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Bose Advanced Math Olympiad: Resources

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Bose Advanced Math Olympiad is suitable for College Students.


  • 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.


  • 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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Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.