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MSc Maths Syllabus


MSc Maths syllabus will surely appeal to students who wish to see themselves as research mathematicians in the future. The syllabus is so designed that if you are an undergraduate student specialising in maths, statistics, or physics, there are ample opportunities for you to enhance your knowledge further. MSc Maths syllabus has a brilliant mix of independent research and lecture-based modules. What's more, students have an opportunity to explore elective subjects of their choice in the final year of their program. If you still have doubts about the MSc Maths Syllabus but are interested in knowing more about it, this blog is for you, and we hope you learn all that you need to know. So, let's go ahead with the blog without further ado.

MSc Maths Course Highlights

Course Name

Master of Science Maths

Education Level



1-2 Years (Depends on the university)

Entrance Exams 


Top Universities

University of Oxford, Imperial College London, UCL London, The University of Edinburg, University of Michigan – Ann Arbor

Basic Eligibility Criteria

Should have completed 3- or 4-years Bachelor’s degree from a mainstream university with required grades, Minimum requirement of 2.1 degree in mathematics, physics, engineering, or applied mathematics

Career Prospects

Algorithm Engineer, Risk Manager, Data Analyst, Research Analyst, Quantitative Analyst

MSc Maths Subjects

There are many essential subjects taught to students during their MSc Maths program.

Some of these include:

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

MSc Maths Syllabus: Semester Wise

Semester 1

Theorems on Principle, Maximal and Prime Ideals, Finite and Infinite Sets, Eminent Mathematicians and the History of Mathematics, The Riemann – Stieltjes Integrallsomorphism Theorems and its Related Problems, Euclidean spaces, Linear Differential Equations of nth Order, Modelling with Recurrence Relations with Examples of Fibonacci Numbers, Extended real number system

Semester 2

Partial Differential Equations, First-Order Partial Differential Equations, Bolzano Weierstrass theorem, Recapitulation: Rings, Some Special Classes of Rings, The Conjugate Space H* of a Hilbert Space, Monotone and bounded sequences, Phragmen -Lindel of the theorem, Second-Order Partial Differential Equations, Alexandroff’s One Point Compactification

Semester 3

Continuous functions, Calculus on Euclidean Space, Mathematical Methods, Abstract Group Theory, Numerical Solution of Partial Differential Equations, Types of Discontinuity, Volterra and Fredholm Integral Equations, the limit of a function, Meaning of First and Second-order Ordinary Derivatives, Comparison test, Integral test, Two-dimensional Flows of Inviscid Fluids

Semester 4

Measure and Integration, Lebesgue Integral, Riemannian Connections and their Components, Connections, Mean value theorem, The derivative of a function, Partitions: Definition of Partition of a +ve Integer, Convergence Theorems and Lebesgue Integral, Mean value theorem, Asymptotic Values and Asymptotic Curves, Planarity – Plane and Planar Graphs, Riemannian Metric

The above given MSc Maths syllabus is presented for indicative purposes only. Depending on the university chosen, the course curriculum, duration, etc., may vary.

Also Read: BSc Maths Syllabus

Electives in MSc Maths Syllabus

In addition to several multidisciplinary subjects, you can choose from a wide range of electives in MSc Maths to expand your knowledge in areas you are interested in. 

Some of these electives include:

  • Number Theory
  • Algebra
  • Real Analysis
  • Rings and Modules
  • Applications of Special Relativity
  • Canonical Transformations
  • The Four-Vector Formulation of Special Relativity
  • Electromagnetism in Special Relativity
  • Linear Programming
  • Fluid Mechanism
  • Derivation of Special Relativity
  • Lagrange's Theory of Holonomic and Non-Holonomic Systems
  • Stability Theory
  • Advanced Uncertainty Quantification
  • Approximation Theory and Finite Element Analysis
  • Dynamical Systems
  • Numerical Optimisation and Inverse Problems
  • Numerical Linear Algebra

TOP Universities in Abroad to Study MSc Maths

S. No

Name of the University





University of Oxford


Mathematical Modelling and Scientific Computing

1 Year


Imperial College London


MSc Mathematics and Finance

1 Year


UCL London


Financial Mathematics MSc

1 Year


The University of Edinburgh


Computational Applied Mathematics MSc

1 Year


University of Michigan – Ann Arbor


Mathematics MS

1 Year


University of Toronto


MSc Mathematics

1 Year


McGill University


MSc Mathematics and Statistics

1 Year


The Australian National University


Master of Science in Mathematical Sciences

2 Years


The University of Manchester


MSc Mathematical Finance

1 Year


Northwestern University


MS Engineering Sciences and Applied Mathematics

1 Year

MSc Maths: Scholarships

Name of the University



Australian National University

ANU Chancellor’s International Scholarship

25% or 50% fee waiver of tuition for the entire study period

The University of Manchester

GREAT Scholarships 2022

£10,000 towards tuition fees

The University of Edinburgh

School of Mathematics Taught Postgraduate Funding

Waiver of some of the costs of studies – Students need to contact the university for details

