B.A. Mathematics Syllabus: Year-wise Subjects & Topics

Choosing the right course starts with knowing the syllabus, and if you are planning to study B.A. Mathematics, you’re in the right place. B.A. Mathematics syllabus covers everything from algebra, calculus, and geometry to advanced topics like real analysis, probability, and statistics, spread across six semesters. This blog breaks down the complete syllabus in detail, semester-wise, along with core subjects and elective subjects. Let’s understand everything you need to know about the syllabus of B.A. Mathematics in 2025.

B.A. Mathematics Syllabus: Quick Highlights

The B.A. Mathematics syllabus is designed to give students a strong base in both pure and applied mathematics. It is taught across 6 semesters, covering algebra, calculus, analysis, statistics, and more. Here is the quick overview of the syllabus structure for easy understanding.

Year	Semester	Key Subjects Covered
1st Year	Semester I	Algebra I, Differential Calculus, Geometry
	Semester II	Integral Calculus, Vector Calculus, Trigonometry
2nd Year	Semester III	Differential Equations, Real Analysis I, Probability Theory
	Semester IV	Linear Algebra, Complex Analysis, Mathematical Statistics
3rd Year	Semester V	Abstract Algebra, Real Analysis II, Numerical Methods
	Semester VI	Linear Programming, Mechanics, Advanced Calculus

What Is B.A. Mathematics? 

B.A. Mathematics is a three-year undergraduate degree where you study math as a way to solve real-life problems. Unlike B.Sc. Mathematics, which is more science-heavy, B.A. Mathematics blends core math with subjects from the arts and humanities. This means you get to explore algebra, calculus, geometry, statistics, and also pick electives like economics, philosophy, or computer science, depending on your university. The course is perfect for students who love logic and patterns but also want flexibility to branch into teaching, data analysis, civil services, finance, or research later on.

B.A. Mathematics Syllabus

The B.A. Mathematics syllabus is spread across 3 years and 6 semesters. It is designed by UGC (India) to make sure students learn the basics of pure mathematics, applied areas, and analytical thinking step by step. Although every university tweaks it slightly, the semester-wise flow remains almost the same everywhere in India, and even abroad, BA Math degrees follow a similar pattern but with extra focus on computing, finance, or data science. So here’s the semester-wise syllabus in India.:

Semester 1	Algebra, Calculus–I (Differential Calculus), Mathematical Logic, English / Environmental Studies (AECC)
Semester 2	Calculus–II (Integral Calculus), Analytical Geometry, Elementary Number Theory, Language / Computer Applications
Semester 3	Linear Algebra, Ordinary Differential Equations, Probability Theory, Generic Elective (non-math subject)
Semester 4	Real Analysis–I, Mechanics, Vector Calculus, Generic Elective (like Economics, Sociology, Political Science, Data Science)
Semester 5	Abstract Algebra, Mathematical Methods, Complex Analysis, Discipline-Specific Electives (Numerical Methods / Operations Research)
Semester 6	Topology, Linear Programming, Mathematical Modelling, Discipline-Specific Electives (Graph Theory / Cryptography / Discrete Maths), Project / Dissertation

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Core Subjects & Topic-wise Units 

The mathematics syllabus is packed with core papers that every student has to take. These subjects are chosen to sharpen a specific skill. Here’s how the core subjects break down, with their topic-wise units:

Algebra

Algebra is the first big block of your degree. You’ll study how numbers, equations, and structures work in depth. Major units include:

• Theory of Equations
  
• Relations and Functions
  
• Matrices and Determinants
  
• Vector Spaces and Linear Transformations
  
• Basic Group Theory

Calculus

If you thought calculus in school was bad, here it gets serious. The course is split into units like:

1. Limits and Continuity
   
2. Differentiation and Applications
   
3. Integration and Its Uses
   
4. Improper and Multiple Integrals

Real Analysis

This is where maths turns rigorous. Instead of just solving problems, you’ll be proving why formulas work. Units include:

• Sequences and Series
  
• Limit Theorems
  
• Functions of Several Variables
  
• Riemann Integration

Abstract Algebra

When numbers are no longer enough, this paper introduces advanced structures. It usually covers:

• Group Theory
  
• Ring Theory
  
• Homomorphisms
  
• Introduction to Fields

Differential Equations

This subject explains how to model change, physics, biology, and even economics use it. The core units are:

Unit	Topics
Unit I	First Order Differential Equations
Unit II	Higher Order Linear Equations
Unit III	Partial Differential Equations
Unit IV	Applications in Physical Sciences

Vector Calculus

This paper teaches how calculus works in higher dimensions. Some of the important parts are:

• Gradient, Divergence, Curl
  
• Line Integrals and Surface Integrals
  
• Theorems of Green, Gauss, and Stokes

Complex Analysis

A favourite of many, since it deals with imaginary numbers in real life. You’ll learn:

• Analytic Functions
  
• Cauchy-Riemann Equations
  
• Complex Integration
  
• Residue Theorem and Its Applications

Mechanics

Mechanics connects maths with motion. The course usually includes:

