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B. Sc. in Mathematics (Honours and Generic)

Teaching Plan for All Courses

The department was opened in 1966 at the time of the establishment of the college. Late Akan Chandra Pathak was the founder teacher of the department. Initially he was assisted by Pranjit Kumar Das and late Bipul Kanti Sarma. Pranjit Kumar Das served as the Principal-in-charge of the college for a period of about one year before his retirement as the Vice-Principal of the college. B.Sc. Major in Mathematics was started in 1997 when Major courses were opened for other science subjects. The teachers of the department also teach Business Mathematics in B.Com. 4th semester Honours and in 1st semester B.B.A. B.A. students can also take Mathematics as Honours subject in our college.

A clear vision for learning Mathematics is one where students engage in meaningful mathematical experience through the use of concrete materials. The Mathematics curriculum also helps the students who can develop a positive identity as a mathematics learner and see themselves as mathematically skilled. Our vision is to build a collaborative mathematics community for students in order to support, advocate and influence mathematics education in our area.

To provide an environment where students can learn, become competent users of mathematics in other disciplines. The honours and generic courses of mathematics are designed to prepare students to work in areas which require critical thinking, skills and the ability to work with mathematical concepts. The Mathematics Department of our college creates and sustain an environment that empowers students to learn and apply mathematics to solve various problems and to allow them to achieve their potential as learners and as productive, contributing members of the community. The members of the Mathematics Department are dedicated to provide mathematics education of the highest quality to their students. The Mathematics Department provides students with the necessary mathematical preparation to pursue their chosen field of study, and deal with mathematical processes and skills needed for everyday living.

1. The Bachelor’s Degree in B.Sc. (Honours) Mathematics is award to the students on the basis of knowledge, understanding, skills, attitudes, values and academic achievements sought to be acquired by learners at the end of this program.

2. To demonstrate basic manipulative skills in algebra, geometry, trigonometry and beginning calculus. Bachelor’s degree in Mathematics is the culmination of in-depth knowledge of algebra, calculus, geometry, differential equations and several other branches of Mathematics. This also leads to study of related areas like Computer Science, Financial Mathematics, Mathematical biology, Statistics and many more. Thus, this programme helps learners in building a solid foundation for higher studies in Mathematics. The skill and knowledge gained has intrinsic beauty, which also leads to proficiency in analytical reasoning. This can be utilised in various modelling and solving real life problems. This helps them to learn behave responsibly in a rapidly changing independent society. Students completing this programme will be able to present Mathematics clearly and precisely. Completion of this programme will also enable the learners to join teaching profession in primary and secondary schools. This programme will also help students to enhance their employability for government jobs, jobs in banking, insurance and investment sectors and jobs in various other public and private enterprises.

1. Scientific temper and skill will be developed among the

students. Techniques for solving difficult problems in Mathematics

will also be developed.

2. A student should get adequate exposure to global and local concerns

that explore them many aspects of Mathematical Sciences.

3. Students will be aware of and able to develop solution oriented approach towards various social and Environmental issues.

Course: B.Sc. (Honours and Generic) in Mathematics

Paper Code: MAT-HC-1016: Calculus (including practical)

Course Objectives: The primary objective of this course is to introduce the basic tools of calculus and geometric properties of different conic sections which are helpful in understanding their applications in planetary motion, design of telescope and to the real-world problems. Also, to carry out the hand on sessions in computer lab to have a deep conceptual understanding of the above tools to widen the horizon of students’ self-experience.

Course Learning Outcomes: This course will enable the students to:

i. Learn first and second derivative tests for relative extremum and apply the knowledge in problems in business, economics and life sciences.

ii. Sketch curves in a plane using its mathematical properties in the different coordinate systems of reference.

iii. Compute area of surfaces of revolution and the volume of solids by integrating over cross-sectional areas.

iv. Understand the calculus of vector functions and its use to develop the basic principles of planetary motion.

Paper Code: MAT-HC-1026: Algebra

Course Objectives: The primary objective of this course is to introduce the basic tools of set theory, functions, induction principle, theory of equations, complex numbers, number theory, matrices and determinant understand their connection with the real-world problems.

