Integer partitions; q-series, elementary identities (q-binomial theorem, Heine's transformation, Jacobi's triple product identity, Ramanujan's 1-psi-1 transformation) and corollaries; q-series as partition generating functions; Ramanujan's congruences for the partition function, Rogers- Ramanujan generalizations.
Special Topics in MATH: Integer partitions and q-series. (MATH 58003)
Programs\Type | Required | Core Elective | Area Elective |
Computer Science and Engineering - With Bachelor's Degree | * | ||
Computer Science and Engineering - With Master's Degree | * | ||
Computer Science and Engineering - With Thesis | * | ||
Cyber Security - With Bachelor's Degree | * | ||
Cyber Security - With Master's Degree | * | ||
Cyber Security - With Thesis | * | ||
Data Science - With Thesis | * | ||
Electronics Engineering and Computer Science - With Bachelor's Degree | * | ||
Electronics Engineering and Computer Science - With Master's Degree | * | ||
Electronics Engineering and Computer Science - With Thesis | * | ||
Electronics Engineering - With Bachelor's Degree | * | ||
Electronics Engineering - With Master's Degree | * | ||
Electronics Engineering - With Thesis | * | ||
Energy Technologies and Management-With Thesis | * | ||
Industrial Engineering - With Bachelor's Degree | * | ||
Industrial Engineering - With Master's Degree | * | ||
Industrial Engineering - With Thesis | * | ||
Leaders for Industry Biological Sciences and Bioengineering - Non Thesis | * | ||
Leaders for Industry Computer Science and Engineering - Non Thesis | * | ||
Leaders for Industry Electronics Engineering and Computer Science - Non Thesis | * | ||
Leaders for Industry Electronics Engineering - Non Thesis | * | ||
Leaders for Industry Industrial Engineering - Non Thesis | * | ||
Leaders for Industry Materials Science and Engineering - Non Thesis | * | ||
Leaders for Industry Mechatronics Engineering - Non Thesis | * | ||
Manufacturing Engineering - Non Thesis | * | ||
Manufacturing Engineering - With Bachelor's Degree | * | ||
Manufacturing Engineering - With Master's Degree | * | ||
Manufacturing Engineering - With Thesis | * | ||
Materials Science and Nano Engineering-(Pre:Materials Science and Engineering) | * | ||
Materials Science and Nano Engineering-(Pre:Materials Science and Engineering) | * | ||
Materials Science and Nano Engineering - With Thesis (Pre.Name: Materials Science and Engineering) | * | ||
Mathematics - With Bachelor's Degree | * | ||
Mathematics - With Master's Degree | * | ||
Mathematics - With Thesis | * | ||
Mechatronics Engineering - With Bachelor's Degree | * | ||
Mechatronics Engineering - With Master's Degree | * | ||
Mechatronics Engineering - With Thesis | * | ||
Molecular Biology, Genetics and Bioengineering (Prev. Name: Biological Sciences and Bioengineering) | * | ||
Molecular Biology, Genetics and Bioengineering-(Prev. Name: Biological Sciences and Bioengineering) | * | ||
Molecular Biology,Genetics and Bioengineering-With Thesis (Pre.Name:Biological Sciences and Bioeng.) | * | ||
Physics - Non Thesis | * | ||
Physics - With Bachelor's Degree | * | ||
Physics - With Master's Degree | * | ||
Physics - With Thesis | * |
CONTENT
OBJECTIVE
* to understand the place of integer partitions among counting problems
* to understand various methods of proving a partition identity, and to be able to imitate those proofs to find similar identities
* to be able to construct and manipulate q-series using well-known transformation formulas
* to be able to recognize q-series as partition generating functions
* to be able to manipulate q-series in modular arithmetic, and prove partition congruences.
* to be able to use symbolic computation software and do large scale computational experiments for new discoveries.
Update Date:
ASSESSMENT METHODS and CRITERIA
Percentage (%) | |
Presentation | 40 |
Homework | 60 |
RECOMENDED or REQUIRED READINGS
Textbook |
Andrews, G.E., 1998. The theory of partitions (No. 2). Cambridge university press. Berndt, B.C., 2006. Number theory in the spirit of Ramanujan (Vol. 34). American Mathematical Soc.. |
Readings |
Andrews, G.E. and Eriksson, K., 2004. Integer partitions. Cambridge University Press. Gasper, G., Rahman, M. and George, G., 2004. Basic hypergeometric series (Vol. 96). Cambridge university press. Hirschhorn, M.D., 2017. The Power of q. In Developments in Mathematics (Vol. 49). Springer. |