Bose Olympiad Senior is suitable for kids in Grade 8 and above. There are two levels of this olympiad:

**Curriculum**

- Number Theory
- Combinatorics
- Algebra
- Polynomials
- Complex Numbers
- Inequality

- Geometry

### Number Theory

The following topics in number theory are useful for the Senior round:

- Bezoutâ€™s Theorem and Euclidean Algorithm
- Theory of congruence
- Number Theoretic Functions
- Theorems of Fermat, Euler, and Wilson
- Pythagorean TriplesChinese Remainder Theorem

Here is an example of a Number Theory problem that may appear in Seinor Bose Olympiad:

### Geometry

The following topics in geometry are useful for the Senior Bose Olympiad round:

- Synthetic geometry of triangles, circles
- Barycentric Coordinates
- Miquel Point Configuration
- Translation
- Rotation
- Screw Similarity

Here is an example of a geometry problem that may appear in the Senior Bose Olympiad:

### Algebra

The following topics in Algebra are useful for Intermediate Bose Olympiad:

- Screw similarity, Cyclotomic Polynomials using Complex Numbers
- AM, GM, and Cauchy Schwarz Inequality
- Rational Root Theorem, Remainder Theorem
- Roots of a polynomial

Here is an example of an algebra problem that may appear in Senior Bose Olympiad:

### Bose Olympiad Previous Year Paper

## Reference Books

- Elementary Number Theory by David Burton
- Principles and Techniques in Combinatorics by Chen Chuan Chong and Koh Khee Meng
- Polynomials by Barbeau
- Secrets in Inequalities by Pham Kim Hung
- Complex Numbers from A to Z by Titu Andreescu
- Challenges and Thrills of Pre College Mathematics
- Lines and Curves by Vasiliyev (something else)
- Geometric Transformation by Yaglom
- Notes by Yufei Zhao
- Trigonometric Delights by El Maor
- Trigonometry by S.L. Loney
- 101 Problems in Trigonometry by Titu Andreescu

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