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Understanding the motivation helps address the root problem. Common reasons include:
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1 Logic
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2 Proofs
- 1. Direct Proofs
- 2. Divisibility
- 3. Existence proofs
- 4. Induction
- 5. Uniqueness Arguments
- 6. Indirect Proof
3 Number Theory
- 1. Congruence
- 2. $\Z_n$
- 3. The Euclidean Algorithm
- 4. $\U_n$
- 5. The Fundamental Theorem of Arithmetic
- 6. The GCD and the LCM
- 7. The Chinese Remainder Theorem
- 8. The Euler Phi Function
- 9. The Phi Function—Continued
- 10. Wilson's Theorem and Euler's Theorem
- 11. Public Key Cryptography
- 12. Quadratic Reciprocity
4 Functions
- 1. Definition and Examples
- 2. Induced Set Functions
- 3. Injections and Surjections
- 4. More Properties of Injections and Surjections
- 5. Pseudo-Inverses
- 6. Bijections and Inverse Functions
- 7. Cardinality and Countability
- 8. Uncountability of the Reals
- 9. The Schröder-Bernstein Theorem
- 10. Cantor's Theorem
5 Relations
- 1. Equivalence Relations
- 2. Factoring Functions
- 3. Ordered Sets
- 4. New Orders from Old
- 5. Partial Orders and Power Sets
- 6. Countable total orders