Number Theory

If you have taken some math tuition on number theory, you should be familiar with the concept of prime numbers. Prime numbers are those numbers which are only divisible by 1 and that number itself. Some examples of prime numbers are 2, 3,7,11 13 etc. These numbers can only be divided by themselves or 1 without producing a remainder.

Prime numbers are one of the most beautiful things in mathematics. They are also quite mysterious in some sense. For thousands of years, many great minds have worked with them to uncover some of their mysteries. The first and foremost thing that the mathematicians wanted to find about prime numbers is a definitive pattern in their distribution. For example, let us consider the following
sequences of numbers:

Sequence 1: 2, 4, 6, 8, 10.....

Sequence 2: 2, 4, 8, 16....

Sequence 3: 1, 1,2,3,5,8,13...


In all of the above 3 sequence of numbers, we can see a definitive pattern. In the first sequence, all numbers are separated by an interval of 2 i.e. we get the next number by adding 2 to the current number. All the numbers generated in this sequence will be even if we follow the same pattern, given we start with an even number. If we take the example of the second sequence, each number (apart from the first number of course) is double of the previous number i.e we generate the next number by multiplying 2 to the current number. The third sequence is known as the Fibonacci sequence and there is a definitive pattern to it as well. Can you see the pattern? Well, each number, apart from the first two numbers (i.e. 1 and 1), is the sum of the previous 2 numbers. For example, 3 is 2+1 and 13 is 8+5. As we can clearly see, there is a definite pattern. The mathematicians wanted to find the same thing for prime numbers; they wanted a pattern using which prime numbers could be generated and predicted. Although there was no lack of trying and many great minds of all time wrestled with this particular problem, till date, we have failed to find such a definitive pattern.


Leonhard Euler, one of the greatest mathematicians of all time, in fact came up with a formula for generating prime numbers. Those of you who have taken some math tuition on algebra or number theory might already be familiar with this formula. The formula goes as follows: n2 – n + 41
If we plug-in the values of n, we will indeed generate primes – well, at least in some cases. For example, when we plug-in n=1, we get 41 – prime. If we plug-in n=2, we get 43 – again a prime. If we plug-in n=3, we get 47, a prime!! In fact, this formula works all the way up to 40. The point it fails at is when n=41 when the value of the expression becomes 1763 which is not prime because this number is the product of 43 and 47 and hence devisable by both of them. As a result, although the formula shows some promise early on, it fails at a point. In fact, this formula potentially generates an infinitely many composite numbers. Although we have failed to find a general pattern which predicts the distribution of prime numbers, it is important to mention here that we have been able to find certain patterns which hold true in certain cases. For example, the Ulam spiral, the prime number chains, Gilbreath's conjecture and many others are examples where such patterns are observed.
Number pattern is a familiar topic for maths tuition students in Singapore. Though it starts from the basic primary maths tuition classes in Singapore, maths tuition students are well aware of number patterns. One of the very popular maths questions many years ago was to find the sum of numbers from 1 to 100. This question was for 12 year olds students taking the maths examination.

Maths Tuition – The Best Option for Kids Who Struggle With the Digits

Maths classes that are conducted in the schools are not always the finest options for students when it comes to getting through their exams, particularly for those who are always at daggers drawn with the subject. There are certain students who have a tendency of running away from Maths because they are simply afraid of the subject and this is what makes institutes like Miracle Learning Centre so much pertinent in today’s context.

Going back to the students’ acumen or the lack of it in grasping Maths, there is simply no reason to blame the teachers of the schools. They after all, have the responsibility of taking care of a number of students during a short period of time. Hence, they in most of the cases do not have the time to give that extra bit of time to those who need some special and focused attention. To this hapless chunk of students, maths tuition is the only feasible solution, especially for those who are really struggling to get in terms with even the elementary issues of the subject.

Here, the only point that needs to be taken into account very seriously is the type of tutorial to opt for. Indeed, the tutorial needs to be chosen very immaculately so the move does not have any adverse effect on the psyche of the student in question. Everything needs to be taken into account – right from the qualification of the tutors, to their experience and method of teaching, and last but not the least, their ability to quickly and seamless adapt to the learning style of the student in question. Experienced Maths tutors in tutorials like Miracle Learning Centre encourage students to respond to questions and also clear their doubts. There are certain students who take time to open up with their problems and issues. Tutors who conduct these maths tuition classes come up with specialized methodology of teaching to help these students divulge their problems so that they can be addressed and taken care of in a methodical way as per the mental structure and mental setup of the students. We at Miracle Learning Centre are excellent at this, as we are home to some of the most experienced and trained tutors who take engaging sessions and equip the students with appropriate knowledge in each step and this helps the students to gain confidence and the required knowledge. All these help them subsequently to appear in Maths assessments with the required self-belief and a renewed vigor. This, ultimately reflects on their mark sheets in the long run.

