Exploring Number Theory and Modular Arithmetic in Mathematics
Delve into the fascinating world of number theory and modular arithmetic, uncovering the foundational concepts and applications in mathematics. Understand the significance of these topics in computer science and pure mathematics, paving the way for advanced studies and problem-solving. Featuring insights on the queen of mathematics and the principles of modular arithmetic, this exploration offers a comprehensive view of the interconnectedness of these fields.
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Presentation Transcript
DRP Carl Gauss Mathematics is the queen of sciences Number Theory is the queen of mathematics
Number Theory Whole Numbers Cryptography
Modular Arithmetic (General) Foundation Knowledge Generic Expression A modulo B == C A: dividend Modulo = mod = % B: modulus ==: Indicates congruency C: remainder derived from A/B
Computer Science Algorithm Algorithm for Most Programming Languages: 1. Quotient = RoundToZero(A/B) 2. Remainder = A (Quotient * B)
Pure Math Modular Arithmetic -1 mod 4 == -5, -1, 3, 7 Infinite possible answers, infinite remainders Pure Math handles infinite sets
Applied Math Java Modular arithmetic Application limited to finite sets Java Programming Language Java picks number closest to zero as an ANSWER -1 % 300 == -1 (8 bits) -1 % 300 == 299 (10 bits)
Final Thoughts Staff Book Chief DRP Mentor: Tim Mercure DRP Student: Geri Dunellari Auxiliary Resources: Dr. Larry Washington Corry Bedwell
