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