Department Of Mathematics
The Department of Mathematics was established in the year 2005 and has a privilege to be one of the founding undergraduate departments in the college. Presently, it has the faculty strength of 02 members. The Department of Mathematics offers exciting programs for undergraduate students, while providing the foundation in Mathematics that is crucial to the education of our students.Undergraduate students seeking a Bachelor of Science (B.Sc.) in Mathematics can choose from the following concentrations: differential calculus, integral calculus, real analysis, differential equations, numerical analysis, graph theory and group theory. Additionally, a new Bachelors programme in Information Technology (B.Sc.IT.) has recently been added to already existing courses in the college wherein the Mathematics Departments has a crucial role to exert.The department’s course offerings are broad providing students with the breadth of opportunity associated with much larger educational institutions, along with the personalized attention that is the hallmark of our college.In addition to a rigorous curriculum, the department offers a vibrant environment for professional development and scientific discourse. Regular visitors to the department present on the latest research findings in Mathematics and introduce students to careers that build upon the knowledge base and skill sets developed in our degree programs.
To be among the best Mathematics departments in the state and to establish a reputation as a centre for learning and teaching in Mathematics, our vision is to explore the world of Mathematics, conduct innovative research, teaching and focus on Analysis, Algebra and Applied Mathematics.
The mission of theDepartment of Mathematics is to provide an environment wherestudents can learn and become competent users of Mathematics and mathematicalapplication. Moreover, the department will contribute to the development of students asmathematical thinkers, enabling them to become lifelong learners, to continue to grow intheir chosen professions, and to function as productive citizens.
In pursuing this mission, our primary departmental functions are the development, dissemination,and application of mathematical knowledge and in the areas of Mathematics, mathematicseducation, and Information Technology. We, as a team of faculty, will serve the students to develop in them the mathematical resoning, application of Maths in day-to-day life, analysis, employability to become productive social constituents.
In fulfilling this mission, the department creates an environment where the students continue to grow as teachers, scholars and other professionals.
“Mathematics is queen of the Sciences”
In this era of emerging technologies & advanced sciences, developed nations are focusing on applied research by using knowledge linkages between scientists, engineers, and researchers. Mathematicsforms the backbone of knowledge development for scientists and engineers. Our focus is to produce scholars equipped with modernmathematical tools, with strong understanding towards real world experiences and engineering problems.
I strongly believe that nobody can develop into a prominent Engineer, Scientist or IT professional without a significant knowledge of Mathematics.
As an important human endeavour, Mathematics has come to be recognized as the ‘language of science.’ Mathematics is one of the oldest academic subjects and the most mature and well-developed disciplines of basic sciences. Mathematics, the study of quantity, structure, space, and change, is used as an essential tool in natural sciences, Engineering, Medicine and the Social Sciences. The subject seeks to establish truth by arduous deduction, being the core foundation of the field of Engineering, aids to build analytical, reasoning &logical skills of the future engineers and researchers.
The Department of Mathematics provides services to the entire college for UG students, opting Mathematics, who constitute the basic component of our department. The aim of the department is to pursue excellence in Mathematics throughteaching-learning exercises. Weachieve our objectives through the assistance of significantly well qualified and experienced academic staff.
Dr. Khrusheed Ahmad Thakur
Department of Mathematics
|DEPARTMENT OF MATHEMATICS|
|Programme outcome:||PO1. Demonstrate basic manipulative skills in algebra,geometry and calculus.
PO2. Applying the underlying unifying structures of mathematics (i.e. sets,relations and functions,logic structure) and relationships among them.
PO3. Demonstrate proficiency in writing proofs.
Communicate mathematical ideas both orally and in writing.
PO4. Investigate and apply mathematical problems and solutions in variety of contexts related to science,technology, business and industry and illustrate.these solutions using symbolic,numeric, or graphical methods.
PO5. Investigate and solve unfamiliar mathematical problem.
|Programme Specific Outcomes:||PSO1. Help the students to enhance their knowledge in soft skills and computing skills.
PSO2. Enable the students to equip knowledge in various concepts involved in algebra,differential equations and graph theory.
PSO3. Students are trained in effective manner to attend the competitive exams to brighten their future.
