Syllabus¶

Credits¶

Sets:
- Definition of set, cardinality of sets, finite, countable, and infinite sets.
- Operations on sets and Venn diagrams.
- Principle of inclusion and exclusion and its applications.
- Multisets.
Relations:
- Definition and properties of binary relations, closures of relations.
- Equivalence relations, equivalence classes, and partitions.
- N-ary relations and their representation as tables.
- Partial ordering relations and lattices.
Functions:
- Definition of a function, one-to-one, and onto functions.
- Principles of mathematical induction.
- Concave and convex functions.

Definition and Types: Identity matrix, diagonal matrix, etc.
Operations: Row and column operations; vector and matrix operations (addition, subtraction, multiplication) and their properties.
Identities and Inverses: Existence of additive and multiplicative identity and additive inverse.
Applications and Properties:
- Representing relations using matrices.
- Transpose of a matrix and its properties.
- Symmetric and skew-symmetric matrices.
- Elementary transformation of a matrix.
- Invertible matrices.

Core Concepts: Determinant of a square matrix, minor, cofactor, and Adjoint of a matrix.
Matrix Inversion:
- Finding the inverse using the adjoint method.
- Finding the inverse using elementary transformations.
Rank, Eigenvalues, and Eigenvectors:
- Rank of a matrix and its determination.
- Eigenvalues and Eigenvectors of a matrix (with emphasis on symmetric matrices).
- Cayley-Hamilton theorem.
Linear Equations:
- Cramer’s rule.
- Consistency of a system of linear non-homogenous equations and existence of solutions.
- Solving simultaneous linear equations by the Gaussian elimination method.

Data Representation:
- Types of Data: Attributes and variables.
- Frequency Distribution: Construction of Frequency and Cumulative frequency.
- Graphical Representation: Histogram, Frequency Polygon, Frequency Curve, and Ogive curves.
- Diagrammatic Representation: Simple bar, Subdivided bar, and Pie diagrams.
Descriptive Statistics:
- Measures of Central Tendency: Mean, Median, and Mode.
- Measures of Variation: Range, Interquartile range, Standard Deviation, and Variance.
Discrete Probability:
- Sample space, events, and random variables.
- Basic probability concepts.
- Conditional Probability and Bayes' theorem.