The Teacher Enrichment Workshop is an outreach activity of the National Centre for Mathematics to enrich mathematical instruction at college level. Mathematics teachers from colleges in the vicinity of Jalandhar will be introduced to some interesting topics related to what they already teach. An important component of this Workshop is the discussion hour during which the teachers will have opportunities to get their doubts cleared and work out exercises. This Workshop is meant for mathematics teachers of Arts and Science colleges in and around Jalandhar.** It may be noted that accommodation will NOT be provided to participants.**

**Speakers and Tutors**

- Dinesh Khurana, Panjab University, Chandigarh.
- Amit Kulshrestha, IISER Mohali.
- Chanchal Kumar, IISER Mohali
- D. S. Ramana, HRI Allahabad

**Syllabus**

- Dinesh Khurana: Vector spaces and their basic properties, Linear Transformations and Matrices,Change of Basis, Triangulation and Diagonalization, Modules, Modules versus Vector Spaces, Free Modules, Matrices over PIDs, Smith Normal Form, Finitely Generated Modules over PIDs and their structure, Rational and Jordan Canonical Forms.
- Amit Kulshrestha: Surfaces, Level surfaces, A need for the Implicit Function Theorem, Projecting globe as a 2D-map, Curvature of a curve, Devising notion of curvature for a surface and a need for Taylor’s formula, Normal sections, Normal and Geodesic curvature, Principal curvature, Gauss’ Theorema Egregium.
- Chanchal Kumar: Groups, Subgroups, Quotient groups, Action of groups on a set, Class equations,Syllow’s theorem, Solvable groups, Characterization of small order groups, Some applications of group theory.
- D. S. Ramana: Review of Euclidean Spaces, Derivatives, Partial Derivatives and the Chain Rule, Mean Value Theorem, Taylor’s Formula, Inverse and Implicit Function Theorems.

**Time Table** (Tea Breaks: 10.30 - 11, 3.30 - 4; Lunch: 1 - 2.30; Snacks Break: 5 - 5.30

Date |
9.30 - 10.30 |
11:00 - 12:00 |
12:00 - 1:00 |
2.30 - 3.30 |
4 :00- 5:00 (Discussion) |

May 28 | Khurana | Kulshrestha | Khurana | Kulshrestha | Khurana |

May 29 | Khurana | Kulshrestha | Khurana | Kulshrestha | Kulshrestha |

May 30 | Khurana | Kulshrestha | Khurana | Kulshrestha | Khurana |

May 31 | Kumar | Ramana | Kumar | Ramana | Kumar |

June 1 | Kumar | Ramana | Kumar | Ramana | Ramana |

June 2 | Kumar | Ramana | Kumar | Ramana | Kumar |