PSO4. Facilitate the students to acquire a flair knowledge in discrete mathematics, real analysis and solve problems efficiently.
|Algebra:||CO1. Solve problems on polynomial equations, transformation of equations and reciprocal equations.
CO2. Find the approximate solution of roots of polynomials by suitable methods and solve problems based on exponential and logarithmic series.
CO3 Understand the concepts on skew symmetric, orthogonal matrix, Eigen values, Eigen vector and workout problems related to it.
CO4 Apply the concept of decomposition of composite number as a product of primes uniquely and Euler functions.
CO5. Understand the congruence modulo concept, Fermat’s and Wilson’s theorem
|Numerical analysis:||CO1. Understand the fundamentals of Solutions of Algebraic and Transcendental equations, Bisection method, Iteration Method, Regulafalsi method, Newton Raphsonmethod.
CO2. Acquire knowledge to solve the set of equations by Gauss elimination method, Gauss Jordan method, Gauss Siedal method, Crout’s method.
CO3. Learn the concept of Finite differences- E operators and the relation between them, topics like differences of a polynomial, factorial polynomial, Differences of zero, Summation series also discussed to understand the operators better.
CO4. Understand the concepts of Interpolation with equal intervals by Newtons forward and backward interpolation.
CO5. Understand the concepts of Interpolation with unequal intervals and Inverse interpolation. The knowledge about Divided differences will also gained.
|Differential Calculus:||CO1. Solve problems on successive differentiation and Leibnitz theorem.
CO2. Find the partial derivative of a function of two functions and realise the maxima and minima of functions of two variables.
CO3. Understand and apply the concepts on envelops, Cartesian formula for radius of curvature.
CO4. Apply the concepts of slope of tangent in polar coordinates and angle of intersection of two curves in polar coordinates.
CO5. Understand the asymptote concepts.
|Plane and Solid Geometry:||CO1. Frame the equations of chord, diameter of sphere and conjugate diameters of hyperbola.
CO2. Introduction of the concept of co-normal points, frame the equation of asymptotes of hyperbola.
CO3. Find the equation of the system of planes and the length of perpendicular to a plane and angle between the lines.
CO4. Find the equation of sphere and its intersection with the plane.
CO5. Find the equation of the circle, tangent plane,radical plane, coaxial system of spheres,orthogonal spheres.
|Integral Calculus:||CO1. Understand and apply the reduction formula and Bernoulli’s formula aptly.
CO2. Find the area of curved surfaces, change the variables and integrate.
CO3. Define beta and gamma functions derive their properties and apply them in evaluating integrals.
CO4. Compute gradient, divergence, curl, directional derivative, and unit normal to the surface.
CO5. Apply the theorems of Gauss, Greens and Stokes
|Differential Equations:||CO1. Solve Homogeneous equations, find solutions of exact equations, use the method of reduction of order to find a second linearly independent solution of a second order, linear homogeneous equation when one solution is given.
CO2. Use the method of undetermined coefficients to solve second order, linear homogeneous equations with constant coefficients, Use the method of variation of parameters to find particular solutions of second order, linear homogeneous equations.
CO3. Solve first order linear differential equations, find the solution of homogeneous linear systems of equations.
|Group Theory:||CO1. Understand and solve problems on groups and Lagrange’s theorem.
CO2. Apply the concept of normal sub groups and quotient sub groups and get a clear idea about homomorphism and automorphism.
CO3. Solve problems on Cayley’s theorem and permutation groups.
CO4. Apply the concept of homomorphism of rings, ideal and quotient rings and solve related problems.
CO5 Find the field of quotients of an integral domain and Euclidean Rings.
|Real Analysis-I||CO1. Acquire knowledge on the fundamentals of sets, functions, real valued functions and countable sets.
CO2. Understand the different types of sequences such as convergent, divergent, monotone and its properties.
CO3. Learn the operations of convergent, Cauchy sequences Limit superior and Limit inferior.
CO4. Understand the basic concepts of series such as convergent, divergent, alternating and also the absolute and conditional convergence.
