B.Sc Maths Syllabus: Semester Wise Curriculum [2025]

If you are about to start your undergraduate studies with B.Sc Mathematics, it is important for you to understand the B.Sc Mathematics syllabus, as it is a 3-year undergraduate academic course that focuses on the study of geometry, trigonometry, statistics, calculus, mathematical theories, and their applications.

Moreover, the B.Sc Mathematics coursework is designed to provide students with a strong foundation in their preferred subject. To know more about the B.Sc Mathematics syllabus, here is a blog that highlights it with semester-wise details. Let’s get started without any delay!

What Is the B.Sc Maths Syllabus?

The B.Sc Mathematics syllabus is structured over three years, usually divided into six semesters. Each year of the B.Sc Mathematics introduces progressively advanced topics, thereby building a strong mathematical foundation. Therefore, it is very important to understand the syllabus in depth.

The first year of B.Sc Maths deals with fundamental mathematical concepts such as calculus, algebra, and differential equations. The second year focuses on advanced calculus, group theory, and partial differential equations, and the third year covers advanced topics like metric spaces, complex analysis, and numerical methods.

What Are the Subjects in BSc Mathematics?

Before we jump into the details of the B.Sc Mathematics syllabus, let us first take a look at the subjects that you will come across in the three-year course of B.Sc Mathematics. This will give you clarity about what you are going to study at the undergraduate level. Here are the year-wise subjects:

Year	Subjects
1st Year	Calculus Algebra Real Analysis Differential Equations
2nd Year	Theory of Real Functions Group Theory- I Multivariate Calculus Partial Differential Equations Riemann Integration and Series of Functions Ring Theory and Linear Algebra- I
3rd Year	Metric Spaces Group Theory- II Complex Analysis  Ring Theory and Linear Algebra-II

Note: This is for indicative purposes. The BSc Maths syllabus and subjects can vary from one university to another.

First Year Syllabus for BSc Mathematics

In the first year of the BSc Mathematics course, you will be taught a variety of important topics spanning 4-5 subjects having different course objectives. The major emphasis will be laid on making you understand the concepts pertaining to planetary motion using calculus and geometric properties of conic sections. Differential equations, mathematical modelling, and their various applications will also be covered in the 1st year.

Listed below are the subjects incorporated in the BSc Maths syllabus for the first year:

Semester 1

The first semester of the B.Sc Mathematics focuses on basic topics to develop analytical skills. The following major topics are covered in this semester.

Calculus

• Derivatives for Graphing and Applications
• Sketching and Tracing of Curves
• Volume and Area of Surfaces 
• Introduction to Vector Calculus and Its Applications 

Algebra

• Theory of Equations and Complex Numbers 
• Equivalence Relations and Functions 
• Basic Number Theory 
• Row Echelon Form of Matrices 

Semester 2

Some of the major topics covered in Semester 2 are based on Semester 1. This semester introduces real analysis and differential equations. These topics are as follows:

Real Analysis

• Real Number System R
• Properties of R
• Infinite Series 
• Sequences in R

Differential Equations

• Population Growth Models 
• Differential Equations and Mathematical Modeling 
• Second and Higher-Order Differential Equations 
• Analysis of Mathematical Models 

Also Read: Career after BSc Maths

Second Year Syllabus for BSc Mathematics

As you begin your journey for the second year of the BSc Mathematics course, you will get familiar with a variety of topics that will build a sound foundation for the third year. Key concepts of calculus, continuity, and limits, as well as a study of valued functions, will be taught.

You will get to study in detail the symmetry of groups, along with the fundamental theory of groups and their homomorphism. Here are some important subjects which form an integral part of the BSc Maths syllabus for the second year:

Semester 3

In semester 3, you will be introduced to real functions and group theory. The topics under the 3rd semester of this course are:

Theory of Real Functions

• Continuous Functions and Their Properties 
• Limits of Functions
• Taylor’s Theorem and Its Applications
• Derivability and Its Applications 

Group Theory- I

• Subgroups and Cyclic Groups
• Groups and Their Elementary Properties 
• Group Homomorphism
• Permutation Groups and Lagrange’s Theorem 

Multivariate Calculus

• Double and Triple Integrals
• Calculus of Functions of Several Variables
• Extrema of Functions of Two Variables and Properties of Vector Field 
• Green’s, Stokes and Gauss’s Divergence Theorem 

Semester 4

The syllabus of the fourth semester of BSc Mathematics will cover advanced topics like Riemann integral and ring theory. Here is an overview of the syllabus for semester 4:

