Homepage of Pee Choon Toh

Family Name: Toh
Given Name: Pee Choon

杜丕俊

Contact: peechoon DOT toh AT nie DOT edu DOT sg

Address:
NIE 7-03-35
Mathematics & Mathematics Education
National Institute of Education
Nanyang Technological University
1 Nanyang Walk, Singapore 637616
Google Scholar Profile
ORCID Profile
Web of Science Profile

Research Interests

Mathematics: Number theory, in particular, partition theory, modular forms, elliptic functions and basic hypergeometric series.
Mathematics Education: 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)

Weighted generalized crank moments for k-colored partitions and Andrews-Beck type congruences (with B. L. S. Lin and L. Peng)
Discrete Math., 344 (2021), Article 112450. (13 pages). DOI:10.1016/j.disc.2021.112450 pdf
A variation of the Andrews-Stanley partition function and two interesting q-series identities (with B. L. S. Lin and L. Peng)
Ramanujan J., 56 (2021), 297-307. DOI:10.1007/s11139-020-00315-5 pdf Springer full text
When is the derivative of an eta quotient another eta quotient? (with Z. S. Aygin)
J. Math. Anal. Appl., 480(2019), Article 123366 (22 pages). DOI: 10.1016/j.jmaa.2019.07.056 pdf
The number of representations of a positive integer by triangular, square and decagonal numbers. (with U. Isnaini and R. Melham)
Bull. Korean Math. Soc., 56(2019) 1143-1157. 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) 1234-1243. pdf link
On the crank function of cubic partition pairs. (with B. Kim)
Ann. Comb., 22(2018) 803-818. 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 x²+ky². (with T. P. N. Ho)
Ramanujan J., 45 (2018) 695-717. DOI: 10.1007/s11139-017-9947-9 pdf Springer full text view
On certain pairs of q-series identities.
Ramanujan J., 40 (2016) 359-365. pdf Springer full text view
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 link
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 link
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 link
Representations of certain binary quadratic forms as Lambert series.
Acta Arith. 143 (2010) 227-237. pdf
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 link
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 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)

What is an irrational number?
P. C. Toh
Blog post written for the Singapore Mathematical Society, July 2022. link pdf
Twelve Erroneous Proofs
P. C. Toh
The Mathematician Educator, 2 (2) (2021) 76-85. link pdf
Four Solutions of a Geometry Problem
P. C. Toh, W. K. Ho, Y. H. Leong, E. G. Tay, and C. L. Tong
The Mathematician Educator, 1 (2) (2020) 75-82. link pdf
On Angles Formed by Lines on a Square Lattice
P. C. Toh
Unpublished note, June 2020. pdf
Invariance as a Big Idea
P. C. Toh
In T. L. Toh and J. B. W. Yeo (Eds), Big Ideas in Mathematics, Association of Mathematics Educators: Yearbook 2019 (pp. 139-149). pdf link
Mathematics Instruction: Goals, Tasks and Activities
P. C. Toh and B. L. Chua (Editors)
Association of Mathematics Educators: Yearbook 2018. link
Developing 21st Century Competencies in the Mathematics Classroom
P. C. Toh and B. Kaur (Editors)
Association of Mathematics Educators: Yearbook 2016. link
Learning Experiences to Promote Mathematics Learning
P. C. Toh, T. L. Toh, and B. Kaur (Editors)
Association of Mathematics Educators: Yearbook 2014. link
A Problem on Egyptian Fractions
E. G. Tay and P. C. Toh
Mathematical Medley, 41(2), (2016) 8-10. 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.257-264). link, pdf
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. pdf
Self Learning Laboratory Sessions for Engineering Mathematics,
P. C. Toh
Proceedings of the 16th Asian Technology Conference in Mathematics, Bolu, Turkey, 2011, 187-192. link

Teaching

Conics for H2 Further Math. link

Events

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 )

Current and Past Student Projects

Determinant Evaluations
Binary Quadratic Forms
"Sum of Cubes equals Square of Sum" identities
Quadratic Iteration Digraphs
Eta products represented by univariate theta functions
Restricted partition functions (exactly/at most m parts)
On Distance-Pair Sequences
p-adic 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 Jan 2022