# TEW - Algebra, Linear Algebra, Cryptography

## Speakers and Syllabus

The Teacher’s Enrichment Workshop is a programme funded by the National Centre for Mathematics (NCM) the funding body for various instructional schools conducted at several levels in various places throughout the country. This workshop is also part of the outreach series `Enriching Collegiate Education' of the Institute of Mathematical Sciences (IMSc) Chennai, which co-sponsors the activity. The TEW is meant for college teachers to revisit and update their content-knowledge. The lectures in the workshop cover specific topics which are relevant for the teachers' classroom instruction. An important component of this workshop is the discussion hour during which the teachers will have opportunities to get their doubts cleared and to work out routine to advanced exercises.

This workshop is meant for mathematics teachers of Engineering colleges in and around Chennai. In view of infrastructural difficulties accommodation will NOT be provided for participants.

This particular edition of the workshop is being funded from the J. C. Bose Fellowship grant of Prof. T. R. Ramdas of CMI, Chennai.

**Syllabus:****Algebra** : Basic examples of groups and homomorphisms, equivalences and partitions, group actions and some applications,the orbit - stabilizer formula, class equation, Sylow's theorem, finitely generated abelian groups.**Linear Algebra** : Review of eigenvalues and eigenvectors, inner product spaces and linear transformations, matrix eigen value problem, some applications of eigen value problems, symmetric and orthogonal matrices, singular value decomposition, quadratic forms.**Cryptography** : Elliptic Curves, addition formula, elliptic curves over finite fields, the elliptic curve discrete logarithm problem, double and add algorithm, Elliptic Diffie-Hellman key exchange protocol, Elliptic Elgamal cryptosystem.

Name of the Speaker with affiliation |
Number of Lectures |
DetailedSyllabus |

K. N. Raghavan (KNR) IMSc Chennai | 6 | Algebra |

Pralay Chatterjee (PC) IMSc, Chennai | 6 | Linear Algebra |

K. Srinivas (KS) IMSc Chennai. | 6 |
Cryptography |

## Time Table

(day) |
(date) |
09.30-11 |
11-11: 30 |
11:30-13. 00 |
13.00-14 :00 |
14:-00-15:30 |
15:30-15.4 5 |
15:45-16:45Discussion |
16:45Snacks |

Mon | 25/11/19 | KNR | Tea | KS | Lunch | PC | Tea | D/T | |

Tue | 26/11/19 | KNR | PC | KS | D/T | ||||

Wed | 27/11/19 | KNR | PC | KS | D/T | ||||

Thu | 28/11/19 | KNR | PC | KS | D/T | ||||

Fri | 29/11/19 | PC | KS | KNR | D/T | ||||

Sat | 30/11/19 | PC | KNR | KS | D/T | ||||