Outline  People  Reading  Grading  Academics  Homepage 
Course Outline*  
Lecture  Topic(s)  Notes  Book(s)  

1. Jan 9  Introduction; Fibonacci 

ENT/CINTA


2. Jan 14  Mathematical induction;
the binomial theorem


ENT §1


3. Jan 16  Inductive definition of addition, multiplication, exponentiation; divisibility and division with remainder 

Class notes;
ENT §2


Mon, Jan 21  M. L. King holiday  
4. Jan 23  Euclid's algorithm


ENT §2


5. Jan 28  Extended Euclidean algorithm; diophantine linear equations 

ENT §2;
class notes


6. Jan 30  Continued fractions; Euclid's lemma 

ENT §2


7. Feb 4 
Fundamental theorem of arithmetic


ENT §3  
8. Feb 6

Theorems on primes:
Euclid, Chebyshev, Dirichlet,
Hadamard/de la Vallee Poussin,
GreenTao
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. 6494 (1962).
list of Mersenne primes, factors of Fermat numbers 
ENT §3


9. Feb 11  Catchup; review for first exam 



10. Feb 13  First Exam  Counts 17.5%  
11. Feb 18 
Return of first exam;
equivalence relations, congruence relations


Class notes


12. Feb 20  Congruences 

ENT §4


13. Feb 25 
Congruences continued




14. Feb 27 
The Chinese remainder theorem


ENT §4.4  
Mar 37, 2007  Spring Break, no class  
15. Mar 10 
The little Fermat theorem;
pseudoprimes;
Fermat primality test;

Carmichael numbers

ENT §5.3


16. Mar 12 
Carmichael numbers;
MillerRabin test


ENT §5.2


Wed, Mar 12, 5pm  Last day to drop the course 

17. Mar 17 
Euler's phi function;
sums of divisors


ENT §7


18. Mar 19 
Public key cryptography; the RSA


ENT §7.5


19. Mar 24  Catchup; review for exam 

20. Mar 26  Second exam  Counts 17.5%  
21. Mar 31 
Return of second exam;
primitive roots


ENT §8


22. Apr 2 
Index calculus: order of an integer modulo n
and
existence of primitive roots modulo p

ENT §8


23. Apr 7 
DiffieHellman key exchange;
elGamal public key crypto system;
digital signatures

Class notes



24. Apr 9 
Quadratic residuosity

ENT §9.1


25. Apr 14 
The quadratic reciprocity law

ENT §9.3


26. Apr 16 
Pythagorean triples

ENT §11.1


27. Apr 21 
Fermat's last theorem for n=4

ENT §11.2


28. Apr 23 
Catchup; final exam review



Wed, Apr 30, 9am11am, Harrelson 272: Final exam (counts 25%) 
Online 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 midsemester 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 8% 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  32% 
Final 2hour examination  25% 
First 1hour midsemester exam  17.5% 
Second 1hour midsemester exam  17.5% 
Class attendance  8% 
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:
©2008 Erich Kaltofen. Permission to use provided that copyright notice is not removed.