| Analysis and Linear Algebra (UMA 102) |
Linear Algebra continued: Inner products and Orthogonality; Determinants; Eigenvalues and Eigenvectors; Diagonalisation of symmetric matrices. Multivariable calculus: Functions on Rn, partial and total derivatives; Chain rule; Maxima, minima and saddles; Lagrange multipliers; Integration in Rn, change of variables, Fubini’s theorem; Gradient, Divergence and Curl; Line and Surface integrals in R2 and R3 ; Stokes, Green’s and Divergence theorems. Introduction to Ordinary Differential Equations; Linear ODEs and Canonical forms for linear transformations.
|
A+ |
| Discrete Mathematics (UMC 103) |
Mathematical Logic: Propositional logic: connectives, tautologies, and contradictions, logical equivalences, normal forms and applications. Predicates and quantifiers, interpretation and validity, proving validity, rules of inference. Sets, Functions and Relations: Sets and cardinality, relations, functions, partial orders, total orders, linear orders, equivalence relations, partitions, n-ary relations. Induction and Recursion: Induction, strong induction, well-ordering principle, recursive definitions and structural induction. Basic Counting Principles: Pigeon hole principle, permutations and combinations, Binomial coefficients and identities, elementary applications to discrete probability, recurrence relations and equations, generating function techniques, principles of inclusion and exclusion and its applications. Graph Theory: Graphs and graph models, basic notions and operations, matchings, Hall’s marriage theorem, vertex and edge connectivity, Euler and Hamiltonian circuits, vertex coloring. Trees.
|
A |