The BRABU B.Sc. 1st Year Syllabus of Mathematics Honours is as follows:
Paper I: Calculus
- Limits and continuity
- Differentiation
- Integration
- Application of derivatives and integrals
Paper II: Algebra
- Linear algebra
- Group theory
- Ring theory
- Field theory
Paper III: Differential Equations
- Ordinary differential equations
- Partial differential equations
Paper IV: Discrete Mathematics
- Graph theory
- Combinatorics
- Probability and statistics
Each paper has a duration of 3 hours and carries 100 marks.
Detailed syllabus:
Paper I: Calculus
- Limits and continuity: Definition of limits, one-sided limits, infinite limits, continuity of functions
- Differentiation: Definition of the derivative, rules of differentiation, higher-order derivatives, applications of derivatives to optimization problems
- Integration: Definition of the integral, fundamental theorem of calculus, indefinite and definite integrals, applications of integrals to area, volume, and other geometric problems
Paper II: Algebra
- Linear algebra: Vectors, matrices, determinants, linear transformations
- Group theory: Definition of a group, subgroups, cosets, normal subgroups, homomorphisms
- Ring theory: Definition of a ring, ideals, quotient rings, homomorphisms
- Field theory: Definition of a field, field extensions, homomorphisms
Paper III: Differential Equations
- Ordinary differential equations: First-order equations, second-order equations, systems of equations
- Partial differential equations: First-order equations, second-order equations
Paper IV: Discrete Mathematics
- Graph theory: Basic concepts of graph theory, trees, paths, circuits, Euler tours, Hamiltonian circuits
- Combinatorics: Counting techniques, permutations, combinations, recurrence relations
- Probability and statistics: Basic concepts of probability and statistics, random variables, probability distributions, statistical inference
Recommended textbooks:
- Calculus by Thomas, Finney, and Weir
- Linear Algebra by Gilbert Strang
- Abstract Algebra by Dummit and Foote
- Elementary Differential Equations by Boyce and DiPrima
- Discrete Mathematics by Rosen