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

1. Jan 9  Introduction; Fibonacci 

ENT/CINTA


2. Jan 11  Mathematical induction;
the binomial theorem


ENT §1


Mon, Jan 15  M. L. King Holiday  
3. Jan 16  Inductive definition of addition, multiplication, exponentiation; divisibility and division with remainder 
Maple Worksheet

Class notes;
ENT §2


4. Jan 18  Euclid's algorithm


ENT §2


5. Jan 23  Extended Euclidean algorithm; diophantine linear equations 

ENT §2;
class notes


6. Jan 25  Continued fractions; Euclid's lemma 

ENT §2


7. Jan 30 
Fundamental theorem of arithmetic


ENT §3  
8. Feb 1

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 6  Catchup; review for first exam 



10. Feb 8  Thursday, First Exam  Counts 20%  
11. Feb 13  Equivalence relations, congruence relations, congruences 

Class notes;
ENT §4


12. Feb 15 
Return of first exam;
congruences continued




13. Feb 20 
Congruences continued




14. Feb 22 
The Chinese remainder theorem

Maple Worksheet

ENT §4.4  
15. Feb 27 
The little Fermat theorem;
pseudoprimes;
Fermat primality test;

Carmichael numbers

ENT §5.3


16. Mar 1 
Carmichael numbers;
MillerRabin test

Maple Worksheet

ENT §5.2


Mar 59, 2018  Spring Break, no class  
Mon, Mar 12, 11:59pm Last day to drop the course  
17. Mar 13 
Euler's phi function;
sums of divisors


ENT §7


18. Mar 15 
Public key cryptography; the RSA


ENT §7.5


19. Mar 20  Catchup; review for exam 

20. Mar 22  Thursday, Second exam  Counts 20%  
21. Mar 27 
Index calculus: order of an integer modulo n
and
existence of primitive roots modulo p

ENT §8


22. Mar 29 
Return of second exam;
primitive roots continued


ENT §8


Friday, Mar 30  Spring Holiday, no class  
23. Apr 3 
DiffieHellmanMerkle key exchange;
elGamal public key crypto system;
digital signatures

Class notes



24. Apr 5 
Quadratic and cubic residuosity

Maple Worksheet

ENT §9.1


25. Apr 10 
Legendre symbol,
the quadratic reciprocity law

ENT §9.2, §9.3


26. Apr 12 
Jacobi symbol

ENT §9.3, Problems 1619


27. Apr 17 
Computing squareroots modulo p

Maple worksheet

TonelliShanks
Algorithm


28. Apr 19 
Pythagorean triples,
Fermat's last theorem for n=4

ENT §12.1, §12.2


29. Apr 24 
Final exam review



30. Apr 26 
Snow day slack lecture



Thursday, May 3, 9am11am, Final exam (counts 30%)  
Friday, May 11, 11:59pm, Grades due 
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 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 midsemester exam  20% 
Second midsemester 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, 2018 Erich Kaltofen. Permission to use provided that copyright notice is not removed.