Syllabus of the BSc math AU

B.Sc 1st Year Mathematics Syllabus of Allahabad University

CalculusTopics

• Differential calculus
• Geometrical application of differential calculus
• Asymptotes
• Integral Calculus
• Multiple Integrals

Probability & StatisticsTopics

• Probability and theoretical distributions 
• Transformation of a random variable 
• Testing of hypothesis 
• Correlation and regression 
• Statistical quality control 

Analytical Solid GeometryTopics

• Analytical geometry of two dimensions 
• Analytical geometry of three dimensions 
• Central coincides 
• Paraboloids 
• Transformation of rectangular axes

Differential EquationsTopics

• Solving ordinary differential calculus 
• Differential equations with constant coefficients 
• Formation and solving PDE 
• Homogenous linear differential equations 
• Laplace transforms

B.Sc 2nd Year Mathematics Syllabus of Allahabad University

Real AnalysisTopics

• Sets and Functions
• Real-valued functions
• Equivalence, Countability
• Real Numbers
• Least upper bounds

Abstract AlgebraTopics

• Preliminaries
• Group and commutative group
• Definition of subgroup and examples
• Definition of a cyclic group
• Permutation

MechanicsTopics

• Friction
• Common catenary
• Impact
• Virtual work
• Moment of force

Linear AlgebraTopics

• Vector spaces 
• Inner product spaces
• Linear transformations
• Eigenvalues and Eigenvectors

B.Sc 3rd Year Mathematics Syllabus of Allahabad University

Discrete MathematicsTopics

• Relations
• Division algorithm
• Logic
• Graph theory

Linear Programming & Its ApplicationsTopics

• Under programming problem
• Problem formulation
• Types of solutions
• Linear programming in matrix notation

Complex AnalysisTopics

• Analytical function
• Transformation
• Contour integral
• Taylor and Laurent's theorem
• Evaluation of Integral

Numerical AnalysisTopics

• The direct and iterative method
• Numerical differentiation and integration
• Polynomial approximation
• Numerical solution of ordinary differential equations
• Numerical solution of partial differential methods