Mathematics and Statistics

HISTORY OF THE DEPARTMENT

The Department of MATHEMATICS was established in this college with B.Sc. General Course in the year 1973 with a view to provide Science education to the students of this region. In a bid to impart the computer knowledge, which is the need of the hour, B.Sc. (Mathematics, Physics, Computer Science) was introduced in the academic year 1996-97, B.Sc. (Mathematics, Statistics, Computer Science) was introduced in year 2018-19 and B.Sc. (Mathematics, Statistics, Data Science) was introduced in 2020-21. The Department started from student intake of 60 developed to the present sanctioned strength of 360.

BASIC INFORMATION

Courses offered:

Number of Teachers working against sanctioned post in Dept. of MATHEMATICS during the last four years:

Details Present Teaching Faculty 

1. CURRICULAR ASPECTS

1.1 Curricular Planning and Implementation

The College is affiliated to Osmania University, Hyderabad and the curriculum for the B.Sc courses is prescribed by the Board of Studies, Department of MATHEMATICS of the University. The curriculum planning and implementation work is undertaken in a planned way. The Curriculum is being implemented according to the Almanac provided by the Affiliating University. The In-charge of the Department conducts the review meetings once in a month at their respective department to know the status of the completion of syllabus and to monitor the conduct of other co-curricular activities such as Remedial Coaching Classes, Student Seminars, Quiz Competitions, Assignments and Internal Exams etc. The Department also organizes various programs related to the academics such as Field Trips etc.

1.2 Academic Flexibility

Introduction of CBCS: The Govt. of Telangana introduced Choice Based Credit System (CBCS) in the state as per the guidelines given by the UGC in all the Universities including the Osmania University to which this college is affiliated, from the academic year 2016-17 and later the syllabus revised in 2019-20.

1.3 Value Added Courses:

The Department of MATHEMATICS introduced Value Added Course on “Quantative Techniques in Mathematics” from the year 2015-16 to the B.Sc students with a view to add some additional value to the existing subject knowledge and to enhance their skill.

2.1 Student Enrolment and Profile

 Year-Wise Male and Female Students 

SOCIO-ECONOMIC STATUS OF STUDENTS

2.2 Catering to Student Diversity

The Department of MATHEMATICS takes every measure possible to understand the needs and requirements of the students before the commencement of the program. Students are counseled at the time of admission and an Orientation program is organized in which students are familiarized with the course, mode of internal assessment as well as facilities available in the college. Teachers before beginning their courses informally get the pulse of the students in the class, their knowledge about the course and their comfort level with English as a medium of instruction. Teachers during class interaction identify students’ potential and then devise strategies to reduce the gap in the knowledge and skills.

 2.3 Teaching-Learning Process

Learning at the college has been changed from teacher centrism to the student centric after introduction of the CBCS. The experiential and participant learning are the effective and active modes of learning which are being adopted enormously at the Department of MATHEMATICS. Visits to other institutes, field trips, seminars and talks by experts are organized every year. Students are given individual projects and class assignments, focusing on self-study and independent learning. They are also assigned group projects and activities which promote peer learning and team building. Classroom discussions, debates, seminars, quiz programs, presentations by students.

2.4 Academic Activities

The staff maintains Teaching diaries, Synopsis and prepares Annual Academic plans to have more systematic approach. Departmental meetings are convened every month to discuss various issues pertaining to academic as well as administrative matters. The faculty of the department strictly adheres to the academic schedule as per the almanac furnished by the university. The time table is framed and workload is distributed among the staff as per the time table.

2.5 Extension Lectures

The Department of MATHEMATICS Conducts Extension Lectures on latest topics in the MATHEMATICS Subjects by inviting eminent persons from university and other colleges.

2.6 Student Study Projects

Teachers are encouraged Students to do study Projects on various topics in both curricular and general Mathematics.

2.7 Evaluation Process and Reforms

The department conducts slip tests and assignments regularly for all the years for assessing their performance. Marks lists are prepared and placed in a separate register. The staff also submits the reports of slip tests and assignments conducted in the department in their performance indicators.

2.8 Reforms in Evaluation Process

Introduction of Semester System (CBCS): The examination system for evaluating the students’ performance has been changed from existing year-wise examination to semester wise examination for continuous evaluation of the students since 2016-17 onwards. Moreover, the credit system has replaced the existing awarding of marks system. The Osmania University, to which this college is affiliated, has introduced the new CBCS syllabus, specially designed for semester system, from the academic year 2016-17.

3. RESEARCH, INNOVATIONS AND EXTENSION

The faculty members are actively participated faculty development programs and participated regularly in seminars.  The following data is from 2015-16 to till date and complete details are given in APPENDIX – 1.

