Department of Mathematics offers Maths as an optional subject at undergraduate leval in

1. B.Sc. Non-Med.
    2. B.A. with Mathematics as an elective subject

3.In B.COM in semester II and semester IV

 B.SC/BA 1 SEM 1

 COURSE TITLE : CALCULUS

COURSE OUTCOMES

1.Understand the fundamental concepts of differential calculus and their applications

2.Understand the basic concepts of integral calculus and their applications in problems.

3. Understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus.
4. locate the x and y intercepts, any undefined points, and any asymptotes.
5. determine asymptotes for rational expressions .
6. apply the techniques from the previous section to graph a fourth degree polynomial or higher
7. determine if there is any symmetry to aid in the graphing process.
8. determine the point(s) of intersection of pairs of curves.

COURSE TITLE: DIFFERENTIAL EQUATIONS

COURSE OUTCOMES

1. Student will be able to solve first order differential equations utilizing the standard techniques for separable, exact, linear, homogeneous, or Bernoulli cases.
2. Student will be able to find the complete solution of a nonhomogeneous differential equation as a linear combination of the complementary function and a particular solution.
3. Student will be introduced to the complete solution of a nonhomogeneous differential equation with constant coefficients by the method of undetermined coefficients.
4. Student will be able to find the complete solution of a differential equation with constant coefficients by variation of parameters.
5. Student will have a working knowledge of basic application problems described by second order linear differential equations with constant coefficients.

COURSE TITLE : COORDINATE GEOMETRY

 COURSE OUTCOMES

 After the completion of the course, Students will be able to

1. understand geometrical terminology for angles, triangles, quadrilaterals and circles.
2. measure angles using a protractor.
3. use geometrical results to determine unknown angles.
4. recognise line and rotational symmetries.
5. find the areas of triangles, quadrilaterals and circles and shapes based on these

B.SC BA / 1 SEM II

COURSE TITLE : PARTIAL DIFFERENTIAL EQUATIONS

COURSE OUTCOMES

1. classify partial differential equations and transform into canonical form
2. solve linear partial differential equations of both first and second order
3. apply partial derivative equation techniques to predict the behaviour of certain phenomena
4. apply specific methodologies, techniques and resources to conduct research and produce innovative results in the area of specialisation.
5. extract information from partial derivative models in order to interpret reality.
6. identify real phenomena as models of partial derivative equations.

COURSE TITLE : ALGEBRA AND TRIGNOMETRY

COURSE OUTCOMES

1. Demonstrate knowledge and understanding of topics including, but not limited to divisibility, prime numbers, congruences, quadratic reciprocity, Diophantine equations.
2. Use mathematical induction and other types of proof writing techniques.
3. Evaluate trigonometric and inverse trigonometric functions.
4. Solve trigonometric equations and applications
5. Apply and prove trigonometric identities.

COURSE TITLE: ANALYTICAL GEOMETRY

 COURSE OUTCOME

Course Outcome of Analytical Geometry Students will able to:

• Describe the various forms of equation of a plane, straight line, Sphere, Cone and Cylinder.
• Find the angle between planes, Bisector planes, Perpendicular distance from a point to a plane, Image of a line on a plane, Intersection of two lines
• Define coplanar lines and illustrate
• Compute the angle between a line and a plane, length of perpendicular from a point to a line
• Define skew lines
• Calculate the Shortest distance between two skew lines
• Find and interpret the gradient curl, divergence for a function at a given point.
• Interpret line, surface and volume integrals
• Evaluate integrals by using Green's Theorem, Stokes theorem, Gauss's Theorem

B.SC BA / 2 SEM III

COURSE TITLE : ADVANCE CALCULUS

COURSE OUTCOMES

1. The student is expected to learn about the basic principles of multi-variable calculus with proofs.
2. To have full knowledge of calculus involving the fundamental tools such as continuity and differentiability.
3. Students are able to reason rigorously in mathematical arguments. They can follow abstract mathematical arguments and write their own proofs.
4. Students are able to effectively communicate mathematics: reading, writing, listening, and speaking. Students make effective use of the library, conduct research and make oral and written presentations of their findings.
5. To know Relationship between the increasing and decreasing behavior of f and the sign of f.

