Mathematics

Core 

Course

CC-2 

(Under CCF) For 

SEM 2

Algebra 

Unit – I: Classical Algebra

Unit – II: Abstract Algebra

Unit – III: Linear Algebra

CO-2 

On completion of this course, students gain the knowledge about

1. Complex number, polynomials, inequality which will be needed in studies of real and complex analysis in coming semesters.

2. Sets, relation, mapping and notions of integer, congruence relation are foundation of Modern Algebra as well as discrete mathematics, which is also in UG Course. Moreover they have important implications in practical field like to prepare Credit card, Debit Card, ISBN, ISSN etc.

3. application to linear system of equations will help students in linear algebra course in semesters 4,5,6. Matrix theory plays one of the most important role in various other subjects like computer science, operational research etc. which have nowadays direct implications in almost every aspect of life.

CC-5 

For 

SEM 

3

Theory of Real 

Functions 

Unit I: Limit and Continuity of

functions

Unit II: 

Differentiability of functions.

CO-5 

Limit and Continuity 

This course will help students to know about

Very important notions of limit, continuity, uniform continuity of a real function with ε − δ approach. Many important results including Sequential criterion will help students in due courses.

Differentiability 

Differentiability of a real function at a point, relation between continuity and differentiability of a function and related theorems, Rolle’s theorem, Cauchy’s MVT to be specially mentioned with.

The concept of maxima, minima of a function in an interval and their application. This portion plays important role in applied sciences, specially on ODE and Multivariate Calculus which is also in the UG course.

This course is the base for any further studies of analysis and many other fields and also help them to grow analytical ideas in real field and make mathematical arguments within this system.

CC-6 

For 

SEM 

3

Ring Theory & Linear Algebra I 

Unit – I: Ring

Theory.

Unit – II: Linear

Algebra

CO-6 

Ring Theory 

Ring is an ordered structure with two operators and it is a generalization of group theory which the students have already read in CC4 (semester 1). In this course the students

1. Get to study ring as arbitrary set with two operators. Definition, examples, properties of subring, subfield, integral domains and field and their properties.

2. Acquire knowledge about some well-known theorems such as isomorphism theorem, correspondence theorem.

3. These ideas are very important to study advanced algebra, linear algebra in semester 5 of undergraduate course as well as for further study of any branch of mathematics.

Linear algebra 

The students already had preliminary ideas of vectors and its analysis in semester 1, but in this course they study its algebra. They

1. Get knowledge about vector spaces and its algebra, subspaces of ℝⁿ and its geometric significance which helps them to connect algebra with geometry.

2. Get to know linear transformations, its algebra and representations, Eigen values, Eigen vectors, characteristic equations, Cayley-Hamilton theorem which gives a new method for finding the inverse of a matrix.

CC-7 

For 

SEM 

3

Ordinary 

differential 

equation & 

Multivariate 

calculus I 

Unit – I 

Ordinary differential equation

Unit – II 

Multivariate

Calculus – I

CO-7 

On completion of this course, the students will acquire knowledge on

1. acquire elementary knowledge and skill of solving problems on certain types of linear and non- linear ordinary differential equations, also acquire knowledge on certain types of second order ordinary differential equations and their applications in Applied Science.

2. solving various problems related to Power series solution, Biological & Mechanical model, vector calculus which has useful applications in various branches of Mathematics and Physics.

3. solving various problems related to multivariate calculus, which is a powerful tool for understanding the geometry of real n-dimensional space.

4. Obtain the knowledge on limit, continuity and differentiability of n-dimensional space curves and surfaces.

CC-8 

For 

SEM 

IV

Riemann 

Integration & 

Series of functions 

Unit – I: Riemann Integration

Unit – II: Improper Integral

Unit – III: Series of functions

CO-8 

This course will help students to acquire knowledge about 1. Riemann integration which is a generalisation of definite integration. Concept of negligible set,

primitive, application of Lebesgue theorem and many important properties and theorems.

2. Improper integral and existence of their finite values and Beta Gamma functions with their

application.

3. Sequence and series of functions, power series and their pointwise convergence, uniform convergence to limit function.

All these concepts are widely applied in integral and differential calculus, differential equations to physics problems.

CC-9 

For 

SEM 

IV

Partial Differential Equation & 

Multivariate 

Calculus-II 

Unit – I: Partial

Differential Equation

Unit – II:

Multivariate

Calculus-II

CO-9 

On completion of this course, the students will acquire 1. elementary knowledge and skill for solving problems of certain types of linear and non-linear partial differential equations, also acquire knowledge on certain types of second order partial differential equations and their applications in Mathematical Physics.

