Bose Advanced Math Olympiad is suitable for College Students.

Curriculum

• Linear Algebra
• Abstract Algebra
• Real Analysis
• Miscellaneous

Linear Algebra

• Vector Space, basis and Dimension.
• Linear Transformation, rank-nullity.
• Matrix Algebra.
• Eigenvalues, Eigenvectors, Characteristic and Minimal polynomials.
• Diagonalizability.
• Inner Product space basic properties.

Abstract Algebra

• Groups, Subgroups, Normal and Quotient groups.
• Homomorphisms, isomorphisms and automorphisms.
• Permutation group and Sylow- Theorem.
• Rings, Ideals and Quotient rings.
• Homomorphisms and Isomorphisms.
• Irreducibility criterion of polynomials.
• Different types of integral domains.
• Fields and algebraic field extension.

Real Analysis

• Sequences and Series.
• Limit Continuity, Differentiation and Riemann Integration.
• Sequence and Series of function.
• Point set topology and Metric spaces.

Miscellaneous

• Basics of Number Theory.
• Combinatorics.
• Ordinary Differential Equation.
• Line, surface and Volume integral.

Reference Books

• Linear Algebra Done right by Sheldon Axler
• Algebra by Artin
• Contemporary Abstract Algebra by Gallian
• Dummit Foote
• Introduction to Real Analysis by Bertle and Sherbert
• Principles of Mathematical analysis
• Elementary Number theory by Burton
• Introuction to ODE by Coddington

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