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# Department of Mathematics

## Introduction

The Department of Mathematics is one of the main constituents of UIET since its beginning. From the very start, it has shared the vision of the Institute in serving for excellence in teaching and other activities. The Department is mainly involved in teaching core courses of B.Tech. program. However, it also runs various courses for other disciplines such as BCA, MCA, B Pharm. and M.Sc. Bioinformatics etc. Currently, there are four faculty members in the department who are actively involved in research and other academic activities.

## Faculty

 Dr. V.N. PalAssociate ProfesorPh.D Area of interest: Mathematical Modelling Dr. Varsha Gupta(HOD)Associate ProfesorrPh.D. Area of interest: Numerical Methods Mr.Vaibhav MishraAssistant ProfesorrM.Sc. ,CSIR-NET
 Dr. Manoj Kumar SinghAssistant ProfesorPh.D. Area of interest: Differential GeometryGoogle Scholar Dr. Dharmendra Kumar SinghAssistant ProfesorPh.D. Area of interest: Fractional CalculusGoogle Scholor Dr. Poonam DixitAssistant ProfesorPh.D. Area of interest: Complex Analysis

## Course Curriculum

Mathematics department caters to four streams namely:
2. Master of computer application
3. Bachelor of computer application
4. Bioinformatics

The department runs four courses namely MTH-101, MTH-102, MTH-201 & MTH-301 for B.Tech students to provide them a basic understanding of Engineering Mathematics and to form their background to study higher level of engineering courses. The essential mathematical tools required for other streams are stressed upon so as to expose the students to a wide variety of applications in their respective programs. The broad subject areas being covered during these courses are following:

1. MTH 101: CALCULUS

This paper mainly comprises of sequence and series, power series, definite integral applications, approximation techniques in integration, vector calculus, limit, continuity, differentiability and their applications, multiple integral and applications.

2.MTH 101: LINEAR ALGEBRA AND DIFFERENTIAL EQUATIONS

This section consists of of linear vector space ,linear transformations and matrices, slinear simultaneous algebraic equations, diogonalization and canonical forms in linear algebra ; and first &second order differential equation,initial/boundary value problem system of linear equations,higher order differential equations,Laplace transforms,Series solutions,Sturn liouvilles problems,Bessel functions in differential equations.

3.MTH 201: COMPLEX ANALYSIS AND PARTIAL DIFFERENTIAL EQUATIONS

Function of complex variable, C –R equations, analytic functions, complex integration and contour integration.Probabilty theory and distributions, Fourier series and Fourier integrals.

4.MTH 301 : DISCRETE MATHEMATICS

Elementary combinatorcs, basic counting, permutations and combinations, principle of exclusion and inclusion. Recurrence relationsolving recurrence relation by different techniques , ,digraphs , graphs, spanning tree, planar graphs, Euler’s formula, Hamiltonian graphs.

5.MCA103: MATHEMATICAL FOUNDATION OF COMP. SCIENCE

Set theory: sets, function and Sequences, Relations, Partially ordered sets, Closure, Lattices. Groups and Ring:; Logic; Recurrence Relations and their solutions, Discrete functions and Generating Functions, Manipulations of Numeric functions; Elementary Combinatorics: Permutation, combination, the Principle of Inclusion Exclusion, Pigeonhole Principle, Multinomial Theorem, Binomial Theorem; Boolean Algebra

6. MCA 204 : GRAPH THEORY AND AUTOMATA THEORY

Graphs : Incidence and degree, II and shaking lemma, Isomorphism, subgraphs, Union of graphs, connectedness,walks, paths, circuits, components, connectedness, shortest path algorithms, Eulerian-graph, fleury’s alogorithm, Chinese postman problem, Hamiltonian graphs necessary and sufficient conditions, traveling salesman problem, bipartite graph, Trees, Planer Graphs.

7. PBI 101: BASIC MATHEMATICS :

Differentiation, Integration, Matrices, 3d-Geomrtry, Vector Analysis.

8. PBI 102 :PROBABILITY AND STATISTICS:

Introduction to probability, Conditional expectations, Bayes theorem, Random variables, data representation, joint distribution representation, mean/mode/median/standard deviation etc. Histogram, scatter plot, Distributions (binomial, Poisson and normal), Test of significance (x2 and t) regression and correlation, Analysis of variance. Information and Entropy representation and summary of data ; Statistical distributions as models of data; parametric models, statistical inference: Likelihood; Posterial distribution; Maximum Likelihood; Bios and variance trade off models of dependence: Markov chains; Boltazmann-Gibbs distribution.

9. MBI 101: BASIC MATHEMATICS :

Differentiation, Integration, Matrices, 3d-Geomrtry, Vector Analysis.

10. MBI 102: PROBABILITY AND STATISTICS:

Introduction to probability, Conditional expectations, Bayes theorem, Random variables, data representation, joint distribution representation, mean/mode/median/standard deviation etc. Histogram, scatter plot, Distributions (binomial, Poisson and normal), Test of significance (x2 and t) regression and correlation, Analysis of variance. Information and Entropy representation and summary of data ; Statistical distributions as models of data; parametric models, statistical inference: Likelihood; Posterial distribution; Maximum Likelihood; Bios and variance trade off models of dependence: Markov chains; Boltazmann-Gibbs distribution.