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The syllabus for the Mathematics section of the IISER (Indian Institutes of Science Education and Research) entrance examination may vary slightly from year to year. However, I can provide you with a general overview of the topics commonly included in the IISER Mathematics entrance exam syllabus. It is advisable to refer to the official IISER website or the information brochure for the most accurate and updated syllabus. Here are the main subject areas typically covered:

1. Algebra: Sets, relations, functions, complex numbers, quadratic equations, matrices, determinants, linear equations, mathematical induction, permutations and combination, binomial theorem, etc.

2. Calculus: Limits, continuity, differentiation, applications of derivatives, integration, definitely and indefinite integral, differential equations, sequences and series, etc.

3. Coordinated Geometry: Lies, circles, conic sections, parabola, ellipse, hyperbola, transformation, etc.

4. Differential Equations: First-order differential equations, second-order linear differential equations, homogeneous and non-homogeneous equations, applications of differential equations, etc.

5. Probability and Statistics: Probability theory, random variables, probability distributions (binomial, Poisson, normal), statistical inference, hypothesis testing, correlation and regression, etc.

6. Analytical Geometry: Coordinated geometry of two and three dimensions, lies, plans, vectors, equations of curve and surfaces, etc.

7. Trigonometry: Trigonometric functions, identities, equations, properties of triangles, inverse trigonometric functions, etc.

8. Sequences and Series: Arithmetic and geometric progression, convergence, sum of finite and infinite series, etc.

9. Mathematical Reasoning: Statement, logical operations, quantifiers, implications, logical equivalence, etc.

Please note that the above-mentioned topics provide a general overview of the IISER Mathematics entrance exam syllabus. The specific topics and their weightage may vary from year to year. It is recommended to refer to the official IISER website or the information brochure for the detailed and updated syllabus.

Additional, candidates are advise to thoroughly study their Class 11 and Class 12 mathematics curriculum and textbooks. Practice solving previous years question papers, sample papers, and mock tests to familiarize yourself with the exam pattern and improve your problem-solving skills.

Good luck with your IISER Mathematics entrance exam preparation!