How Can Congruent Mathematics Enhance Number Theory Education?

AI Thread Summary
Introducing congruences in a number theory course can be impactful by focusing on real-world applications like encryption, particularly RSA and elliptic curve cryptography. Engaging students with practical exercises, such as solving a treasure map using RSA, can enhance their understanding and interest. However, it's important to provide foundational knowledge and sample problems in modular arithmetic to prepare them for these challenges. This approach not only makes the learning process more interactive but also highlights the relevance of congruent mathematics in modern technology. Overall, integrating practical applications can significantly enrich the educational experience in number theory.
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What the best way to introduce congruences in a number theory course? I am looking for something which will have an impact. What are the really interesting applications of congruent mathematics?
 
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matqkks said:
What the best way to introduce congruences in a number theory course? I am looking for something which will have an impact. What are the really interesting applications of congruent mathematics?

Encryption. Both RSA and elliptic curve cryptology both use modular arithmetic. If you want it to be interesting, ask your students to google a treasure map in RSA and have them solve it. The modular arithmetic is a bit tough though and would require you give them some background and some sample problems before tackling the treasure map.
 

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