# TEW Algebra, Discrete Mathematics, Complex Analysis (2017) - Speakers and syllabus

The Teacher Enrichment Workshop is a programme funded by the National Council 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 activity `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 covers specific topics which are relevant for the teachers' classroom instructions. 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 routine to advanced exercises.
This Workshop is meant for mathematics teachers of Arts and Science colleges in and around Chennai. In view of infrastructural difficulties accommodation will NOT be provided for participants.

Syllabus:

• Algebra: Group actions and examples: regular action, action by conjugacy, action on cosets; new actions from old: diagonal action, actions on function spaces; restriction.Orbits and stabilisers: structure of an orbit, equivalence class of orbits, transitive actions and homogeneous spaces. Lagrange's theorem; order of an orbit divides order of the group.
Class equation, its variations and applications: action of p-groups; centre of a p-group is non-trivial.
Applications to structure of finite groups: existence or lack thereof of subgroups of a finite group of given orders: theorems of Cauchy and Sylow asserting existence of subgroups of prime power orders (dividing the order of the group); Sylow p-subgroups: theorems of Sylow about their conjugacy and number.
• Discrete Mathematics: Permutations and combinations, combinations with repetition, multinomial coefficients, inclusion-exclusion principle, partitions, bijective proofs of identities, recurrence relations, generating functions, elementary graph theory.
• Complex Analysis : Analytic functions, complex integration, Cauchy’s theorem,Cauchy’s integral formula, maximum modulus principle, zeros of analytic functions, Cauchy’s residue theorem, evaluation of integrals.
 Name of the Speaker with affiliation Number of Lectures Detailed Syllabus K.N. Raghavan (KNR) IMSc Chennai 6 Algebra S. Viswanath (SV)IMSc, Chennai 6 Discrete Mathematics K. Srinivas (KS) IMSc Chennai. 6 Complex analysis

Time- Table

 (day) (date) Speaker 1 09.30-11 Tea 11-11:30 Speaker 2 11:30 to 13.00 Lunch. 13.00to 14:00 Speaker-3 14:00to15:00 Tea 15:00to15.15 Discussion 15:15 to 16:45 Snacks 16:45 Mon 22/05/17 KNR SV KS D/T Tue 23/05/17 KS KNR SV D/T Wed 24/05/17 SV KS KNR D/T Thu 25/05/17 KNR SV KS D/T Fri 26/05/17 KS KNR SV D/T Sat 27/05/17 SV KS KNR D/T