Are you a student of B.Sc Maths and have completed the first year of B.Sc Maths? If yes, and browsing the BSc maths 2nd-year syllabus then I would like to tell you that your search is over because you visited the right site. In this post, you will check out the complete syllabus and subjects of 2nd year BSc maths honours.

As you all know there are two semesters in each bachelor’s degree course. Similarly, BSc maths second year consists of two semesters and the curriculum of the BSc maths course is also divided into semesters. There are three core papers, one skill enhancement and one generic elective paper present in the 3rd and 4th semesters respectively.

Bachelor of Science in mathematics is one of the popular undergraduate courses among students. Generally, students enrol in this course after successfully completing 12th from a recognized board of education.

I hope you know that syllabus of BSc maths may vary from university to university. So, it is not necessary that the below syllabus and the syllabus of your university are the same. The syllabus in this post is based on the University Grant Commission (UGC). However, I tried to cover most of the popular university syllabi.

Now, let’s move toward the syllabus and subjects of BSc 1st year maths.

## BSc 2nd Year Maths: Overview

BSC Full Form | Bachelor of Science |

Branch | Mathematics |

Total Number of Semesters in 2nd Year | 2 Semesters (6 Months Each) |

Complete Course Duration | 3 Years / 4 Years |

Core Subjects | 2 or 3 |

Optional Subjects | 2 |

### BSc Maths 2nd Year Syllabus

Semester III | Semester IV |
---|---|

Theory of Real Functions | Numerical Methods |

Group Theory I | Riemann Integration and Series of Functions |

PDE and Systems of ODE | Ring Theory and Linear Algebra I |

Skill Enhancement Course 1 | Skill Enhancement Course 2 |

Generic Elective 3 | Generic Elective 4 |

### BSc 3rd Semester Maths Syllabus

#### Theory of Real Functions

- Limits of Functions
- Sequential Criterion for Limits
- Limit Theorems
- Infinite Limits and Limits at Infinity
- Sequential Criterion for Continuity and Discontinuity
- Algebra of Continuous Functions
- Intermediate Value Theorem
- Location of Roots Theorem
- Preservation of Intervals Theorem
- Uniform Continuity
- Uniform Continuity Theorem
- Caratheodory’s Theorem
- Algebra of Differentiable Functions
- Rolle’s Theorem
- Mean Value Theorem
- Darboux’s Theorem
- Taylor’s Theorem to Inequalities
- Cauchy’s Mean Value Theorem
- Application of Taylor’s Theorem to Convex Functions
- Relative Extrema
- Intermediate Value Property of Derivatives

#### Group Theory I

- Symmetries of a Square
- Dihedral Groups
- Elementary Properties of Groups
- Subgroups and Examples of Subgroups
- Centralizer
- Product of Two Subgroups
- Properties of Cyclic Groups
- Classification of Subgroups of Cyclic Groups
- Cycle Notation for Permutations
- Properties of Permutations
- Even and Odd Permutations
- Properties of Cosets
- Lagrange’s Theorem
- Cauchy’s Theorem for Finite Abelian Groups
- Group Homomorphisms
- Properties of Homomorphisms
- Cayley’s Theorem
- Properties of Isomorphisms

#### PDE and Systems of ODE

- Partial Differential Equations
- Mathematical Problems
- First-Order Equations
- Canonical Forms of First-order Linear Equations
- Derivation of Heat Equation
- Wave Equation and Laplace Equation
- Cauchy Problem of an Infinite String
- Initial Boundary Value Problems
- Equations with Non-homogeneous Boundary Conditions
- Non-Homogeneous Wave Equation
- Method of Separation of Variables
- Solving the Heat Conduction Problem
- Systems of Linear Differential Equations
- Basic Theory of Linear Systems in Normal Form
- Homogeneous Linear Systems with Constant Coefficients
- The Method of Successive approximations
- The Runge-Kutta Method

#### Skill Enhancement Course 1

##### Logic and Sets

- Propositions
- Conjunction and Disjunction
- Biconditional Propositions
- Propositional Equivalence
- Predicates and Quantifiers
- Quantifiers
- Binding Variables and Negations
- Sets
- Laws of Set Theory and Venn Diagrams
- Examples of Finite and Infinite Sets
- Finite Sets and Counting Principle
- Empty Set, Properties of Empty Set
- Standard Set Operations
- Classes of Sets
- Difference and Symmetric Difference of Two Sets
- Set Identities
- Relation
- Types of Relations
- Partial Ordering Relations

##### Computer Graphics

- Development of Computer Graphics
- Raster Scan and Random Scan Graphics Storages
- Displays Processors and Character Generators
- Points, Lines and Curves
- Two-dimensional Viewing
- Coordinate Systems
- Linear Transformations
- Line and Polygon Clipping Algorithms

