MSc Maths Syllabus

MSc Maths Syllabus

Mathematics is considered as one of the toughest subjects to crack. But for those who love calculations and want to learn its advanced and intricate concepts, opting for BSc Mathematics after completing high school is a suitable step to begin your higher education with. Further, completing your graduation, if you are interested in specialising with a master’s degree, MSc Mathematics can help you explore the advanced concepts and components of mathematics and equip you with the extensive skills to pursue a career in research as well. But before pursuing any course, it is significant to familiarise yourself with the course content. This blog brings you a detailed overview of MSc Maths syllabus, major subjects covered, career scope and more. 

Also Read: Applied Mathematics and Computation

Course Overview

Generally offered as a two-year degree course, MSc Mathematics aims to impart students with the knowledge of advanced principles and theories of Pure and Applied Mathematics. Many universities incorporate imperative research projects under the MSc Maths syllabus in order to encourage students to develop research and analytical abilities. Studying this course, you will get to explore subjects like algebraic geometry, probability theory, number theory, theoretical computer science etc. 

MSc Maths Syllabus 

MSC Mathematics is generally divided into 4 semesters offering covering a varied range of topics under Applied and Pure Mathematics. Here is a semester-wise breakdown of the MSc Maths syllabus.

Semester Syllabus 
Semester 1Theorems on Principle, Maximal and Prime Ideals,
The Riemann – Stieltjes IntegralIsomorphism
Theorems and its Related Problems, Finite and Infinite Sets,
Linear Differential Equations of nth Order,
Modelling with Recurrence Relations with
Examples of Fibonacci Numbers,
Extended real number system,
Euclidean spaces,
Eminent Mathematicians and the History of Mathematics.
Semester 2Recapitulation: Rings, Some Special Classes of Rings,
Phragmen-Lindel of the theorem,
Alexandroff ’s One Point Compactification,
First-Order Partial Differential Equations,
Second-Order Partial Differential Equations,
The Conjugate Space H* of a Hilbert Space,
Monotone and bounded sequences,
Bolzano Weierstrass theorem,
Partial Differential Equations.
Semester 3Calculus on Euclidean Space,
Volterra and Fredholm Integral Equations,
Two-dimensional Flows of Inviscid Fluids,
Numerical Solution of Partial Differential Equations,
Meaning of First and Second-order
Ordinary Derivatives,
Abstract Group Theory,
Partial sums, Root and ratio tests,
Integral test, Comparison test,
The limit of a function,
Continuous functions,
Types of discontinuity, Mathematical Methods.
Semester 4Lebesgue Integral, Convergence Theorems
and Lebesgue Integral, Riemannian Metric;
Connections; Riemannian Connections and their Components,
Partitions: Definition of Partition of a +ve Integer,
Asymptotic Values and Asymptotic Curves,
Planarity:- Plane and Planar Graphs,
The derivative of a function;
Mean value theorem,
Continuity of derivatives, Measure and Integration. 

Note: The aforementioned syllabus is for indicative purposes. The course curriculum, duration and offerings can vary from one university to another.

Subjects Covered in MSc Maths Syllabus

Now that you are familiar with core MSc Maths syllabus, let’s take a look at some of the essential subjects taught during this program:

  • Algebra
  • Real Analysis
  • Topology
  • Ordinary Differential Equations
  • Discrete Mathematics
  • Eminent Mathematicians and the History of Mathematics
  • Complex Analysis
  • Functional Analysis
  • Partial Differential Equations
  • Differential Geometry
  • Mathematical Methods
  • Fluid Mechanics
  • Measure And Integration

Electives in MSc Maths Syllabus

Apart from multidisciplinary subjects, you will be accustomed to a range of electives to help you explore the topics you are interested in. Tabulated below is the comprehensive list of electives in MSc Maths syllabus:

Real AnalysisAlgebraNumber Theory
Electromagnetism in Special RelativityApplications of Special Relativity The Four-Vector Formulation of Special Relativity 
Linear ProgrammingLagrange’s Theory of Holonomic and Non-Holonomic SystemsDerivation of Special Relativity 
Canonical Transformations Fluid MechanicsRings and Modules 

Now that you know the course content and offerings of MSc Maths syllabus, here are the major universities offering this course and its variants in India and abroad:

Top Universities in India Top Universities Abroad
St. Stephens College, DelhiCity University of London
Christ University, BangaloreUniversity of Warwick
Loyola College, ChennaiUniversity of York
Hans Raj College, DelhiUniversity of Stirling 
Presidency College, ChennaiUniversity of Manchester
Jadavpur University, KolkataUniversity of Exeter
Miranda House, DelhiUniversity of Bristol 
Annamalai University, CuddaloreUniversity of Sheffield
IIT, KanpurUniversity of Essex
St. Xavier’s College, MumbaiSwansea University 

Career Scope

Certainly, Mathematics is one of the fascinating and intriguing fields of study. It offers lucrative opportunities with excellent salary packages in top-notch companies, startups, scientific organizations as well as consultancies. Concluding MSc Maths, you can explore a wide range of job profiles across the public and private sectors and some of these are:

  • Mathematics Specialist
  • Professor
  • Quantitative Risk Analyst
  • Quantitative Developer
  • Interest Rate Trending Strategist
  • Data Analyst
  • Numerical Analyst
  • Equity Quantitative Analyst
  • Cryptanalyst
  • Senior Business Analyst
  • Training Manager
  • Operation Manager

Also Read: PhD in Mathematics

Hope this blog has provided you with a comprehensive analysis of MSc Maths Syllabus. Aspiring to study an MSc in Mathematics? Our Leverage Edu experts are just a click away to provide you with the best guidance and assistance throughout the process of choosing the right course and university to sorting the admission procedure and ensuring that you get successfully shortlisted!

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