Memorandum of Understanding (MOU):

4. INFRASTRUCTURE AND LEARNING RESOURCES

The department is located in the ground floor of the C block of the college with internet facility and the departmental library is having 134 books in the concerned subjects for reference both for staff and students to facilitate teaching and learning.

5. STUDENT SUPPORT AND PROGRESSION

• Majority of the students are covered under scholarship scheme by the state govt.
• Coaching for P.G and other Entrance Examinations are given to the students.
• The students are provided with sets of Previous question papers.
• Students are given Departmental Library books in addition with Central Library.
• Students are provided with access to N-List facility.
• Providing study material to students.
• Some students are joined PG in Central and State Universities

6. GOVERNANCE, LEARDERSHIP AND MANAGEMENT

6.1 Vision, Mission and Objectives

Vision

To explore the innate mathematical genius among student and instill curiosity in investigating new methodologies for future applications in Mathematics.

Mission

• To apply math in real life situations and seek solutions in day to day life.
• To impart the knowledge of mathematical science with precision and motivate the students to pursue research in various science fields
• To generate mathematical thinking to solve complex problems by providing mathematical experiences.
• To use numbers and symbols and relevant applications in the study and understanding of quantities, operations and measurements.

Objectives

The students should be able to:

1. Recognize that mathematics is an art as well as a powerful foundational tool of science with limitless applications.
2. Demonstrate an understanding of the theoretical concepts and axiomatic underpinnings of mathematics and an ability to construct proofs at the appropriate level.
3. Demonstrate competency in mathematical modeling of complex phenomena, problem solving and decision making.
4. Demonstrate a level of proficiency in quantitative and computing skills sufficient to meet the demands of society

6.2 Performance Appraisal System

The IQAC appraises the performance of the teaching staff by adopting two methods such as Feedback System and Self-Appraisal Forms (API).

The performance of the Teachers is assessed based on the feedback received from the students. The feedback is collected annually through a structured questionnaire, across various teaching quality parameters and analysed to assess the performance and to take necessary steps to plug the loopholes if any.

7. BEST PRACTICES

• Awareness program for High School students on Higher Studies
• Writing of Mathematical Formulae
• Preparing various Mathematical 3-D models and Charts
• Provides previous Question papers and Material to PG Entrance and other Competitive Examinations

Action Plan for the next Five Years

• To conduct National seminars and workshops
• To apply Major/ Minor Research Projects
• To Start More Job Oriented Certificate Courses
• To start inter disciplinary Research

STRENGTHS, WEAKNESSES, OPPORTUNITITES & CHALLENGES:

Strengths                     :           Qualified and Experienced Faculty

Weaknesses                :           Students with poor basics

Opportunities              :           To excel Research

Challenges                  :           High student teacher ratio

APPENDIX-1: RESEARCH PUBLICATIONS AND SEMINARS

APPENDIX-2: B.SC (CBCS) SYLLABUS AND STRUCTURE

APPENDIX-3: TEACHERS’ PERSONAL PROFILES

APPENDIX-4: SNAP SHOTS OF DEPARTMENTAL ACTIVITIES

APPENDIX-1: RESEARCH PUBLICATIONS AND SEMINARS

Research Publications

1. A K Tripathy, S. Panigrahi, and P. Rami Reddy, Oscillation of a class of fourth order functional dynamic equations, Functional Differential Equations, Vol.22 2015, No 1-2, pp 69-91.
2. P. Rami Reddy, N. Sikender and M. Venkata Krishna, Classification of solutions of second order neutral delay dynamic equations on time scales, IOSR Journal of Mathematics (IOSR-JM), e-ISSN: 2278-5728, P-ISSN: 2319-765X Vol. 12, Issue 5 Ver. I (Sep. – Oct. 2016), PP 72-81.
3.   N. Sikender, M. Venkata Krishna and P. Rami Reddy, Classification of solutions of second order nonlinear neutral delay dynamic equations with positive and negative coefficients, International Journal of Mathematics Trends and Technology (IJMTT) – Volume 37 Number 1-20, September 2016.
4. S. Panigrahi, and P. Rami Reddy, Oscillatary behavior of higher order nonlinear homogeneous neutral delay dynamic equation with positive and negative coefficients, J. Appl. Anal 2018: 24(2); 139-154
5. N. Sikender, P. Rami Reddy, M. Venkata Krishna and M. Chenna Krishna Reddy, Classifications of solutions of second order nonlinear neutral delay dynamic equations of mixed type, International Journal of Mathematical Archive 9(2), (2018), 284-294.
6. P. Narasimha Swamy, C. Saraswathi and T. Srinivas, “Interval Valued Fuzzy Near-algebra Over Interval Valued Fuzzy Field”, International Review of Pure and Applied Mathematics, Volume 14, Number 1,87-94(2018)
7. C. Saraswathi, P. Narasimha Swamy, K. Vijay Kumar and L. Bhaskar, “Bipolar Fuzzy Gamma Near-algebra Over Bipolar Fuzzy Field”, AIP Conference Proceedings (ICMSA 2019), Published (Scopus).
8. C. Saraswathi, P. Narasimha Swamy and L. Bhaskar, Interval Valued Fuzzy Ideals of Near algebras, Malaya Journal of Mathematik, Vol. S, No. 1, 177-182(2020)

