Integrated B.Sc. - B.Ed.

The department offers disciplinary/interdisciplinary 4-years integrated B.Sc. - B.Ed. program from the academic year 2024-25. The current students’ strength is 22. Admission to B.Sc. - B.Ed. Program through your score in the National Common Entrance Test (NCET). Click the Link for details.

B.Sc. - B.Ed. Course Structure

Semester - I

Responsive Course Table
Sr. Course Code Course Name Credits L-T-P-S-C
1. HB101 Language 1: English 4 4-0-0-8
2. HB102 Understanding India (Indian Ethos and Knowledge Systems) 2 2-0-0-4
3. HB103 Evolution of Indian Education 4 4-0-0-8
4. HB104 Art Education (Performing and Visual) 1 2 2-0-0-4
5. PB101 Introductory Physics 3 3-1-0-5-3
6. CB101 Introductory Chemistry 3 3-1-0-5-3
7. MB101 Calculus 4 4-0-0-8
Total Credits: 22

Semester-II

Responsive Course Table
Sr. Course Code Course Name Credits L-T-P-S-C
1. HB105 Language 2 (as per the 8th schedule of the Constitution of India.) Sanskrit 4 4-0-0-8
2. HB106 Understanding India (Indian Ethos and Knowledge Systems) 2 2-0-0-4
3. HB107 Teacher and Society 2 2-0-0-4
4. MB102 Discrete Mathematics 4 4-0-0-8
5. MB103 Matrices and Linear Algebra 5 4-0-2-10
6. MB104 Coordinate geometry and Trigonometry 4 4-0-0-8
Total Credits: 21

Semester-III

Responsive Course Table
Sr. Course Code Course Name Credits L-T-P-S-C
1. HB201 Child Development & Education Psychology 4 4-0-0-8
2. HB202 Basics of pedagogy 4 4-0-0-8
3. MB201 Algebra 4 4-0-0-8
4. MB202 Advanced Calculus 4 4-0-0-8
5. MB204 Probability and Statistics 4 4-0-0-8
Total Credits: 20

Semester-IV

Responsive Course Table
Sr. Course Code Course Name Credits L-T-P-S-C
1. HB203 Philosophical and Sociological perspectives of education-1 4 4-0-0-8
2. MB200 Pedagogy for Mathematics 4 3-0-2-7
3. MB203 Differential Equations 4 4-0-0-8
4. MB205 Real & Complex Analysis 4 4-0-0-8
5. MB206 Number Theory 4 4-0-0-8
Total Credits: 20

B.Sc. - B.Ed. Courses

Real numbers, Functions and their graphs, Limits and continuity of single variable functions, Differentiation and applications of derivatives, Rolle’s theorem, Cauchy’s mean value theorem, Indeterminate forms, Taylor’s and Maclaurin‘s theorems with remainders, Maxima and Minima, Concavity and convexity of a curve, Points of inflexion, Asymptotes and Curvature, Definite integrals, Fundamental theorem of calculus, Mean value theorems, Applications to length, Moments and center of mass, Surfaces of revolutions, Sequences, Series and their convergence, Absolute and Conditional convergence, Power series, Taylor’s and Maclaurin’s series, Convergence of improper integrals, Tests of convergence,Convergence of Beta and Gamma functions.Differentiation under integral sign, differentiation of integrals with variable limits – Leibnitz rule, Conic section and polar coordinates.

Logic and Proofs: Propositional Logic Predicates and Quantifiers, Proof Methods.

Set Theory: Basic Set Structure, Cardinality of a Set.

Relations, Induction and Recurrences: Relations and Their Properties, Closure of Relations, Equivalence Relations, Partial Orderings, Induction, Strong Induction, Recursive Definitions. Counting Techniques: Pigeonhole Principle, Permutations and Combinations, Binomial Coefficients, Recurrence Relations, Generating Functions, Inclusion-exclusion principle.

Number Theory and Cryptography: Modular arithmetic, Euclid’s Algorithm, Primes, Solving Congruences; Public key Cryptography. Graph Theory: Basic terminology and Special type of graphs, Connectivity, Eulerian and Hamiltonian graphs, Planar graphs, Graph Coloring, Shortest Path, Minimum Spanning Trees.

Boolean Algebra: Boolean Functions, Logic Gates.

Tentative Syllabus:

Unit 1 – Basic operation of matrices: Matrices, algebra of matrices, determinants, fundamental properties, minors and cofactors, product of determinant, adjoint and inverse of a matrix, Rank and nullity of a matrix, Eigen values, Eigen vectors of amatrix.

