Math 406 – Introduction to Number Theory

Spring 2005

Lectures

Section 0201:

        TuTh 12:30pm-1:45pm (MTH 0403)

 

Section 0301:

        TuTh 2:00pm-3:15pm (MTH 0303)
 

Instructor

Professor Niranjan Ramachandran (atma at math dot umd dot edu)

Office: Math Building 4115 (405-5080)

Office hours: Tuesdays 3:30 - 4:30pm, Wednesdays 11:00am - Noon.

 

Class web page

http://www.math.umd.edu/~atma/math406.html


Text

Elementary Number Theory and its applications by Kenneth H. Rosen (Fifth Edition). The book has many weblinks

and other resources. The Number Theory Web is amazing.

 

Topics

The integers

Divisibility                       

Prime numbers                      

Greatest common divisor                    

Euclidean algorithm                      

Unique factorization                 

Congruences                      

Basic properties                      

Modular arithmetic                      

Euler's phi function                      

Fermat's, Euler's and Wilson's theorems                     

Chinese remainder theorem                  

Multiplicative Functions                 

Möbius inversion formula                 

Number and Sum of Divisors

Primitive roots

            Existence of primitives roots

Index arithmetic           

Quadratic Residues

Legendre and Jacobi symbols

Quadratic Reciprocity 

Additional Topics                      

Perfect numbers, Mersenne primes                

Continued Fractions 

Pythagorean Triples

Fermat’s Last Theorem

Sums of squares

Pell’s equation

Gaussian Integers

Tests

There will be two 90-min tests (in class) with 125 points for each test.

No make-up tests will be given.

If you have to miss a test and you have a written excuse according to the University Policies, then you will be given 50% extra credit on the final.

The final exam (worth 150 points) will be on

Section 0201: Friday May 20th (1:30pm – 3:30pm) in MTH 0403.

Section 0301: Thursday May 19th (10:30am – 12:30pm) in MTH 0303.


Please see the webpage Final Exam for the official schedule.
 


Please see the university regulations on academic integrity.
 

Homework

Homework problems will be assigned everyday and they are due Tuesdays in class.
 

Grading

Two 90-minute exams

 250 points

Final Exam

 150 points

Homework

 100 points

Total

 500 points

 

Test dates (tentative)

Test 1: Tuesday, 1st of  March, in class. Update: now changed to Thursday 3/3/05.Covers Chapter 1 and Sections 3.1 through 3.5 (inclusive). No calculators.

Test 2: Tuesday, 5th of April, in class

Final exam: See above for informaton from Testudo

 

Testbank (previous final exams)
 

Homework problems  (to be updated during the semester)

Homework 1 (due 2/8/05) Solutions

Sect 1.1: 4,8,11,28,34,39,40

Sect 1.2: 3,8,15,17

 

Homework 2 (due 2/15/05) Solutions

Sect 1.3: 7,20,27

Sect 1.4: 4,14

Sect 1.5: 8,17,34,36,39

 

Homework 3 (due 2/22/05) Solutions to 3.3 and 3.4 , Solutions to others including Homework 4

Sect 3.1: 3,6,13,16

Sect 3.2: 3,10,12,16

Sect 3.3: 5,16

 

Homework 4 (due 3/1/05) (Solutions are above)

Sect 3.3: 21,23,32

Sect 3.4: 1,3,21

Sect 3.5: 9,11,14,15,45

 

Homework 5 (due 3/15/05)

Sect 4.1: 6,13,19,27

Sect 4.2: 9,13,15

Sect 4.3: 4,9,13

 

Homework 6 (due 3/31/05) Solutions to 4.1,4.2,4.3, 6.1, 6.3 ,

Sect 6.1: 2,16,24,28,34

Sect 6.3: 6,8,10

 

Homework 7 (due 4/19/05)

Sect 7.1: 6,12,16

Sect 7.2: 8,16

Sect 9.1: 6,8,14

Sect 9.2: 6,10,16

 

Homework 8 (due 4/26/05)

Sect 11.1: 6,10,12,14,20,28(a)

Sect 11.2: 4,6,8

 

Homework 9 (due 5/3/05)

Sect 13.1: 4,6,8,12,16,18

Sect 13.2: 4,6,10,20 Solutions to all problems from 7.1 onwards

 

Last modified: 26 April 2005