Family Name: Toh
Given Name: Pee Choon
杜丕俊
Contact: peechoon DOT toh AT nie DOT edu DOT sg
Address:
NIE 70335
Mathematics & Mathematics Education
National Institute of Education
Nanyang Technological University
1 Nanyang Walk, Singapore 637616
ORCID Profile
Google Scholar Profile
Research Interests
 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, proofs and reasoning, and the teaching of mathematics at the undergraduate level.
My Erdös number is at most 3, via Toh  Hirschhorn  Loxton  Erdös
Publications (Number theory, partition theory, theta functions and modular forms)
 The number of representations of a positive integer by triangular, square and decagonal numbers. (with U. Isnaini and R. Melham)
Bull. Korean Math. Soc., to appear. pdf
link
 On a symmetric identity of Ramanujan involving the sum of two squares function. (with H. H. Chan)
J. Math. Anal. Appl., 473(2019) 12341243. pdf
link
 On the crank function of cubic partition pairs. (with B. Kim)
Ann. Comb., 22(2018) 803818. pdf
Springer full text view
 On some congruences for Andrews' singular overpartitions. (with U. Isnaini)
Integers, 18 (2018) A5 (17 pages). pdf link
 A general transformation for theta series associated with the quadratic form x^{2}+ky^{2}. (with T. P. N. Ho)
Ramanujan J., 45 (2018) 695717. DOI: 10.1007/s1113901799479 pdf
Springer full text view
 On certain pairs of qseries identities.
Ramanujan J., 40 (2016) 359365. pdf Springer full text view
 Theta series associated with certain positive definite binary quadratic forms. (with H. H. Chan)
Acta Arith., 169 (2015) 331356. pdf
 On a certain vector crank modulo 7. (with M. Hirschhorn)
Electron. J. Combin., 22 (2015) #P1.25. pdf link
 On representations by figurate numbers: A uniform approach to the conjectures of Melham.
Int. J. Number Theory, 9 (2013) 10551071. pdf
 Ramanujan type identities and congruences for partition pairs.
Discrete Math. 312 (2012) 12441250. pdf link
 Differential equations satisfied by Eisenstein series of level 2.
Ramanujan J., 25 (2011) 179194. pdf
 A new class of theta function identities in two variables. (with R. Chapman and W. Hart)
J. Comb. Number Theory, 2 (2010) 201208. pdf
 New analogues of Ramanujan's partition identities. (with H.H. Chan)
J. Number Theory 130 (2010) 18981913. pdf link
 Representations
of certain binary quadratic forms as Lambert series.
Acta Arith. 143 (2010) 227237.
pdf
 Quintic and septic Eisenstein series. (with S. Cooper)
Ramanujan J., 19 (2009) 163181. pdf
 Determinant identities for theta functions. (with S. Cooper)
J. Math. Anal. Appl., 347 (2008) 17. pdf link
 Generalized mth order Jacobi theta functions and the Macdonald identities.
Int. J. Number Theory, 4 (2008) 461474. pdf
 Ramanujan's Eisenstein series and powers of Dedekind's etafunction.(with H.H. Chan and S. Cooper)
J. London Math. Soc., 75 (2007) 225242. pdf
 The 26th power of the Dedekind's eta function.(with H.H. Chan and S. Cooper)
Adv. Math., 207 (2006) 532543. pdf link
Click on pdf for the submmitted versions of the papers which may differ from the published versions. For published versions that are available for download, click on link.
Other Publications (Selected)
 Invariance as a Big Idea
P. C. Toh
In T. L. Toh and J. B. W. Yeo (Eds), Big Ideas in Mathematics, Association Mathematics Educators: Yearbook 2019 (pp. 139149). pdf link
 Mathematics Instruction: Goals, Tasks and Activities
P. C. Toh and B. L. Chua (Editors)
Association Mathematics Educators: Yearbook 2018. link
 Developing 21st Century Competencies in the Mathematics Classroom
P. C. Toh and B. Kaur (Editors)
Association Mathematics Educators: Yearbook 2016. link
 Learning Experiences to Promote Mathematics Learning
P. C. Toh, T. L. Toh, and B. Kaur (Editors)
Association Mathematics Educators: Yearbook 2014. link
 A Problem on Egyptian Fractions
E. G. Tay and P. C. Toh
Mathematical Medley, 41(2), (2016) 810. 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 Psychology of Mathematics Education, Vancouver, 2014, Vol 5, (pp.257264).
link,
pdf
 What is the next number in this sequence?
P. C. Toh and E. G. Tay
Math. Spectrum, 46 (2014) 125131. 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) 241255. 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, 736743.
pdf
 Self Learning Laboratory Sessions for Engineering Mathematics,
P. C. Toh
Proceedings of the 16th Asian Technology Conference in Mathematics,
Bolu, Turkey, 2011, 187192.
link
Teaching
 Conics for H2 Further Math. link
Events

International workshop on Number theory, partitions, qseries and RogersRamanujan identities (67 March 2014)

Seminar series on Number theory, partitions, qseries and related research (npqr² )
Current and Past Student Projects
 padic numbers
 Stirling Numbers
 Simplicity of Alternating Group of degree n
 Rational Points on Curves
 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).pdf
 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 May 2019