Partial Differential Equations 

• First-Order PDE and Method of Characteristics 
• The Cauchy Problem and Wave Equations 
• Mathematical Models and Classification of 2nd Order Linear PDE 
• Method of Separation of Variables 

Riemann Integration and Series of Functions

• Riemann Integration
• Improper Integral
• Sequence and Series of Functions
• Power Series

Ring Theory and Linear Algebra-I

• Introduction of Rings
• Ring Homomorphisms
• Introduction of Vector Spaces
• Linear Transformations

Third Year Syllabus for BSc Maths

The final year of your BSc Mathematics journey will constitute topics like Metric Spaces, Contour Integral, Numerical Analysis, etc, through which you will be equipped with a deep understanding of metrics of closed or open balls along with various other areas of study.

Furthermore, you will gain an in-depth understanding of the essential topics of abstract algebra and their applications. Enlisted below are the major subjects in the BSc Maths syllabus for the 3rd year:

Semester 5

The syllabus for the fifth semester of B.Sc. Mathematics gives a detailed introduction to topology and advanced algebra. Here is an overview of it:

Metric Spaces

• Topology and Metric Spaces 
• Basic Concepts 
• Connectedness and Compactness
• Continuity & Uniform Continuity in Metric Spaces 

Group Theory- II

• Automorphism and Properties 
• Group Action 
• Sylow Theorems and Applications
• External and Internal Direct Products of Groups

Semester 6

The final semester syllabus of B.Sc. Mathematics focuses on complex analysis and advanced applications. Here is an overview of it:

• Complex Analysis:
  • Analytic functions and Cauchy’s theorem
  • Contour integrals and the residue theorem
  • Power series and Laurent series
• Ring Theory and Linear Algebra-II:
  • Advanced ring theory
  • Canonical forms and applications
  • Quadratic forms
• Elective (Choose One):
  • Graph Theory
  • Differential Geometry
  • Mathematical Finance

University-Specific BSc Maths Syllabus

In India, different universities may have unique syllabi tailored to their academic standards. Below are examples from prominent Indian universities, updated for 2025.

BSc Maths Syllabus for DU

The Delhi University’s syllabus emphasizes both theoretical and applied mathematics. As per the DU syllabus for BSc Maths, the following segregation is found.

Semesters	Subjects
Semester 1	-Calculus -Algebra
Semester 2	-Real Analysis -Differential Equations
Semester 3	-Theory of Real Functions -Group Theory-I -Multivariate Calculus
Semester 4	-Partial Differential Equations -Riemann Integration and Series of Functions -Ring Theory and Linear Algebra-I
Semester 5	-Metric Spaces -Group Theory-II
Semester 6	-Complex Analysis – Ring Theory and Linear Algebra-II

BSc Maths Syllabus for Kumaun University

The Kumaun University BSc Mathematics syllabus emphasizes both theoretical and applied mathematics, preparing students for advanced study and research in areas such as nonlinear analysis, dynamical systems, and differential geometry. Here is an overview of the Kumaun University BSc Mathematics course.

Semester	Subjects
Semester 1	-Elementary Algebra and Trigonometry -Differential Calculus -Geometry and Vector Analysis
Semester 2	-Group Theory  -Integral Calculus -Analytical Geometry
Semester 3	-Advanced Algebra  -Differential Equations  -Mechanics
Semester 4	-Vector spaces and Matrices  -Real Analysis  -Mathematical Methods
Semester 5	-Linear Algebra -Complex Analysis  -Functions of several variables and Partial Differential Equations
Semester 6	-Numerical Methods -Mathematical Statistics  -Operations Research

Banaras Hindu University (BHU) BSc Maths Syllabus

BHU’s curriculum integrates practical applications and research-oriented topics. Here is an overview of the Banaras Hindu University’s B.Sc Mathematics syllabus.

Semester	Subjects
Semester 1	Calculus, Elementary Algebra, Trigonometry
Semester 2	Differential Equations, Analytical Geometry, Probability
Semester 3	Real Analysis, Group Theory, Vector Calculus
Semester 4	Linear Algebra, PDEs, Numerical Analysis
Semester 5	Metric Spaces, Complex Analysis, Linear Programming (Elective)
Semester 6	Abstract Algebra, Differential Geometry, Mathematical Statistics (Elective)

IGNOU BSc Maths Syllabus (Distance Education)

IGNOU offers a flexible syllabus for distance learners, focusing on core and elective courses. Here is an overview of the IGNOU’s B.Sc Mathematics syllabus for distance learning education.

