Course module

Mathematics - I, II, III, IV — DSSSB TGT Computer Science 2026 Section B

Explore the module outline and lessons below. Enroll free to begin studying here.

Lessons: 537
Duration: 43 hr 22 min
PYQs: 81
Practice: 468

Exam importance: 2.2% of the exam, based on section capacity, PYQ history and paper recency.

Syllabus index

Lessons in this module

537 linked lessons

Permutation and Combination

Basic Concepts & Counting Principles

Permutations (with & without Repetition)

Circular & Grouping Permutations

Combinations (with & without Repetition)

Special Applied Problems

Advanced Counting Theorems

Logarithm

Basic Concepts and Terminologies

Laws or Properties or Rules of Logarithms

Solving Logarithmic Expressions and Equations

Linear Algebra

Matrix and Vectors - Definition and Types

Matrix Addition and Multiplication

Transpose of a Matrix

Elementary Row and Column Operations

Determinant of a Matrix

Adjoint and Inverse of a Matrix

Rank of a Matrix

System of Linear Equations

Trace of a Matrix

Algebra

Basic Concepts & Fundamental Operations

Laws & Identities of Algebra

Factorization & Simplification

Linear Equations

Quadratic Equations

Polynomials & Algebraic Expressions

Simplification Based Problems

Calculus

Limits

Continuity

Differentiability and Differentiation

Maxima and Minima

Integration

Numerical Methods

[Notes] Numerical Methods Yash Jain Sir Knowledge Gate AIPdf

Trigonometry

Basics of Trigonometry (Foundation)

Trigonometric Functions and Angles

Compound Angle and Transformation Formula

Trigonometric Identities and Simplification

Vectors

Vector Basics (Foundation)

Dot Product and Its Applications

Cross Product and Its Applications

Set Theory

Sets, Representation of Sets and Hierarchy of numbers

Finite, Infinite, Countable, and Uncountable Sets

Null, Universal, Subsets, Proper Subsets

Power Set and its Cardinality

Set Operations – Union, Intersection, Set Difference, Symmetric Difference, and Complement

Functions

Definition of a Function – Domain, Co-domain, Range, and Count of Possible Functions

Composition of Functions – Definition, Properties, and Examples

One-to-One (Injective) Function – Definition, Count, and Properties

Onto (Surjective) Function – Definition, Count, and Properties

Bijective Function – Definition, Count, and Properties

Inverse of a Function – Definition, Existence Conditions, and Examples

Relations

Cartesian Product, Relation, Inverse & Complement

Reflexive Irreflexive Relation – Count, and Properties

Symmetric Anti-Symmetric Asymmetric Relation and Properties

Transitive Relation – Definition, Count, and Properties

Equivalence Relation, Equivalence Classes, Partitions of a Set

Partial Order Relation – Properties, Partially Ordered Set (Poset), and Total Order Relation

Hasse Diagram, Greatest Element, Least Element, Upper Bound, Lower Bound

Propositional and Predicate Logic

Introduction to Propositions, Laws of Contradiction and Excluded Middle

Types of Propositions – Atomic and Compound

Logical Operators – Negation, Conjunction, and Disjunction

Implication and Bi-Conditional Operators in Logic

Types of Logical Cases – Tautology, Contradiction, Contingency, Satisfiability, and Validity

Introduction to First Order Predicate Logic

Quantifiers – Universal and Existential

Practice Problems on Quantifiers and Predicate Logic

Research Process Steps

Types of Variables (Independent, Dependent, Control, Extraneous, etc.)

Measurement Scales (Nominal, Ordinal, Interval, Ratio & Attitudinal Scales)

Formulating Hypothesis

Step - 4 Formulating HypothesisDrm Video

True, Quasi & Non-Experimental Designs

Randomisation, Types & Experimental Constraints

RandomisationDrm Video

Sampling Fundamentals – Types, Probability & Non-Probability Sampling

Sampling & Non-Sampling Errors

Statistical Properties of Data (including Skewness & Kurtosis)

Testing of Hypothesis & Variables

Parametric Tests – t-test, z-test, ANOVA

Non-Parametric Tests – Chi-square, Mann-Whitney, K-S, Runs Test, etc.

Assumptions, Advantages & Limitations of Tests

Graph Theory

Introduction to Graphs – Definitions, Terminology (Loops, Parallel Edges, Adjacent Vertices)

Types of Graphs – Finite, Infinite, Null, Trivial, Complete

Bipartite, Cycle, Regular, and Complement of a Graph

Number of Graphs – Counting of Simple, Undirected, Unlabeled

Degree of Vertex – Isolated and Pendant Vertices, Handshaking Lemma, and Degree Sequence

Minimum and Maximum Degree – Relationships, Degree Constraints, and Havel-Hakimi Theorem

Graph Traversal – Walk, Path, Trail, Circuit, and Connected Graphs

Euler and Hamiltonian Graphs – Definitions, Conditions, and Examples

Planar Graphs – Kuratowski’s Theorems, Homorphism and examples

Euler Formula – Planar Graph Formula, Applications, and Derived Relations

Graph Coloring – Vertex Coloring, Edge Coloring, Chromatic Number, and Coloring Theorems

Trees – Definitions, Properties, Eccentricity, Diameter, Radius, and Center

Spanning Tree and Spanning Forest – Definition, Construction, and Applications

Cut Set and Connectivity – Edge Connectivity, Vertex Connectivity, and Cut Set Concepts

Previous-year questions