Mathematical Foundation for Computer Application
The mathematics a computer application degree actually runs on — matrices, logic, sets, graphs and numerical methods.
- Code
- BCA1B01T
- Semester
- 1
- Credits
- 4
- Contact
- 4 hours / week
- Modules
- 5
Modules
Module 1
9 topics
Matrices
From notation to eigenvalues. Every named type of matrix, every standard operation, and every method the exam asks for — worked in full.
- Definition, order, types of matrices
- Addition, scalar multiplication and multiplication of matrices
- Transpose, symmetric and skew-symmetric matrices
- Determinants and their properties
- Minors, cofactors, adjoint and inverse
- Elementary transformations, echelon form and rank
- Solution of linear equations — Cramer's rule, matrix method, Gauss elimination
- Eigenvalues, eigenvectors and the Cayley–Hamilton theorem
Module 2
In preparation
Mathematical Logic
Propositions, connectives, truth tables, tautologies, normal forms, rules of inference and predicate calculus.
- Propositions and logical connectives
- Truth tables, tautology and contradiction
- Logical equivalence and implication
- Normal forms — CNF and DNF
- Rules of inference and validity of arguments
- Predicates and quantifiers
Module 3
In preparation
Set Theory, Relations and Functions
Set operations and Venn diagrams, Cartesian products, types of relations, equivalence classes and functions.
- Sets, subsets and set operations
- Venn diagrams and De Morgan's laws
- Cartesian product and relations
- Types of relations; equivalence relations and partitions
- Functions — injective, surjective, bijective; composition and inverse
Module 4
In preparation
Graph Theory
Graphs, degrees, paths and circuits, trees, and the matrix representations that connect back to Module 1.
- Graphs, vertices, edges and degree
- Types of graphs; subgraphs and isomorphism
- Paths, circuits, Euler and Hamiltonian graphs
- Trees and spanning trees
- Adjacency and incidence matrices
Module 5
In preparation
Numerical Methods
Solving equations and interpolating data when an exact answer is out of reach.
- Errors in numerical computation
- Bisection, Regula Falsi and Newton–Raphson methods
- Iterative solution of linear systems — Gauss–Seidel
- Finite differences and interpolation
- Numerical integration