Unit 2 – Types of matrices: Transpose of matrix, symmetric matrix, orthogonal matrix, idempotent matrix, nilpotent matrix and their basic properties.

Unit 3 – System of Linear equations: Systems of linear equations (homogenous and non-homogonies), row reduction and echelon forms, solution sets of linear systems, applications of linear systems.

Unit 4 – Basics on Vector spaces: Vector spaces, subspaces, examples, algebra of subs paces, quotient spaces, linear combination of vectors, linear span, linear independence, basis and dimension, dimension of subspaces.

Unit 5 – Linear Transformations: Linear transformations, null space, range, rank and nullity of a linear transformation.

References:

  1. 1. Richard Bronson, Theory and Problems of Matrix Operations, Tata McGraw Hill, 1989.
  2. 2. Roger A. Horn, Charles R. Johnson – Topics in Matrix Analysis-Cambridge University Press (2008)
  3. 3. David C. Lay, Linear Algebra and its Applications, 3rd Ed., Pearson Education Asia, Indian Reprint, 2007.
  4. 4. S. Lang, Introduction to Linear Algebra, 2nd Ed., Springer, 2005.
  5. 5. Gilbert Strang, Linear Algebra and its Applications, Thomson, 2007.
  6. 6. A.I. Kostrikin, Introduction to Algebra, Springer Verlag, 1984.

General equation of second degree. Tracing of conics. Tangent at any point to the conic, chord of contact, pole of line to the conic, director circle of conic. System of conics. Confocal conics. Polar equation of a conic, tangent and normal to the conic.

Sphere: Plane section of a sphere. Sphere through a given circle. Intersection of two spheres, radical plane of two spheres. Co-oxal system of spheres.

Cones: Right circular cone, enveloping cone and reciprocal cone.

Cylinder: Right circular cylinder and enveloping cylinder.

Central Conicoids: Equation of tangent plane. Director sphere. Normal to the conicoids. Polar plane of a point. Enveloping cone of a coincoid. Enveloping cylinder of a coincoid.

Paraboloids: Circular section, Plane sections of conicoids. Generating lines. Confocal conicoid. Reduction of second degree equations.

De Moivre’s Theorem and its Applications. Expansion of trigonometrical functions. Direct circular and hyperbolic functions and their properties. Inverse circular and hyperbolic functions and their properties. Logarithm of a complex quantity. Gregory’s series. Summation of Trigonometry series.

References:

  1. 1. R. J. T. Bill; Elementary Treatise on Coordinary Geometry of Three Dimensions, MacMillan India Ltd. 1994.
  2. 2. S. L. Loney; Plane Trigonometry Part – II, Macmillan and Company, London.
  3. 3. S. L. Loney; The elements of co-ordinate geometry, EduGorrila Community Pvt. Ltd.

Unit – 1: The real number system: Finite, countable and uncountable sets, Order and fields axioms of R, upper bounds and lower bounds, the least upper bound property, the Archimedean property. Intervals, limits and interior points of sets, open and closed sets of R, connected and compact sets, the Heine-Borel and the Bolzano-Weierstrass theorems.

Unit – 2: Metric Spaces: Definition and Basic Examples: metric, discrete metric, sup metric, Open, and closed balls, open and closed sets, Interior, closure, boundary; limit points, and isolated points. Bounded and unbound sets, Compact sets.

Unit – 3: Riemann Integrals: Riemann upper sums and lower sums, Riemann integral of a function and its properties, Fundamental theorems for integral calculus.

Unit – 4: The complex number system: The complex number system, real and imaginary parts, algebra of complex numbers, contumacy and its properties, modulus, reciprocal of complex numbers, polar coordinates, conversion of polar coordinates to Cartesian coordinates, arguments and Euler form.

Unit 5: Functions of Complex Variables: Functions of complex numbers, limits and continuity. Uniform continuity, The exponential function, the trigonometric and hyperbolic functions, logarithmic function.

Unit 6: Linear and Bilinear transformations: Elementary transformations, Linear and Bilinear transformations, properties and geometrical interpretation of bilinear transformations, determinations, Cross ratios and its invariance, fixed points of bilinear transformations, some special bilinear transformations, classification of bilinear transformations.

Unit 7: Functions of Complex Variables: Differentiability of complex functions, Cauchy–Riemann equations: necessary and sufficient conditions for differentiability, Standard Differentiation Formulas, non-differentiable functions. Analytic functions and their properties, Harmonic functions: relation with analytic functions.