Course Learning Out comes: This course will enable the students to:

i) Employ De Moivre’s theorem in a number of applications to solve numerical problems.

ii) Learn about equivalent classes and cardinality of a set.

iii) Use modular arithmetic and basic properties of congruences.

iv) Recognize consistent and inconsistent systems of linear equations by the row echelon form of the augmented matrix.

v) Learn about the solution sets of linear systems using matrix method and Cramer’s rule

Paper Code: MAT-HG-1026: Analytical Geometry

Course Objectives: The primary objective of this course is to introduce the basic tools of two-dimensional coordinate systems, general conics, and three-dimensional coordinates systems. Also, introduces the vectors in coordinate systems with geometrical properties

Course Learning Out comes: This course will enable the students to:

i) Transform coordinate systems, conic sections

ii) Learn polar equation of a conic, tangent, normal and related properties

iii) Have a rigorous understanding of the concept of three-dimensional coordinate systems

iv) Understand geometrical properties of dot product, cross product of vectors

Paper Code: MAT-HC-2016: Real Analysis

Course Objectives: The course will develop a deep and rigorous understanding of real line R and of defining terms to prove the results about convergence and divergence of sequences and series of real numbers. These concepts have wide range of applications in real life scenario.

Course Learning Out comes: This course will enable the students to:

i) Understand many properties of the real line R, including completeness and Archimedean properties.

ii) Learn to define sequences in terms of functions from N to a subset of R.

iii) Recognize bounded, convergent, divergent, Cauchy and monotonic sequences and to calculate their limit superior, limit inferior, and the limit of a bounded sequence.

iv) Apply the ratio, root, alternating series and limit comparison tests for convergence and absolute convergence of an infinite series of real numbers.

Paper Code: MAT-HC-2026: Differential Equations (including practical)

Course Objectives: The main objective of this course is to introduce the students to the exciting world of differential equations, mathematical modeling and their applications.

Course Learning Outcomes: The course will enable the students to:

i) Learn basics of differential equations and mathematical modeling.

ii) Formulate differential equations for various mathematical models.

iii) Solve first order non-linear differential equations and linear differential equations of higher order using various techniques.

iv) Apply these techniques to solve and analyze various mathematical models.

Paper Code: MAT-HG-2016/MAT-RC-2016: Algebra

Course Objectives: The primary objective of this course is to introduce the basic tools of theory of equations, complex numbers, number theory, matrices, determinant, along with algebraic structures like group, ring and vector space to understand their connection with the real-world problems.

Course Learning Outcomes: This course will enable the students to:

i) Learn how to solve the cubic and biquadratic equations, also learn about symmetric functions of the roots for cubic and biquadratic

ii) Employ De Moivre’s theorem in a number of applications to solve numerical problems.

iii) iii) Recognize consistent and inconsistent systems of linear equations by the row echelon form of the augmented matrix. Finding inverse of a matrix.

iv) Recognize the mathematical objects that are groups, and classify them as abelian, cyclic and permutation groups, ring etc.

Paper Code: MAT-HC-3016: Theory of Real Functions

Course Objectives: It is a basic course on the study of real valued functions that would develop an analytical ability to have a more matured perspective of the key concepts of calculus, namely; limits, continuity, differentiability and their applications.

Course Learning Outcomes: This course will enable the students to:

i) Have a rigorous understanding of the concept of limit of a function.

ii) Learn about continuity and uniform continuity of functions defined on intervals.

iii) Understand geometrical properties of continuous functions on closed and bounded intervals.

iv) Learn extensively about the concept of differentiability using limits, leading to a better understanding for applications.

v) Know about applications of mean value theorems and Taylor’s theorem

Paper Code: MAT-HC-3026: Group Theory-I

Course Objectives: The objective of the course is to introduce the fundamental theory of groups and their homomorphisms. Symmetric groups and group of symmetries are also studied in detail. Fermat’s Little theorem is studied as a consequence of the Lagrange’s theorem on finite groups.

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) Link the fundamental concepts of groups and symmetrical figures.

iii) Analyze the subgroups of cyclic groups and classify subgroups of cyclic groups.

iv) Explain the significance of the notion of cosets, normal subgroups and factor groups.

v) Learn about Lagrange’s theorem and Fermat’s little theorem.

vi) Know about group homomorphisms and group isomorphisms.

Paper Code: MAT-HC-3036: Analytical Geometry

Course Objectives: The primary objective of this course is to introduce the basic tools of two-dimensional coordinates systems, general conics, and three-dimensional coordinate systems.

Course Learning Outcomes: This course will enable the students to:

i) Learn conic sections and transform co-ordinate systems

ii) Learn polar equation of a conic, tangent, normal and properties

iii) Have a rigorous understanding of the concept of three-dimensional coordinates systems.