Orientation / Refresher Courses, FDPs, Seminars, Conferences etc.

Mathematics Dept. Faculty

Sl.No.	Photo	Name	Designation	Profile
1		Dr K Venkateswarlu M.Sc., Ph.D	Associate Professor	Profile
2		T. NAVEEN CHANDAR RAJU M.Sc.(Mathematics)	Assistant Professor	Profile
3		Ms N Jayaleela M.Sc,APSET	Lecturer	Profile
4		Ms.C. SARASWATHI PhD, MTech	Assistant Professor	Profile

Statistics Dept. Faculty

Sl.No.	Photo	Name	Designation	Profile
1		Santi vinod Msc statistics	Lecturer	Profile

Department of Mathematics

Course:  B.Sc.
Program: Mathematics.

Mathematics Program Outcomes:

1. Demonstrate basic manipolative skills in algebra, geometry, trigonometry, and beginning calcolus
2. Apply the underlying unifying structures of mathematics (i.e. sets, relations and functions, logical structure) and the relationships among them
3. Demonstrate proficiency in writing proofs
4. Communicate mathematical ideas both orally and in writing
5. Investigate and apply mathematical problems and solutions in a variety of contexts related to science, technology, business and industry, and illustrate these solutions using symbolic, numeric, or graphical methods
6. Investigate and solve unfamiliar math problems
7. Classes develop student abilities and aptitudes to apply mathematical methods and ideas not only to problems in mathematics and related fields such as the sciences, computer science, actuarial science, or statistics, but also to virtually any area of inquiry.

Programme Specific Outcome of B.Sc., Mathematics:

1. Think in a critical manner.
2. Know when there is a need for information, to be able to identify, locate, evaluate, and effectively use that information for the issue or problem at hand.
3. Formolate and develop mathematical arguments in a logical manner.
4. Acquire good knowledge and understanding in advanced areas of mathematics and statistics, chosen by the student from the given courses.
5. Understand, formolate and use quantitative models arising in social science, business and other contexts.

Course Outcome of B. Sc. Mathematics:

Course Outcome of Analytical Geometry 3D and Vector Calcolus:

Students will able to

1. Describe the various forms of equation of a plane, straight line, Sphere, Cone and Cylinder.
2. Find the angle between planes, Bisector planes, Perpendicolar distance from a point to a plane, Image of a line on a plane, Intersection of two lines
3. Define coplanar lines and illustrate
4. Compute the angle between a line and a plane, length of perpendicolar from a point to a line
5. Define skew lines
6. Calcolate the Shortest distance between two skew lines
7. Find and interpret the gradient curl, divergence for a function at a given point.
8. Interpret line, surface and volume integrals
9. Evaluate integrals by using Green’s Theorem, Stokes theorem, Gauss’s Theorem.

Course Outcome of Theory of Equation, Theory of Numbers and Inequalities:

Students will able to

1. Describe the relation between roots and coefficients
2. Find the sum of the power of the roots of an equation using Newton’s Method.
3. Transform the equation through roots moltiplied by a given number, increase the roots, decrease the roots, removal of terms
4. Solve the reciprocal equations.
5. Analyse the location and describe the nature of the roots of an equation.
6. Obtain integral roots of an equation by using Newton’s Method.
7. Compute a real root of an equation by Horner’s method. • Illustrate the Division and Euclidean Algorithm
8. Describe the properties of prime numbers
9. Show that every positive integer can be expressed as product of prime power in unique way
10. Write a formola for the number of positive integers less than n that are relatively prime to n
11. Define congruences and describe the properties of congruences
12. Find the Sum, product of all the divisors of N.
13. Find the smallest number with N divisors.
14. Solve the system of linear congruences
15. State Chinese Remainder Theorem, Fermat’s and Wilson’s theorem.

