Family Name: Toh
Given Name: Pee Choon
Contact: peechoon DOT toh AT nie DOT edu DOT sg
Mathematics & Mathematics Education
National Institute of Education
Nanyang Technological University
1 Nanyang Walk, Singapore 637616
- My main research focus is on number theory, in particular, elliptic functions, modular forms, partition theory and basic hypergeometric series.
- I'm also interested in Problem Solving and the teaching of mathematics at the undergraduate level.
My Erdös number is at most 3, via Toh - Hirschhorn - Loxton - Erdös
International workshop on Number theory, partitions, q-series and Rogers-Ramanujan identities (6-7 March 2014)
Seminar series on Number theory, partitions, q-series and related research (npqr² )
Publications (Number theory, partition theory, theta functions and modular forms)
- On certain pairs of q-series identities.
Ramanujan J., 40 (2016) 359-365. pdf
- Theta series associated with certain positive definite binary quadratic forms. (with H. H. Chan)
Acta Arith., 169 (2015) 331-356. pdf
- On a certain vector crank modulo 7. (with M. Hirschhorn)
Electron. J. Combin., 22 (2015) #P1.25. pdf
- On representations by figurate numbers: A uniform approach to the conjectures of Melham.
Int. J. Number Theory, 9 (2013) 1055-1071. pdf
- Ramanujan type identities and congruences for partition pairs.
Discrete Math. 312 (2012) 1244-1250.pdf
- Differential equations satisfied by Eisenstein series of level 2.
Ramanujan J., 25 (2011) 179-194. pdf
- A new class of theta function identities in two variables. (with R. Chapman and W. Hart)
J. Comb. Number Theory, 2 (2010) 201-208 pdf
- New analogues of Ramanujan's partition identities. (with H.H. Chan)
J. Number Theory 130 (2010) 1898-1913. pdf
of certain binary quadratic forms as Lambert series.
Acta Arith. 143 (2010) 227-237.
- Quintic and septic Eisenstein series. (with S. Cooper)
Ramanujan J., 19 (2009) 163-181. pdf
- Determinant identities for theta functions. (with S. Cooper)
J. Math. Anal. Appl., 347 (2008) 1-7. pdf
- Generalized m-th order Jacobi theta functions and the Macdonald identities.
Int. J. Number Theory, 4 (2008) 461-474. pdf
- Ramanujan's Eisenstein series and powers of Dedekind's eta-function.(with H.H. Chan and S. Cooper)
J. London Math. Soc., 75 (2007) 225-242. pdf
- The 26th power of the Dedekind's eta function.(with H.H. Chan and S. Cooper)
Adv. Math., 207 (2006) 532-543. pdf
These are the submmitted versions of the papers and may differ from the published versions. For copies of the published version, please write to me.
Other Publications (Selected)
- A Problem on Egyptian Fractions
E. G. Tay and P. C. Toh
Mathematical Medley, 41(2), (2016) 8-10. link, pdf
- Designing Tasks for Conjecturing and Proving in Number Theory
P. C. Toh, Y. H. Leong, T. L. Toh and F. H. Ho
Proceedings of the 38th Conference of the International Group for the Pyschology of Mathematics Education, Vancouver, 2014, 5-257-264.
- What is the next number in this sequence?
P. C. Toh and E. G. Tay
Math. Spectrum, 46 (2014) 125-131. link, pdf
- The Problem Solving Approach in the Teaching of Number Theory
P. C. Toh, Y. H. Leong, T. L. Toh, J. Dindyal, K. S. Quek, E. G. Tay and F. H. Ho
Int. J. Math. Ed. Sci. Technol., 45 (2014) 241-255. link, pdf
- Use of Practical Worksheet in Teacher Education at the Undergraduate and Postgraduate Levels,
P. C. Toh, T. L. Toh, F. H. Ho and K. S. Quek
Proceedings of the 35th Mathematics Education Research Group of Australiasia Conference,
Singapore, 2012, 736-743.
- Self Learning Laboratory Sessions for Engineering Mathematics,
P. C. Toh
Proceedings of the 16th Asian Technology Conference in Mathematics,
Bolu, Turkey, 2011, 187-192.
- Conics for H2 Further Math. link
Current and Past Student Projects
- Catalan Numbers
- The Extended Staircase Problem
- Very Odd Sequences
- Cubic Equations and Beyond
- On Divisibility in the Rings Z[i], Z[sqrt(-2)], Z[w]
- Gaussian Integers
- The Law of Quadratic Reciprocity
- Introduction to Coding Theory
- Bijections in the theory of Partitions
- Pell's Equation
- Sums of Squares and Sums of Triangular Numbers
- Applications of Graphs
- Repunit Polygonal Numbers. (Student paper appeared in Mathematical Medley Vol 38 No. 2.)
- Properties of Lattice Polygon Duals
- Finite Calculus
- The Mathematics of Google's PageRank (Student project won silver award in SSEF2010.)
- Fourier Series and the Riemann Zeta Function
updated April 2017