Faculty of Science

Model (No 12)

Course Specification : تحليل عددى (1) - منطق رياضى ونظرية الأعداد وجبر

2010 - 2011

 
Farabi Quality Management of Education and Learning - 23/11/2024
University :Mansoura University
Faculty :Faculty of Science
Department :Mathematics Department
1- Course data :-
Code: 15303
Course title: تحليل عددى (1) - منطق رياضى ونظرية الأعداد وجبر
Year/Level: ثالثة الإحصاء وعلوم الحاسب
Program Title:
  • Statistics & Computer science
Specialization:
Teaching Hours: Theoretical: 6Tutorial: 2Practical:
2- Course aims :-
  1. The aim of the course is to provide the student with a firm introduction to the basic algorithms used in scientific computations, their design and analysis and implement similar algorithms for the solution of related scientific problems. By the end of the course students will be able to • Present the basic mathematical foundations of numerical analysis and scientific computing; • Give the students hands-on experience in solving nonlinear equations. • Provide useful tools for scientists, engineers and others.
  2. The goal of the course is to provide the student with the basics of number theory ( including unique factorization , congruence , the distribution of primes , and divisibility ) and logical argument; theorem, lemma, corollary, proof by contradiction. The course unit will introduce the student to the idea of formalizing arguments, both semantically and syntactically, and to the fundamental connection between these approaches.
3- Course Learning Outcomes :-
4- Course contents :-
NoTopicsWeek
1Introduction to computer science and number system and type of errors
2Roots of Non-Linear Equations
3Lagrange interpolation
4Divided difference formula
5Numerical integration
6Numerical solution to ODE
7Gaussian Elimination
8Logic & number theory & algebra:
9Statements, Connectives and Symbolic forms, Truth Tables,
10Logical Equivalence, Valid Arguments
11Boolean Functions and Disjunctive Normal Form, Logic Circuits.
12Karnaugh Maps.
13Postulates for the integers.
14Divisibility. Prime Factors and Greatest Common Divisor.
15Congruence of Integers.- Congruence Classes.
16Revision

5- Teaching and learning methods :-
SMethod
Lectures, exercise sheets and solution sheets
Tutorials
Internet facilities
Workshops
Computer labs

6- Teaching and learning methods of disables :-
  1. -Science students are usually normal. Therefore, no specific teaching and learning methods are needed.

7- Student assessment :-
A. Timing
NoMethodWeek
1Oral Examination14
2Final_Term Examination 15
B. Degree
NoMethodDegree
1Mid_term examination0
2Final_term examination90
3Oral examination 10
4Practical examination 0
5Semester work0
6Other types of asessment0
Total100%

8- List of books and references
SItemType
1H. B. Enderton, A Mathematical Introduction to Logic (second edition), Academic Press ISBN 0122384520, 2001
2E. Mendelson, Introduction To Mathematical Logic, Wadsworth & Brooks, ISBN 0442306768, 1971.
3D. M. Burton, Elementary Number Theory (McGraw-Hill), 1997.
4Burden R.L. and J. D. Faires, Numerical Analysis, Sixth edition, Brooks/Cole, Pacific Grove, CA, 1997.
5Mathews, J. H., and K. D. Fink. Numerical Methods Using MATLAB®. 3rd ed. Prentice Hall, 1999.

9- Matrix of knowledge and skills of the course
SContentStudy week
Introduction to computer science and number system and type of errors
Roots of Non-Linear Equations
Lagrange interpolation
Divided difference formula
Numerical integration
Numerical solution to ODE
Gaussian Elimination
Logic & number theory & algebra:
Statements, Connectives and Symbolic forms, Truth Tables,
Logical Equivalence, Valid Arguments
Boolean Functions and Disjunctive Normal Form, Logic Circuits.
Karnaugh Maps.
Postulates for the integers.
Divisibility. Prime Factors and Greatest Common Divisor.
Congruence of Integers.- Congruence Classes.
Revision

Course Coordinator(s): -
  1. Elmetwaly Mohamed Elabassy Elabassy
Head of department: -
Ahmed Habeb Mohamed Nageb Elbassiony