2. Concept of Cauchy problem, Cauchy-Kowalewskaya theorem, Cauchy problem of finite & infinite string and their applications in Mathematical Physics.

3. elementary knowledge and skill of solving problems on multiple integral and centre of gravity, surface and volume of revolution. knowledge on vector calculus and their applications in Mathematical Physics.

CC-10 

For 

SEM 

IV

Mechanics 

Unit – I: Statics

Unit – II: Particle Dynamics

Unit – III: Many

Particle System

CO-10 

On completion of this course, the students will acquire knowledge on

(a) Reduction of forces in 2D and 3D system.

(b) condition of stability and instability of a system by a system of forces

(c) how the frictional force work with the interaction two bodies and also the stability in the environment of frictional force

(d) virtual work and one can check the condition of stability using virtual work done.

(e) rectilinear motion of a particle in straight line and in two and three dimension

(f) orbital motion and its stability. It will help in research of artificial satellite.

(g) work, power, energy and energy conservation maintain in different systems.

(h) linear and angular momentum principal and energy conservation in many particle systems.

(i) over all study help to research in particle physics.

CC-11 

For 

SEM 

V

Probability and Statistics. 

Unit I: Probability Unit II: Statistics.

CO-11 

This course will introduce students to

1. the theory of probability, basic knowledge about one and two dimensional probability distribution,

distribution function, conditional probability,

expectation, some special distributions, generating functions etc. and problems related to all these topics. 2. the statistical theory build up on the basis of probability theory and help students in solving problems on parameter estimation viz., point and interval estimation, level of significance, concept of hypothesis and their various applications based on real life data.

This course lay foundation to one of the most beautiful and practically oriented subject Statistics.

CC-12 

For 

SEM 

V

Group theory II & Linear Algebra II 

Unit I: Group theory.

Unit II: Linear

Algebra

CO-12 

Group theory II 

The students who had preliminary ideas of definition and properties of groups, now in this course

1. Acquire conceptual knowledge about automorphism group and its properties and applications of factor group to automorphism groups.

2. Can extend their skills to study further about external and internal direct product of groups, the existence of some well-known theorems such as Cauchy theorem, converse of Lagrange’s theorem and Fundamental theorem only on finite Abelian groups.

Linear Algebra II 

This course is an extension of Linear Algebra I in CC6. In this course the students go through the study of advanced linear algebra such as

1. Inner product spaces, Gram-Schmidt process of orthogonalization and orthonormalization of vectors, Bessel’s inequality, linear operators, linear bilinear quadratic form of vectors, Sylvester’s law of inertia etc.

2. Dual spaces, transpose of linear transformation and its matrix in the dual basis, annihilators, eigen spaces, diagonalizability, inverse and subspaces, Jordan and rational canonical form.

These concepts are very essentials for further studies as well as for competitive examinations.

CC-13 

For 

SEM 

VI

Metric space & Complex analysis 

Unit I: Metric space.

Unit II: Complex analysis

CO-13 

Metric space 

Metric space is a generalization of Real line. On completion of study of metric space, the students

1. get the idea of abstraction of modulus distance function from real line to abstract field to form a metric space by axiomatic approach.

2. acquire knowledge of extension of real analysis i.e., open set, interiors, closure, convergence of sequence, continuity, uniform continuity, various types of compactness, connectedness, contraction maps, etc. in arbitrary Meric space.

3. know about Banach Fixed Point theorem which has an application for solving ordinary differential equations.

These ideas help the students to study arbitrary vector spaces and topological spaces.

Complex analysis: 

In semester 2, the students already had ideas of real analysis and a set of complex numbers in a superset of real numbers. Here, in this course, students get to know about

1. Well-known stereographic projection, complex plane, differential calculus and integral calculus of complex numbers

2. Uniform and absolute convergence of power series, radius of convergence

Difference between real analysis and complex analysis.

CC-14 

For 

SEM 

VI

Numerical Analysis 

Unit I: Rounding of real and machine

numbers, Errors,

Numerical

algorithms

Unit II: 

Approximations,

Interpolations.

Unit III: Numerical Differentiations.

Unit IV: Solution of Transcendental and Polynomial

equations

Unit V: Solution of Ordinary Differential equations.

CO-14 

Nowadays, application of numerical analysis spreads in various areas in social sciences. Those problems are difficult to solve in an analytic method but it can be solved through a numerical method. But has a limitation that there may involve small errors that do not affect much. On completion of this course, the students will acquire knowledge on

(a) numerical calculation, which gives most of the time some errors. Here is a scope to learn different types of errors that appear during calculation.

(b) different interpolation, numerical differentiation and numerical integration rule.

(c) finding roots of polynomial and transcendental equations in different methods. In general, we cannot find the roots of transcendental equations in an analytic method. (d) to find the solution of a system of linear equations in different numerical methods.

