MSc in Mathematics Syllabus & Subjects 2024

  • SaveSave
  • Request a callbackRequest a callback
  • AskAsk us
author
Jan 10, 2024 20:17PM IST

MSc Mathematics Syllabus & Subjects Overview

MSc Mathematics Syllabus is a two-year study focusing on advanced Mathematics such as Geometry, Calculus, Algebra, Number Theory, dynamic systems, Differential Equations, and so on. The core and elective MSc Mathematics subjects are included in all four semesters of the degree. However, the elective subjects may vary depending on the university. In the MSc Mathematics course, the students’ minds are augmented to encompass advanced mathematical reasoning.

The MSc Mathematics syllabus and subjects create a perfect blend of research, and reasoning that aims at providing students with a thorough understanding of advanced mathematics. To be eligible for this course, applicants must have graduated from a recognised university with a minimum average of 50% aggregate marks in a Science-related field. Banks, colleges, stock exchanges, space agencies, research institutes, and other organisations provide excellent work possibilities for professionals in this field. Students are placed in reputable businesses since Mathematics has a high employment market internationally. This page provides an in-depth understanding of the MSc Mathematics syllabus & subjects to help students become aware of what the course entails.

Show More

MSc Mathematics Year Wise Syllabus

The primary goal of the MSc Mathematics syllabus is to provide students with the tools and strategies they must employ for solving a variety of algebraic expressions, mathematical problems, and so forth The first-semester programme for the MSc in Mathematics includes a set of programmes that address every mathematical fundamental topic. Thus, those who want to pursue this programme should be familiar with the subjects they will be taught during their educational journey. The MSc Maths syllabus is available for download on each university's official website where this degree is offered. The following is a discussion about the semester-wise MSc Mathematics syllabus that students can use for reference.

MSc Mathematics 1st Year Syllabus

The following table outlines the semester-wise MSc Mathematics syllabus for 1st year:

Semester 1Semester 2
Real Analysis IGroups and Rings
Ordinary Differential EquationsReal Analysis II
Linear AlgebraNumerical Analysis
Fuzzy Set Theory and Topology IFunctional Analysis
Complex AnalysisFuzzy Set Theory and Topology II
Algebra IAlgebra II

MSc Mathematics 2nd Year Syllabus

The following table outlines the semester-wise MSc Mathematics syllabus for 2nd year:

Semester 3 Semester 4 
Topology IReal Analysis
Theory of NumbersAdvanced Graph Theory
Mathematical MethodsTopology II
Discrete MathematicsOperator Theory
CryptographyDifferential Geometry
Analytical Dynamics and Fluid MechanicsMeasure and Integration
Elements of Functional Analysis-
Show More

Stream Wise MSc Mathematics Syllabus

MSc in Mathematics is commonly pursued with honours and applied Maths. These are the popular branches of Maths postgraduate courses that students take to pursue their degree programmes. The following is a discussion of the stream-wise MSc Mathematics syllabus and subjects.

MSc Applied Maths Syllabus

The following table highlights the semester-wise subjects for MSc Applied Maths:

Semester-I

Semester-II

Linear AlgebraFunctional Analysis
Elements of Probability and StatisticsMeasures and Integration
Discrete Maths StructureRings and Modules 1
Applied MathsTopology
Real Analysis 2
Ordinary Differential Equations
Complex Analysis
Linear Programming
C Programming
Real Analysis 1

Semester-III

Semester-IV

Numerical AnalysisFluid Mechanics
Non- Linear ProgrammingClassical Mechanics
Mathematical MethodsAdvanced courses on differential equations
Functional AnalysisDynamical Systems

MSc Maths Honours Syllabus

The following table highlights the semester-wise subjects for MSc Maths Honours:

