TIFR GS 2025 Mathematics Syllabus: Direct Link to PDFs, Important Topics & More

Updated By Sudeshna chakrabarti on 22 Nov, 2024 11:02

Tata Institute of Fundamental Research has released the latest TIFR GS 2025 syllabus on its official website www.tifr.res.in. Check here for more details regarding the TIFR GS syllabus. Also, get direct links to download the subject-wise syllabus PDFs!

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TIFR GS 2025 Mathematics Syllabus Overview

Getting familiar with the TIFR GS 2025 Mathematics Syllabus is key to a well-organized and effective study plan. In this guide, you’ll find a complete overview of the syllabus, along with direct links to PDF downloads and a breakdown of the most important topics to focus on. You’ll also get insights into the exam pattern and specific syllabus details for the PhD program at TIFR’s Centre for Applicable Mathematics (TIFR CAM), so you know exactly what’s expected for success in this program.

The syllabus spans a range of critical mathematical areas, so knowing where to focus can help you create a strategic study plan. Here, you can explore each section of the syllabus in depth, review major highlights, and get a clear sense of the exam’s format. Use the direct PDF links to access the complete syllabus, focus on essential topics, and prepare confidently for the TIFR GS 2025 Mathematics exam.

Check Here: TIFR GS 2025 Syllabus

Highlights on TIFR GS 2025 Mathematics Syllabus

As mentioned earlier, students willing to pursue PhD from TIFR CAM, Bangalore, are required to follow a different curriculum whereas, for I-PhD and PhD at other institutes, a more conceptual approach in the syllabus has been prescribed. Find below some key highlights on the TIFR GS 2025 Mathematics Syllabus:

Particulars

Details

Name of Exam

TIFR GS

Category

Syllabus

Status

Released

Released by

Tata Institute of Fundamental Research

Exam Level

National

Question Type

MCQ and subjective type questions

Number of section

2(Part A and B)

Duration

3 hours

Topic to cover

Algebra, Geometry, Real Analysis, Linear Algebra, Measure Theory


TIFR GS 2025 Mathematics Syllabus Details

TIFR GS 2025 Mathematics Syllabus for PhD and integrated PhD in institutes other than TIFR CAM will test students' fundamental knowledge of concepts of real numbers, complex numbers, integers, matrices, determinants, series, and sequences. We have provided details on topics you must cover for the Mathematics paper.

Topics

Sub Topics

Algebra

  • Definitions and examples of groups
  • Matrices
  • Symmetric Matrices
  • Minimal Polynomials
  • Integers
  • Group Actions and Sylow Theorems

General

  • Pigeon-hole principle
  • Induction
  • Elementary probability theory
  • Elementary zoning with graphs

Analysis

  • Basic facts about real and complex numbers
  • Continuity 
  • Trigonometric functions
  • Sequences and series of functions and their various types of convergence
  • Differentiability 

Geometry/Topology

  • Elementary geometric properties of common shapes and figures in 2 and 3-dimensional Euclidean spaces
  • Definition and properties of metric spaces
  • Continuity of functions between metric spaces

TIFR GS 2025 Mathematics Syllabus for PhD from TIFR CAM

Are you aiming for TIFR CAM, Bangalore? The mathematics syllabus for TIFR GS 2025 will be different for you. The questions will be objective, unlike the pattern for other courses. Get a clear idea regarding the topic you need to prepare from the TIFR GS 2025 Mathematics Syllabus from the table below and set effective study goals.

Topics

Sub Topics

Real Analysis

  • Riemann integration
  • Directional derivative
  • Inverse and implicit function theorems
  • Uniform convergence
  • Fixed point theorems

Linear Algebra

  • Vector space
  • Linear transformation
  • Algebraic and geometric multiplicities
  • Minimal polynomial
  • Spectral theorems

Complex Analysis

  • Cauchy-Riemann equations
  • Cauchy’s integral formula
  • Conformal mappings
  • Morera’s theorem
  • Schwarz reflection principle
  • Argument principle

Ordinary Differential Equations

  • Stability of linear ODEs
  • Existence and uniqueness of solutions of initial value problem for first-order ODEs
  • General theory of homogenous and non-homogenous linear ODEs

Functional Analysis

  • Normed linear spaces
  • Banach spaces
  • Weak convergence
  • Hilbert space
  • Open mapping theorem
  • Uniform boundedness principle

Measure Theory

  • Lebesgue measure
  • Lebesgue integral
  • Fubini theorem

Probability

  • Combinatorial and discrete probability
  • Limit theorems
  • Borel-Cantelli and its applications
  • Distribution function of random variable
  • Random variables and their probability mass function/density function

Topology

  • Topological spaces
  • Induced topology
  • Product topology
  • Compactness
  • Connectedness

TIFR GS Mathematics Exam Pattern 2025

Alongside covering the TIFR GS 2025 Mathematics Syllabus, you need to closely scrutinise the paper pattern. Try thoroughly checking the difficulty level of questions, topic-wise mark distribution, number of sections, and nature of questions. The mathematics paper will be divided into two parts; Part A and B. Part A comprises objective-type questions and it is compulsory for those willing to enroll in the PhD program at TIFR CAM, Bangalore. However, for others both Part A and B are compulsory. You need to apply logical thinking when solving statement-based questions in Part B. 

Find the complete details on the TIFR GS exam pattern 2025 for mathematics below:

Particulars

Details

Number of sections

Parts A and B

Type of questions

  • Part A: MCQ
  • Part B: True/False questions

Number of questions

20 each for Part A and B

Duration

3 hours

Note: Students aspiring to enroll in PhD Mathematics at TIFR CM, Bangalore will be evaluated based on Part A only. 

Marking criteria for TIFR GS Mathematics 2025

Sections

Correct Answer

Incorrect Answer

Unanswered

Part A

+2

-1

0

Part B

+2

-2

0


Read Here: TIFR GS 2025 Preparation Tips

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