Imperial College London

Inlaks Shivdasani Foundation Scholarships

Up to $10,000 to cover program tuition as well as one-way airfare, healthcare, and living expenses

Career after MSc Maths

If you are interested in pursuing an MSc Maths course abroad, there is good news for you. After completing the course, the job opportunities before you will be vast and rewarding. The best part about the job opportunities after MSc Maths is that they will be prosperous and stable, with private and public enterprises opening the doors for you.

There is always a need for mathematicians to manage business and data models. After all, every business enterprise deals with data management and financial activity for guaranteed success and better improvement. Therefore, it is common to see organisations with positions like accountants and numerical operators open. It is not just the junior or entry-level positions that MSc Maths graduates can look forward to; there are many top-tier or senior-category job positions one can target after acquiring some experience after the course. 

These job positions come with an excellent pay package and career growth opportunities.

1. Mathematics Lecturer: 

Suppose you are passionate about teaching students with an MSc Maths background. In that case, you can easily get a job as a Mathematics lecturer at a university near you. Getting this job is even higher when you have an MSc Maths degree from a prestigious university abroad, like in the US, the UK, Canada, Australia, New Zealand, Ireland, etc. Most universities and colleges only require a minimum score in MSc Maths to be considered for the job position. With some experience and upskilling, you can easily become a professor later in your career. This job is not just secure but also financially rewarding.

2. IT and Computers: 

There is a strong connection between computer science and MSc Maths. A career in the burgeoning world of computers is lucrative and fulfilling for an MSc Maths graduate. ICT (Information and Communication Technology) offers an excellent platform for MSc Maths students, especially in developing ICT, logical skills, programming skills, design and manufacturing parts, etc.

3. General Management: 

It does not matter the industry you are targeting; there is an opening for MSc Maths graduates in general management. Typically, this role requires handling employees and business organising skills that MSc Maths students possess. However, graduates need to be able to handle departmental management and branch management. Some additional skills, like organisational skills, interpersonal skills, customer awareness, etc., provide an advantage when applying for this position.

4. Scientific Officer: 

Being a Scientific Officer can be a great career option if you are good at maths and calculation. Top government sectors always have openings for scientific officers. They are always on the lookout for competitive and experienced MSc Maths graduates. Top scientific organisations of the world, like NASA, EUSPA, ASA, NZSA, UKSA, etc., hire scientific officers in varying capacities. For these roles, having an MSc Maths degree is beneficial.

5. Data Science Modellers: 

Data Science professionals are in high demand these days for their ability to convert available data into useful information. Data science modellers present useful information sheets to the company's decision-makers to make informed decisions. And some of the required skills data science modellers require are data analytics, computer science, advanced analytics, business domain knowledge, statistics, and mathematics. Therefore, MSc Maths graduates have a fair chance of making it big as data science modellers if they make the most of the opportunities that come their way.

Quick Read: Career after Bsc Maths

TOP Recruiters – MSc Maths

  • Ernst & Young
  • Deloitte
  • Amazon
  • Capgemini
  • NASA
  • Boeing
  • Intel
  • National Security Agency
  • US Department of Energy
  • US Census Bureau
  • JP Morgan, etc.

MSc Maths: Roles and Salaries Offered


Average Salary (USD)

Quantitative Analyst


Operations Research Analyst


Mathematics Lecturer


Data Analyst


Budget Analyst


Research Analyst


Financial Modeler


Research Scientist


Risk Manager


Algorithm Engineer


AECC is a reputed player in international education services. We help students study at an international location in a program of their choice and a university matching their needs. Suppose you are passionate about maths and are interested in pursuing an MSc degree in Mathematics. In that case, we can assist you all the way through. Our experienced and friendly counsellors can guide you through various MSc Maths programs offered by prestigious universities across the US, the UK, Canada, Australia, New Zealand, and Ireland. Make sure you get to study in a program of your choice and within your budget. Get in touch with AECC today and give yourself the chance to make it big in mathematics.


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