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Course Code |
Course Title |
L |
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MTH101 |
Pedagogy of Mathematics |
3 |
1 |
0 |
4 |
COURSE OUTCOMES
CO1. Understanding instructional objectives of different topics of mathematics.
CO2. Applying suitable methods appropriate to transact the subject matter.
CO3. Analyzing the importance of different instructional strategies and using different resources for effective teaching.
CO4. Evaluating the techniques of evaluation and developing the competency in preparing tools of evaluation in mathematics.
UNIT – I Foundation of Mathematical Education
a. Meaning, nature and structure of mathematics.
b. Value of teaching mathematics.
c. History of Mathematics with special reference to Indian Mathematics
(Aryabhatta and Sriniwas Ramanajum)
UNIT – II Aims, Objectives and curriculum form:
a. General aims and objectives of teaching mathematics in different level of education.
b. Bloom's Taxonomy and specification of objectives in terms of learning outcomes.
c. Correlation of mathematics with other school subjects language, social science and science.
d. Rationale, objectives, principles in the recent curricular reforms.
UNIT – III Methods, Techniques and Lesson Planning of Mathematics:
a. Skills of Teaching: Skill of Introducing the lesson. Skill of Illustration with Examples, Skill of Reinforcement, Skill of Probing questions and Skill of Stimulus Variation
b. Different methods approaches and techniques of teaching mathematics.
b. Teacher Centered and Child Centered Method of mathematics teaching.
c. Meaning & approaches of lesson planning, preparation of unit plan and lesson plan.
UNIT – IV Learning resources in Mathematics:
a. Text books, teacher manuals - importance and characteristics.
b. Co-curricular activities i.e. Mathematics field trip.
c. Audio-visual aids.
d. Print Media etc.
UNIT – V Evaluation in Mathematics:
a. Meaning and purpose of evaluation.
b. Types of test items - Objective, short-answer & essay types.
c. Continuous and comprehensive evaluation:
(i) Summative
(ii) Formative
d. Error analysis & conduct remedial teaching.
Practical Assignments/Field engagement (Any one):
● Construction and administration of achievement test in Mathematics.
● Identifying and Evaluating ICT resources (MOOCs & OERs) suitable for teaching Mathematics.
● Develop a Multi-Media lesson using appropriate ICT resources and transacting the same before peers in simulated teaching exercise.
● Preparation and presentation of lesson based on any one value of teaching Mathematics
● Preparation of album or video on contributions Indian and Western Mathematicians
● Preparation and presentation of an action research report on different problems faced by teachers/students in the mathematics classroom
● Construction of blue print for unit test, achievement test.
● Developing online games, video for mathematical concepts.
● Preparation of case study of slow or gifted learner in mathematics
SUGGESTED READINGS
∙ Alen, D.W and Ryan, K.A. (1969).Micro teaching, reading. Masschusetts, Falifornia: Addition
Wesley.
∙ Bloom, B.Se. (1956). Taxonomy of Educational objectives. Handbook No. 1, New York:
Longmans Green.
∙ Dave, R.H. and Saxena, R.C. (1970). Curriculum & Teaching of Maths in Secondary Schools. A Research Monograph, Delhi: NCERT
∙ Davis, D.R. (1951). The teaching of Mathematics. London: Addison Wesclyh Press.
∙ Kulshrestha, A.K. (2007). Teaching of Mathematics. Meerut: R.Lal Book Depot. ∙ Mangal, S.K. (2007). Teaching of Mathematics, New Delhi: Arya Book Depot.
∙ Shankaran and Gupta, H.N. (1984). Content- cum – Methodology of teaching Mathematics. New Delhi: NCERT
- Teacher: DEVANSHU SINGH
|
BSP 340 |
Numerical Analysis & Operations Research |
L |
T |
P |
C |
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3 |
0 |
0 |
3 |
COURSE OUTCOMES
CO1. Understanding the application of various numerical techniques for variety of problems occurring in daily life.
CO2. Evaluating the use of different methods for numerical solution of Ordinary differential equations
CO3. Applying the basic concepts of transportation problems and its related problems in operations research.
CO4. Solving Transportation problems.
Course Learning Outcomes
Part A (Numerical Analysis)
UNIT I
- Solution of equations: bisection, Secant, Regular Falsi, Newton Raphson’s method, Newton’s method for multiple roots,
- Interpolation, Lagrange and Hermite interpolation,
- Difference schemes, Divided differences, Interpolation formula using differences
UNIT II
- Numerical differentiation, Numerical Quadrature: Newton Cotes Formulas, Gaussian Quadrature Formulas, System of Linear equations:
- Direct method for solving systems of linear equations (Gauss elimination, LU Decomposition, Cholesky Decomposition), Iterative methods (Jacobi, Gauss Seidel, Relaxation methods). The Algebraic Eigen value problem:
- Jacobi’s method, Givens method, Power method.
UNIT III
- Numerical solution of Ordinary differential equations:
- Euler method, single step methods, Runge-Kutta method, Multi-step methods:
- Milne-Simpson method, Types of approximation:
- Last Square polynomial approximation, Uniform approximation, Chebyshev polynomial approximation.
