NAMEPRACTICAL/TUTORIAL GROUP
Unit Course book
Number Theory
Course code:MthP 315 NT
Unit Coordinator
Woria M. Sediq
2012/2013
Soran University
Faculty of Science
Department of Mathematics
Stage 3 (Pure)
Welcome to department of mathematics at Soran University. This handbook summarise all the general information you need to guide you during the third stage of your selected course. This booklet also describes in details the content of number theory unit, the names of academic staff who will teach the unit, and what you will be expected to do to make sure your success in this unit. We hope you enjoy the unit and that you will find the work inspiring and challenging.
Keep in mind that good attendance at lectures and tutorials is important to give you a good basis for work throughout the course. If any students may experience difficulty with this unit, is important to sort things out as soon as possible. Make an appointment with unit coordinator who may be able to help, your year tutor, or other academic staff that involved with this unit.
Please note: you are provided with a hardcopy of teaching materials. It may be necessary to change the order of lectures, deadlines etc, which you will be informed. Therefore, it is ESSENTIAL that you check the Department of Mathematics notice board regularly in order to keep up to date with any changes.
Course Overview and Goals
This course is a year-long introduction to Number Theory. Number theory is the study of properties of numbers in particular the integers and rational numbers. Questions in elementary number theory include divisibility properties of integers (e.g. the Euclidean algorithm), properties of primes (e.g. there are infinitely many), congruences, quadratic reciprocity and integer solutions to basic equations (e.g. Diophantine equations). Even though number theory is one of the oldest disciplines in mathematics, it has recently contributed to many practical problems such as coding theory, cryptography, hashing functions or other tools in modern information technology. In this course we will discuss classical topics including primality, congruences, Linear Diophantine Equation and number-theoretic functions. The class is primarily based on Chapters 1-7 of Burton's book: “Elementary Number Theory 5th Edition [David M. Burton]”.
Learning Outcomes
After successful completion of this course, the student will be able to:
* Apply Divisibility properties and the Fundamental Theorem of Arithmetic.
* Prove results involving divisibility and common.
* Use the Euclidean algorithm to find the GCF of two integers.
* Find integral solutions to specified linear Diophantine equations.
* Apply the Chinese Remainder theorem.
* Solve systems of linear congruences.
* Apply properties of number-theoretic functions.
* Apply Fermat’s Little Theorem to prove relations involving prime numbers.
* Use mathematical induction to prove a given formula.
Communications with Academic Staff
This handbook gives information on how to contact and communicate with staff.
We provide room numbers and email addresses of staff to you. The staffs in this department want to help you as much as possible so that you will be successful in your programme. We also want to encourage you to take responsibility for yourselves and for your learning so it will help you in your future careers.
The email rules
* Write your email in acceptable English.
* In your emails you must include: full name, stage, department and the unit title.
* We only respond to queries from students using genuine/Soran University email accounts.
* Appointments can be arranged through the email system, if you wish.
* We respond to genuine problems and queries as soon as possible, normally within 7 days.
* We will not respond to emails which do not have a subject line.
Staff associated with the unit
Staff
Room Number
Email
Woria M. SediqInstructors Room in Math Dep.soran_math.woria@yahoo.com
Soran University
Department of Mathematics
Unit: Number Theory
Credit: 3
Method of Assessment:
Lectures: 2 sessions / week, 2 hours / session
Examination and grading
ACTIVITIES PERCENTAGESHomework 5%Exams 35%Final exam 60%
Homework
There will be HW assignment every time we finish a subject. Any time we assign HW It will be due next Monday and I will not accept any late homework.
Tutorials & Assessments
Attendance at tutorials & Assessments is necessary in order to gain marks for the given exercise.
Course of Action
1. There are penalties for late submission of coursework.
2. There are penalties for plagiarism and collusion.
Unit Timetable/Content
University Academic Week
Lecture Title & Content 1Introduction and Proof By Induction2Strong form of PMI3Divisibility4The Division Algorithm5Linear Combination Theorem6Consequences of LCT7Linear Diophantine Equation8Fundamental Theorem of Arithmetic9The Sieve of Eratosthenes10The Goldbach Conjecture11Arithmetic of Remainders12Polynomials and Congruenc13Fermat's Little Theorem14Winter Holiday15Wilson's Theory16History of Numbers17Number Theoretic Functions18Multiplicative Functions19Euler's Phi Function20Some Properties of Phi Function21Final Exam
Recommended Reading
• David M. Burton, Elementary Number Theory, 5th ed, McGraw Hill Companies.
• Andrew Adler, John E. Coury, The Theory of Numbers, Jones & Bartlett Publishers.