Complex Analysis
Course Objectives: This course aims to introduce the basic ideas of analysis for complex functions in complex variables with visualization through relevant Practicals. Particular emphasis has been laid on Cauchy’s theorems, series expansions and calculation of residues. Course Learning Outcomes: The completion of the course will enable the students to: i) Understand the significance of differentiability of complex functions leading to the understanding of Cauchy-Riemann equations. ii) Evaluate the contour integrals and understand the role of Cauchy-Goursat theorem and the Cauchy integral formula. iii) Expand some simple functions as their Taylor and Laurent series, classify the nature of singularities, find residues and apply Cauchy Residue theorem to evaluate integrals. iv) Represent functions as Taylor, power and Laurent series, classify singularities and poles, find residues and evaluate complex integrals using the residue theorem.
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Course Objectives: The course objective is to introduce students to the fundamental theory of groups and their homomorphisms. Symmetric groups and symmetries in groups, Lagrange's theorem are also studied in depth. Course Learning Outcomes: The course will enable the students to: i) recognize the mathematical objects that are groups, and classify them as abelian, cyclic and permutation groups, etc; ii) analyze consequences of Lagrange’s theorem iii) learn about structure preserving maps between groups and their consequences. iv) explain the significance of the notion of cosets, normal subgroups, and factor groups.
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Enzymology
To understand methods of active site determination, role of enzymes and its cofactors in microbial physiology
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