Semester-I

Semester-II

Solid Geometry

Programming in Visual Basic

English

Vector Calculus

Regression Analysis and Probability

English-II

Discrete Maths and Descriptive Statistics

Number Theory and Trigonometry

Computer Fundamentals and MS Office

Ordinary Differential Equations

Algebra and Calculus

Discrete Maths-II

Semester-III

Semester-IV

Special Functions and Integral Transforms

Groups and Rings

Sequences and Series

Practical / Computational work to be performed on computers using EXCEL / SPSS)

Programming in C and Numerical Methods

Integral Equations

Hydrostatics

Methods of Applied Maths

Elementary Inference

Real Analysis and Numerical Analysis

Data Structures using C

-

Show More

MSc Mathematics Subjects

Projects and homework assignments are part of the MSc Mathematics curriculum, which aids students in developing a thorough understanding of the subjects for MSc Maths that they can apply to real-world issues. The candidate's final grades are determined by their performance on both internal and external assessments, which comprise assignments, tests, attendance, theses, and presentations. Nearly every college or university offers the following MSc Mathematics subjects:

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

MSc Mathematics Common Subjects for All Semester

Common subjects for this course are the ones that share the same mathematical methods, formulae, methods of integration and derivation, and so on. These are also sometimes termed the core subjects that are usually incorporated into the curriculum of most universities providing specialisations in this programme. The following is a list of MSc Mathematics common subjects for all semesters:

  • Topology I & II
  • The History of Mathematics
  • Real Analysis
  • Partial Differential Equations
  • Ordinary Differential Equations
  • Measure And Integration
  • Mathematical Methods
  • Functional Analysis
  • Eminent Mathematicians 
  • Discrete Mathematics
  • Differential Geometry
  • Complex Analysis I & II
  • Algebra I & II
Show More

MSc Mathematics Optional Subjects

Optional subjects are often referred to as elective subjects as they can be opted by a student according to their interests or professional career goals. Nevertheless, the curriculum for optional subjects may vary from one university to another. The following is a list of MSc Mathematics optional subjects:

  • Applications of Special Relativity
  • Canonical Transformations
  • Fluid Mechanics
  • Discrete Mathematics
  • Electromagnetism in Special Relativity
  • Rings and Modules
  • The Four-Vector Formulation of Special Relativity
Show Less

Detailed MSc Mathematics Subjects

The following table highlights a list of detailed MSc Mathematics subjects along with the topics that will be covered during the course:

Subject NameTopics Included
Topology 
  • Connected sets on the real line
  • Connectedness - connected spaces
  • Path connectedness
  • Set-theoretic preliminaries
Reliability and Queueing Theory 
  • Introduction
  • Definition of probability
  • Failure data
  • Graphical plots
  • Mean failure rate
  • Mean Time Between Failure (MTBF)
  • Mean Time to Failure (MTTF)
Probability Theory
  • Bayes Theorem
  • Combinatorial formula
  • Conditional probability
  • Distribution Function
  • Independent events
  • Probability axioms
  • Random events
  • Random Variables
Partial Differential Equations 
  • Cauchy Problem order equation
  • Characteristics Compatible system
  • First order non-linear
  • Formation and solution of PDE
  • Integral surfaces
  • Orthogonal surfaces
Ordinary Differential Equations 
  • Non-linear equations
  • Power Series solutions
  • Qualitative Properties of solutions of ordinary differential equations of order two
  • Second-order linear equations
Linear Algebra 
  • Linear independence
  • Projections and their relation with direct sum Decomposition of vector spaces
  • Similarity of matrices and linear transformations
  • Vector spaces
Commutative Algebra 
  • Exact sequences of modules
  • Direct sums
  • Finitely generated modules
  • Free modules
  • Modules and modules homomorphisms
  • Nakayama Lemma
  • Simple modules
  • Submodules and quotient modules
Combinations and Graph Theory 
  • Application to switching circuits
  • Boolean Algebra
  • Boolean expressions
  • Complements
  • Complete lattices
  • Distributive lattices
  • Lattices
  • Partially ordered sets
Analysis 
  • Bounded sequences
  • Countable and uncountable sets
  • Finite and infinite sets
  • Numerical sequences and their convergence
  • Relations and functions
Algebra 
  • Basic properties and examples of ring
  • Cayley's theorem
  • Dihedral groups and their elementary properties
  • Domain division ring and field
  • Group action
  • Group of symmetries
Show More

