1,720,986 research outputs found
3rd Lee Peng Yee Symposium: Celebrating Mathematics (18 - 19 Nov 2013)
No full textSome participants at the Symposium dinner: Mdm Chua Kwee Gek, Prof. Lee Peng Yee, Mdm. Yeo Shumei, Prof. Berinderjeet Kaur, (back row) A/P Tay Eng Guan and A/P Toh Pee Choon
A construction of the double-angle trigonometric formulae
No full textA visual construction is used to double the base angle of a right triangle, thereby deriving the double-angle trigonometric formulae.Accepted versio
Twelve erroneous proofs
No full textAssessing how well students understand proofs is difficult. One way to achieve this is to present an erroneous proof and require students to identify the error. Twelve erroneous proofs on various topics in mathematics at the Secondary school level are presented as examples.Published versio
On representations by figurate numbers: A uniform approach to the conjectures of Melham
No full textUsing known formulas for R(a;b)(n), the number of representations of n as a times a square plus b times a square, we prove 21 conjectured formulas of Melham on the number of representations of n as sums of triangular, pentagonal and heptagonal numbers. We also demonstrate how our technique can be used to prove the other 277 conjectured formulas of Melham concerning representations by other gurate numbers.Accepted versio
On certain pairs of q-series identities
No full textHirschhorn recently proved a pair of q-series identities that inter-linked the coefficients of two infinite products. We use the theory of modular forms to extend his results from p = 5 to other primes and provide other
examples of infinite products sharing similar properties.Accepted versio
On the crank function of cubic partition pairs
No full textWe study a crank function M(m, n) for cubic partition pairs. We show that the function M(m, n) explains a cubic partition pair congruence and we also obtain various arithmetic properties regarding M(m, n). In particular, using the Θ-operator, we confirm a conjecture on the sign pattern of c(n), the number of cubic partition pairs of n, weighted by the parity of the crank.Accepted versionRI 3/12 TP
Differential equations satisfied by Eisenstein series of level 2
No full textRamanujan’s differential equations for the classical Eisenstein series are of great importance to many areas in number theory and special functions. H.H. Chan recently demonstrated that these differential equations can be derived from the triple product identity and the quintuple product identity in an elementary manner. In this article, we extend this method in a uniform manner to derive corresponding differential equations for the Eisenstein series of level 2. Several applications of these differential equations are also given.Accepted versio
On a certain vector crank modulo 7
No full textWe de ne a vector crank to provide a combinatorial interpretation for a certain Ramanujan type congruence modulo 7.Published versio
Ramanujan type identities and congruences for partition pairs
No full textAbstractUsing elementary methods, we establish several new Ramanujan type identities and congruences for certain pairs of partition functions
The Mathematician Educator special issue: Mathematics instruction for the future
No full textPublished versio
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