B.Sc. Mathematics – Course Outcomes

Semester II

Course 3: Differential Equations & Problem Solving Sessions (T & P)

Course Outcomes:

1. Solve first order first degree linear differential equations.

2. Convert a non-exact homogeneous equation to exact differential equation by using an integrating factor.

3. Know the methods of finding solution of a differential equation of first order but not of first degree.

4. Solve higher-order linear differential equations for both homogeneous and non-homogeneous, with constant coefficients.

5. Understand and apply the appropriate methods for solving higher order differential equations.
    

Course 4: Analytical Solid Geometry & Problem Solving Sessions (T & P)

Course Outcomes:

1. Understand planes and system of planes.

2. Know the detailed idea of lines.

3. Understand spheres and their properties.

4. Know system of spheres and coaxial system of spheres.

5. Understand various types of cones.

Semester III

 

Course 5: Group Theory & Problem Solving Sessions (T & P)

Course Outcomes:

1. Acquire the basic knowledge and structure of groups.

2. Get the significance of the notion of a subgroup and cosets.

3. Understand the concept of normal subgroups and properties of normal subgroup.

4. Study the homomorphisms and isomorphisms with applications.

5. Understand the properties of permutation and cyclic groups.

 

Course 6: Numerical Methods & Problem Solving Sessions (T & P)

Course Outcomes:

1. Difference between the operators Δ, ∇, E and the relation between them.

2. Know about the Newton – Gregory Forward and backward interpolation.

3. Know the Central Difference operators δ, μ, σ and relation between them.

4. Solve Algebraic and Transcendental equations.

5. Understand the concept of Curve fitting.

Course 7: Laplace Transforms & Problem Solving Sessions (T & P)

Course Outcomes:

1. Understand the definition and properties of Laplace transformations.

2. Get an idea about first and second shifting theorems and change of scale property.

3. Understand Laplace transforms of standard functions like Bessel, Error function etc.

4. Know the reverse transformation of Laplace and properties

5. Get the knowledge of application of convolution theorem.
    

 

Course 8: Special Functions & Problem Solving Sessions (T & P)

Course Outcomes:

1. Understand the Beta and Gamma functions, their properties and relation between these two functions; understand the orthogonal properties of Chebyshev polynomials and recurrence relations.

2. Find power series solutions of ordinary differential equations.

3. Solve Hermite equation and write the Hermite Polynomial of order (degree) n; find the generating function for Hermite Polynomials; study the orthogonal properties of Hermite Polynomials and recurrence relations.

4. Solve Legendre equation and write the Legendre equation of first kind; find the generating function for Legendre Polynomials; understand the orthogonal properties of Legendre Polynomials.

5. Solve Bessel equation and write the Bessel equation of first kind of order n; find the generating function for Bessel function; understand the orthogonal properties of Bessel function.

Semester IV

Course 9: Ring Theory & Problem Solving Sessions (T & P)

Course Outcomes:

1. Understand the definition and basic properties of rings.

2. Study the properties of subrings and ideals.

3. Learn about quotient rings and ring homomorphisms.

4. Understand integral domains, fields, and their properties.

5. Apply ring theory concepts to solve related problems.

 

Course 10: Introduction to Real Analysis & Problem Solving Sessions (T & P)

Course Outcomes:

1. Understand the concept of real numbers and their properties.

2. Learn the basic ideas of sequences and their convergence.

3. Study series of real numbers and tests for convergence.

4. Understand limits and continuity of real-valued functions.

5. Apply real analysis concepts to solve practical problems.

 

Course 11: Integral Transforms & Problem Solving Sessions (T & P)

Course Outcomes:

1. Understand Fourier series and their convergence.

2. Learn Fourier transforms and their properties.

3. Study applications of Fourier transforms to boundary value problems.

4. Understand Hankel and Z-transforms and their uses.

5. Apply integral transform techniques to solve differential equations.

 

Semester V

Course 12: Linear Algebra & Problem Solving Sessions (T & P)

Course Outcomes:

1. Understand vector spaces and subspaces.

2. Learn about linear independence, basis, and dimension.

3. Study linear transformations and their matrix representations.

4. Understand eigenvalues, eigenvectors, and diagonalization.

5. Apply linear algebra concepts to real-world problems.

 

Course 13: Vector Calculus & Problem Solving Sessions (T & P)

Course Outcomes:

1. Understand scalar and vector fields.

2. Learn gradient, divergence, and curl operations.

3. Study line, surface, and volume integrals.

4. Apply Green’s, Gauss’s, and Stokes’ theorems.

5. Use vector calculus in physical and engineering problems.

 

Course 14 (Elective): Functions of a Complex Variable / Advanced Numerical Methods

Course Outcomes (Functions of a Complex Variable):

1. Understand analytic functions and Cauchy-Riemann equations.

2. Learn complex integration and Cauchy’s integral theorem.

3. Study Taylor and Laurent series expansions.

4. Understand residues and evaluation of improper integrals.

5. Apply complex variable methods to physical problems.

Course Outcomes (Advanced Numerical Methods):

1. Understand advanced interpolation techniques.

2. Solve systems of linear equations using numerical methods.

3. Study numerical solutions of differential equations.

4. Learn numerical integration methods.

5. Apply numerical techniques in scientific computations.

 

Course 15 (Elective): Number Theory / Mathematical Statistics

Course Outcomes (Number Theory):

1. Understand divisibility, primes, and congruences.

2. Learn properties of arithmetic functions.

3. Study quadratic residues and reciprocity law.

4. Understand Diophantine equations.

5. Apply number theory concepts in cryptography and coding theory.

Course Outcomes (Mathematical Statistics):

1. Understand random variables and probability distributions.

2. Study mathematical expectation and moments.

3. Learn correlation and regression analysis.

4. Study sampling distributions and statistical inference.

5. Apply statistical techniques to data analysis.

 

Semester VI

(Internship/Apprenticeship – 12 Credits, no specific paper-wise outcomes, practical/project-based learning.)