UNIT IV
- Difference Equations and their solutions, Shooting method and Difference equation method for solving
- Linear second order differential equation with boundary conditions of first, second and third type.
Part B (Operational Research)
UNIT V
- Introduction, Linear programming problems, statement and formation of general linear programming problems, graphical method, slack and surplus variables, standard and matrix forms of linear programming problem, basic feasible solution.
UNIT VI
- Convex sets, fundamental theorem of linear programming, basic solution,
- Simplex method, introduction to artificial variables, two phase method Big-M method and their comparison.
UNIT VII
- I Resolution of degeneracy, duality in linear programming problems, primal dual relationships, revised simplex method, sensitivity analysis.
UNIT VIII
- Transportation problems, assignment problems.
Suggested Readings
(Part-A Numerical Analysis):
- Numerical Methods for Engineering and scientific computation by M. K. Jain, S.R.K. Iyengar& R.K. Jain.
- Introductory methods of Numerical Analysis by S. S. Sastry
- Suggested digital plate form: NPTEL/SWAYAM/MOOCs
- Course Books published in Hindi may be prescribed by the Universities.
(Part-B Operation Research):
- Taha, Hamdy H, "Opearations Research- An Introduction ", Pearson Education.
- KantiSwarup , P. K. Gupta , Man Mohan Operations research, Sultan Chand & Sons
- Hillier Frederick S and Lieberman Gerald J., “Operations Research”, McGraw Hill Publication.
- Winston Wayne L., “Operations Research: Applications and Algorithms”, Cengage Learning, 4th Edition.
- Hira D.S. and Gupta Prem Kumar, “Problems in Operations Research: Principles and Solutions”, S Chand & Co Ltd.
- Kalavathy S., “Operations Research”, S Chand.
- Course Books published in Hindi may be prescribed by the Universities.
- Teacher: Narendra Kumar
|
BSP 338 |
METRIC SPACES & COMPLEX ANALYSIS |
L |
T |
P |
C |
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3 |
0 |
0 |
3 |
CO1. Analyzing various physical phenomena that will provide foundation in mathematics.
CO2. Understanding fundamental concepts in Mathematics.
CO3. Describing the concepts of metric space, basic concepts and developments of complex analysis
CO4. Evaluating Exponential function and Logarithmic function.
Course Content
Part A (Metric Spaces)
UNIT I
- Metric spaces: Definition and examples,
- Sequences in metric spaces,
- Cauchy sequences,
- Complete metric space.
UNIT II
- Open and closed ball,
- Neighborhood, Open set, Interior of a set, limit point of a set, derived set, closed set, closure of a set, diameter of a set,
- Cantor’s theorem,
- Subspaces, Dense set.
UNIT III
- Continuous mappings,
- Sequential criterion and other characterizations of continuity,
- Uniform continuity,
- Homeomorphism,
- Contraction mapping,
- Banach fixed point theorem.
UNIT IV
- Connectedness, Connected subsets of Connectedness and continuous mappings,
- Compactness, Compactness and boundedness,
- Continuous functions on compact spaces.
Part B (Complex Analysis)
UNIT V
- Functions of complex variable, Mappings; Mappings by the exponential function,
- Limits, Theorems on limits, Limits involving the point at infinity,
- Continuity, Derivatives, Differentiation formulae, Cauchy-Riemann equations,
- Sufficient conditions for differentiability;
- Analytic functions and their examples.
UNIT VI
- Exponential function, Logarithmic function, Branches and derivatives of logarithms, Trigonometric function,
- Derivatives of functions, Definite integrals of functions,
- Contours, Contour integrals and its examples,
- Upper bounds for moduli of contour integrals.
UNIT VII
- Anti-derivatives, Proof of anti-derivative theorem,
- Cauchy-Goursat theorem, Cauchy integral formula;
- An extension of Cauchy integral formula, Consequences of Cauchy integral formula,
- Liouville’s theorem and the fundamental theorem of algebra.
UNIT VIII
- Convergence of sequences and series,
- Taylor series and its examples;
- Laurent series and its examples,
- Absolute and uniform convergence of power series,
- Uniqueness of series representations of power series, Isolated singular points,
- Residues, Cauchy’s residue theorem, residue at infinity;
- Types of isolated singular points,
- Residues at poles and its examples
Suggested Readings
(Part-A Metric Space):
- Mathematical Analysis by Shanti Narain.
- Shirali, Satish&Vasudeva, H. L. (2009). Metric Spaces, Springer, First Indian Print.
- Kumaresan, S. (2014). Topology of Metric Spaces (2nd ed.). Narosa Publishing House. New Delhi.
- Simmons, G. F. (2004). Introduction to Topology and Modern Analysis.Tata McGraw Hill. New Delhi.
- Suggested digital plateform:NPTEL/SWAYAM/MOOCS.
- Course Books published in Hindi may be prescribed by the Universities.
(Part-B Complex Analysis):
- Function of Complex Variable by Shanti Narain.
- Complex variable and applications by Brown & Churchill.
- Suggested digital plateform:NPTEL/SWAYAM/MOOCS.
- Course Books published in Hindi may be prescribed by the Universities
- Teacher: Narendra Kumar