Suggested textbooks and references:

  1. 1. R.G. Bartle and D R Sherbert, “ Introduction to ot Real Analysis”, 3rd Edition, Wiley India, 2010.
  2. 2. S. Ponnusamy, Foundations of Complex Analysis, Narosa Publications, 2011.
  3. 3. Tom M. Apostol, Mathematical Analysis, 2nd Edition, Addison-Wesley, 1974.
  4. 4. Kenneth A. Ross, Elementary analysis – The Theory of Calculus, 2nd Edition, Springer, 2013.
  5. 5. S.C. Malik and Savita Arora, Mathematical Analysis, 2nd Edition, New Age International Publishers, 2010.
  6. 6. Theodore W. Gameli, Complex analysis, Springer, 2001.
  7. 7. S Kumaresan, A Pathway to Complex Analysis, Techno World Publishers, 2021.
  8. 8. Hemant Kumar Pathak, “Complex Analysis and Applications, Springer, 2015.

Responsive Course Table

Objectives: The course aims to develop awareness among student-teachers and educators about the nature of mathematics, effective teaching and learning processes, and learners’ identities. It encourages inquiry, reflection, and critical examination of beliefs and practices to enhance mathematics teaching and learning using teaching aids like charts, models etc.

Content:
1. Development of Mathematics from a historical perspective. Importance of Mathematics knowledge in everyday life.
2. Aims and objectives of teaching Mathematics at secondary stage. Linkages of Mathematics with other school subjects and place in school curriculum.
3. Implication of various approaches of teaching Mathematics – inductive deductive, analytical synthetically, constructivist, blended learning, experiential learning.
4. Learner-centric and participative methods of teaching of Mathematics: lecture cum demonstration, problem-solving, laboratory, project based.
5. Techniques of teaching learning Mathematics: oral, written, drill work, homework, self-study, group study, supervised study.
6. Techniques of teaching learning Mathematics: concept-mapping, learning, art and sports integrated Learning. (continued)
7. Teaching learning materials: meaning and importance for secondary school Mathematics.
8. Types of teaching learning resources: print media (Mathematics textbook, teachers’ manual / handbook, laboratory manual), non-print and digital media for offline/ online classroom teaching and learning. Mathematics resource room/ laboratory – equipment and management, concept of virtual laboratories.
9. Analysis for identification of axioms, concepts, rules, formulas, theorems, corollaries; Developing annual plan, unit plan, lesson plan – need, main consideration, and format.
10. Strategies for method-based lesson plan for secondary classes. Inductive-deductive, analytical-synthetical, lecture cum demonstration, problem-solving, laboratory, and project based.
11. Need for and importance of how to learn 21st century skills such as practicing imagination, spatial visualization, mathematical reasoning, problem solving for learners and teachers of Mathematics.
12. Scope and importance of ICT for teaching and learning Mathematics. Use of ICT (digital repository, Augmented Reality (AR), Virtual Reality (VR).
13. Artificial Intelligence (AI) based digital resources, open education resources, blogs, forums, interactive boards, and devices) in the teaching learning, assessment and resource management of secondary Mathematics. Use of tools, software, and platforms such as national teacher’s portal, DIKSHA, SWAYAM.
14. Planning and developing teachers made tests in Mathematics Table of Specification (TOS), question paper setting and preparing answer key.

Labs:
  1. 1. Class room arrangement models.
  2. 2. Teaching aids – 2D Models on topic 1 (From NCERT Mathematics textbooks from Class V to X).
  3. 3. Teaching aids – 2D Models on topic 2 (From NCERT Mathematics textbooks from Class V to X).
  4. 4. Teaching aids – 2D Models on topic 3 (From NCERT Mathematics textbooks from Class V to X).
  5. 5. Teaching aids – 2D Models on topic 4 (From NCERT Mathematics textbooks from Class V to X).
  6. 6. Teaching aids – 2D Models on topic 5 (From NCERT Mathematics textbooks from Class V tso X).
  7. 7. Teaching aids – 3D Models on topic 1 (From NCERT Mathematics textbooks from Class V to X).
  8. 8. Teaching aids – 3D Models on topic 2 (From NCERT Mathematics textbooks from Class V to X).
  9. 9. Teaching aids – 3D Models on topic 3 (From NCERT Mathematics textbooks from Class V to X).
  10. 10. Teaching aids – 3D Models on topic 4 (From NCERT Mathematics textbooks from Class V to X).
  11. 11. Teaching aids – 3D Models on topic 5 (From NCERT Mathematics textbooks from Class V to X).
  12. 12. Teaching aids – mathematics puzzle on topic 1 (from NCERT Mathematics textbooks from Class V to X).
  13. 13. Teaching aids – mathematics puzzle on topic 21 (from NCERT Mathematics textbooks from Class V to X).
  14. 14. Teaching aids – Video model on topic (from NCERT Mathematics textbooks from Class V to X).

