Number Theory Fundamentals

37 chapters

Chapters

1. Core Definitions
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2. The Division Algorithm
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3. GCD and the Euclidean Algorithm
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4. LCM
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5. Definition and Fundamental Theorem
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6. Distribution of Primes
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7. Infinitude of Primes
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8. Arithmetic Properties
   Number Theory Fundamentals · 3:27
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9. The Ring ℤ/nℤ
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10. Linear Congruences
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11. The Chinese Remainder Theorem
    Number Theory Fundamentals · 3:23
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12. Euler's Totient Function
    Number Theory Fundamentals · 4:19
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13. Fermat's Little Theorem
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14. Euler's Theorem (Generalization)
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15. The Legendre Symbol
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16. The Law of Quadratic Reciprocity
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17. Key Functions
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18. Multiplicativity
    Number Theory Fundamentals · 6:11
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19. Möbius Inversion
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20. Linear Diophantine Equations
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21. Pythagorean Triples
    Number Theory Fundamentals · 3:22
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22. Fermat's Last Theorem (Statement)
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23. Infinitude of Primes (The Inexhaustible Supply)
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24. Fundamental Theorem of Arithmetic (The Atomic Theory of Numbers)
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25. Fermat's Little Theorem (The Cycling of Powers)
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26. Quadratic Reciprocity (The Secret Handshake)
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27. 6 Homomorphisms and Isomorphisms
    Number Theory Fundamentals · 3:38
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28. Mathematical Induction
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29. 5 Normal Subgroups and Quotient Groups
    Number Theory Fundamentals · 3:37
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30. 2 Splitting Fields and Galois Groups
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31. 1 Modules
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32. Cantor's Theorem (The Never-Ending Staircase)
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33. The Law of Large Numbers
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34. 3 Root Systems and Classification
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35. Cardinality via Functions
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36. 11 Essential Equations and Formulas
    Number Theory Fundamentals · 3:37
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37. 7 Inner Product Spaces
    Number Theory Fundamentals · 3:34
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