Paper Code: MAT-SE-3024: Combinatorics and Graph Theory

Course Objectives: This course aims to provide the basic tools of counting principles, pigeonhole principle. Also introduce the basic concepts of graphs, Eulerian and Hamiltonian graphs, and applications to dominoes, Diagram tracing puzzles, Knight’s tour problem and Gray codes.

Course Learning Outcomes: This course will enable the students to:

i) Learn about the counting principles, permutations and combinations, Pigeon hole principle

ii) Understand the basics of graph theory and learn about social networks, Eulerian and Hamiltonian graphs, diagram tracing puzzles and Knight’s tour problem.

Paper Code: MAT-HG-3016/MAT-RC-3016: Differential Equations

Course Objectives: The main objective of this course is to introduce the students to the exciting world of ordinary differential equations, mathematical modeling and their applications.

Course Learning Out comes: The course will enable the students to:

i) Learn basics of differential equations and mathematical modelling.

ii) Solve first order non-linear differential equations and linear differential equations of higher order using various techniques.

Paper Code: MAT-HC-4016: Multivariate Calculus

Course Objectives: To understand the extension of the studies of single variable differential and integral calculus to functions of two or more independent variables. Also, the emphasis will be on the use of Computer Algebra Systems by which these concepts may be analyzed and visualized to have a better understanding. This course will facilitate to become aware of applications of multivariable calculus tools in physics, economics, optimization, and understanding the architecture of curves and surfaces in plane and space etc.

Course Learning Outcomes: This course will enable the students to:

i) Learn the conceptual variations when advancing in calculus from one variable to multivariable discussion.

ii) Understand the maximization and minimization of multivariable functions subject to the given constraints on variables.

iii) Learn about inter-relationship amongst the line integral, double and triple integral formulations.

iv) Familiarize with Green\'s, Stokes\' and Gauss divergence theorems

Paper Code: MAT-HC-4026: Numerical Methods (including practical)

Course Objectives: To comprehend various computational techniques to find approximate value for possible root(s) of non-algebraic equations, to find the approximate solutions of system of linear equations and ordinary differential equations. 27 Also, the use of Computer Algebra System (CAS) by which the numerical problems can be solved both numerically and analytically, and to enhance the problem solving skills.

Course Learning Outcomes: The course will enable the students to:

i) 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.

ii) Know about methods to solve system of linear equations, such as False position method, Fixed point iteration method, Newton’s method, Secant method, LU decomposition.

iii) Interpolation techniques to compute the values for a tabulated function at points not in the table.

iv) Applications of numerical differentiation and integration to convert differential equations into difference equations for numerical solutions.

Paper Code: MAT-HC-4036: Ring Theory

Course Objectives: The objective of this course is to introduce the fundamental theory of rings and their corresponding 28 homomorphisms. Also introduces the basic concepts of ring of polynomials and irreducibility tests for polynomials over ring of integers.

Courses Learning Outcomes: On completion of this course, the student will be able to:

i) Appreciate the significance of unique factorization in rings and integral domains.

ii) Learn about the fundamental concept of rings, integral domains and fields.

iii) Know about ring homomorphisms and isomorphisms theorems of rings.

iv) learn about the polynomial rings over commutative rings, integral domains, Euclidean domains, and UFD

Paper Code: MAT-SE-4024: Latex and HTML (practical)

Course Objectives: The purpose of this course is to acquaint students with the latest type setting skills, which shall enable them to prepare high quality typesetting, beamer presentation and webpages

Course Learning Outcomes: After studying this course the student will be able to:

i) Create and typeset a LaTeX document.

ii) Typeset a mathematical document using LaTex.

iii) Learn about pictures and graphics in LaTex.

iv) Create beamer presentations.

v) Create web page using HTML

Paper Code: MAT-HG-4016/MAT-RC-4016: Real Analysis

Course Objectives: The course will develop a deep and rigorous understanding of real line R and of defining terms to prove the results about convergence and divergence of sequences and series of real numbers. These concepts have wide range of applications in real life scenario.

Course Learning Outcomes: This course will enable the students to:

i) Understand many properties of the real line R, including completeness and Archimedean properties.

ii) Learn to define sequences in terms of functions from R to a subset of R.

iii) Recognize bounded, convergent, divergent, Cauchy and monotonic sequences and to calculate their limit superior, limit inferior, and the limit of a bounded sequence.

iv) Apply the ratio, root and limit comparison tests for convergence and absolute convergence of an infinite series of real numbers.

