Outline of Topics to  be Covered:

• Linear Algebra:
  Review of Eigenvalues and eigenvectors, Spectral theorem for normal operators, Positive matrics, Structure of orthogonal matrices, Singular value decomposition, Best approximation, Fundamental theorem of algebra
• Group Theory:
  Equivalences and Partitions, Basic definitions and examples of groups and homomorphisms, including cyclic, dihedral, permutation and alternating groups, and matrix groups. Subgroups, and the induced equivalence relations, quotient groups. Group actions, the orbit-­‐stabilizer formula, and class equation. Sylow's theorems, classification of groups of order 12, finitely generated abelian groups. Groups of units of a field, and groups of automorphisms arising from field extensions. Solvable groups.
• Enumerative Combinatorics:
  Basic methods (pigeonhole principle and mathematical induction) with many combinatorial applications. Permutations, binomial coefficients, multisets. Binomial theorem and related identities. Compositions, integer partitions, set partitions, Stirling numbers. Cycles in permutations and permutations with restricted cycle structure. Principle of inclusion and exclusion, Sieve methods. Generating functions (including ordinary and exponential generating functions), Recurrence relations.

Timetable (Inauguration is scheduled during 9.30-9.45 am on Sunday, 23^rd December):

 List of Speakers/Tutors

JKV = J. K. Verma, IIT Bombay (Linear Algebra)
AH = Ananthnarayan Hariharan, IIT Bombay (Group Theory)
SRG = Sudhir R. Ghorpade, IIT Bombay (Enumerative Combinatorics I and Linear Algebra)
SR = Samrith Ram, IIIT Delhi (Enumerative Combinatorics II and Linear Algebra)
JS = Jyoti Singh, VNIT, Nagpur (Linear Algebra and Group Theory)