Course Outcome of Complex Analysis :

Students will able to

1. Compute sums, products, quotients, conjugate, modolus, and argument of complex numbers.
2. Calcolate exponentials and integral powers of complex numbers.
3. Write equation of straight line, circle in complex form
4. Define reflection points, concyclic points, inverse points
5. Understand the significance of differentiability for complex functions and be familiar with the Cauchy-Riemann equations.
6. Determine whether a given function is analytic.
7. Define Bilinear transformation, cross ratio, fixed point.
8. Write the bilinear transformation which maps real line to real line, unit circle to unit circle, real line to unit circle.
9. Find parametrizations of curves, and compute complex line integrals directly.
10. Use Cauchy’s integral theorem and formola to compute line integrals. • Represent functions as Taylor, power and Laurent series.
11. Classify singolarities and poles.
12. Find residues and evaluate complex integrals, real integrals using the residue theorem.

Course Outcome of Modern Analysis :

Students will able to

1. Define countable, uncountable sets
2. Write Holders and Minkowski inequality
3. Define and recognize the concept of metric spaces, open sets, closed sets, limit points, interior point.
4. Define and Illustrate the concept of completeness
5. Determine the continuity of a function at a point and on a set.
6. Differentiate the concept of continuity and uniform continuity
7. Define connectedness • Describe the connected subset of R.
8. Define compactness.

Course Outcome of Linear Algebra :

Students will able to

1. Define Vector Space, Quotient space Direct sum, linear span and linear independence, basis and inner product.
2. Discuss the linear transformations, rank, nollity.
3. Find the characteristic equation, eigen values and eigen vectors of a matrix.
4. Prove Cayley- Hamilton theorem, Schwartz inequality, Gram Schmidt orthogonalization process.
5. Solve the system of simoltaneous linear equations.

Course Outcome of Numerical Analysis :

Students will able to

1. Define Basic concepts of operators ∆, Ε, ∇
2. Find the difference of polynomial
3. Solve problems using Newton forward formola and Newton backward formola.
4. Derive Gauss’s formola and Stirling formola using Newton forward formola and Newton backward formola.
5. Find maxima and minima for differential equation
6. Derive Simpson’s 1/3 ,3/8 roles using trapezoidal role
7. Find the solution of the first order and second order equation with constant coefficient
8. Find the summation of series finite difference techniques
9. Find the solution of ordinary differential equation of first by Eoler, Taylor and Runge-Kutta methods.

Course Outcome of Sequence and Series:

Students will able to

1. Define different types of sequence.
2. Discuss the behaviour of the geometric sequence.
3. Prove properties of convergent and divergent sequence.
4. Verify the given sequence in convergent and divergent by using behaviour of Monotonic sequence.
5. Prove Cauchy’s first limit theorem, Cesario’s theorem, Cauchy’s Second limit theorem.
6. Explain subsequence’s and upper and lower limits of a sequence.
7. Give examples for convergence, divergence and oscillating series.
8. Discuss the behaviour of the geometric series.
9. Prove theorems on different test of convergence and divergence of a series of positive terms.
10. Verify the given series is convergent or divergent by using different test.

Course Outcome of Differential equations and its applications:

Students will able to

1. Extract the solution of differential equations of the first order and of the first degree by variables separable, Homogeneous and Non-Homogeneous methods.
2. Find a solution of differential equations of the first order and of a degree higher than the first by using methods of solvable for p,x and y.
3. Compute all the solutions of second and higher order linear differential equations with constant coefficients, linear equations with variable coefficients.
4. Solve simoltaneous linear equations with constant coefficients and total differential equations.
5. Form partial differential equations.
6. Find the solution of First order partial differential equations for some standard types.
7. Use inverse Laplace transform to return familiar functions
8. Apply Laplace transform to solve second order linear differential equation and simoltaneous linear differential equations.

Department of Statistics

Course Outcome of Statistics:

Students will able to

1. Define Resoltant, Component of a Force, Coplanar forces, like and unlike parallel forces, Moment of a force and Couple with examples.
2. Prove the Parallelogram of Forces, Triangle of Forces, Converse of the Triangle of Forces, Polygon of Forces, Lami’s Theorem, Varignon’s theorem of moments.
3. Find the resoltant of coplanar couples, equilibrium of couples and the equation to the line of action of the resoltant.
4. Discuss Friction, Forces of Friction, Cone of Friction, Angle of Friction and Laws of friction.
5. Define catenary and obtain the equation to the common catenary.
6. Find the tension at any point and discuss the geometrical properties of a catenary.

Course Outcome of Statistics:

Students will able to

1. Define Moments Skewness and Kurtosis.
2. Fit a straight line.
3. Calcolate the correlation coefficient for the given data.
4. Compute Rank correlation for the given data.
5. Define attributes, consistency of data, independence of data.
6. Find index numbers for the given data.
7. Define Probability, Conditional probability.
8. Derive Baye’s theorem.