Mathematical research in high school: The PRIMES experience

Document Type : Translation Paper

Authors

Sheikhbahaee University

Abstract

This paper is a translation of the the following paper into Persian:
[P. Etingof, S. Gerovitch and T. khovanova, [P. Etingof, S. Gerovitch and T. khovanova, Mathematical research in high school: The PRIMES experience, Notices of the American Mathematical Society, 62 no. 8 (2015) 910–918.], Notices of the American Mathematical Society, 62 no. 8 (2015) 910–918.]
 
High level original mathematical research is possible by high-school students. In particular, chosen research programs properly and supervised by expert mentors, produces young mathematical researchers. Program for Research in Mathematics, Engineering, and Science, has proved such an experience.
 
 
 

[1] S. Bhupatiraju, P. Etingof, D. Jordan, W. Kuszmaul and J. Li, Lower central series of a free associative algebra over the integers and finite fields, J. Algebra, 372 (2012) 251–274.
[2] L. M. Braswell and T. Khovanova, On the Cookie Monster Problem, http://arXiv:1309.5985.
[3] L. M. Braswell and T. Khovanova, Cookie Monster devours Naccis, College Math. J., 45 no. 2 (2014) 129–135.
[4] Y. Chen, P. Etingof, D. Jordan and M. Zhang, Poisson traces in positive characteristic, http://arXiv:1112.6385.
[5] C. Chen, Maximizing volume ratios for shadow covering by tetrahedra, http://arXiv:1201.2580.
[6] C. Chen, T. Khovanova and D. A. Klain, Volume bounds for shadow covering, Trans. Amer. Math. Soc., 366 no. 3 (2014) 1161–1177.
[7] S. Devadas and S. Sam, Representations of rational Cherednik algebras of G(m, r, n) in positive characteristic, J. Commut. Algebra, 6 no. 4 (2014) 525–559.
[8] F. Ding and A. Tsymbaliuk, Representations of infinitesimal Cherednik algebras, Represent. Theory, 17 (2013) 557–583.
[9] C. Lian, Representations of Cherednik algebras associated to symmetric and dihedral groups in positive characteristic, arXiv:1207.0182.
[10] Yael Fregier and Isaac Xia, Lower Central Series Ideal Quotients Over Fp and Z, http://arXiv:1506.08469.
[11] N. Golowich, Resolving a Conjecture on degree of regularity of linear homogeneous equations, Electro. J. Combin., 21 (2014) no. 3.
[12] R. Jagadeesan, A new Gal( )-invariant of dessins d’enfants, http://arXiv:1403.7690.
[13] Shashwat Kishore and Augustus Lonergan, Signatures of Multiplicity Spaces in tensor products of sf2 and Uq(sf2). Repre-sentations, arXiv:1506.02680.
[14] T. Khovanova and J. Xiong, Cookie Monster plays games, arXiv:1407.1533.
[15] T.-Y. Jiang, Z. Scully and Y. X. Zhang, Motors and impossible firing patterns in the parallel chipfiring game, SIAM J. Discrete Math., 29 (2015) 615–630.
[16] J. Zurier, Generalizations of the Joints Problem, math.mit.edu/research/highschool/primes/ materials/2014/Zurier.pdf
Volume 2, Issue 2
June 2017
Pages 19-34
  • Receive Date: 06 November 2015
  • Revise Date: 01 June 2016
  • Accept Date: 01 June 2016
  • Publish Date: 23 August 2017