Saturday, December 31, 2011

Sri Ramanujan


 Sri Ramanujan


(22 December 1887 – 26 April 1920) was a Indian mathematician and autodidact who, with almost no formal training in pure mathematics, made extraordinary contributions to mathematical analysis, number theory, infinite series and continued fractions. Ramanujan's talent was said by the English mathematician G.H. Hardy to be in the same league as legendary mathematicians such as Gauss, Euler, Cauchy, Newton and Archimedes and he is widely regarded as one of the towering geniuses in mathematics.[1]

Born in Kumbakonam, Tamil Nadu, India, to a poor Brahmin family, Ramanujan first encountered formal mathematics at age 10. He demonstrated a natural ability, and was given books on advanced trigonometry written by S. L. Loney.[2] He mastered them by age 12, and even discovered theorems of his own, including independently re-discovering Euler's Identity. He demonstrated unusual mathematical skills at school, winning accolades and awards. By 17, Ramanujan conducted his own mathematical research on Bernoulli numbers and the Euler–Mascheroni constant. He received a scholarship to study at Government College in Kumbakonam, but lost it when he failed his non-mathematical coursework. He joined another college to pursue independent mathematical research, working as a clerk in the Accountant-General's office at the Madras Port Trust Office to support himself.[3] In 1912–1913, he sent samples of his theorems to three academics at the University of Cambridge. Only Hardy recognized the brilliance of his work, subsequently inviting Ramanujan to visit and work with him at Cambridge. He became a Fellow of the Royal Society and a Fellow of Trinity College, Cambridge, dying of illness, malnutrition and possibly liver infection in 1920 at the age of 32.

During his short lifetime, Ramanujan independently compiled nearly 3900 results (mostly identities and equations).[4] Although a small number of these results were actually false and publish work in all areas of mathematics influenced by his work.

Shakuntala Devi: That’s Incalculable!

 Shakuntala Devi: That’s Incalculable!


In 1976 the New York Times reported that an Indian woman named Shakuntala Devi (b. 1939) added 25,842 + 111,201,721 + 370,247,830 + 55,511,315, and then multiplied that sum by 9,878, for a correct total of 5,559,369,456,432, all in less than twenty seconds. Hard to believe, though this uneducated daughter of impoverished parents has made a name for herself in the United States and Europe as a lightning calculator. Unfortunately, most of Devi’s truly amazing feats not done by obvious “tricks of the trade” are poorly documented. Her greatest claimed accomplishment—the timed multiplication of two thirteendigit numbers on paper—has appeared in the Guinness Book of World Records as an example of a “Human Computer.” The time of the calculation, however, is questionable at best. Devi, a master of the criss-cross method, reportedly multiplied 7,686,369,774,870 x 2,465,099,745,799, numbers randomly generated at the computer department of Imperial College, London, on June 18, 1980. Her correct answer of 18,947,668,177,995,426,773,730 was allegedly generated in an incredible twenty seconds. Guinness offers this disclaimer:

“Some eminent mathematical writers have questioned the conditions under which this was apparently achieved and predict that it would be impossible for her to replicate such a feat under highly rigorous surveillance.” Since she had to calculate 169 multiplication problems and 167 addition problems, for a total of 336 operations, she would have had to do each calculation in under a tenth of a second, with no mistakes, taking the time to write down all 26 digits of the answer. Reaction time alone makes this record truly in the category of “that’s incalculable!” Despite this, Devi has proven her abilities doing rapid calculation and has even written her own book on the subject.

Wednesday, December 28, 2011

Bar Model and Table and Arrow Diagram

How can younger students be introduced to algebraic thinking before they are ready for formal algebra?

In discussing multiplicative structures, ergnaud (1988, 1994) argued for less formal representations to make algebraic thinking accessible to younger students.  he introduced table and arrow diagrams to repsent multiplication problems

Vergnaud argued that the table and arrow diagrams are helpful conceptual learning tools - the vertical arrows indicate ratios and the horizontal arrow represent functions

He also claimed that the table and arrow diagram is a pre-algebraic representation  that is less abstract and more accessible to younger students than formal algebra.