Semester	Subjects
Semester 1	Calculus, Linear Algebra
Semester 2	Real Analysis, Differential Equations
Semester 3	Abstract Algebra, Probability and Statistics
Semester 4	Numerical Methods, Vector Calculus
Semester 5	Complex Analysis, Mathematical Modeling (Elective)
Semester 6	Graph Theory, Operations Research (Elective)

BSc Maths Syllabus for Lucknow University

The BSc Mathematics curriculum for Lucknow University is designed to develop analytical and problem-solving skills, covering core areas such as algebra, calculus, and statistics, as well as options for optional subjects in advanced topics. Here are the important subjects from the Lucknow University syllabus-

• Matrices & Differential Equations
• Differential Calculus
• Integral Calculus
• Geometry
• Algebra
• Mathematical Methods 
• Mechanics
• Differential Equations

BSc Maths Syllabus for Calicut University

The syllabus of BSc Mathematics for Calicut University emphasizes core mathematical concepts, practical applications, and interdisciplinary connections with computer science and statistics. Here are the important subjects from the Calicut University syllabus-

• Foundations of Mathematics 
• Informatics and Mathematical Software
• Calculus
• Calculus and Analytic Geometry
• Vector Calculus
• Abstract Algebra
• Basic Mathematical Analysis
• Numerical Methods
• Real Analysis
• Complex Analysis 
• Differential Equations
• Number Theory and Linear Algebra 
• Open Courses offered by other departments

BSc Maths Syllabus with Subject Codes

BSc Mathematics course descriptions usually include codes for subjects as these uniquely identify courses, organize the curriculum, and simplify record-keeping, along with academic tracking for BSc Mathematics. Below is a list of BSc Mathematics courses with subject codes.

Subject Code	Subject	Credits
MTE-01	Calculus	4
MTE-02	Linear Algebra	4
MTE-04	Elementary Algebra	2
MTE-05	Analytical Geometry	2
MTE-06	Abstract Algebra	4
MTE-07	Advanced Calculus	4
MTE-08	Differential Equations	4
MTE-09	Real Analysis	4
MTE-10	Numerical Analysis	4
MTE-11	Probability and Statistics	4
MTE-12	Linear Programming	4
MTE-13	Discrete Mathematics	4
MTE-14	Mathematical Modelling	4
MTE-03	Mathematical Methods	4

Note that subject codes and specific topics may vary slightly depending on the institution, but the structure above represents a comprehensive and widely adopted framework.

What Is the Eligibility Criteria for B.Sc Mathematics?

Before submitting the application for admission to BSc Mathematics, students must satisfy certain eligibility requirements as specified by the university. Although it can vary from university to university, here is a general idea about the eligibility criteria:

• Students must have completed their higher secondary education (10+2) in PCM (Physics, Chemistry, and Mathematics).
• Candidates must also secure a minimum of 60-70% aggregate in their 12th class.

Also Read: PhD in Mathematics

10 Best Universities Abroad to Study BSc Mathematics

Various universities around the world are renowned for their academic excellence and strong mathematics programs, providing an ideal environment for aspiring mathematicians. To help you find the best university, here is a list of top universities abroad that offer a BSc in Mathematics. 

University	Course Name
University of Bath	Mathematics BSc (Hons)
Imperial College London	BSc Mathematics
University College London	Mathematics BSc
University of York	BSc (Hons) Mathematics
The University of Manchester	BSc Mathematics
Stanford University	BSc Mathematics
Vancouver Island University	BSc Mathematics
University of British Columbia	BSc Mathematics
University of Manitoba	Mathematics (BSc)
University of Southampton	BSc Mathematics with German

The BSc Mathematics program offers a robust foundation in mathematical theories and their real-world applications, making it an excellent choice for students passionate about numbers and problem-solving. BSc Mathematics syllabus is well-structured, covering calculus, algebra, real analysis, and advanced topics like complex analysis and metric spaces, this degree prepares graduates for rewarding careers in data science, finance, research, and more.

FAQs

Hopefully, through this blog, you are now familiar with the BSc Maths syllabus and the course content. If you aspire to get your career started in this field but are unsure of the admission process, then our experts at Leverage Edu will lend you a helping hand. From helping you draft an impressive SOP to completing the application formalities, assistance will be provided throughout the admission journey!

Related Reads

Statistics Class 9	Analytical Reasoning For Competitive Exams
Commerce With Maths	Branches of Mathematics
Branches of Science	How to Become a Software Developer in India?