# BRABU B.Sc. 1st Year Syllabus Of Mathematics Honours

#### 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
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