(e) to find the eigen values of a real symmetric matrix. (f) solution of initial and boundary value problem. All the above said numerical methods are hugely used in solving different research problems in the real world. So it gained serious attention to the students of science background.

SEC-A 

For 

SEM 

III

C Programming

Language

CO-15 

Computer programming is now very much essential for the study of different areas of social science. Software wholly depends on computer programming. On completion of this course, the students will acquire knowledge

(a) on basic keywords, functions and data type used in C programming language

(b) on condition, loop and structure that used to make computer program

(c) on defining array, user defined function, pointer and creating a file through C.

Thus students will learn a soft-skill in the area of computer science and can take entry to the software industry.

SEC-B 

For 

SEM 

IV

CO-16 

On completion of this course, the students will acquire knowledge

(a) on advance computing up to desired accuracy (b) on programming technique

(c) on plotting different kinds of function that help to predict the behaviour of the function. This is an extra feature inbuilt in this software than other programming compilers.

Thus study of SageMath helps students to move in research motivation.

DSE 

A1 

For 

SEM 

V

Advanced 

Algebra 

Unit – I: Group

Theory

Unit – II: Ring

Theory

CO-17 

After successful completion of this particular course the students has extended their knowledge about

1. Group action & permutation representation associated with a given group action, basic applications of group actions, Generalised Cayley’s theorem and Index theorem

2. Generalised theory of Ring, basic idea of which they have already read in CC6. In this part of ring theory they also acquire knowledge about Principal Ideal Domain and Its properties Euclidean domain, Factorisation domain, Unique factorisation Domain & inter relations among them.

3. Polynomial ring as an example of Factorisation domain, Euclidean algorithm, Eisenstein criterion etc.

4. Regular rings, its examples & properties ideals etc. which are very much essential to study higher course of pure mathematics as well as in the research field.

DSE 

-B1 

For 

SEM 

V

CO-18 

On completion of this course, the students will acquire

1. fundamental knowledge on the theory of basic and basic feasible solutions and their properties, convex sets based on the knowledge of linear algebra studied in previous semesters.

2. the skills on the solution of a Linear Programming Problem by Simplex Method. Also acquire knowledge on duality, transportation problem, assignment problem and travelling salesman problem.

This course is very much important in present day Mathematics, like in the field of Operation Research, Modelling, Financial Mathematics.

DSE 

A2 

For 

SEM 

VI

Mathematical 

Modelling

CO-19 

On completion of this course,the students will acquire knowledge

1. Concept of power series solution of Bessel’s & Legendre’s equation, Laplace transform and their application in Mathematical Physics.

DSE 

A2 

For 

SEM 

VI

Point Set Topology 

Unit – I: Topological spaces.

Unit – II:

Countability and

Separation Axioms

Unit – III:

Compactness and Connectedness

CO-20 

Topology is an abstraction of real analysis and a generalization of metric spaces which the students have already read in 1^st semester CC3 and 6^th semester CC13 courses. In this course the students

1. Realize that there are various extensions of real numbers in which the set of reals is a subset of them. 2. Understand the construction of real numbers is relatively unimportant to get a topology on it.

3. Get knowledge about axiomatic set theory which is one of the pivotal concept of set theoretic approach of topology.

4. Get ideas of the extension of topological open sets, closed sets limit points, neighbourhood, convergence, continuity etc. from the set of real numbers to arbitrary topological spaces and topological properties like compactness, connectedness, separation axioms etc., some of which hold in the set of real numbers but not all.

5. Acquire knowledge about ℝⁿ(n copies of ℝ) as well as ℝw arbitrary product of ℝ. Not only that, but they also come to know about many well-known examples of topological space.

6. Get experience to construct topology in an arbitrary space and can solve problems which makes them able to study further branch of advanced theory of pure mathematics.

SEM I 

CC1/ 

GE1

Unit-1 : Algebra-I

Unit-2 : Differential

Calculus-I

Unit-3 : Differential

Equation-I

Unit-4 : Coordinate

Geometry

CO-21 

The knowledge of basic mathematical ideas of algebra, differential calculus and its applications, 1^st and 2^nd order differential equations and two and three dimensional geometry, which are generalizations of mathematics syllabus which students already studied at +2 level. These ideas will help them to develop mathematical practice to enter in the next level of study in GE2.

SEM II 

CC2/ 

GE2

Unit-1 : Differential

Calculus-II

Unit-2 : Differential

Equation-II

Unit-3 : Vector Algebra Unit-4 : Discrete

Mathematics

CO-22 

The course of GE2 is so designed that students will be able to gain the knowledge about the next part of GE1, i.e., differential calculus II, differential equation II, vector algebra as a generalization of geometry and discrete mathematics which is very essential nowadays in application to computer science and modern algebra, graph theory as well as in our Everyday life while using Debit and Credit Cards, ISBN number for Books, Bar code for any product etc. .

