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I.S.I. Entrance Problems

Math Olympiad

College mathematics

Research Tracks

Arithmetical Dynamics: Part 6

Arithmetical Dynamics: Part 6

Arithmetical dynamics is the combination of dynamical systems and number theory in mathematics. Again, we are here with the Part 6 of the Arithmetical Dynamics Series. Let's get started.... Consider fix point of \( R(z) = z^2 - z \) . Which is the solution of $$ R(z)...

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Arithmetical Dynamics: Part 5

Arithmetical Dynamics: Part 5

Arithmetical dynamics is the combination of dynamical systems and number theory in mathematics. The basic objective of Arithmetical dynamics is to explain the arithmetic properties with regard to underlying geometry structures. Again, we are here with the Part 5 of...

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Arithmetical Dynamics: Part 0

Arithmetical Dynamics: Part 0

Arithmetical dynamics is the combination of dynamical systems and number theory in mathematics. We are here with the Part 0 of the Arithmetical Dynamics Series. Let's get started.... Rational function \( R(z)= \frac {P(z)}{Q(z)} \) ; where P and Q are polynimials ....

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Arithmetical Dynamics: Part 4

Arithmetical Dynamics: Part 4

We are here with the Part 4 of the Arithmetical Dynamics Series. Let's get started.... Arithmetical dynamics is the combination of dynamical systems and number theory in mathematics. \( P^m(z) = z \ and \ P^N(z)=z \ where \ m|N \Rightarrow (P^m(z) - z) | (P^N(z)-z) \)...

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Arithmetical Dynamics: Part 3

Arithmetical Dynamics: Part 3

We are here with the Part 3 of the Arithmetical Dynamics Series. Let's get started.... Arithmetical dynamics is the combination of dynamical systems and number theory in mathematics. Theory: Let \( \{ \zeta_1 , ......., \zeta_m \} \) be a ratinally indifferent cycle...

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Arithmetical Dynamics: Part 2

Arithmetical Dynamics: Part 2

We are here with the Part 2 of the Arithmetical Dynamics Series. Let's get started.... Arithmetical dynamics is the combination of dynamical systems and number theory in mathematics. The lower bound calculation is easy . But for the upper bound , observe that each \(...

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Arithmetical Dynamics: Part 1

Arithmetical Dynamics: Part 1

We are here with the Part 1 of the Arithmetical Dynamics Series. Let's get started.... Arithmetical dynamics is the combination of dynamical systems and number theory in mathematics. Definition: Suppose that \( \zeta \in C \) is a fixed point of an analytic function...

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Research for School

Research for School

Research projects for school students, in mathematics and data science. For advanced learners who are in love with mathematical science.

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Arithmetical Dynamics: Two possible problems

Today, we are going to discuss two possible problems for Arithmetical Dynamics in this post. 1.1. Existence of (pre)Periodic Points. These are the topics expanding on I.N. Baker’s theorem. Related reading: (1) Silverman Arithmetic of Dynamical Systems: p 165....

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