MSc Mathematics Entrance Exam Syllabus

Certain schools, institutions, and even states may administer entrance tests for admittance to the MSc in Mathematics programme. Algebra, probability theory, number theory, real analysis, and many other topics are covered in the exam, which provides graduates with a general understanding of the programme. Check out these MSc Mathematics entrance exams’ syllabi.

CUET: The Common University Entrance Test (CUET) includes topics such as Computer Science/Informatics Practices, Economics/Business Economics, Engineering Graphics, Entrepreneurship, Environmental Studies, Geography/ Geology, History, Home Science, Knowledge Tradition-Practices India, Legal Studies, Mass Media/Mass Communication, Visual Arts/ Fine Arts/ Commercial Art, etc.

NEST: The National Entrance Screening Test (NEST) includes topics from Chemistry, Mathematics, Biology, and Physics such as Aldehydes and Ketones, Alkenes and Alkynes, Atomic structure and chemical bonding, Biology of Animal Systems, Biotechnology, Carbohydrates, Chemical equilibrium, Coordination compounds, Ecology, Ethers, Gaseous and liquid states, Haloalkanes (Alkyl halides), Humans and Environment, p-Block elements, Phenols, Thermodynamics, and more.

IIT JAM: The Joint Admission Test for Masters (IIT JAM) includes questions from academic disciplines like Biotechnology, Geology, Mathematical Statistics, Economics, Chemistry, Mathematics, and Physics. The topics include Biochemistry, Evolution, Plant Biology, Biochemical techniques, Physical and chemical properties of compounds, Probability, Laws of motion, Moving charges and magnetic field, nuclei and nuclear physics, and so on.

DUET: TheDelhi University Entrance Test (DUET) mainly includes questions related to degrees such as BTech and BMS/ BA (Hons)/ BBA (FIA). The syllabus for the entrance examination includes topics such as Alphabet Test, Analogy and data Sufficiency, Blood Relations, Data Interpretation: Table and Combination, Direction Sense Test, Geometry, Input-Output, Linear and Quadratics Equations, Mensuration: 2D and 3D, Number Sequence, Profit and Loss, Trigonometry, etc.

Show More

MSc Mathematics Important Books

The best books give students a thorough understanding of the MSc Maths subject while also enabling them to go further into their area of speciality. The course books are available for students to purchase both online and offline. By meticulously reviewing the programme's prerequisites, candidates who get the course materials beforehand registering can make an informed decision. The following is a list of the best books for MSc Mathematics that students can use for reference:

  • Methods of Real Analysis by author RR Goldberg
  • Linear Algebra: Geometric Approach by author S Lang
  • Foundations in Discrete Mathematics by author KD Joshi
  • Differential Equations by author GF Simmons
  • Complex Analysis by author Ahlfors
Show More

MSc Mathematics Course Structure

The MSc Math syllabus's structure allows it to cover a range of mathematical disciplines such as probability theory, algebraic geometry, number theory, and theoretical computer science. The majority of the syllabus consists of project work that is weighted toward course completion. Candidates must also focus on their optional courses if they wish to pass the course. Given below is the course structure of MSc Mathematics:

  • IV Semester
  • Core Subjects
  • Elective Subjects
  • Project Work
  • Assessment
  • Dissertation Submission
Show More

FAQs about Master of Science in Mathematics Syllabus

Which colleges offer the best curriculum for BSc Environmental Sciences courses?

Colleges that offer the best curriculum for BSc Environmental Sciences courses are Patna Science College, IISC Banglore, Fergusson College Pune, Vidhya Jyoti University Chandigarh, and Vallia College for Women Chennai.