• Newton’s Laws of Motion
  
• Work, Energy, and Power
  
• Dynamics of Particles
  
• Motion of Rigid Bodies

Topology

By the final year, students are introduced to abstract spaces. The subject covers:

1. Sets and Functions
   
2. Open and Closed Sets
   
3. Continuity
   
4. Connectedness and Compactness

Probability and Statistics

This subject prepares you for data-heavy jobs. You’ll work through:

• Basic Probability Rules
  
• Random Variables
  
• Distributions
  
• Statistical Inference

Mathematical Methods

This is a toolbox paper, giving you practical tricks like:

• Fourier Series
  
• Laplace Transforms
  
• Numerical Approximation Techniques

Electives & Specializations in B.A. Mathematics

Core subjects build the base, but electives are what let you personalize your degree. They give you the freedom to go deep in areas that match your career plan. Different universities in India and abroad offer different electives, but most follow a similar set of themes.

Popular Elective Options

Instead of forcing everyone to study the same thing, BA Maths gives you a choice. Common electives include:

• Operations Research: Optimisation, game theory, and decision-making models.
  
• Number Theory: Prime numbers, modular arithmetic, and cryptography basics.
  
• Discrete Mathematics: Best for computer science aspirants (graphs, logic, algorithms).
  
• Linear Programming: Tools for solving real-world business and resource problems.
  
• Mathematical Modelling: Equations that explain natural and social phenomena.

Technology-Focused Electives

Some universities now include tech-driven papers. These help maths students step into IT and data roles. Example units:

Elective	Key Topics
Computer Programming with Python	Basics of coding, data structures, and problem-solving
Data Science & Big Data	Probability models, statistical tools, introduction to machine learning
Mathematical Software	MATLAB, Mathematica, R programming

Finance & Applied Math Specialisations

If you lean towards banking or economics, these electives make sense:

• Actuarial Science: Risk analysis, life tables, insurance models.
  
• Financial Mathematics: Interest theory, portfolio optimisation, stock market maths.
  
• Econometrics: Applying maths to economic data and policy predictions.

Pure Math Specialisations

For students dreaming of research or higher studies (M.A./PhD), the electives often focus on deeper theory:

1. Advanced Algebra: Field extensions, Galois theory.
   
2. Functional Analysis: Banach spaces, Hilbert spaces.
   
3. Differential Geometry: Curves, surfaces, manifolds.
   
4. Advanced Topology: Homotopy, compactness, connectedness.

Interdisciplinary Electives

Some colleges also let you blend maths with other fields, making your degree more versatile:

• Mathematical Biology: Modelling diseases, genetics, population growth.
  
• Environmental Mathematics: Climate modelling, pollution analysis.
  
• Mathematical Psychology: Decision theory, learning curves.

Specialisation Tracks (Final-Year Options)

By the final year, many universities let you pick a track. For example:

Specialisation Track	Focus Area
Pure Mathematics	Deep theory, research prep, abstract structures
Applied Mathematics	Real-world problems, physics, engineering models
Computational Mathematics	Algorithms, simulations, computer-heavy maths
Statistics	Data analysis, probability, inferential methods
Financial Mathematics	Banking, actuarial, and stock markets

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B.A. vs B.Sc. Mathematics: Syllabus Comparison

Both B.A. Mathematics and B.Sc. Mathematics are math degrees, but the syllabus focus is different.

• B.A. Mathematics: Designed as a mix of mathematics and humanities. It covers pure and applied maths but balances it with social sciences, language papers, and electives from arts disciplines.
  
• B.Sc. Mathematics: More technical and science-heavy. It dives deeper into theory, lab work, and applications in physics, computer science, and engineering.

Feature	B.A. Mathematics	B.Sc. Mathematics
Core Approach	Balanced: maths + arts subjects	Intensive: maths + science subjects
Core Maths Papers	Algebra, Calculus, Differential Equations, Real Analysis, Linear Algebra	Same as BA but with extra depth, plus Advanced Analysis, Abstract Algebra, Mechanics
Supporting Subjects	English, Economics, Statistics, History, Philosophy (depending on college)	Physics, Computer Science, Programming, Mathematical Modelling
Electives	Operations Research, Mathematical Biology, Financial Maths, Discrete Maths	Computational Maths, Quantum Mechanics, Numerical Methods, Data Science
Practical Component	Usually, less lab work, more theoretical assignments	Strong lab/practical work with experiments, simulations,and  software training
Career Alignment	Teaching, civil services, finance, economics, and data entry jobs	Research, IT, data science, academia, engineering-linked roles

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This was all about B.A. Mathematics syllabus in detail. Mathematics as a subject is becoming more important with its role in data, finance, technology, and even research-driven fields. With the right understanding of the syllabus, students can prepare better for exams, explore higher studies like M.A. or M.Sc., or build careers in teaching, analytics, finance, and government jobs. For more such helpful guides on courses, careers, and study abroad options, make sure to check out the Leverage Edu blog and stay updated.