Text Book: NCERT(2012), Pedagogy of Mathematics- textbook for Two year B.Ed course, New Delhi.

References:
  1. 1. Butler and Wren (1965), The Teaching of Secondary Mathematics- Fourth Edition, London, McGraw Hill Book company.
  2. 2. Cooney T J and others (1975), Dynamics of Teaching Secondary School Mathematics, Boston: Houghton Miffilin.
  3. 3. Madhu Sahni, Pedagogy Of Mathematics, Vikas Publishing house India, 2019.
  4. 4. T V Somashekar, G Viswanathappa and Anice James (2014), Methods of Teaching Mathematics, Hyderabad, Neelkamal publications Pvt Ltd.

Binary operations, Semigroups, groups, Symmetries of a square, Dihedral groups, groups of integers modulo n, matrix groups, groups of quaternions, symmetric groups, permutations, properties of groups, subgroups, Cyclic groups, classification of subgroups of cyclic groups, Lagranges theorem, Normal sub-groups, Quotient groups, Homomorphisms, Isomorphism Theorems, Cayleys Theorem, Automorphism, Inner automorphism, automorphism group, automorphism group of finite and infinite cyclic groups.
    Definition and examples of rings, properties of rings, subrings and ideals, integral domains, Division rings and fields, characteristic of a ring, ideals and factor rings, ideal generated by a subset of a ring, algebra of ideals, prime and maximal ideals. Polynomial Rings over commutative rings, division algorithm and consequences, Eisensteins irreducibility criterion, Ring homomorphisms, properties of ring homomorphisms, Isomorphism theorems.

Textbooks:

  1. 1. J. A. Gallian, Contemporary Abstract Algebra, (4th ed.), Narosa, 1999.
  2. 2. M. Artin, Abstract Algebra,(2th ed.), Pearson, 2011.

Unit – 1: Vectors and geometry of spaces: The space R^n, distance between vectors, norm, dot product, cross product and angle. Cauchy’s inequality, triangle inequality, Polar coordinate system and its parametric representation., Cylindrical and spherical coordinate systems.

Unit – 2: Limits and Continuity of Functions of Several Variables: Functions of several variables, level curves, level sets, limits and continuity of functions of several variables.

Unit – 3: Multivariable Differential Calculus: Partial derivatives, Tangent planes and Linear approximation, Increments and total derivative or differential, implicit derivatives, The chain rule, gradients and directional derivatives, Taylor’s formula, Taylor’s approximations, Hessian matrix, Extreme values and saddle points, Lagrange multipliers.

Unit – 4: Multiple integrals: Double integrals over rectangles and general regions, Change of variables, double integral in polar coordinates, Area, moments and centre of masses, surface area, triple integral over rectangular coordinates, Spherical and Cylindrical coordinates, Applications to volume computations, Improper Integrals, Improper Multiple Integrals.

Unit – 5: Vector Calculus: Vector fields, work, circulation and flux, line integrals, fundamental theorem for line integrals, path independence, potential functions and conservative fields, Green’s theorem, curl and divergence, surface area and surface integrals, parametrised surfaces, Stokes’ theorem and the Divergence theorem.

Suggested textbooks and references:

  1. 1. George B. Thomas, Jr, Maurice D. Weir, Joel Hass and Christopher Heil, “Thomas Calculus”, 15th Edition, Pearson. 2015.
  2. 2. James Stewart, “Early Transcendentals- Calculus”, Indian Edition, Thomson, 2015.
  3. 3. Gilbert Strang, “Calculus”, Wellesley-Cambridge Press; 2nd edition, 2010.
  4. 4. G. B. Thomas and R. L. Finney, Calculus and Analytic Geometry, 9th edition, Addison-Wesley/Narosa, 1998.

