Cavelin, a truly gifted kid who entered college at 8.
Ideally, only students who are genuinely interested in learning should be prepped for GEP. As the Chinese proverb 拔苗助长 tells us, there is no point pushing a child artificially beyond what he/she wishes to learn. But for those children who have curiosity to learn, books like Match Wits With Mensa: The Complete Quiz Book will be a good brainteaser for them. If one is looking for books to help prepare for GEP, the average assessment books sold in bookstores would not be of much help since they are catered to the mass market, not gifted children.
Amazon actually has a long list of books for gifted children and their parents: Books for Gifted Children. Gifted children are like raw unpolished diamonds. As the Chinese proverb 玉不琢，不成器 goes, even jade needs to be polished and cut before it can become a piece of jewellery, hence even gifted children need guidance to unlock their full potential. There is no single book that after reading it can get into the GEP. The GEP tests for a wide range of knowledge in the Math and English subjects and hence students need to read widely to acquire a broad spectrum of knowledge.
The above 3 GEP English Literature books are fun to read, and contain a lot of useful and advanced vocabulary and idioms. It is a good idea to read these books to get a hang of what GEP English is about (very different from normal mainstream English). One important technique to improve English by reading is to highlight any new words, and then record it in a notebook, followed by copying down the dictionary definition. From time to time, revise the notebook to refresh your memory. Soon, as the notebook grows, so will your vocabulary.
Remember to use the above technique of using the dictionary and recording in a notebook; simply skimming and flipping the pages is not likely to improve English! As Singapore follows British English, it is important to get a British English dictionary like Paperback Oxford English Dictionary. Try not to use Webster / Google as those are American English, which can be quite different.
Gifted students have the potential to learn material earlier and faster, to handle more complexity and abstraction, and to solve complex problems better. This potential, however, needs stimulating experiences from home and school or it will not unfold. These books are designed to help teachers provide the stimulating curricula that will nurture this potential in school. The units presented in this series are based on research into how these students actually think differently from their peers and how they use their learning styles and potential not merely to develop intellectual expertise, but to move beyond expertise to the production of new ideas.
The Math book includes units that ask students to develop a financial portfolio that includes high- and low-risk stocks, options and margins, AAA and junk bonds, mutual funds, and money markets; use math, science, engineering, technology, and art to design and build a miniature golf course; develop games based on probability; and run a real-life small business.
Grades 6–8
GEP Psychology Book
Mindset is the key to success. I highly recommend this book Mindset: The New Psychology of Success to students and parents. A psychologist has written this book, and it has many new insights. For instance, praising your child “intelligence and ability doesn’t foster self-esteem and lead to accomplishment, but may actually jeopardize success.” This is new psychological research supported by evidence. The correct way is actually to praise the child’s effort. Find out more tips and stories by reading this book.
Rubik’s Cube (Dayan Zhanchi)
For parents, buying a Rubik’s cube for your child is a great investment. Playing with the Rubik’s cube is a major intellectual challenge (it has 43 quintillion permutations, only 1 of which is correct), which will develop the child’s brain for logical thinking, which is especially useful for Math and Science. Most importantly, it is fun!
Special note for buying Dayan Zhanchi from Singapore:
If you are buying the Dayan Zhanchi from Singapore, at first it seems like the Dayan ZhanChi does not ship to Singapore. It actually does! We just have to choose the correct seller, Cube Puzl, which ships to Singapore.
Even though the GEP Screening/Selection Test does not test science, it is a good idea to get acquainted with science from a young age since the Sciences (Chemistry, Physics, Biology) form the bulk of the Singapore education system from upper primary school onwards till university. For example in Junior College, 3 out of 4 subjects will be sciences, for those in the Science Stream.
SINGAPORE: Education Minister Heng Swee Keat has said that two important shifts must be made in the education system in order to prepare the young for the future.
In a Facebook post on Friday evening, Mr Heng said firstly, the education system must help the young acquire deep skills and integrate theory with practice through applied learning.