#### Generic Elective 3

##### Cryptography and Network Security

- Public Key Cryptography Principles & Applications
- Algorithms
- Message Authentication
- One Way Hash Functions
- Public Key Infrastructure
- Network Attacks
- Network Scanning
- Denial of Service Attacks
- Smurf Attacks
- IP Security Architecture
- Virtual Private Network Technology
- Network Management Security
- Overview of SNMP Architecture
- Types of Firewalls

##### Information Security

- Overview of Security
- Protection Versus Security
- Privacy
- Security Threats
- System Threats
- Communication Threats
- Cryptography
- Diffie-Hellman Key Exchange
- Message Authentication
- Digital Signatures
- Security Mechanisms
- System-call Monitoring

### BSc 4th Semester Maths Syllabus

#### Numerical Methods

- Use of a Scientific Calculator is Allowed
- Algorithms
- Transcendental and Polynomial Equations
- System of Linear Algebraic Equations
- Gauss Jacobi Method
- Gauss-Seidel Method and Their Convergence Analysis
- Interpolation
- Lagrange and Newton’s Methods
- Finite Difference Operators
- Gregory Forward and Backward Difference Interpolation
- Numerical Integration
- Trapezoidal Rule
- Composite Trapezoidal Rule
- Composite Simpson’s Rule
- Ordinary Differential Equations

#### Riemann Integration and Series of Functions

- Riemann Integration
- Riemann Conditions of Integrability
- Equivalence of Two Definitions
- Properties of the Riemann Integral
- Intermediate Value Theorem for Integrals
- Fundamental Theorems of Calculus
- Improper Integrals
- Series of Functions
- Limit Superior and Limit Inferior
- Cauchy Hadamard Theorem
- Differentiation and Integration of Power Series
- Abel’s Theorem
- Weierstrass Approximation Theorem

#### Ring Theory and Linear Algebra I

- Definition and Examples of Rings
- Properties of Rings
- Characteristic of a Ring
- Ideal Generated by a Subset of a Ring
- Ring Homomorphisms
- Properties of Ring Homomorphisms
- Dimension of Subspaces
- Linear Transformations
- Matrix Representation of a Linear Transformation
- Algebra of Linear Transformations
- Isomorphisms Theorems
- Invertibility and Isomorphisms
- Change of Coordinate Matrix

#### Skill Enhancement Course 2

##### Graph Theory

- Definition
- Examples and Basic Properties of Graphs
- Bi-partite Graphs
- Isomorphism of Graphs
- Eulerian Circuits
- Hamiltonian Cycles
- Travelling Salesman’s Problem
- Dijkstra’s Algorithm
- Floyd-Warshall Algorithm

##### Operating System: Linux

- Linux
- Linux History
- Overview of Linux Architecture
- The Ext2 and Ex3 File Systems
- User Management
- The Powers of Root
- Using the Command Line
- GUI Tools
- Resource Management in Linux
- File and Directory Management
- Memory Management
- Library and System Calls for Memory

#### Generic Elective 4

##### Applications of Algebra

- Balanced Incomplete Block Designs (BIBD)
- Incidence Matrix of a BIBD
- Construction of BIBD from Difference Sets
- Coding Theory
- Hamming Codes
- Decoding and Cyclic Codes
- Symmetry Groups and Color Patterns
- Colouring and Colouring Patterns
- Polya Theorem and Pattern Inventory
- Generating Functions for Non-Isomorphic Graphs
- Special Types of Matrices
- Positive Semi-definite Matrices
- Symmetric Matrices and Quadratic Forms
- Applications of Linnear Transformations
- Least Squares Methods
- Linear Algorithms

##### Combinatorial Mathematics

- Basic Counting Principles
- Binomial Theorem
- Principle of Inclusion and Exclusion
- Generating Functions
- Recurrence Relations
- Integer Partitions
- Systems of Distinct Representatives
- Polya Theory of Counting
- Polya’s Theorems and Their Immediate Applications
- Combinatorial Designs

**Also Read:-** BSc 1st Year Maths Syllabus

### BSc 2nd Year Maths Syllabus Kamaun University

Semester III | Semester IV |
---|---|

Advanced Algebra | Vector Spaces and Matrices |

Differential Equations | Real Analysis |

Mechanics | Mathematical Methods |

### BSc 2nd Year Maths Syllabus CSJM University

Paper I | Linear Algebra and Matrices |

Paper II | Differential Equations and Integral Transforms |

Paper III | Mechanics |

### BSc 2nd Year Maths Syllabus Kota University

3rd Semester | 4th Semester |
---|---|

Real Analysis | Real Analysis and Partial Differential Equation |

Differential Equations | Mechanics |