Welcome to Government College Department : Maths
INTRODUCTION
Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding." This profound insight by William Paul Thurston reflects the guiding philosophy of our Department of Mathematics. Established in 1945,our department has long been a cornerstone of academic excellence within the college. Over the decades, it has evolved into a hub for innovation and critical thinking, equipped with modern facilities and a vibrant community of learners and scholars. We provide a strong education in Mathematics with a focus on understanding and solving realworld problems. Our department is wellequipped and offers a lively environment where students can learn and grow. With regular guest speakers, we aim to prepare students for successful careers in mathematics.
VISION :
 Imparting of quality mathematics education and the inculcating of the spirit of research through innovative teaching and research methodologies.
 To achieve high standards of excellence in generating and propagating knowledge in Mathematics. Department is committed to providing an education that combines rigorous academics with joy of discovery.
 To provide an environment where students can learn, become competent users of mathematics, and understand the use of mathematics in other disciplines.
MISSION :
The mission of the mathematics department is to provide an environment where students can learn and become competent users of mathematics and mathematical application. Moreover, the department will contribute to the development of students as mathematical thinkers, enabling them to become life long learners, to continue to grow in their chosen professions, and to function as productive citizens.
Teaching Staff
Name: Dr. Dalvinder Singh
Designation: Assistant Professor
Joining Date: 19980907
Qualification: M.Sc ,M.Phil,Ph.D.in Mathematics , B.ed
Area of Specialisation:Pure Mathematics
Email: [email protected]
Mobile: 9814421031
Vidwan ID : 382537
Appointment Type : Regular
Research Papers :
 Fixed point theorems for nonexpansive mappings in Banach space  Published in Indian J. Sci. Res. 1(2) : (2010), 9195.
 Common Fixed point theorem of Siterative schemes for nonexpansive mappings in Banach Space  Accepted for Publication Indian Mathematical Society 76th Annual Conference December 2730 (2010).
 Fixed point theorems for contraction mapping using iteration methods  Published in International Journal of Physical Sciences Ultra Scientist, Vol. 22(3)M, (2010) 839844
 Convergence theorems of iterative schemes for nonexpansive mappings Sent For Publication In Thai Journal of Mathematics
 Common fixed point theorems of iterative schemes for nonexpansive mappings in uniformaly convex banach space  Send for publication In Kodai Mathematical Journal, Tokyo.
Books :
Numerical Methods Published by Sharma Publications
Edited Chapters in books :
Numerical Methods Published by Sharma Publications
Papers presented in conference/Seminars :
1 .Presented Paper at National Level Conference Futuristic Vision Qualitative Literacy for new Millennium at 42nd Indian Social Science Association Conference in 201011 held at Govt. T.R.S (Auto) College Rewa (M.P)
2. Advances in Mathematical & Information Sciences in a National Level Seminar at S.G.T.B. Khalsa College,Sri Anandpur Sahib
Name: Dr. Kirti Bhagirath
Designation: Assistant Professor
Joining Date: 20181203
Qualification: M.Sc. (Hons), CSIR UGC NET qualified , B.ed
Area of Specialisation:Applied Mathematics
Email: [email protected]
Mobile: 8054111979
Vidwan ID : 382648
Appointment Type : Guest Faculty
Research Papers :
 Model to describe a small outbreak of damaged grains due to insects.
 To develop and validate a mathematical model to analyze the effect of S. cerealella on grains in the environmental Ecosystem.
 Analysis of growth in population through nonlinear stochastic process.
Papers presented in conference/Seminars :
 Model to describe a small outbreak of damaged grains due to insects.
 To develop and validate a mathematical model to analyze the effect of S. cerealella on grains in the environmental Ecosystem.
 Analysis of growth in population though nonlinear stochastic process.
Participation in conferences :
 Analysis of growth in population through nonlinear stochastic process. (RAFAS 2021)
 Mathematical modeling to predict the population dynamics of Rusty Grain Beetle in Stored Bulk wheat (International Conference on Materials for Emerging Technologies (ICMET21)).
