The syllabus for the ISI entrance exam in mathematics

 The Indian Statistical Institute (ISI) conducts entrance exams for admission to its undergraduate and postgraduate programs in mathematics, statistics, computer science, and other related subjects. The syllabus for the ISI entrance exam in mathematics is as follows:

1. Algebra:

• Groups, subgroups, normal subgroups, quotient groups, homomorphisms, isomorphisms
• Rings, subrings, ideals, quotient rings, homomorphisms, isomorphisms
• Fields, subfields, extensions, algebraic extensions, transcendental extensions
• Linear algebra, matrices, determinants, systems of linear equations, eigenvalues and eigenvectors

2. Analysis:

• Real numbers, sequences, limits, continuity, differentiability, Riemann integration
• Metric spaces, completeness, compactness
• Complex numbers, complex functions, Cauchy-Riemann equations, complex integration, Cauchy's theorem and formula, singularities, residues

3. Geometry:

• Euclidean geometry, triangles, circles, quadrilaterals, conic sections
• Differential geometry, curves, surfaces, curvature, torsion

4. Number theory:

• Divisibility, primes, congruences, Euler's phi function, quadratic residues, Diophantine equations
• Continued fractions

5. Probability:

• Basic probability theory, conditional probability, Bayes' theorem, independence, random variables, probability distributions, expectation, variance, covariance, correlation

6. Miscellaneous:

• Set theory, functions, relations, logic

It is important to note that the above syllabus is indicative and may vary from year to year. Candidates are advised to check the ISI website for the most up-to-date information on the entrance exam syllabus and pattern.

Previous year question papers of ISI entrance exam

Previous year question papers of ISI entrance exam are available on the official website of the institute. Candidates can download question papers from the website to get an idea about the exam pattern and difficulty level. To access previous years question papers of ISI entrance exam, follow these steps: Visit the official website of Indian Statistical Institute - https://www.isical.ac.in/ Click on the 'Admission' tab and select 'Admission Information'. Click on 'Previous Years Question Papers' under 'Admission to Degree/Diploma Programs 2022-2023' section. Download the question paper for the desired programme. Candidates are advised to solve previous years question papers to get an idea about the exam pattern, type of questions asked and time management. This will also help them to identify their strengths and weaknesses and focus on those areas which require more preparation. Candidates must note that the exam pattern and syllabus may vary from year to year, so they must also check the latest syllabus and exam pattern before starting their preparation.