The Monty Hall Problem

If you have been taking some maths tuition on statistics, you might have heard about the Monty Hall problem already. It is an extremely interesting problem. For those who are not familiar with statistics, fear not. It does not require any in-depth knowledge of statistics to understand the problem.

Introduction

The Monty Hall problem is a famous puzzle in statistics which has one of the most counter intuitive answers. Steve Selvin, a professor of biostatistics at UC Berkeley published a letter in the scientific journal “The American Statistician”. In this letter, he wrote about a problem loosely based on the game show “Let’s Make a Deal” and he dubbed the problem as “The Monty Hall” problem. Since then, the problem has achieved a cult status and has enjoyed immense popularity amongst maths enthusiasts.

The Problem

The Monty Hall problem goes like this. There are three closed doors marked as A,B and C. Behind each door, there is a prize. There are two goats behind two doors and behind one door, there is a car. You are now given an option to choose one of the three doors. Let’s say you pick door A. The game’s host Monty Hall, who knows what prize sits behind each door, will now open one of the remaining doors which has a goat. Let’s say he opens the door C which has a goat. Now Mr. Monty Hall comes up with a proposition. He offers you the option of changing your initial choice and swapping the doors. That is, if you wanted, you could choose door B and let go of door A. The Monty Hall problem asks what you should do in order to maximize your chance of winning the car. Should you take the option and swap doors or should you stick with your original choice? Before reading on, please take a moment to think about it.

The Analysis

It is most common mistake to think that swapping does not make any difference and your chances will remain the same. However, in order to maximize your chances of winning, you should swap every time you are given such a choice. In reality, if you swap, you are twice as likely to win – a whopping 100% increase in terms of probability. So how does this work? Let us see. At first, you have 3 choices i.e. there are 3 doors that you can choose from. The car sits behind just one door. Those of you who have already taken some maths tuition on probability and statistics will be able to quickly point out the fact that the probability of you winning the car is 1/3 or around 33.33%. Similarly, the chance that you have chosen a door which has a goat behind it is 2/3 i.e. 66.66%. As you can see, when you choose for the first time, you are twice as likely to choose a door which has a goat behind it than choosing the one which has the car. Next, Mr. Monty Hall reveals one of the doors which has a goat behind it. Since it was more likely that you had chosen a door with a goat (66.66&), if you switch, you will increase your chances of winning and in fact, you will be winning the car 66.66% of the time if you switch compared to the meagre 33.33% if you did not switch.

Best Maths Tuition in Singapore

Miracle Learning Centre Pte Ltd is conveniently located in Bukit Timah, and started in 2008 as a centre specializing in Mathematics and Science. Because we were founded with one simple aim – “achieving excellence in mathematics and science”, we have been able to stay focused, and deliver consistent results. We must be doing something right!Our institute MIRACLE LEARNING isn't completely qualification institute, it's a platform wherever we have a tendency to tend to tend to undertake and provide our greatest to create rock bottom of youngsters about science. we have a tendency to tend to tend to start out to creating rock bottom of scholars from Primary level to Secondary level and put together level categories. we have a tendency to tend to tend to undertake and facilitate students to induce through their difficulties throughout this such a stimulating subject mentioned as “SCIENCE”.

What is Mathematics?

Mathematics is a subject which gives us knowledge about main concepts of any kind of calculations happening throughout the world. Maths is based on numbers, quantity, several kind of shapes like : square, rectangle, triangle, oval, pyramids, cubes etc., counting, calculations, measurements, mathematical proof, logic and abstraction. Famous Mathematician Galileo Galilei said “The universe cannot be read until we have learned the language and become familiar with the characters in which it is written. It is written in Mathematical language, and the letters are triangles, circles and other geometrical figures.” Nowadays we find several methods of calculations in this interesting subject called Mathematics like : Algebra, Differentiation, Calculus and Analysis, Geometry and topology, Trigonometry, Combinatorics, Logic, Number theory, Applied mathematics etc. All these chapters help people understand this subject better by giving us clear concept about particular things. If we observe with a little effort we can see that in our surrounding whatever is going on most of it related to Maths. For example : we set our alarm clock by counting time; in schools, colleges, at work our schedule is based on time; while shopping we count money for payment or budget; when drinking tea or coffee or cooking something we measure sugar and spices with right measurement; when engineers build house, offices, building, shopping malls all of their work is based on measurement etc. So you can understand application of this subject ‘Mathematics’ is how important in our daily life.