Secondly, the system should make it easier for students to continue learning in their areas of strength and interest, and encourage lifelong learning.
Mr Heng said the education system needs to better link the interest and strengths of students to jobs of the future.
He explained that when students develop a deep interest, when their imagination is captured, they can go on to do wonderful things.
Math is logical, functional and just … awesome. Mathemagician Arthur Benjamin explores hidden properties of that weird and wonderful set of numbers, the Fibonacci series. (And reminds you that mathematics can be inspiring, too!)
Look out for this movie on Indian math genius Ramanujan starring Dev Patel from “Slumdog Millionaire”!
Ramanujan was a self-taught maths genius from India who had little to no formal education. Yet he was able to come out with stunning formulas such as this approximation for Pi:
(Reuters) – A new Hollywood film starring Dev Patel as Srinivasa Ramanujan will put the spotlight on the Indian math genius best known for his work on the theory of prime numbers.
Ramanujan, who died in 1920, was considered one of the brightest minds in mathematics, despite his lack of a formal education.
Patel, who caught Hollywood’s eye in 2008’s Oscar-winning film “Slumdog Millionaire”, has been cast as the lead. Filming begins in September with a British actor playing G.H. Hardy, the mathematician who recognized Ramanujan’s talent and brought him to England in 1914.
“The subject matter of Ramanujan is an Indian story but it is the story of the relationship of India and the West,” the film’s co-producer Edward Pressman told Reuters over the phone.
Researchers found that higher scores were related to greater sleep quality, especially less awakenings rather than the actual length of time asleep.
The team of researchers, led by Dr Jennifer Cousins at the University of Pittsburgh, studied 56 adolescents and compared their sleep patterns with their exam grades.
They found those that enjoyed deeper, less disturbed, sleep were the most successful, especially in maths but also in English and history.
Those who fell asleep and awoke easily – especially at weekends – were found to have better exam results.
Higher maths scores were related to less night awakenings, less time spent in bed, higher sleep efficiency and great sleep quality.
Try out this simple and effective time management and study strategy, named the Pomodoro Technique.
It helps to break up big tasks into smaller tasks, so that we don’t feel so overwhelmed by the task. Sometimes, students feel overwhelmed by the huge amount of material to study, so they don’t feel like starting. Using this method may be effective for beating procrastination and increasing efficiency.
Minister for Education Heng Swee Keat (Photo: MOE)
. It covers the areas of Algebra, Geometry, Counting and Probability, and Number Sense, over 500 examples and problems with fully explained solutions.
is said to be connected if there does not exist a separation of 
, 
of disjoint nonempty open subsets of 
continuous 
.
be the set of all rational numbers in the interval ![[0,1]](https://s0.wp.com/latex.php?latex=%5B0%2C1%5D&bg=ffffff&fg=1a1a1a&s=0&c=20201002)
, and since 
. In hindsight, the dyadic rationals approach in other sources may be more explicit and clearer.
if for every neighborhood ![[-1,0)\cup (0,1]](https://s0.wp.com/latex.php?latex=%5B-1%2C0%29%5Ccup+%280%2C1%5D&bg=ffffff&fg=1a1a1a&s=0&c=20201002)
of 
is not connected, but it is locally connected. The topologists’ sine curve is connected but not locally connected.
. This useful concept is not found in the book Topology, nor the other book Essential Topology.
” should be “
” instead. Upon consulting an errata list, there was only one page of errors.
contains research that shows that IQ can be increased.)
page for more details)
to have an all-round knowledge of the world and science.
to get an idea of the IMO (International Math Olympiad).
(Past Official P4 GEP Literature Book)
(P5 GEP Literature Book)
(P6 GEP Literature Book)
. Try not to use Webster / Google as those are American English, which can be quite different.
to students and parents. A psychologist has written this book, and it has many new insights. For instance, praising your child “intelligence and ability doesn’t foster self-esteem and lead to accomplishment, but may actually jeopardize success.” This is new psychological research supported by evidence. The correct way is actually to praise the child’s effort. Find out more tips and stories by reading this book.
Mathtuition88 