SEM III 

CC3/ 

GE3

Unit-1 : Integral Calculus

Unit-2 : Numerical Methods

Unit-3 : Linear

Programming

CO-23 

Integral Calculus 

From this course, students acquire knowledge of integral calculus and its application in geometry, numerical analysis and linear programming problems, each of which is very necessary for further study in any field of science as well as in the competitive examinations.

Numerical Methods 

Nowadays, application of numerical analysis spreads in various areas in social sciences. Those problems are difficult to solve in an analytic method but it can be solved through a numerical method. On completion of this course, the students will acquire knowledge on

(a) numerical calculation, which gives most of the time some errors. Here is a scope to learn different types of errors that appear during calculation.

(b) different interpolation, numerical differentiation and numerical integration rule.

(c) finding roots of polynomial and transcendental equations in different methods. In general, we cannot find the roots of transcendental equations in an analytic method.

(d) to find the solution of a system of linear equations in different numerical methods.

All the above said numerical methods are hugely used in solving different research problems in the real world. So it gained serious attention to the students of science Background.

Linear Programming 

On completion of this course, the students will acquire

1. fundamental knowledge on the theory of basic and basic feasible solutions and their properties, convex sets based on the knowledge of linear algebra studied in previous semesters.

2. the skills on the solution of a Linear Programming Problem by Simplex Method. Also acquire knowledge on duality, transportation problem, assignment problem and travelling salesman problem.

This course is very much important in present day Mathematics, like in the field of Operation Research, Modelling, Financial Mathematics.

SEM IV 

CC4/GE4 

Unit-1 : Algebra-II

Unit-2 : Computer

Science & Programming Unit-3 : Probability & Statistics

CO-24 

In this course students study modern algebra, computer science and methods of programming and also probability and statistics which play important roles in present day mathematics.

SEM V 

DSE – A (Any 

one)

CO-25 

Students acquire the knowledge of

(a) rectilinear motion of a particle in straight line and in two and three dimension

(b) orbital motion and its stability. It will help in research of artificial satellites.

(c) work, power, energy and energy conservation are maintained in different systems.

(d) linear and angular momentum principle and energy conservation in many particle systems.

CO-26 

On Completion of This Course, the students will acquire knowledge of basic graph theory, paths, circuits, trees and their application in Mathematical algorithms. To find the shortest path using Dijkstra’s algorithm, Floyd-Warshall algorithm.

SEM VI 

DSE B 

Advanced 

Calculus

CO-27 

This course is an extension of Real Analysis. Here students will study the concept of point-wise and Uniform convergence of sequence of functions and series of functions. They also learn periodic Fourier series and it’s convergence, Laplace Transform, it’s properties and application to the solution of ordinary Differential equations.

SEM VI 

SEC – B 

CO-28 

Boolean algebra as a skill enhancement course is very helpful for students to develop skill about Boolean algebra as a distributive lattice, Boolean polynomials, Karnaugh diagram, switching circuits which plays a very crucial role in present day Mathematics and Computer science.

CO7 

CO8 

CO9 

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CO10 

CO11 

CO12 

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CO13 

CO14 

CO15 

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Sl. 

No.

Assessment 

Description

frequency 

Once for newly

It is a surprise test taken at the beginning of

admitted 1st Sem

the study of UG syllabus to assess students’

(year) students

knowledge at the (+2) level of study.

Internal

Assessment Test

Once in a semester

Internal Assessment is taken on full

on each course

syllabus after completion. It will be for 10

marks of each course..

In 6th semester

End Semester practical examinations assess

only

whether all the students have acquired the

practical applications of the particular

subject by hands-on training.

Examinations are held along with the

theoretical schedule,

Tutorial

Examination

Once in a semester

15 % of the total marks is assigned to the

on each course

tutorial exam in each course which is

distributed in equal marks distribution in

Project copy, project presentation and

viva-voce. These are conducted to assess

student’s conception, communication and

presentation skills along with depth of the

subject knowledge.

As per CU rules Total 10 Marks is allotted for all CBCS courses:

The marks obtained of every course from

Class Attendance by the students is the

following manner.

6 marks for attending 60% or above but less

than 75% of the number of lectures

delivered

8 marks for attending 75% or above but less

than 90% of the number of lectures

delivered 10 marks for attending 90% or

above of lectures delivered, and such

attendance are calculated from the date of

commencement of classes or date of

admission whichever is later)