Best Maths Tuition in Singapore

MIRACLE LEARNING is an institute where we teach students the importance of Maths. We give Maths tuition to children to make their base about this subject strong. We know how some students get scared of the name of this subject. But here we are who can help them get through their difficulties. Children cannot grasp everything in their school among all the race of classes. They need extra care and patience sometimes. Our institute has trained NIE teachers who are fully capable of taking care of children’s inconvenience. First of all children need to understand the basic things of their chapters otherwise the whole concepts can’t mean anything to them. That’s why we are here !! Our education system has 3 levels. Our specialization in Maths tuition starts from Primary level to Secondary level and even junior College level. We give tuition AT HOME too !! This process can be very fun-filled cause it includes parents too. Children are always fond of their parents, so it makes them more enthusiastic to concentrate in their studies. We can use several kind of study kits or household things besides textbooks to make their study more enjoyable. They will learn about all types of geometrical shapes from these equipments. This process WILL NOT cost any extra charges !! Miracle learning is not just a professional institute, we try our best to give children by showing them proper way to overcome their combated situation. Our belief is that if we try to guide children in right direction at their tender age, they can fight their own battle easily. We believe in trust and reliability !!

Best Maths Tuition in Singapore

Mathematics is a subject which is really interesting and knowledgeable if you find. Maths means factors of quantity, numbers, size, structure, space etc. Mathematics is the study of arithmetic calculations and equations. This subject helps us understand how to count things, how to express anything with formulated calculations etc. In this world everything around us is related to Mathematics. When we count time or points, when we count distance of our destination, while counting hours, in our school college office timing hours, when mechanics/ engineers build buildings, ships, cars, other vehicles etc with countless of equations. So you can see that everything around us is based on the concept of Mathematics. There are many renowned scientists throughout the whole world who had been invented millions of mathematical formulas, theories and equations. Some names of famous Mathematicians are : Isaac Newton, Aristotle, Archimedes, Blaise Pascal, Leonardo Fibonacci, Albert Einstein and many more. According to Aristotle Mathematics is “Science of Quantity”. Its true that Maths means trick of Calculations.

Careers Open For You If You Have Got Brilliant Maths Skills

MIRACLE LEARNING is an institute which gives Maths tuition to children who need extra attention after their school. Its really understandable if children can’t grasp everything at their school. We try to get through their difficulties by taking care of their inconvenience. Maths can become very interesting subject if children can understand the main basic factors of their chapters. We are here to give them clearer view of Mathematics and we make sure that they can get whatever we are trying to teach them. We give tuitions at home too !! This process can become fun-filled to children cause its involved their parents. Children need their parents all the time to be by their side in each and every step. We can use several household things or our funny kits to make student’s lesson more interesting and enjoyable. Our education system divided in 3 levels to make our learning pattern understand easier. We have trained NIE teachers who are totally capable of giving right suggestions and taking care of children. Our specialisation in Maths starts from Primary level to Secondary level and even junior College level. We are not just an professional institute. We try to give our best that children can overcome their combated situation regarding this most interesting subject called Mathematics. We encourage students to attend regular classes, so that they don’t get to miss any portions. We make sure that we can prepare them fully for final exams by giving the children proper instructions. Miracle learning believes that children need extra care and patience. We try to make study enjoyable that students don’t get bored by their study. Regular attending of our classes will build their concept of Maths clearer and they will learn how to get through their own combated situation. We believe in trust and reliability !! Its our duty to show the children right path in their life. So here we are to be by your side all the time.

Best Maths Tuition in Singapore

Miracle Learning Centre Pte Ltd is conveniently located in Bukit Timah, and started in 2008 as a centre specializing in Mathematics and Science. Because we were founded with one simple aim – “achieving excellence in mathematics and science”, we have been able to stay focused, and deliver consistent results. We must be doing something right! Do you notice the actual fact that maths applies to nearly any field you'll be able to probably consider. affirmative you detected it right it applies to any attainable field you'll be able to return up with, together with science, engineering, textiles, business, medicine, social sciences and etc. Despite its importance, science ar one thing feared by several students, in order that they fail to grasp the ideas in science and this leads them into taking a maths tuition. Nowadays students have created it a trend to require maths tuition, because the level will increase the difficulties will increase with increase and variations in ideas. "O" level students specially face issues in maths owing to the actual fact that each downside has two to three attainable solutions in several ways in {which} which results in confusion among the coed. the actual fact has it that ninety nine students take maths tuition for his or her learning, and this can be not alittle range. On the opposite hand, this range shows the scholars have positive response towards their not understanding concerning science.

The Monty Hall Problem

If you have been taking some maths tuition on statistics, you might have heard about the Monty Hall problem already. It is an extremely interesting problem. For those who are not familiar with statistics, fear not. It does not require any in-depth knowledge of statistics to understand the problem.