 International Web Conference on Perspective on Agricultural and Applied Sciences in COVID19 Scenario (PAAS2020) to
Participation in Workshops :
1. Five Day workshop on Research methodology : Techniques , Analysis and Presentation.
Conducted/Attended FDP :
 NATIONAL LEVEL FACULTY DEVELOPMENT PROGRAMME ON MAKING CLASSES AND LESSONS MORE INTERACTIVE .
 One day Faculty Development Programme ob Use of ICT TOOLS CURRENT PERSPECTIVE
Attended Short Term Courses :
2 days course on Data Science using Python conducted by NIELTS
Name: Mr. Jagjit Singh
Designation: Assistant Professor ( Guest Fa
Joining Date: 19960520
Qualification: M.sc Mathematics, CSIRUGC NET
Area of Specialisation:Pure Mathematics
Email: [email protected]
Mobile: 8146051171
Vidwan ID : 382630
Appointment Type : Guest Faculty
Participation in Workshops :
Three Day Live Online Workshop on "Mathematica for Beginners (A Technical Computing System)"
Conducted/Attended FDP :
1. Five Day National Level FDP on " RESEARCH METHODOLOGY: TECHNIQUES, ANALYSIS AND PRESENTATION", 2. Seven Day FDP on "Together for Education Embracing Changes Amid Technological Challenges", 3. A Six Day eFDP on "Applies Mathematics and Related Fields (AMRF2020)",
Lesson Plans
20222023Lesson plansBsc 1st maths 202223.pdfBsc 2nd Maths 202223.pdf Bsc 3rd Maths 202223.pdf 
20212022Lesson plansBsc 1st Maths 202122.pdfBsc 2nd Maths 202122.pdf Bsc 3rd Maths 202122.pdf 
20202021Lesson plansBsc 1st Maths 202021.pdfBsc 2nd Maths 202021.pdf Bsc 3rd Maths 202021.pdf 
20192020Lesson plansBsc 1st maths 201920.pdfBsc 2nd Maths 201920.pdf Bsc 3rd Maths 201920.pdf 
20182019Lesson plansBsc 1st Maths 201819.pdfBsc 2nd Maths 201819.pdf Bsc 3rd Maths 201819.pdf 
Courses Offered
Department of Mathematics offers Maths as an optional subject at undergraduate leval in

B.Sc. NonMed.
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.
 Understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus.
 locate the x and y intercepts, any undefined points, and any asymptotes.
 determine asymptotes for rational expressions .
 apply the techniques from the previous section to graph a fourth degree polynomial or higher
 determine if there is any symmetry to aid in the graphing process.
 determine the point(s) of intersection of pairs of curves.
COURSE TITLE: DIFFERENTIAL EQUATIONS
COURSE OUTCOMES
 Student will be able to solve first order differential equations utilizing the standard techniques for separable, exact, linear, homogeneous, or Bernoulli cases.
 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.
 Student will be introduced to the complete solution of a nonhomogeneous differential equation with constant coefficients by the method of undetermined coefficients.
 Student will be able to find the complete solution of a differential equation with constant coefficients by variation of parameters.
 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
 understand geometrical terminology for angles, triangles, quadrilaterals and circles.
 measure angles using a protractor.
 use geometrical results to determine unknown angles.
 recognise line and rotational symmetries.
 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
 classify partial differential equations and transform into canonical form
 solve linear partial differential equations of both first and second order
 apply partial derivative equation techniques to predict the behaviour of certain phenomena
 apply specific methodologies, techniques and resources to conduct research and produce innovative results in the area of specialisation.
 extract information from partial derivative models in order to interpret reality.
 identify real phenomena as models of partial derivative equations.
COURSE TITLE : ALGEBRA AND TRIGNOMETRY
COURSE OUTCOMES
 Demonstrate knowledge and understanding of topics including, but not limited to divisibility, prime numbers, congruences, quadratic reciprocity, Diophantine equations.
 Use mathematical induction and other types of proof writing techniques.
 Evaluate trigonometric and inverse trigonometric functions.
