Department of Mathematics

Programme: B.Sc(H) Mathematics

Courses offered by Department of Mathematics under B.Sc(H) Mathematics

Category: Core

Course outcomes

After completing the course, students should be able to

• Learn first and second derivative tests for relative extrema and apply the knowledge in problems in business, economics and life sciences.
• Sketch curves in a plane using its mathematical properties in the different coordinate systems of reference.
• Compute area of surfaces of revolution and the volume of solids by integrating over cross-sectional areas.
• Understand the calculus of vector functions and its use to develop the basic principles of planetary motion.

Category: Core

Course outcomes

After completing the course, students should be able to

• Employ De Moivre’s theorem in a number of applications to solve numerical problems.
• Learn about equivalent classes and cardinality of a set.
• Use modular arithmetic and basic properties of congruences
• Recognize consistent and inconsistent systems of linear equations by the row echelon form of the augmented matrix.
• Find eigenvalues and corresponding eigenvectors for a square matrix.

Category: Core

Course outcomes

After completing the course, students should be able to

• Understand many properties of the real line ℝ, including completeness and Archimedean properties.
• Learn to define sequences in terms of functions from ℕ to a subset of ℝ
• Recognize bounded, convergent, divergent, Cauchy and monotonic sequences and to calculate their limit superior, limit inferior, and the limit of a bounded sequence
• Apply the ratio, root, alternating series and limit comparison tests for convergence and absolute convergence of an infinite series of real numbers.

Category: Core

Course outcomes

After completing the course, students should be able to

• Learn basics of differential equations and mathematical modeling
• Formulate differential equations for various mathematical models
• Solve first order non-linear differential equations and linear differential equations of higher order using various techniques.
• Apply these techniques to solve and analyze various mathematical models.

Category: Core

Course outcomes

After completing the course, students should be able to

• Have a rigorous understanding of the concept of limit of a function
• Learn about continuity and uniform continuity of functions defined on intervals
• Understand geometrical properties of continuous functions on closed and bounded intervals
• Learn extensively about the concept of differentiability using limits, leading to a better understanding for applications.
• Know about applications of mean value theorems and Taylor’s theorem.

Category: Core

Course outcomes

After completing the course, students should be able to

• Recognize the mathematical objects that are groups, and classify them as abelian, cyclic and permutation groups, etc
• Link the fundamental concepts of groups and symmetrical figures.
• Analyze the subgroups of cyclic groups and classify subgroups of cyclic groups.
• Explain the significance of the notion of cosets, normal subgroups and factor groups
• Learn about Lagrange’s theorem and Fermat’s Little theorem.
• Know about group homomorphism and group isomorphism.

Category: Core

Course outcomes

After completing the course, students should be able to

• Learn the conceptual variations when advancing in calculus from one variable to multivariable discussion
• Understand the maximization and minimization of multivariable functions subject to the given constraints on variables.
• Learn about inter-relationship amongst the line integral, double and triple integral formulations
• Familiarize with Green's, Stokes' and Gauss divergence theorems.

Category: SEC

Course outcomes

After completing the course, students should be able to

• Create and typeset a LaTeX document.
• Typeset a mathematical document using LaTex
• Learn about pictures and graphics in LaTex.
• Create beamer presentations
• Create web page using HTML.

Category: Core

Course outcomes

After completing the course, students should be able to

• Formulate, classify and transform first order PDEs into canonical form.
• Learn about method of characteristics and separation of variables to solve first order PDE’s.
• Classify and solve second order linear PDEs.
• Learn about Cauchy problem for second order PDE and homogeneous and nonhomogeneous wave equations.
• Apply the method of separation of variables for solving many well-known second order PDEs.

Category: Core

Course outcomes

After completing the course, students should be able to

• Learn about some of the classes and properties of Riemann integrable functions, and the applications of the Fundamental theorems of integration.
• Know about improper integrals including, beta and gamma functions.
• Learn about Cauchy criterion for uniform convergence and Weierstrass M-test for uniform convergence.
• Know about the constraints for the inter-changeability of differentiability and integrability with infinite sum
• Approximate transcendental functions in terms of power series as well as, differentiation and integration of power series.

Category: Core

Course outcomes

After completing the course, students should be able to

• Learn about the fundamental concept of rings, integral domains and fields
• Know about ring homomorphisms and isomorphisms theorems of rings.
• Learn about the concept of linear independence of vectors over a field, and the dimension of a vector space.
• Basic concepts of linear transformations, dimension theorem, matrix representation of a linear transformation, and the change of coordinate matrix.

