Outline | People | Reading | Grading | Academics | Homepage |
Course Outline* | |||||
Lecture | Topic(s) | Notes | Book(s) | ||
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1. Jan 10 | Introduction; Fibonacci |
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ENT/CINTA
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2. Jan 12 | Mathematical induction;
the binomial theorem
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ENT §1
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Mon, Jan 16 | M. L. King Holiday | ||||
3. Jan 17 | Inductive definition of addition, multiplication, exponentiation; divisibility and division with remainder |
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Class notes;
ENT §2
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4. Jan 19 | Euclid's algorithm
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ENT §2
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5. Jan 24 | Extended Euclidean algorithm; diophantine linear equations |
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ENT §2;
class notes
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6. Jan 26 | Continued fractions; Euclid's lemma |
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ENT §2
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7. Jan 31 |
Fundamental theorem of arithmetic
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ENT §3 | ||
8. Feb 2
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Theorems on primes:
Euclid, Chebyshev, Dirichlet,
Hadamard/de la Vallee Poussin,
Green-Tao
Conjectures on primes: Goldbach, twin, Mersenne, Fermat |
sequences
of equidistant primes;
Barkley Rosser, Lowell Schoenfeld.
Approximate formulas of some functions of prime numbers.
Illinois J. Math. vol. 6, pp. 64--94 (1962).
list of Mersenne primes, factors of Fermat numbers |
ENT §3
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9. Feb 7 | Catch-up; review for first exam |
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10. Feb 9 | Thursday, First Exam | Counts 20% | |||
11. Feb 14 | Equivalence relations, congruence relations, congruences |
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Class notes;
ENT §4
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12. Feb 16 |
Return of first exam;
congruences continued
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13. Feb 21 |
Congruences continued
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14. Feb 23 |
The Chinese remainder theorem
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ENT §4.4 | ||
15. Feb 28 |
The little Fermat theorem;
pseudoprimes;
Fermat primality test;
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Carmichael numbers
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ENT §5.3
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16. Mar 2 |
Carmichael numbers;
Miller-Rabin test
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ENT §5.2
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Mar 6-10, 2017 | Spring Break, no class | ||||
Mon, Mar 13, 11:59pm Last day to drop the course | |||||
17. Mar 14 |
Euler's phi function;
sums of divisors
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ENT §7
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18. Mar 16 |
Public key cryptography; the RSA
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ENT §7.5
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19. Mar 21 | Catch-up; review for exam |
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20. Mar 23 | Thursday, Second exam | Counts 20% | |||
21. Mar 28 |
Index calculus: order of an integer modulo n
and
existence of primitive roots modulo p
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ENT §8
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22. Mar 30 |
Return of second exam;
primitive roots continued
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ENT §8
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23. Apr 4 |
Diffie-Hellman key exchange;
el-Gamal public key crypto system;
digital signatures
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Class notes
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24. Apr 6 |
Quadratic residuosity
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ENT §9.1
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25. Apr 11 |
Legendre symbol,
the quadratic reciprocity law
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ENT §9.2, §9.3
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26. Apr 13 |
Jacobi symbol
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ENT §9.3, Problems 16-19
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Friday, Apr 14 | Spring Holiday, no class | ||||
27. Apr 18 |
Computing squareroots modulo p
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Maple worksheet
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Tonelli-Shanks
Algorithm
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28. Apr 20 |
Pythagorean triples,
Fermat's last theorem for n=4
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ENT §12.1, §12.2
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29. Apr 25 |
Final exam review
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30. Apr 27 |
Snow day slack lecture
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Tuesday, May 2, 9am-11am, Final exam (counts 30%) |
On-line information: All information on courses that I teach (except individual grades) is now accessible via html browsers, which includes this syllabus. My web page listing all my courses' is at
There will be four homework assignments of approximately equal weight, two mid-semester examinations during the semester, and final examination. Depending on time constraints, I may only grade a selection of homework problems.
I will check who attends class. You will forfeit 5% of your grade if you miss 3 or more classes without a valid justification. I you miss a class because you are sick, etc., please let me know. I may require you to document your reason.
Grade split up | |
Accumulated homework grade | 25% |
Final examination | 30% |
First mid-semester exam | 20% |
Second mid-semester exam | 20% |
Class attendance | 5% |
Course grade | 100% |
If you need assistance in any way, please let me know (see also the University's policy).
Collaboration on homeworks: I expect every student to be his/her own writer. Therefore the only thing you can discuss with anyone is how you might go about solving a particular problem. You may use freely information that you retrieve from public (electronic) libraries or texts, but you must properly reference your source.
Late submissions: All programs must be submitted on time. The following penalties are given for (unexcused) late submissions:
©2010, 2014, 2016, 2017 Erich Kaltofen. Permission to use provided that copyright notice is not removed.