BSc Maths 3rd Year Subjects, Syllabus, Elective, Optional, Colleges, Books

BSc Maths 3rd Year Syllabus

In BSc Maths 3rd year, there are two semesters - the fifth and sixth semesters. Each semester is four to six months. The syllabus of BSc Maths 3rd year is listed below.

BSc Maths 3rd Year Subjects

The subjects in BSc Maths 3rd year are numerical methods, probability, statistics, group theory, metric space, and graph theory. The details of every subject are listed below.

BSc Maths 3rd Year Subjects: Numerical Methods

• Representations of numbers: The topics covered in this subject are Roundoff error, truncation error, significant error, and error in numerical computations.
• Solution of transcendental and algebraic equations: The topics covered are Bisection, secant, fixed-point, Regula Falsi, Graffe's methods, and Newton-Raphson.
• Interpolation: The topics covered are interpolation formulas using differences, Lagrange and Newton interpolation, Divided differences, and Hermite interpolation.
• Numerical differentiation: The topics covered are Methods based on interpolations and Methods based on finite differences.
• Numerical integration: The topics covered are Trapezoidal, Simpson's, and Weddle's rules, and Gauss Quadrature Formulas.
• Solution of linear equations: The topics covered are Gauss elimination, Gauss-Jordan elimination, LU decomposition, Jacobi, and Gauss-Siedel.
• Ordinary differential equations: The topics covered are Euler's method, Single-step methods, Runge Kutta's method, and multi-step methods.

See Also

BSc Maths 3rd Year Subjects: Probability

• Notion of probability: The topics covered are the random experiment, sample space, axioms of probability, elementary properties of probability, and equally likely outcome problems.
• Random variables: The topics covered are Concept, cumulative distribution function, discrete and continuous random variables, expectation, mean, variance, and moment-generating function. 
• Discrete random variables: The topics covered are Bernoulli random variable, Binomial random variable, Poisson random variable, and geometric random variable.
• Continuous random variables: The topics covered are Uniform random variable, Gamma random variable, exponential random, Conditional probability, and conditional expectations, Bayes theorem, and Normal random variable.
• Bivariate random variables: The topics covered are Joint distribution, joint and conditional distributions, Bivariate normal distribution, and the correlation coefficient.

BSc Maths 3rd Year Subjects: Statistics

• Sampling and Sampling Distributions: The topics covered are Populations and Samples, distribution of the sample, Random Sample, and Simple random sampling with and without replacement.
• Sampling Distributions: The topics covered are statistics, Sample moments, Sample variance, Sampling from the normal distribution, Chi-square, t, and F-distributions.
• Statistical hypothesis: The topics covered are Simple and composite hypotheses, alternative hypotheses, null hypotheses, one-sided and two-sided hypotheses, Power function of a test, etc.
• Bivariate frequency Distribution: The topics covered are Bivariate data, Correlation, Scatter diagram, Linear Regression, the principle of least squares, and fitting of polynomials and exponential curves.

See Also:

BSc Maths 3rd Year Subjects: Group Theory

• Group Theory: The topics covered are Automorphism, inner automorphism, automorphism groups of finite and infinite cyclic groups, automorphism groups, applications of factor groups to automorphism groups, External direct product, and its properties, the converse of Lagrange’s theorem for the finite abelian group, etc.

BSc Maths 3rd Year Subjects: Metric Space

• Metric Space: The topics covered are definitions and examples of metric spaces, open ball, open set, limit point and closure of a set, properties of interior, closure, and boundary, bounded set and diameter of a set, Convergent sequence, Cauchy sequence, Cantor’s intersection theorem, Continuous mappings, Uniform continuity, Banach Fixed point Theorem, etc.

BSc Maths 3rd Year Subjects: Graph Theory

• Graph Theory: The topics covered in graph theory are definition, examples, and basic properties of graphs, pseudographs, complete graphs, bipartite graphs, isomorphism of graphs, paths, and circuits, Eulerian circuits, Hamiltonian cycles, the adjacency matrix, weighted graph, traveling salesman’s problem, shortest path, Dijkstra’s algorithm, Floyd?Warshall algorithm. 

See Also:

Elective Courses in BSc 3rd Year Maths Syllabus

The elective courses in the third year of BSc Maths are listed below. 

• Advanced Algebra
• Bio Mathematics
• Industrial Mathematics
• Discrete Mathematics
• Linear Programming
• Boolean Algebra & Automata Theory
• Differential Geometry
• Mathematic Modeling

See Also:

Optional Papers in BSc Maths 3rd Year

Students have to select any one out of the set of these three papers.

• Advanced Algebra
• Bio Mathematics
• Industrial Mathematics

The second set of papers out of which students have to select any one paper is listed below.

• Discrete Mathematics
• Linear Programming
• Boolean Algebra & Automata Theory