What is the entrance exam syllabus for BSc Environmental Sciences?

The entrance exam syllabus for BSc Environmental Sciences includes topics such as Geography, English and basic scientific aptitude, Hindi, History, Reasoning, Geography, Plants and Animals, Climate and Weather, Common Diseases, Environment & its Pollution, History, Human Body, Human Health, Natural Resources, and more.

What is the syllabus of BSc Environmental Sciences?

The syllabus of BSc Environmental Sciences consists of both core and elective subjects such as English Communication Skills, Environmental Chemistry, Fundamentals of Environmental Science, Ecology and Environmental Studies, Environmental Geology and Remote Sensing, Environmental Economics and Sustainable Development, Environmental Ethics and Philosophy, and so on.

Which is the best subject to pursue BSc Environmental Sciences courses?

Any subject related to the Science (PCB) stream is best to pursue BSc Environmental Sciences courses. As this field is related to the ecosystem, an understanding of the geography, climatic conditions, animal habitat, etc. is preferred. By completing the BSc Environmental Sciences syllabus, students acquire the skills and knowledge required to protect and manage the environment positively.

What are the BSc Environmental Sciences subjects for 1st semester?

The BSc Environmental Sciences subjects for 1st semester are basic topics that usually help students revise concepts they have learned in their class 12. The list of topics includes Fundamentals of Environmental Science, Physics, English Communication Skills, Chemistry, and Maths. During their degree course, candidates will require this fundamental knowledge to learn the advanced concepts based on it.

What are the BSc Environmental Sciences subjects for 2nd semester?

The BSc Environmental Sciences subjects for 2nd semester are common topics that introduce the students to the advanced concepts they will be taught in the remaining course of their degree. The list of topics includes Ecology and Environmental Studies, Geology and Soil Science, Environmental Chemistry, Biodiversity and Conservation, and Computer Fundamentals and Applications.

What are the BSc Environmental Sciences subjects for the 3rd semester?

The BSc Environmental Sciences subjects for the 3rd semester introduce students to the real-world techniques and procedures going on to conserve natural resources. The list of topics includes Environmental Pollution and Control, Environmental Biotechnology, Environmental Microbiology, Environmental Geology and Remote Sensing, and Environmental Impact Assessment and Auditing.

What are the BSc Environmental Sciences subjects for the 4th semester?

The BSc Environmental Sciences subjects for the 4th semester acquaint students with advanced knowledge about environmental sustainability and the policies and laws they can use for nature’s conservation. The list of topics includes Environmental Toxicology, Environmental Economics and Sustainable Development, Environmental Laws and Policies, and Environmental Monitoring and Management.

What are the BSc Environmental Sciences subjects for the 5th semester?

The BSc Environmental Sciences subjects for the 5th semester introduce students to the elective or optional subjects and research methodologies they can use to save natural habitats. The list of topics includes Climate Change and Environmental Sustainability, Research Methodology and Project Planning, Natural Resource Management, Urban Ecology, Environmental Ethics and Philosophy, etc.

What are the BSc Environmental Sciences subjects for the 6th semester?

The BSc Environmental Sciences subjects for the 6th semester incorporate performing environment research, building real-time projects, and hands-on training. The list of topics includes Environmental Data Analysis and Modeling, Internship/Industrial Training, Environmental Risk Assessment and Disaster Management, Environmental Project and Field Work, etc.

Are the BSc Environmental Sciences subjects tough to understand?

No, the BSc Environmental Sciences subjects are not tough to understand provided students have a good idea of the core subjects such as physics, geology, chemistry, and scientific methodology. Environmental science is still a relatively difficult major, therefore students who prefer learning outside of the classroom would be the best fit for this programme.

Does the BSc Environmental Sciences syllabus incorporate research?