Pre-requisites: Calculus

First Order Ordinary Differential Equations: Separable Equations, Exact Differential Equations, Integrating Factors, Linear First Order Equations, Substitutions-Bernoulli Equation, Homogeneous Equations, Substitution to Reduce Second Order Equations to First Order, Applications and Examples of First Order Ordinary Differential Equations.

Linear Differential Equations: Homogeneous Linear Equations, Nonhomogeneous Linear Equation, Second Order Linear Equations-Reduction of Order, Undetermined Coefficients, Variation of Parameters, Applications of Second Order Differential Equations.

Higher Order Linear Differential Equations: Undetermined Coefficients, Variation of Parameter, Euler’s Equation, Power Series Solutions-Legendre Equation, Bessel Equation. System of Linear Differential Equations, Existence and Uniqueness Theorems, Numerical Approximations-Euler’s Method, Runge-Kutta Methods. First Order Linear Partial Differential Equation. Homogeneous Linear Partial Differential Equation with constant.

Suggested textbooks and references:

  1. 1. George F. Simmons, Differential Equations with Applications and Historical Notes, 2nd Edition CRC Press.
  2. 2. Walter A. Strauss, Partial Differential Equations: An Introduction, John Wiley & Sons.
  3. 3. V. I. Arnold, Ordinary Differential Equations, Springer Science & Business Media.

Basic Concepts of Probability, Sample Space, Events, and Probability of Events, Probability Rules: Addition and Multiplication Rules, Conditional Probability and Independence, Bayes’ Theorem (simple applications), Permutations and Combinations (Basic problems).

Random Variables: Discrete and Continuous Random Variables, Probability Mass Function (PMF) and Probability Density Function (PDF), Cumulative Distribution Function (CDF), Standard Probability Distributions.

Discrete Distributions: Binomial, Geometric, Negative Binomial, Poisson (applications in teaching and basic science).

Continuous Distributions: Uniform, Exponential, Normal (emphasis on the Normal distribution for educational purposes), Expectation, Variance, Skewness, Kurtosis, Probability Generating Function, Characteristic Function, Moment Generating Functions, Law of Large Numbers, Central Limit Theorems.

Definition, Importance, and Applications in real-life and education, Types of data: Qualitative and Quantitative, Tabulation, and Graphical Representation (Bar Graphs, Histograms, Pie Charts).

Measures of Central Tendency: Arithmetic Mean, Median, Mode.

Measures of Dispersion: Range, Quartiles, Variance, Standard Deviation, Coefficient of Variation.

Correlation Analysis: Pearson’s and Spearman’s Rank Correlation Coefficient, Sampling Methods, Sampling Distributions Point Estimation, Unbiased Estimators, Interval Estimation, Hypothesis Testing.

Regression Analysis: Simple and Multiple Linear Regression, Line of Best Fit, Interpretation of Slope and Intercept, One-way ANOVA.

Suggested textbooks and references:

  1. 1. K.L. Chung. Elementary Probability Theory and Stochastic Process, Springer International Student Ed. (Eighth reprint).
  2. 2. Sheldon M. Ross. Introduction to Probability and Statistics for Engineers and Scientists, 5th Ed. 2014, Academic Press.
  3. 3. Walpole, Myers, Myers and Ye. Probability and Statistics for Engineers and Scientists, 9th Ed. 2011, Pearson Education, Inc.
  4. 4. J. S. Milton and J. C. Arnold. Introduction to Probability and Statistics: Principles and Applications for Engineering and the Computing Sciences, 2002, McGraw-Hill.

Division Algorithm, Greatest common divisors, Euclidean algorithm, Diophantine equations, The Fundamental theorem of Arithmetic, The Sieve of Eratosthenes, The Golbach conjecture, The theory of congruences and its properties, Linear congruences, Fermat’s Little theorem, Wilson’s theorem. Number theoretic functions and their properties, Euler’s phi functions and Euler’s theorem.

Primitive roots and theirs properties, Order of an integer modulo n, Theory of indices, The quadratic reciprocity law, Legendre symbol and its properties, quadratic congruencies with composite moduli, Perfect numbers, Mersenne primes, Fermat Numbers, Pythagorean triplets, The Fermat Last Theorem, Sum of two squares, Sum of four squares, Fibonacci numbers and their properties, Continued Fractions, Pell equations.

Suggested textbooks and references:

  1. 1. D. M . Burton, Elementary Number Theory
  2. 2. G Jones and J Jones, Elementary number theory
  3. 3. Niven, Zuckerman, Montgomery, The theory of Numbers

Scroll to Top