COURSE TITLE : ANALYSIS

COURSE OUTCOMES

1. Students will be able to understand the concept of limit for real functions and be able to calculate limits of standard functions and construct simple proofs involving this concept;
2. Student will be introduced to the concept of continuity and be familiar with the statements and proofs of the standard results about continuous real functions;
3. Student will understand the concept of the differentiability of a real valued function and be familiar with the statements and proofs of the standard results about differentiable real functions.
4. Student will have a working knowledge of differentiability for complex functions and be familiar with the Cauchy-Riemann equations;
5. Student will evaluate integrals along a path in the complex plane and understand the statement of Cauchy's Theorem

COURSE TITLE : STATISTICS

COURSE OUTCOMES

1. An ability to construct free-body diagrams and to calculate the reactions necessary to ensure static equilibrium.
2. An understanding of the analysis of distributed loads.
3. A knowledge of internal forces and moments in members.
4. An ability to calculate centroids and moments of inertia.

B.SC BA / 2 SEM IV

COURSE TITLE : DYNAMICS

COURSE LEARNING OUTCOMES: This course will enable the students to:

1. i) Understand the reduction of force system in three dimensions to a resultant force acting at a base point and a resultant couple, which is independent of the choice of base of reduction.
2. ii) Learn about a nul point, a nul line, and a nul plane with respect to a system of forces acting on a rigid body together with the idea of central axis.

 iii) Know the inertia constants for a rigid body and the equation of momental ellipsoid together with the idea of principal axes and principal moments of inertia and to derive Euler’s equations of motion of a rigid body, moving about a point which is kept fixed.

1. iv) Study the kinematics and kinetics of fluid motions to understand the equation of continuity in Cartesian, cylindrical polar and spherical polar coordinates which are used to derive Euler’s equations and Bernoulli’s equation.
2. v) Deal with two-dimensional fluid motion using the complex potential and also to understand the concepts of sources, sinks, doublets and the image systems of these with regard to a line and a circle.

COURSE TITLE : ANALYSIS II

COURSE OUTCOME

 Students will able to

• Compute sums, products, quotients, conjugate, modulus, and argument of complex numbers

. • Calculate exponentials and integral powers of complex numbers.

• Write equation of straight line, circle in complex form
• Define reflection points, concyclic points, inverse points
• Understand the significance of differentiability for complex functions and be familiar with the Cauchy-Riemann equations.
• Determine whether a given function is analytic.
• Define Bilinear transformation, cross ratio, fixed point.
• Write the bilinear transformation which maps real line to real line, unit circle to unit circle, real line to unit circle.
• Find parametrizations of curves, and compute complex line integrals directly.
• Use Cauchy’s integral theorem and formula to compute line integrals.
• Represent functions as Taylor, power and Laurent series.
• Classify singularities and poles.
• Find residues and evaluate complex integrals, real integrals using the residue theorem.

COURSE TITLE : ADVANCE CALCULUS II

 COURSE OUTCOME

Students will able to

• Solve Basic Integral Calculus problems.
• Explain properties of definite integrals.
• Prove reduction formulae and solve some problems by using this formulae.
• Evaluate double and triple integrals.
• Apply change variable method to find the value of double and triple integral.
• Explain properties of Beta functions.
• Derive relation between Beta and Gamma functions.
• Evaluate integrals by using Beta and Gamma functions.
• Find Fourier series expansions for given functions.
• Find Cosine and Sine series expansions for given function

B.SC/BA 3 SEM V

COURSE TITLE : ALGEBRA 1

COURSE OUTCOMES

1. Solve systems of linear equations,
2. Analyze vectors in R^n geometrically and algebraically

, 3. Recognize the concepts of the terms span, linear independence, basis, and dimension, and apply these concepts to various vector spaces and subspaces

4. Use matrix algebra and the related matrices to linear transformations,
5. Identify and construct linear transformations of a matrix.
6. Characterize linear transformations as onto, one-to-one. 3. Solve linear systems represented as linear transforms.
7. Express linear transforms in other forms, such as as matrix equations, and vector equations.
8. Characterize a set of vectors and linear systems using the concept of linear independence.