Category: Sec

Course outcomes

After completing the course, students should be able to

• Use of computer algebra systems (Mathematica/MATLAB/Maxima/Maple etc.) as a calculator, for plotting functions and animations
• Use of CAS for various applications of matrices such as solving system of equations and finding eigenvalues and eigenvectors.
• Understand the use of the statistical software R as calculator and learn to read and get data into R.
• Learn the use of R in summary calculation, pictorial representation of data and
• exploring relationship between data. Analyze, test, and interpret technical arguments on the basis of geometry.

Category: Core

Course outcomes

After completing the course, students should be able to

• Learn various natural and abstract formulations of distance on the sets of usual or unusual entities. Become aware one such formulations leading to metric spaces.
• Analyse how a theory advances from a particular frame to a general frame.
• Appreciate the mathematical understanding of various geometrical concepts, viz. balls or connected sets etc. in an abstract setting.
• Know about Banach fixed point theorem, whose far-reaching consequences have resulted into an independent branch of study in analysis, known as fixed point theory.
• Learn about the two important topological properties, namely connectedness and compactness of metric spaces.

Category: Core

Course outcomes

After completing the course, students should be able to

• Learn about automorphisms for constructing new groups from the given group.
• Learn about the fact that external direct product applies to data security and electric circuits.
• Understand fundamental theorem of finite abelian groups.
• Be familiar with group actions and conjugacy.
• Understand Sylow theorems and their applications in checking non-simplicity.

Category: DSE

Course outcomes

After completing the course, students should be able to

• Learn some numerical methods to find the zeroes of nonlinear functions of a single variable and solution of a system of linear equations, up to a certain given level of precision.
• Know about methods to solve system of linear equations, such as Gauss−Jacobi, Gauss−Seidel and SOR methods.
• Interpolation techniques to compute the values for a tabulated function at points not in the table.
• Applications of numerical differentiation and integration to convert differential equations into difference equations for numerical solutions

Category: DSE

Course outcomes

After completing the course, students should be able to

• Understand the notion of ordered sets and maps between ordered sets.
• Learn about lattices, modular and distributive lattices, sublattices and homomorphisms between lattices.
• Become familiar with Boolean algebra, Boolean homomorphism, Karnaugh diagrams, switching circuits and their applications.
• Learn about basics of graph theory, including Eulerian graphs, Hamiltonian graphs.
• Learn about the applications of graph theory in the study of shortest path algorithms.

Category: DSE

Course outcomes

After completing the course, students should be able to

• Learn the significance of differentiability of complex functions leading to the understanding of Cauchy−Riemann equations.
• Learn some elementary functions and valuate the contour integrals.
• Understand the role of Cauchy−Goursat theorem and the Cauchy integral formula.
• 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

Category: DSE

Course outcomes

After completing the course, students should be able to

• Appreciate the significance of unique factorization in rings and integral domains.
• Compute the characteristic polynomial, eigenvalues, eigenvectors, and eigenspaces, as well as the geometric and the algebraic multiplicities of an eigenvalue and apply the basic diagonalization result.
• Compute inner products and determine orthogonality on vector spaces, including Gram−Schmidt orthogonalization to obtain orthonormal basis.
• Find the adjoint, normal, unitary and orthogonal operators.

Category: DSE

Course outcomes

After completing the course, students should be able to

• Learn about probability density and moment generating functions.
• Know about various univariate distributions such as Bernoulli, Binomial, Poisson, gamma and exponential distributions.
• Learn about distributions to study the joint behavior of two random variables.
• Measure the scale of association between two variables, and to establish a formulation helping to predict one variable in terms of the other, i.e., correlation and linear regression.
• Understand central limit theorem, which helps to understand the remarkable fact that the empirical frequencies of so many natural populations, exhibit a bellshaped curve, i.e., a normal distribution

Category: DSE

Course outcomes

After completing the course, students should be able to

• Learn about the graphical solution of linear programming problem with two variables.
• Learn about the relation between basic feasible solutions and extreme points
• Understand the theory of the simplex method used to solve linear programming problems.
• Learn about two-phase and big-M methods to deal with problems involving artificial variables.
• Learn about the relationships between the primal and dual problems.
• Solve transportation and assignment problems
• Apply linear programming method to solve two-person zero-sum game problems.