Competition resources

Notes 1: Arithmetic, Geometric, Fibonacci sequences

• Problem Set 1 - General term & Sequence pattern

• Problem Set 2 - Arithmetic sequence

• Problem Set 3 - Geometric sequence

• Problem Set 4 - Fibonacci sequence

Notes 2: Recursively defined sequences

• Problem Set 5 - Recurrence relation

• Problem Set 6 - Recurrence practical problems

Notes 3: Polynomial interpolation of sequences

• Problem Set 7 - Sum of k-th powers of 1 to n

• Problem Set 8 - Polynomial interpolation

Notes 4: Convergence of sequences

Notes 5: Convergence of series

• Problem Set 9 - Sequence and series convergence

Notes 6: Harmonic series

• Problem Set 10 - Harmonic series

Notes 7: Finding values of series (Part 1)

• Problem Set 11 - Shifting terms

• Problem Set 12 - Telescoping sum

• Problem Set 13 - Partial fraction

Notes 8: Finding values of series (Part 2)

• Problem Set 14 - Generating function

• [Link] List of mathematical series

Notes 1: Radicals (Internal access only)

• Problem set 1 - Nested radical

Notes 2: Logarithms and Number system (Internal access only)

• Problem set 2 - Number system

Notes 3: Functions (Internal access only)

• Problem set 3 - Functions

• Problem set 4 - Absolute value function 

• Problem set 5 - Floor and Ceiling functions

Notes 4: Inequalities (Internal access only)

• Problem set 6 - Inequalities

Notes 1: Factors and Multiples

• Problem set 1 - Divisibility test

• Problem set 2 - Factors and Multiples

• Problem set 3 - Factorial & Trailing zeros

• Problem set 4 - No. of factors and Sum of factors

• Problem set 5 - Factor equation

Notes 2: The Euclidean algorithm

• Problem set 6 - H.C.F. and L.C.M.

• Problem set 7 - Euclidean algorithm

• Problem set 8 - Linear Diophantine equation

Notes 3: Modular arithmetic

Notes 4: Euler-phi function, Special congruences, Fast modular exponentiation

• Problem set 9 - Modular arithmetic (Remainder)

• Problem set 10 - Modular arithmetic (Congruence system)

• Problem set 11 - Modular arithmetic (Miscellaneous)

Notes 5: Application of Number theory (Internal access only)

• Problem set 12a - Letter equation (Addition & Subtraction)

• Problem set 12b - Letter equation (Multiplication)

• Problem set 12c - Letter equation (Division)

Outline of Topics

Combinatorics notes (Internal access only)

Handwritten note on Recurrence and Markov chain

[Link] Stars and bars (combinatorics)

[Link] 日本科学未来館『フカシギの数え方』

[Link] Meaning of expected value: St. Petersburg paradox