 Solve trigonometric equations and applications
 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
 The student is expected to learn about the basic principles of multivariable calculus with proofs.
 To have full knowledge of calculus involving the fundamental tools such as continuity and differentiability.
 Students are able to reason rigorously in mathematical arguments. They can follow abstract mathematical arguments and write their own proofs.
 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.
 To know Relationship between the increasing and decreasing behavior of f and the sign of f.
COURSE TITLE : ANALYSIS
COURSE OUTCOMES
 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;
 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;
 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.
 Student will have a working knowledge of differentiability for complex functions and be familiar with the CauchyRiemann equations;
 Student will evaluate integrals along a path in the complex plane and understand the statement of Cauchy's Theorem
COURSE TITLE : STATISTICS
COURSE OUTCOMES
 An ability to construct freebody diagrams and to calculate the reactions necessary to ensure static equilibrium.
 An understanding of the analysis of distributed loads.
 A knowledge of internal forces and moments in members.
 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:
 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.
 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.
 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.
 v) Deal with twodimensional 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 CauchyRiemann 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
 Solve systems of linear equations,
 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
 Use matrix algebra and the related matrices to linear transformations,
 Identify and construct linear transformations of a matrix.
 Characterize linear transformations as onto, onetoone. 3. Solve linear systems represented as linear transforms.
 Express linear transforms in other forms, such as as matrix equations, and vector equations.
 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
 understand the importance of algebraic properties with regard to working within various number systems.
 extend group structure to finite permutation groups (Cayley's Theorem).
 understand Sylow's Theorems.
 generate groups given specific conditions.
 investigate symmetry using group theory.
 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:
 i) Learn about partially ordered sets, lattices and their types.
 ii) Understand Boolean algebra and Boolean functions, logic gates,switching circuitsand their applications.
iii) Solve reallife problems using finitestate and Turing machines.
 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::
 i) Understand the concepts of vector spaces, subspaces, bases, dimension and their properties.
 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.
 iv) Realise importance of adjoint of a linear transformation and its canonical form
 v) Understand the basic concepts of group actions and their applications.
 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.
 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.
 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.
 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 simpleinterestbased 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 decisionmaking 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
 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 : MSOFFICE 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.
 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
 A) Understand the concepts of database and techniques for its management.
 B) Different Data Models at Conceptual and Logical level.
 C) Differentiate between the role of DBA and Data Architect
 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:
 Establish and indepth understanding of Database Administration using the Oracle DBMS interfaces.
 SVRMGR, OEM tools, Command Line interface and SQL*Plus.
 Apply the Relational Database Model to understand the Logical and Physical aspects of the DBMS architecture.
 Understand the functions of the Oracle Database Server and Oracle Database Client.
 Create, maintain and manipulate an Oracle Database.
 Understand and apply the Data Dictionary.
 Understand and apply database statistics in relation to performance and integrity of the database.
 Create and understand the application of user roles, privileges, and the security of the database.
 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
Facilities
 ICT Facility is available for the students in the department.
 Departmental Library is there to help the economically weak students and even other students who want to supplement their learning.
Activities
 Inter Department Quiz competition has been conducted to improve student’s general awareness.
 Cleanliness drive has been organized in the Department and its surroundings under Swacch Bharat Abhiyaan which helps in developing team work and coordination among the students.
 Various competitions has been conducted for the students to improve their presentation skills and creativity.
 Students have been participating in various events at district and university level such as Quiz, Giddha, Bhangra, Debate and declamation.
Various students are encouraged for participation in inter college competitions and youth festivals.
Dr.CV RAMAN SCIENCE SOCIETY
The staff and students of Maths,physics and chemistry Department collectively forms this society and all activities are carried out under this society. Students celebrate science day every year on the eve of Dr. CV Raman’s birthday. Various competitions are organized including debates ,power point presentations ,science quiz etc.
Student progression & Achievement.
Most of the graduates in Maths department pursue post graduation or bachelor of education.
 Many students are also doing jobs in industrial field and various pharmaceutical companies.
 Some students are being recruited as officials in army ,navy and air force.
 Large number of students are doing jobs in educational institutes.