**Lecture 1:**Warm up (1) Algorithms on trees (8/1/2014), Scribe: Prafullkumar P Tale [pdf]**Lecture 2:**Warm up (2) Algorithms on t-decomposible graphs (9/1/2014), Scribe: Anantha Padmanabha MS [pdf]**Lecture 3:**Defining Tree Decompositions and their existence (10/1/2014), Scribe: Aditya Potukuchi [pdf]**Lecture 4:**Another equivalent definition of Tree Decompositions (13/1/2014), Scribe: Diptapriyo Majumdar [pdf]**Lecture 5:**An Approximation Algorithm for finding Tree Decomposition of a graph (14/1/2014), Scribe: Roohani Sharma [pdf]**Lecture 6:**Nice Tree Decompositions and Dynamic Programming on them (15/1/2014), Scribe: Prafullkumar P Tale [pdf]**Lecture 7:**Determinants, PIT and reducing Perfect Matching to PIT (20/1/2014), Scribe: Anantha Padmanabha MS [pdf]**Lecture 8:**Finding weight of minimum weighted cycle in a graph (21/1/2014), Scribe: Aditya Potukuchi [pdf]**Lecture 9:**Pfaffian of a Matrix (22/1/2014), Scribe: Diptapriyo Majumdar [pdf]**Lecture 10:**Counting number of Perfect Matchings in a graph using Pfaffian orientation (27/1/2014), Scribe: Roohani Sharma [pdf]**Lecture 11:**Finding Perfect Matching in O(n^(w+1)) time (28/1/2014), Scribe: Prafullkumar P Tale [pdf]**Lecture 12:**Finding Perfect Matching in O(n^w) time (Hervey's Algorithm) (28/1/2014), Scribe: Anantha Padmanabha MS [pdf]**Lecture 13:**Introduction to Matroids (1/2/2014), Scribe: Sanjukta Roy [pdf]**Lecture 14:**Representability of Matroids, Reduction of graph problems to Matroid Intersection and Matroid Parity (1/2/2014), Scribe: Sanjukta Roy [pdf]**Lecture 15, 16:**Solving Matroid Parity (3/2/2014, 5/2/2014), Scribe: Aditya Potukuchi [pdf]**Lecture 17, 18:**An O(mr^w) Algorithm for Matroid Parity (12/3/2014, 17/3/2014), Scribe: Aditya Potukuchi [pdf]**Lecture 19:**An O(m^w) algorithm for deciding Matroid Parity (19/3/2014), Scribe: Aditya Potukuchi [pdf]**Lecture 20:**An O(mr^(w-1)) algorithm for Matrid Parity (24/3/2014), Scribe: Aditya Potukuchi [pdf]**Lecture 21:**Matrix Multiplication and some applications (26/3/2014), Scribe: Diptapriyo Majumdar [pdf]**Lecture 22, 23:**All pair Shortest Paths in O(n^w log n) time (5/4/2014), Scribe: Roohani Sharma [pdf]**Lecture 24:**Finding the witness matrix in almost O(n^w) time (26/3/2014), Scribe: Sanjukta Roy [pdf]**Presentation 1:**Lemma of Gessel Viennot (22/4/2014), Diptapriyo Majumdar [pdf]**Presentation 2:**Proof of Tutteās Matrix Tree Theorem using Gessel Viennot lemma (23/4/2014), Sanjukta Roy [pdf]**Presentation 3:**Counting Steiner Trees and Hamiltonian Cycles on bounded treewidth graphs (25/4/2014), Aditya Potukuchi [pdf]**Presentation 4:**Courcelle's Theorem (25/4/2014), Anantha Padmanabha MS [pdf]**Presentation 5:**Solving Minimum Steiner Tree on bounded treewidth graphs using Guassian elimination (2/5/2014), Roohani Sharma [pdf]**Presentation 6:**Construction of Almost k-wise Independent Random Variables (11/5/2014), Prafullkumar P Tale [pdf]