B.sc math shorts syllabus of part 1, 2 and 3 for all University

The Bachelor of Science (B.Sc.) in Mathematics is typically a three-year undergraduate program divided into three parts or six semesters, depending on the university’s structure. The syllabus can vary across institutions, but core topics are generally consistent. Below is an overview of the typical subjects covered in each part:

Part I (First Year):

1. Calculus:

   • Differential Calculus: Limits, continuity, differentiability, successive differentiation, Leibniz’s theorem, tangents and normals, curvature, asymptotes, partial differentiation, Euler’s theorem, and applications.
   • Integral Calculus: Integration techniques, definite integrals, applications to areas, volumes, and surfaces of revolution.

2. Algebra:

   • Set theory, relations, functions, binary operations, group theory, subgroups, cyclic groups, rings, integral domains, fields, and their properties.

3. Analytical Geometry:

   • Two-dimensional geometry: Conic sections, tangents and normals, polar equations.
   • Three-dimensional geometry: Planes, straight lines, spheres, cones, cylinders, and conicoids.

4. Trigonometry:

   • De Moivre’s theorem, hyperbolic functions, and series expansions.

Part II (Second Year):

1. Real Analysis:

   • Sequences and series, convergence tests, continuity, differentiability, mean value theorems, Taylor and Maclaurin series.

2. Abstract Algebra:

   • Group theory, including homomorphisms, isomorphisms, and Sylow theorems; ring theory, including ideals and quotient rings; field theory.

3. Differential Equations:

   • First-order and higher-order differential equations, methods of solution, applications to physical problems.

4. Vector Calculus:

   • Vector differentiation and integration, line, surface, and volume integrals, theorems of Gauss, Green, and Stokes.

Part III (Third Year):

1. Complex Analysis:

   • Analytic functions, Cauchy-Riemann equations, complex integration, Cauchy’s theorem, Laurent series, residues, and applications.

2. Linear Algebra:

   • Vector spaces, linear transformations, matrices, eigenvalues, eigenvectors, Cayley-Hamilton theorem.

3. Numerical Methods:

   • Numerical solutions of equations, interpolation, numerical differentiation and integration, numerical solutions of differential equations.

4. Mechanics:

   • Statics and dynamics, including forces, equilibrium, motion of particles and rigid bodies, central forces, and planetary motion.

5. Optional Topics:

   • Depending on the university, optional papers may include subjects like number theory, probability theory, mathematical statistics, or operations research.

For instance, Patna University offers a detailed syllabus for its B.Sc. Mathematics program, which includes topics such as numerical analysis, spherical astronomy, probability theory, and computational methods in the final year. citeturn0search0

Please note that the exact syllabus can vary between universities. It’s advisable to consult the specific curriculum provided by the university you are interested in for precise information.