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Final Exam.
Answers.
Meeting 39. Recursive solutions to Pell equations.
Newton's method.
Newton basins.
Meeting 38. Pell equations.
Archimedes Cattle Problem.
Meeting 37. Comments on continued fractions.
Meeting 36. No meeting. Spree Day.
Meeting 35. Harmonic theory.
Meeting 34. More on continued fractions.
Meeting 33. Introduction to continued fractions.
Second test, Wednesday, Apr. 5.
Sample questions.
Second test.
Answers.
Alternate test.
Alternate test answers.
Student questionnaire
Meeting 29. Writing up proofs; decimal fractions.
Meeting 28. Decimal expansion of rational numbers.
Meeting 27. More on Pythagorean triples. Fermat's
method of descent.
Meeting 26. Pythagorean triples.
Quiz answers.
Meeting 24. Diophantine equations. Fermat/Wiles
theorem.
Meeting 23. More on public-key cryptograpy. The
Public Key Applet.
Meeting 22. Public-key cryptography, the mathematics behind
the RSA algorithm. Illustration with 143.
Meeting 21. The group of totatives, the order of a totative,
primitive roots.
Meeting 20. Fermat's little theorem and Euler's theorem.
Pseudoprimes. Multiplicativity of Euler's phi function.
Meeting 19. Exercises on congruence and CRT.
Meeting 18. Totatives and Euler's phi function.
Meeting 17.
Linear congruences, the Chinese remainder theorem.
First test, Wednesday, Feb. 22.
Sample questions.
Test.
Answers.
Meeting 14. Linear congruences.
Meeting 13. N, Z, Q, R, C,
Zn, squares modulo n.
Meeting 12. Polynomials and congruence.
Meeting 11. Congruence modulo n.
Meeting 10. Linear Diophantine equations.
Meeting 9. Divisors of a number, their number and their sum.
Multiplicative functions. Perfect numbers.
Meeting 8. Irrationality of surds.
Meeting 7. The unique factorization theorem.
Meeting 6. More on divisibility, the Euclidean algorithm,
and greatest common divisors.
Meeting 5. Some elementary properties of divisibility,
prime numbers, greatest common divisors, and the Euclidean algorithm.
Meeting 4. What are numbers and what should they be?
Meeting 2. An Innocent Investigation.
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Asmt. 13, due Mon, Apr 3, from page 161, one of the
exercises 3, 5 completely.
Asmt. 12, due Fri, Mar 31, from page 155, one of the
exercises 1, 2, 7 completely.
Asmt. 11, due Fri, Mar 14, from page 148, exercises 1, 4; and
from page 151, exercises 3, 7, 11.
Asmt. 10, due Fri, Mar 17, from page 106, exercises 2, 4, 5, 9; and
from page 108, misc. exercises 8, 15.
Asmt. 9, due Fri, Mar 3, from page 82, exercises 1, 2, 4, 10; and
from page 86, exercises 1, 2, 6, 7.
Asmt. 8, due Wed, Mar 1, from page 76, exercises 1-3, 7-9, 11-13, 17, 20.
Asmt. 7, due Fri, Feb 17, from page 54, exercises 1-5, 8, 10; and
from page 63, exercises 1, 4-6, 8, 9, 13, 19-21.
Asmt. 6, due Wed, Feb 15, from page 47, exercises 3-8, 10.
Asmt. 5, due Fri, Feb 10, from page 43, exercises 2, 3, 5, 6, 7.
Asmt. 4, due Wed, Feb 8, from page 35, exercises 1, 2.
Asmt. 3, due Mon, Feb 6, from page 32, exercises 5, 7, 12, 13, 15.
Asmt. 2, due Wed, Feb 1, from page 26, exercises 2, 3, 4, 5, 6, 11, 12, 13.
Asmt. 1, due Wed, Jan 25, from page 14, Misc. exercises: 1, 2, 3, 4.
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