Yes, the BSc Environmental Sciences syllabus incorporates research at a minimum level related to their environmental fieldwork and projects. Given that it is an undergraduate-level degree, the scope of performing research is less. Therefore, if individuals are interested in researching about the Environmental Sciences, they can opt for courses like MSc Environmental Sciences, MPhil, or PhD.

What are the BSc Environmental Sciences elective subjects?

The list of BSc Environmental Sciences elective subjects includes topics such as Remote Sensing and Geographical Information Systems, Environmental Chemistry, Water and Watershed, Forestry Management, Environmental Management, Occupational Safety and Health, Wildlife Management, Disaster Management, and so on. However, optional subjects may vary from one institute to another.

What are the core subjects of BSc Environmental Sciences?

The core subjects of BSc Environmental Sciences are Biology, Chemistry, Ecology, Environmental Biology, Geology, Physics, Soil Science, and more. These are the fundamental topics covered in the BSc Environmental Sciences degree curriculum, which students should comprehend to pass their semester-long exams.

What is the BSc Environmental Sciences course structure?

The BSc Environmental Sciences course structure is divided into six semesters that contain both core and elective subjects along with hands-on industrial training and project work. Various topics are covered in the BSc Environmental Sciences syllabus, including natural resource degradation, pollution, mitigation, and more.

What methodologies and techniques are used to teach BSc Environmental Sciences subjects?

Some methodologies and techniques used to teach BSc Environmental Sciences subjects incorporate both traditional in-class instructions and on-field work. The following list denotes the same:

  • Reading
  • Process-based & Problem-based Experimental
  • Lecturing
  • Hands-on Activities
  • Discussion
  • Concept Mapping
  • Collaborative

What is the BSc Environmental Sciences syllabus for entrance exams?

The BSc Environmental Sciences syllabus for entrance exams is divided into disciplines such as Biology, Chemistry, Mathematics, Geography, and Physics. It includes topics such as Climate and Weather, Common Diseases, Environment and Pollution, Moving Charges and Magnetism, Organic Chemistry principles and Techniques, Sentence Correction, Statements and Conclusions, Trigonometry, and more.

Can I download the BSc Environmental Sciences syllabus & subjects PDF?

Yes, students can download the BSc Environmental Sciences syllabus & subjects PDF to get specific subject descriptions, semester-by-semester subject codes, number of credits, reference materials, and other details. For this, candidates must access the subject/syllabus page of their desired university's official website, and click ‘download PFD’.

Is project work a part of the BSc Environmental Sciences curriculum?

Yes, project work is a part of the BSc Environmental Sciences curriculum that includes minimum research and hands-on experience. Candidates should submit their project in the sixth semester along with their thesis. Students will get the chance to integrate their knowledge from the MSc Environmental Sciences course and apply it to their potential careers during their projects.

What are the popular BSc Environmental Sciences project topics?

The list of popular BSc Environmental Sciences project topics includes the following:

  • Urban Ecology
  • Renewable Energy
  • Remote Sensing and Geographic Information Systems
  • Noise Pollution
  • Limnology
  • Environmental Justice
  • Conservation Biology
  • Bioremediation

What are the best reference books to study BSc Environmental Sciences subjects?

The best reference books to study BSc Environmental Sciences subjects include the following:

  • Primer of Ecological Restoration by author Karen F Holl
  • Fundamentals of Environmental Studies by author Mahua Basu
  • Textbooks of Environmental Studies by author Erach Bharucha 
  • Environmental Science by author Richard T Wright
  • Recharge Methods of Environmental Studies by author Mark Kanazawa

What BSc Environmental Sciences subjects are common for all semesters?

BSc Environmental Sciences subjects that are common for all semesters incorporate topics from Geology, Geography, Chemistry, Physics, Biology, and Social Sciences. The list of topics for the same includes Sustainable development, Soil Science, Environmental pollution and control, Environmental Physics, Environmental management, Environmental Geology, Environmental Chemistry, Environmental Biology, Ecology, and more.

Show More