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Course Description form
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Course Title
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English Code /No
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ARABIC code/no.
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credits
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Th.
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Pr.
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Tr.
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TCH
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Number Theory
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Math.444
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ر. 444
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3
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-
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-
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Pre-requisites
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Math 342
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Brief contents, to be posted in university site and documents(4-5 lines):
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Divisibility theorem in the integers - primes and their distribution - The theory of congruencies - Fermat's theorem, Wilson's theorem and their Applications - Primitive roots. Applications of congruencies - The quadratic reciprocity law.
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Faculties and departments requiring this course (if any): Faculty of
Science/Department of Mathematics.
Objectives: Prefer In points
1- The student will improve his logical thinking and learn the
techniques of the proofs of the theorems.
2- The student will be equipped with the methods of solved exercises.
3- It is expected that the students may apply the techniques learn in
this course to apply of the theorems of number theory.
Contents: Prefer In points
1- Divisibility theorem in the integers, primes and
their distribution
2- The theory of congruencies
3- Fermat's theorem, Wilson's theorem and their
Applications
4- Primitive roots
5- Applications of congruencies
6- The quadratic reciprocity law
Course Outcomes:
A- Knowledge:
(i) Description of the knowledge to be acquired
The student will improve his logical thinking and learn the
techniques of the proof of theorems. As a result he will be
equipped with the methods of solved exercises.
(ii) Teaching strategies to be used to develop that knowledge
In class lecturing where the previous knowledge is linked to the current and future topics. It is expected that the students may apply the techniques learnt in this course to apply of the theorems of group theory. Homework assignments.
(iii) Methods of assessment of knowledge acquired
In class short MCQ quizzes. Major and final exams
B-Cognitive Skills:
(i) Cognitive skills to be developed
1.The student will improve his logical thinking and learn the
techniques of the proof of theorems. As a result he will be
equipped with methods of solved exercises.
2. It is expected that the students may apply the techniques
learn in this course to apply of the theorems of group
theory.
(ii) Teaching strategies to be used to develop these cognitive
skills
1. Homework assignments.
2. Problem solving.
3. Case studies related to the course topics.
(iii) Methods of assessment of the cognitive skills
1. In class short MCQ quizzes.
2. Major and final exams.
3. Checking the problems solved in the homework
assignments.
C- Interpersonal skills and responsibilities:
(i) Description of the interpersonal skills and capacity to carry
responsibility to be developed
1. Work independently and as part of a team.
2. Mange resources, time and other members of the group.
3. Communicate results of work to others.
(ii) Teaching strategies to be used to develop these skills and abilities
1. Writing group reports.
2. Solving problems in groups.
(iii) Methods of assessment of student's interpersonal skills and
capacity to carry responsibility: Grading homework assignments.
D- Analysis and communication:
(i) Description of the skills to be developed in this domain.
1. Use computational tools.
2. Report writing.
(ii) Teaching strategies to be used to develop these skills.
1. Report writing.
2. Incorporating the use and utilization of computer in course
requirements.
(iii) Methods of assessment of students numerical and
communication skills.
Test questions require interpretation of simple statistical
information. Assessments of students assignment and
project work include expectation of adequate of numerical
and communication skills. Five percent of marks allocated for
standard of presentation using ICT.
Assessment methods for the above elements: Discussions, Homework,
Periodic tests and final test
Text book:
David M. Burton, Elementary number theory, fifth Edition Mc
Graw-Hill.
Supplementary references:
Kenneth H. Rosen, Elementary number theory and its applications. Fifth
Edition Greg Tobin.
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Time table for distributing Theoretical course contents
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Remarks
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Experiment
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weak
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Mathematical induction, The Binomial theorem, Early number theory
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1
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The division algorithm, The greatest common divisor, The Euclidean Algorithm
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2
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The Fundamental theorem of Arithmetic, Special divisibility tests
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3
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Basic properties of congruence, Linear congruence
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4
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Fermat's Factorization method and examples
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5
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Wilson's theorem, Applications on Fermat and Wilson Theorems, first quizzes
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6
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The order of an integer and primitive roots, Primitive roots for primes
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7
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Existence of primitive roots, and its examples
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8
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Primitive tests using orders of integers and primitive roots, and examples
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9
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primitive roots, and examples and second quizzes
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10
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Linear congruencies generation power residues
Divisibility tests, check digits, and examples
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11
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Divisibility tests, check digits, and its examples Euler's criterion, and its examples
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12
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Euler's criterion, and its examples Quadratic reciprocity, and its examples
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13
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Quadratic reciprocity, and its examples
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14
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Revision
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15
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Final exam.
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