In the introduction of the model method in Singapore schools to address students  difficulities in solving word problem, Kho similarly argued that "the model method is less abstract than the algebraic method and can be introduced before students learn to solve algrebraic equation".  In fact students will appreciate better the use of symbols to represent quantities as they have experienced using bars to represent quantities in the model method.

Infinite Math Book




Sunday, December 25, 2011

Why Math is Important










Bar Model - Introduction





Syllabus for Simpang Lima - Speed Math

1    Complements   
2    Speed Addition   
3    Speed Subtraction   
4    Speed Subtraction II   
5    Doubling and Halving   
6    Speed Division   
7    Digital Root   
8    Multiply by Nine   
9    Multiply by 11   
10    Multiply by 12   
11    Base Multiplication I   
12    Base Multiplication II   
13    Above and Below   
14    Crosswise and Vertical (2 Digit)   
15    Cross Wise and Vertical (Three Digit)   
16    Divisibility   
17    SPECIAL MULTIPLICATION    

Bar Model Syllabus for Simpang Lima

1    Bar Model – Whole and Part 1   
2    Bar Model – Whole and Part II   
3    Bar Model - Whole and Part III (UPSR Question)   
4    Bar Model - Comparision Model I   
5    Bar Model - Comparision Model II   
6    Bar Model – Fraction Model  1       
7    Bar Model – Fraction Model II (USPR Question)   
8    Bar Model – Ratio Model I   
9    Bar Model – Ratio Model II (UPSR Question
10    Bar Model - Percentage I
11     Bar Model - Percentage II (UPSR Question)   
12    Model Method and Algebra

Annoucement for Simpang Lima for 2011

Our programme for Simpang Lima will continue on 8th Jan 2011 Sunday from 9 to 11 am every morning for the next 10 months.  Our programme will include

a) Speed Math 4 months

b) Bar Model - Singapore Method of Problem Solving ( 3 months)

c) Olympiad Math - Problem Solving (3 months)

The above programme are suitable for students from Std 4 to Std 6.  Students from Form 1 to Form 3 are also encouraged to join in into our program.

If you are interested pls email ptbestari@gmail.com or infinitemathmal@gmail.com.  Those who registered before or on the 8th of Jan 2012 will received 3 books free.

Friday, December 16, 2011

Infinite Interview

Infinite Learning Academy at Simpang Lima

Infinite Learing Academy will be at Simpang Lima Tamil school frm 8 am to 10.30 am on Sunday 18th of Dec 2011.

Classses for Infinite Math will continue in the month of January every Sunday 9 am to 11 am.

Monday, December 5, 2011

Week 2 at Simpang Lima

Day 1 Revision of the previous week
Day 2 Cross and Vertical - 3 digit
Day 3 Digital root - checking method of basic arithmetic operation
Day 4 Subtraction

Friday, November 25, 2011

Olympiad Math

Dear Parents


We are also planning to organize Olympiad Math Program for Primary and Secondary School Students. More information will be provided later

Week 1 in Simpang Lima Elementary

Day1 - Exam and Discussion with Parents

Day2 - Introduction to Finger Math with all the hand sign. Left hand and right hand and basic addition using finger
Day3 - Introduction of Small Friend which is used when you want to add 3 + 4 which 3 + 5 -1


Day 4 Introduction of Big Friend which is used when you want to add 9 + 3 which is 9 + 10 -7
Day 5 : Mix Operation Using both Small Friend and Big Friend

Week 1 in Simpang Lima Beginners

Day 1 - Exam and Discussion with Parent
Day 2 - Complements and Revision on basic arithmetic operation

Day 3 - Base Multiplication
Focus on how to quickly multiply 98 x 96 or similar number which is near to base 100.
It also focus on numbers above 100 such multiplying 102 x 108

Day 4 - Above and Below and Multiplying with 9
Focus on multiplying 98 (below) x 102 (above).  Base 100 was used in class.  Other base such 50, 20 will be taught in future class
Three technique on how to multiply any number with 9, 99 or 999 was taught.

