MATH: P-13 Number Theory and Graph Theory(e-PGP) (English)

   Tuesday, January 24, 2023   

Starting a new Lecture Notes Series on MATH: P-13 Number Theory and Graph Theory(e-PGP)

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MATH: P-13 Number Theory and Graph Theory(e-PGP)
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Lecture Description of this above Topic:

Lecture 1: Introduction to arithmetic functions (MATH)

Lecture 2: Properties of Euler’s Phi-function (MATH)

Lecture 3: Euler’s Theorem and Dirichlet product (MATH)

Lecture 4: nth roots of unity (MATH)

Lecture 5: Primitive roots (MATH)

Lecture 6: Quadratic residues/non-residues (MATH)

Lecture 7: Gauss Lemma (AMTH)

Lecture 8: Quadratic Reciprocity Law (MATH)

Lecture 9: The Gaussian Integers (MATH)

Lecture 10: Pythagorean Triples (MATH)

Lecture 11: Pell’s Equation (MATH)

Lecture 12: Introduction to graph theory (MATH)

Lecture 13: Some known graph families and their properties (MATH)

Lecture 14: Construction of new graphs from old graphs (MATH)

Lecture 15: Connectedness of a graph (MATH)

Lecture 16: Graph isomorphism and automorphism group of a graph (MATH)

Lecture 17: Trees (MATH)

Lecture 18: Eulerian and Hamiltonian Graphs (MATH)

Lecture 19: Planar graphs and coloring (MATH)

Lecture 20: Matching and covering (MATH)

Lecture 21: Network flows (MATH)

Lecture 22: Review of eigenvalues and eigenvectors of a square matrix (MATH)

Lecture 23: Adjacency matrix of a graph (MATH)

Lecture 24: Bounds of eigenvalues of subgraphs and eigenvalues of regular graphs (MATH)

Lecture 25: Eigenvalues of some known graphs/digraphs (MATH)

Lecture 26: Automorphisms of graphs and adjacency matrix (MATH)

Lecture 27: Nonnegative matrices (MATH)

Lecture 28: Incidence matrix of a graph (MATH)

Lecture 29: Laplacian matrix of a graph (MATH)