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