Paper Code: MAT-HC-5016: Complex Analysis (including practical)

Course Learning Outcomes: The completion of the course will enable the students to:

i) Learn the significance of differentiability of complex functions leading to the understanding of Cauchy−Riemann equations.

ii) Learn some elementary functions and valuate the contour integrals.

iii) Understand the role of Cauchy−Goursat theorem and the Cauchy integral formula.

iv) 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.

Paper Code: MAT-HC-5026: Linear Algebra

Course Objectives: The objective of this course is to introduce the fundamental theory of vector spaces, also emphasizes the application of techniques using the adjoint of a linear operator and their properties to least squares approximation and minimal solutions to systems of linear equations.

Course Learning Outcomes: The course will enable the students to:

i) Learn about the concept of linear independence of vectors over a field, and the dimension of a vector space.

ii) Basic concepts of linear transformations, dimension theorem, matrix representation of a linear transformation, and the change of coordinate matrix.

iii) 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.

iv) Compute inner products and determine orthogonality on vector spaces, including Gram−Schmidt orthogonalization to obtain orthonormal basis.

v) Find the adjoint, normal, unitary and orthogonal operators.

Paper Code: MAT-HE-5026: Mechanics

Course Objectives: The course aims at understanding the various concepts of physical quantities and there late defects on different bodies using mathematical techniques. Item phasizes knowledge building for applying mathematics in physical world.

Course Learning Outcomes: The course will enable the students to:

i) Know about the concepts in statics such as moments, couples, equilibrium in both two and three dimensions.

ii) Understand the theory behind friction and center of gravity.

iii) Know about conservation of mechanical energy and work-energy equations.

iv) Learn about translational and rotational motion of rigid bodies.

Paper Code: MAT-HE-5056: Spherical Trigonometry and Astronomy

Course Objectives: This main objective of this course is to provide the spherical triangles, Napier’s rule of circular parts and Planetary motion

Course Learning Outcomes: This course will enable the students to:

i) Learn about the properties of spherical and polar triangles

ii) Know about fundamental formulae of spherical triangles

iii) Learn about the celestial sphere, circumpolar star, rate of change of zenith distance and azimuth

iv) Learn about Kepler’s law of planetary motion, Cassini’s hypothesis, differential equations or fraction

Paper Code: MAT-HC-6016: Riemann Integration and Metric spaces

Course Objectives: To understand the integration of bounded functions on a closed and bounded interval and its extension to the cases where either the interval of integration is infinite, or the integrand has infinite limits at a finite number of points on the interval of integration. Up to this stage, students do study the concepts of analysis which evidently rely on the notion of distance. In this course, the objective is to develop the usual idea of distance into an abstract form on any set of objects, maintaining its inherent characteristics, and the resulting consequences.

Course Learning Outcomes: The course will enable the students to:

i) Learn about some of the classes and properties of Riemann integrable functions, and the applications of the Fundamental theorems of integration.

ii) Know about improper integrals including, beta and gamma functions.

iii) 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.

iv) Analyse how a theory advances from a particular frame to a general frame.

v) Appreciate the mathematical understanding of various geometrical concepts, viz. Balls or connected sets etc. in an abstract setting.

vi) 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.

vii) Learn about the two important topological properties, namely connectedness and compactness of metric spaces.

Paper Code: MAT-HC-6026: Partial Differential Equations (including practical)

Course Objectives: The main objectives of this course are to teach students to form and solve partial differential equations and use them in solving some physical problems.

Course Learning Outcomes: The course will enable the students to:

i) Formulate, classify and transform first order PDEs into canonical form.

ii) Learn about method of characteristics and separation of variables to solve first order PDE’s.

iii) Classify and solve second order linear PDEs.

iv) Learn about Cauchy problem for second order PDE and homogeneous and non-homogeneous wave equations.

v) Apply the method of separation of variables for solving many well-known second order PDEs.

Paper Code: MAT-HE-6066: Group Theory-II

Course Objectives: The course will develop an in-depth understanding of one of the most important branch of the abstract algebra with applications to practical real-world problems. Classification of all finite abelian groups (up to isomorphism) can be done.

Course Learning Outcomes: The course shall enable students to:

i) Learn about automorphisms for constructing new groups from the given group.

ii) Learn about the fact that external direct product applies to data security and electric circuits.

iii) Understand fundamental theorem of finite abelian groups.

iv) Be familiar with group actions and conjugacy in Sn.

v) Understand Sylow’s theorems and their applications.

Paper Code: MAT-HE-6086: Project

In this paper each student is asked to submit a project on an assigned topic. After the examination of the project, they have to present themselves with their topic before an interview board and ultimately evaluation process of the paper is completed.

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