COURSE TITLE MATHEMATICAL METHODS I

COURSE OUTCOMES:

After the completion of the course, Students will be able to

1. understand the importance of algebraic properties with regard to working within various number systems.
2. extend group structure to finite permutation groups (Cayley's Theorem).
3. understand Sylow's Theorems.
4. generate groups given specific conditions.
5. investigate symmetry using group theory.
6. understand the three major concrete models of Boolean algebra: the algebra of sets, the algebra of electrical circuits, and the algebra of logic.

COURSE TITLE : DISCRETE MATHEMATICS I

COURSE LEARNING OUTCOMES: This course will enable the students to:

1. i) Learn about partially ordered sets, lattices and their types.
2. ii) Understand Boolean algebra and Boolean functions, logic gates,switching circuitsand their applications.

 iii) Solve real-life problems using finite-state and Turing machines.

1. iv) Assimilate various graph theoretic concepts and familiarize with their applications.

B.SC/BA 3 SEM VI

COURSE TITLE: ALGEBRA II .

COURSE LEARNING OUTCOMES: This course will enable the students to::

1. i) Understand the concepts of vector spaces, subspaces, bases, dimension and their properties.
2. ii) Relate matrices and linear transformations, compute eigen values and eigen vectors of linear transformations.

 iii) Learn properties of inner product spaces and determine orthogonality in inner product spaces.

1. iv) Realise importance of adjoint of a linear transformation and its canonical form
2. v) Understand the basic concepts of group actions and their applications.
3. vi) Recognize and use the Sylow theorems to characterize certain finite groups.

 vii) Know the fundamental concepts in ring theory such as the concepts of ideals, quotient rings, integral domains, and fields.

 viii) Learn in detail about polynomial rings, fundamental properties of finite field extensions, and classification of finite fields.

COURSE TITLE : MATHEMATICAL METHODS II

COURSE OUTCOMES

i)To introduce the concepts of partial differential equations, Calculus of Finite differences, statistics, Fourier series and Fourier transform. Identify real phenomena as models of partial derivative equations.

1. ii) Solve real problems by identifying them appropriately from the perspective of partial derivative equations.

iii) To apply the concept of probability to find the physical significance of various distribution phenomena.

1. iv) To understand the concept of solving differentiation and integration using approximation methods. Able to solve algebraic and differential equations using numerical method.·

COURSE TITLE : DISCRETE MATHEMATICS II

 COURSE OUTCOMES

i)The course aims at introducing the concepts of ordered sets, lattices, sublattices and homomorphisms between lattices.

ii)It also includes introduction to modular and distributive lattices along with complemented lattices and Boolean algebra.

iii) Some important applications of Boolean algebra are discussed in switching circuits.

1. iv) The second part of this course deals with introduction to graph theory, paths and circuits, Eulerian circuits, Hamiltonian graphs and finally some applications of graphs to shortest path algorithms.

B.COM SEM II

COURSE TITLE:BUSSINESS MATHEMATICS

LEARNING OUTCOMES

Upon successful completion of this course, students will be able to

• Demonstrate mastery of mathematical concepts that are foundational in business mathematics, including functions and their mappings, linear systems and their solutions, and descriptive statistics and their applications.
• Demonstrate an understanding of basic marketing mathematics by solving relevant problems, including trade discounts, cash discounting, and markup and markdown calculations.
• Apply the principles of simple interest to solve relevant problems in financial applications such as simple-interest-based loans.
• Use the principles of compound interest to solve relevant problems in financial applications, for example, those involving annuities, loans and mortgages, bonds and sinking funds, and investment decisions.