Introduction

The Monty Hall problem is a famous puzzle in statistics which has one of the most counter intuitive answers. Steve Selvin, a professor of biostatistics at UC Berkeley published a letter in the scientific journal “The American Statistician”. In this letter, he wrote about a problem loosely based on the game show “Let’s Make a Deal” and he dubbed the problem as “The Monty Hall” problem. Since then, the problem has achieved a cult status and has enjoyed immense popularity amongst maths enthusiasts.

The Problem

The Monty Hall problem goes like this. There are three closed doors marked as A,B and C. Behind each door, there is a prize. There are two goats behind two doors and behind one door, there is a car. You are now given an option to choose one of the three doors. Let’s say you pick door A. The game’s host Monty Hall, who knows what prize sits behind each door, will now open one of the remaining doors which has a goat. Let’s say he opens the door C which has a goat. Now Mr. Monty Hall comes up with a proposition. He offers you the option of changing your initial choice and swapping the doors. That is, if you wanted, you could choose door B and let go of door A. The Monty Hall problem asks what you should do in order to maximize your chance of winning the car. Should you take the option and swap doors or should you stick with your original choice? Before reading on, please take a moment to think about it.

The Analysis

It is most common mistake to think that swapping does not make any difference and your chances will remain the same. However, in order to maximize your chances of winning, you should swap every time you are given such a choice. In reality, if you swap, you are twice as likely to win – a whopping 100% increase in terms of probability. So how does this work? Let us see. At first, you have 3 choices i.e. there are 3 doors that you can choose from. The car sits behind just one door. Those of you who have already taken some maths tuition on probability and statistics will be able to quickly point out the fact that the probability of you winning the car is 1/3 or around 33.33%. Similarly, the chance that you have chosen a door which has a goat behind it is 2/3 i.e. 66.66%. As you can see, when you choose for the first time, you are twice as likely to choose a door which has a goat behind it than choosing the one which has the car. Next, Mr. Monty Hall reveals one of the doors which has a goat behind it. Since it was more likely that you had chosen a door with a goat (66.66&), if you switch, you will increase your chances of winning and in fact, you will be winning the car 66.66% of the time if you switch compared to the meagre 33.33% if you did not switch.

Best Maths Tuition in Singapore

Miracle Learning Centre Pte Ltd is conveniently located in Bukit Timah, and started in 2008 as a centre specializing in Mathematics and Science. Because we were founded with one simple aim – “achieving excellence in mathematics and science”, we have been able to stay focused, and deliver consistent results. We must be doing something right! Classes conducted in the school are not always enough to help your kids get through in their exams. This is especially true with maths, as many kids find it hard to keep up with the ongoing maths lessons in the class. However, there is no point in blaming the teacher, who is faced with the task of tending several students during the short period of the class. Hence, maths tuition can be the only solution, particularly if the child is struggling even with the elementary concepts.

Maths Tuition - The Best Solution for Kids Who Are Struggling With Maths

It is important to select maths tutors carefully, with respect to their qualification, experience and their capability to adapt to the child's learning style. Over the course of a few sessions, you can evaluate certain things that will convey whether or not the tuition will be successful for your child. However, it is best to be proactive with the choice, as it may be too late if your child's progress is not satisfactory even after several sessions. A good tutor must provide detailed updates regarding the progress of your child. An accurate feedback on assignments is also essential, as it will help the parent understand whether the child is prepared for the test. On your part, you must inform the tutor about the concepts or topics that are challenging for your child. Experienced maths tutors encourage the student to speak up while responding to questions and also clear their doubts without hesitation. They use several resources, including metaphors and multiple examples to explain the lesson to the student. Instead of letting them memorize things, they teach the students to identify where and how to apply the concepts in the right context. In other words, tuition sessions are more engaging and helpful to equip the student with the appropriate knowledge at each step. This approach not only makes the homework easier, but also interesting. Apart from these, tutors must have a compliant personality and attitude, so that they are both realistic and optimistic about the student's performance. Children need a special interactive environment to learn well. Further, maths tuition requires a special routine, as new concepts will be based on what is already learned. Out-of-the-school maths tutors will help kindle the child's interest in the subject. You can find tutors to guide your child individually or with a group of students, as in tuition centers. Today, online tuition is widespread because of the convenience associated with learning from home. Learning websites use interactive learning tools and assign individual tutors to each student. With flexible learning hours, plenty of resources and assistance of tutors, an interesting learning atmosphere can be created in the home. Tutors also give assignments and provide feedback about the progress of the student. When it comes to maths tuition, it is not advisable to wait too long once you discover that your child needs additional coaching. This is because your child has to catch up a lot to stay current with the lessons, and any undue delay can make him or her feel completely lost.