Number Theory 
Instructor Sorin Popescu (office: Math 4119, tel. 6328358, email sorin@math.sunysb.edu)
Time and Place TuTh 02:20pm03:40pm, SBU 226
Prerequisites 
Either MAT 312 (Applied algebra), or MAT 313 (Abstract Algebra) or MAT 318 (Classical Algebra) are mandatory prerequisites for this class. In general basic algebra exposure is required and assumed, but I will try to keep prerequisites to a minimum.
Textbook(s) 
Elementary Number Theory and Its Applications , by Kenneth Rosen, (fourth edition)
AddisonWesley 2002. This is a very nice textbook that integrates classical (elementary) topics in number theory with lots and lots of applications to cryptology, computer science, etc. It also features a number of computer (programming) projects, mainly for Mathematica and Maple. There are many other excellent undergraduate books on the subject. Here is a sample (all of them available in our library):

Course description & Homework assignments 
We will cover only part of the textbook and the following schedule may/will be adjusted based on students' preparation and progress. Problems marked with an asterisk (*) are for extra credit.
Date  Topic  Homework  Notes  
Wk 1  
1/23  1.1 Numbers, sequences, and sums  p14/2,4,26,27;
p22/5,10,16,30; p28/4,8,22; due 02/04; solutions 

Wk 2  1/28  1.2 Mathematical induction; 1.3 Fibonacci numbers  Fibonacci links  
1/30  1.4 Divisibility; 3.1 Prime numbers  p34/4,16,28; p76/2,6,10; p84/6,7,13,31; due 02/11; solutions 
Half hour pretest  
Wk 3  2/4  3.2 Greatest common divisor  Primes links  
2/6  3.33.4 Euclidean algorithm, Fundamental theorem of arithmetic  p94/5,7,19*; p123/2, 3, 6 p104/4, 10, 16*, 32, 35, 46; due 02/18; solutions 

Wk 4  2/11  3.6 Linear Diophantine equations  
2/13  4.14.5: Congruences  p123/4, 21; p135/5, 22, 26, 28, 38*; p141/2, 6, 8; due 02/25; solutions 

Wk 5  2/18  p149/4a)b), 12, 22, 24; p159/1, 10; p167/2, 4, 8b, 14* due 03/04; solutions 

2/20  p177/12,19,22; p195/8,12,13,16,17 due 03/11; solutions 

Wk 6  2/25  
2/27  5.1 Divisibility tests  
Wk 7  3/4  6.16.2 Wilson's theorem, Fermat's little theorem, pseudoprimes 
p202/3, 12, 15, 20, 22, 23; p213/2, 7 due 03/27; solutions 
First project due 
3/6  
Wk 8  3/11  Midterm [exam] [solutions]  
3/13  6.3 Euler's theorem  
Recess  
Wk 9  3/25  7. Multiplicative functions  p218/1, 6, 8, 12; p227/1, 2(c,e), 3, 5, 14, 35
due 04/3; solutions 

3/27  
Wk 10  4/1  p235/2(ac), 21, 22, 23, 24, 34*, 37*
p257/1(a,b), 15,17,18,23; due 04/10; solutions 

4/3  8. Cryptography  
Wk 11  4/8  p267/3, 14, 15 p278/1, 3, 4*, 13, 18, 19 p290/1, 3, 4*, 6, 7, 11*; due 04/22; solutions 

4/10  
Wk 12  4/15  p304/1, 6, 10; p313/1, 6, 10, 18*;
due 04/29; solutions 
04/1604/18 no classes Passover 

9. Primitive roots  
Wk 13  4/22  p319/3, 8, 12, 16; p337/2, 4, 9
due 05/06 
Second project due  
4/24  
Wk 14  4/29  11. Quadratic residues  
5/1  
Wk 15  5/6  
5/8  Review  
5/20  Final exam 2:004:30pm (SBU 226)  
5/20  Review 05/16, 4:00pm5:30pm (Math Towers P131) 
Projects, Homework & Grading 
Homework (see above) and projects (TBA) are an integral part of the course. Problems marked with an asterisk (*) are for extra credit. In addition you will be required to hand in 2 research/scholarship/computing projects. Projects with a nontrivial writing component may be used to satisfy the Mathematics Upper Division Writing Requirement.
Your grade will be based on the weekly homeworks (20%), two projects (15% each), midterm (20%), and the final exam (30%). The two lowest homework grades will be dropped before calculating the average.
The Math Learning Center (MLC), located in Room S240A of the Math Tower, is an important resource. It is staffed most days and some evenings by mathematics tutors (professors and advanced students). For more information and a schedule, consult the MLC web site.
Software 
Links 
The following is a short list of web sites devoted to number theory or number theoretic related topics relevant for our class:
Special needs 
If you have a physical, psychiatric, medical or learning disability that may impact on your ability to carry out assigned course work, you may contact the Disabled Student Services (DSS) office (Humanities 133, 6326748/TDD). DSS will review your concerns and determine, with you, what accommodations may be necessary and appropriate. I will take their findings into account in deciding what alterations in course work you require. All information on and documentation of a disability condition should be supplied to me in writing at the earliest possible time AND is strictly confidential. Please act early, since I will not be able to make any retroactive course changes.
Sorin Popescu