SEM IV

COURSE TITLE : OPERATIONAL RESEARCH

LEARNING OUTCOMES

• Identify and develop operational research models from the verbal description of the real system.
• Understand the mathematical tools that are needed to solve optimisation problems.
• Use mathematical software to solve the proposed models.
• Develop a report that describes the model and the solving technique, analyse the results and propose recommendations in language understandable to the decision-making processes in Management studies.

ADD ON COURSE

The department of mathematics also offers an ADD ON course namely Data Care Management to all undergraduate courses.The course is divided into three year as

1. I) CERTIFICATE COURSE IN DATA CARE MANAGEMENT

SEM I

PAPER A : FUNDAMENTALS OF INFORMATION TECHNOLOGY

 Learning Outcomes:

 At the end of this course, student should be able to

 (a) Understand basic concepts and terminology of information technology.

(b) Have a basic understanding of personal computers and their operations.

(c) Be able to identify issues related to information security.

SEM II

PAPER B : MS-OFFICE AUTOMATION TOOLS

LEARNING OUTCOMES

Upon completion of this course students will be able to

: Demonstrate an advanced knowledge of the Word Processing package, MS Office and a· knowledge of how to design & create effective and structured documents like technical reports, letters, brochures, etc.,

Demonstrate the skills in the appropriate use of various features of the spread sheet· package MS Excel and also to create useful spreadsheet applications like tabulated statements, balance sheets, statistical charts, business statements, etc.

Demonstrate the skills in making an effective presentation with audio and video effects· using the MS Excel package

 Draw graphical pictures, flow charts, block diagrams etc., using the drawing tools· available in MS Word or MS Power Point and incorporate them into documents and presentations.

1. II) DIPLOMA COURSE IN DATA CARE MANAGEMENT :

SEM III

PAPER A : Database Management System

Learning Outcomes:

 At the end of the course, student should be able to

1. A) Understand the concepts of database and techniques for its management.
2. B) Different Data Models at Conceptual and Logical level.
3. C) Differentiate between the role of DBA and Data Architect
4. D) Understanding Data Security standards and Methods and MS Access

SEM IV

PAPER B: Advance Database Management Systems and PL/SQL

Learning Outcomes: 

A)Understand database concepts and structures and query language

Understand the E R model and relational model

B)To design and build a simple database system and demonstrate competence with the fundamental tasks involved with modeling, designing, and implementing a DBMS.

C)Understand Functional Dependency and Functional Decomposition.

D)Apply various Normalization techniques

F)Perform PL/SQL programming using concept of Cursor Management, Error Handling, Package and Triggers

G)Execute various advance SQL queries related to Transaction Processing & Locking using concept of Concurrency control.

H)Understand query processing and techniques involved in query optimization.

Understand the principles of storage structure and recovery management.

III) ADVANCE DIPLOMA IN DATA CARE MANAGEMENT

SEM V

PAPER A : Database Administration of Oracle

 Learning Outcomes:

1. Establish and in-depth understanding of Database Administration using the Oracle DBMS interfaces.
2. SVRMGR, OEM tools, Command Line interface and SQL*Plus.
3. Apply the Relational Database Model to understand the Logical and Physical aspects of the DBMS architecture.
4. Understand the functions of the Oracle Database Server and Oracle Database Client.
5. Create, maintain and manipulate an Oracle Database.
6. Understand and apply the Data Dictionary.
7. Understand and apply database statistics in relation to performance and integrity of the database.
8. Create and understand the application of user roles, privileges, and the security of the database.
9. Discuss and understand the concepts of Backup and Recovery Procedures.

SEM VI

PAPER B: Advance Database Administration of Oracle

 LEARNING OUTCOMES

 Successful students will be able to:

• Installing Oracle Software
• Creating an Oracle Database Using DBCA
• Managing Database instances and ASM instances
• Managing and controlling database network environment
• t Define and devise transaction management, concurrency control, crash recovery components
• Managing storage structure
• Controlling user security
• Designing Database backup and recovery procedures
• Take Decisions related with Database Maintenance