CO5. Learn the operations of limits of functions and metric spaces and reformulations.
|Linear Algebra:||CO1. Understand and solve problems on linear independence and bases.
CO2. Apply the concepts on dual spaces and solve related problems.
CO3. Find the inner product spaces and solve problems related to it.
CO4. Find the linear transformation and their characteristics roots.
CO5. Solve problems on matrices, canonical forms and triangular forms.
|Graph Theory:||CO1. Understand the definition of graphs, subgraphs and fundamental concepts related to the same.
CO2. Understand degree sequences, Connectedness and operations on graphs.
CO3. Understand Eulerian and Hamiltonian graphs.
CO4. Characterize planar graphs and solve problems related to trees.
CO5 Understand digraphs, matrices and tournaments.
Attainment of Programme outcome, programme specific outcome, and course outcome are evaluated by the department/ institution.
The assessment tools and processes used for measuring the attainment of each of the program outcomes and program specific outcomes are as mentioned below:
Method of assessment of POs / PSOs: The program outcomes and program specific outcomes are assessed with the help of course outcomes of the relevant courses through direct and indirect methods. Direct methods are provided through direct examinations or observations of student knowledge or skills against measurable course outcomes. The knowledge and skills described by the course outcomes are mapped to specific problems on university examination, internal exams and home assignment. Throughout the semester the faculty records the performance of each student on each course outcome.
At the end of each session university conducts examinations based on the syllabus published by university. The course outcomes are measured based on the course attainment level fixed by the program. The Direct mode is used for the same. .Assignments are given at the end of each chapters/unit. The assignments are provided to the students, so that the students will refer the text books and good reference books to find out the answers and understand the expected objective of the given problem. It is the responsibility of the concerned subject teacher to ensure that most students are able to work out the assignments honestly. The questions asked in assignments are mostly aligned with course outcome of the respective subject according to the performance of the student in answering each question. Mapping is carried out with the respective COs for assessing the attainment level of the specific COs of the subject are conducted. The Direct mode is used for the same.
To make conscious mind professionals.
To increase the ratio of competitive learners.
To develop scientific temper in students.
To assess the teaching learning based on feedback.
To make students skill oriented.
To inculcate quality education in students.
To improve efficiency and effectiveness of the higher education in the state and institutions selected under the programme.
Course outcome are evaluated by the department by:
|S.No.||Nature of Posts||Number|
PROFILE OF THE FACULTY MEMBERS
|S.No||Name / Mobile/Email ID||Designation||Qualification||Specialization||Teaching Experience||Photograph||CV Attached|
|1.||Dr. Khrusheed Ahmad Thakur||Associate Professor||PhD|
|2.||Mr. Ajaz Rasool||Assistant Lecturer||M.Sc.,|
|1.||Mr.Bilal Ahmad Mir
|Differential Geometry||07 years|
|Ex-Assistant Lecturer||M.Sc. MPhil.
|Generating Functions||01 year|
DETAIL OF COURSE OFFERING
|S.No.||Title of the Course||Semester||Core Course/ Skill Enhancement Course (SEC)||Link to the Syllabus|
|1||Differential calculus/integral calculus.||1st.||Core||View Syllabus|
|2||Differential Equations/special functions||2nd.||Core||View Syllabus|
|3||Real analysis||3rd.||Core||View Syllabus|
|4||Abstract Algebra||4th.||Core||View Syllabus|
|5||Plane and solid geometry/
Theory of probability
|Gender||Semester I||Semester II||Semester III||Semester V||TOTAL|
|S.No||Year of Pass-Out||Semester||Number of Students|
|S.No||Name of the Student||Current Status of the Student|
|1.||Waseem Ahmad Hajam||M.Sc. Mathematics(KU)|
|2.||Waseem Ahmad Lone||M.Sc. Mathematics (KU)|
|3.||Mohd Asif Wani||M.Sc.Mathematics (KU)|
|4.||Khushboo Hassan||M.Sc. Mathematics (KU)|
|5.||Safoora Hamid||M.Sc. Mathematics (KU South Campus)|
Academic Events Organized by the Department During the last Academic Year:
- Students counseling-cum special classes for PG entrance (2018) were conducted by the faculty of Mathematics Department.