Day 5 - Vertical and Crosswise
Focus on multiplying any 2 digit numbers  such as 77 x 44

Monday, November 21, 2011

Infinite Math Class in Simpang Lima

Classes for Infinite Math will start tomorrow at 8am at SRJK Simpang Lima.

For elementary the focus will on basic addition using finger and for beginners the focus will be on complements and revision on addition, subtraction, division and multiplication

Monday, November 14, 2011

Infinite Math Exam at Simpang Lima Tamil School

Dear Parents and Students

Infinite Learning Academy will held it first Infinite Math Exam at Simpang Lima on Thursday 17th Nov 2011 from 8pm to 9pm followed by a informal meeting with the parents.

Friday, November 11, 2011

Week 1 Classes for Infinite Math

Elementary Class

The focus will on finger math
- introduction of the hand sign
- on how to do addition and subtraction faster using finger.
- oral exercise for all the student.


Beginner Class
The focus will be on
- Complements
- Fast addition and subtraction
- Revision on multiplication and division.
The aim is to make sure all the students have mastered the basic technique before going in to advance classes

Wednesday, November 9, 2011

Our Instructor

Mr Arivu - Speed Math Expert
Mr Sri - FingerMath Expert
Mrs LatchmiDevi - Bar Model Expert



Infinite Math Exam at Infinite Learning Academy



Our first exam was conducted before the start of the program at Infinite Learning Academy Puchong

Infinite Math at SRJK(T) Simpang Lima

Teacher Latchmi explaining Bar Model concept to the parents


Mr Ari watching himself on the multiplication video of himself


Mr Sri explaining fast subtraction to students and parents

Mr Ari involved in a serious discussion with students and parents


Solving the math problem on the spot

Friday, October 28, 2011

Beginners Updated Syllabus

CHAPTER 1 : COMPLEMENTS
1.1 : Complements
1.2 : High Speed Addition
1.3 : Easy Addition 1
1.4 : Easy Addition 2
1.5 : Easy Subtraction
1.6 : Easy Multiplication
1.7 : Easy Division

CHAPTER 2 : BASE MULTIPLICATION
2.1 : Multiplications Single Digit Numbers
2.2 : Multiplication using a base of 100
2.3 : Multiplication above the base
2.4 : Mixed Multiplication


CHAPTER 3 : MULTIPLICATION ABOVE AND BELOW
3.1 Above and Below
3.2 Multiply by 9
3.2.1 Multiply by 9 - Single Digit
3.2.2 Multiply by 9 - Type 1
3.2.3 Multiply by 9 - Type 2
3.2.4 Multiply by 9 - Type 3
3.3 Math Genius

CHAPTER 4 : BASE MULTIPLICATION
4.1 Base Multiplication (Using Different Base)
4.2 Exercise
4.3 Math Genius

CHAPTER 5 : MULTIPLICATION
5.1 : Vertically and CrossWise -2 digit
5.2 : Vertically and CrossWise - 3 digit

CHAPTER 6 : MULTIPLICATION 11 and 12
6.1 Mulitply by 11
6.2 Multiply by 12

CHAPTER 7 : DIVISION
7.1 Division without Remainders
7.2 Division with Remainder
7.3 Dividing with 9 and 8

CHAPTER 8 : DIVISION
8.1 Division with base 10
8.2 Division with base 100
8.3 Exercise

CHAPTER 9 : SUBTRACTION
9.1 Finding Complement
9.2 Subtraction Using Complement
9.3 Exercise


CHAPTER 10 : DIGITAL ROOT
10.1 Digital Root
10.2 Cast out Nine
10.3 Checking for Addition
10.4 Checking for Subtraction
10.5 Checking for Division
10.6 Checking for Multiplication