
Number Theory with Applications, 1/e
James A. Anderson, University of South CarolinaSpartanburg Published October, 1996 by Prentice Hall Engineering/Science/Mathematics
 
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Provides over 1000 practice problems — of various types, covering all theory and applications presented. Surveys the historical context of number theory and the people who developed the theorems. Offers a selfcontained treatment of tools necessary to understand and construct proofs — e.g., set theory and proof logic. Covers Peano Postulates — a concise and historically important set of axioms from which number theory can be developed. 0. SETS.
2. Functions. 3. Generalized Set Operations. 1. Elementary Properties of Integers.
2. Axioms for the Integers. 3. Principle of Induction. 4. Division. 5. Representation. 6. Congruence. 7. Application: Random Keys. 8. Application: Random Number Generation I. 9. Application: Two's Complement.
2. Prime Factorization. 3. Distribution of the Primes. 4. Elementary Algebraic Structures in Number Theory. 5. Application: Pattern Matching. 6. Application: Factoring by Pollard's r.
2. Chinese Remainder Theorem. 3. Matrices and Simultaneous Equations. 4. Polynomials and Solutions of Polynomial Congruences. 5. Properties of the Function f 6. The Order of an Integer. 7. Primitive Roots. 8. Indices. 9. Quadratic Residues and the Law of Reciprocity. 10. Jacobi Symbol. 11. Application: Unit Orthogonal Matrices. 12. Application: Random Number Generation II. 13. Application: Hashing Functions. 14. Application: Indices. 15. Application: Cryptography. 16. Application: Primality Testing.
2. Multiplicative Functions. 3. The Möbius Function. 4. Generalized Möbius Function. 5. Application: Inversions in Physics.
2. Convergents. 3. Simple Continued Fractions. 4. Infinite Simple Continued Fractions. 5. Pell's Equation. 6. Application: Relative Rates. 7. Application: Factoring.
2. Preliminaries. 3. Bertrand's Postulate.
2. Pythagorean triples. 3. Integers as Sums of Two Squares. 4. Quadratic Forms. 5. Integers as Sums of Three Squares. 6. Integers as Sums of Four Squares. 7. The Equation ax^2 + by^2 + cz = 0. 8. The Equation x^4 + y^ 4 = z^2.
2. Propositional Calculus. 3. Arguments. 4. Predicate Calculus. 5. Mathematical Proofs.
