Courses 5

 

College:

Faculty of science

Department:

Mathematics

Course Title:

Differential Equations(2)

Course Code:

Math 305

Credit Hours:

3

Prerequisite:

Differential Equations 1 Math 204

Text Books:

1.

Shepley L. Ross: Differential Equations:3rd. Edit. (1998): John Wiley & Sons. , Inc

2.

D. Rainville and P. E. Bedient: Elementary Differential Equations, (1995) MacMillan Pub. Co. Inc. N. Y.

3.

Course Description:

System of linear ordinary differential equations with an emphasis on applications on initial value problems. Topics include power series solutions, Laplace transform, solution of initial value problems, and nonlinear differential equations.

Learning Objectives:

1- Let the student present the importance and applications of the differential equations in Physics, Chemistry and Engineering Science

2- Let the student study the methods for solving ODE, series solution, solutions by Laplace transform.

3- Let the student acquire the concept of nonlinear differential equations.

Grading: 

No.

Assessment

Evaluation

1.

Med semester exam 1

25%

2.

Med Semester exam 2

25%

3.

Home works

5%

4.

Quizzes

5%

5.

Final Exam

40%

Total

100 %

Methods of Teaching: (Lectures, Laboratory, Individual exercises, In-class discussion, Selection of Readings,…)

1.

Lectures

2.

Tutorials

3.

Homework

4.

Quizzes

Course Outline:

Week

Lecture Topics

1.

System of first-order equations- Introductory remarks

2.

Homogenous linear system with constants coefficients

3.

Introduction and review of power series

4.

Series solutions of first-order DE

5.

Second order differential equations – ordinary points

6.

Laplace transform, introduction

7.

First Term Exam,  

8.

Derivatives and integrals of Laplace transform

9.

Convolutions,

10.

Applications to Differential Equations

11.

Nonlinear differential equations- Introduction

12.

The Unit step function ,TheImpulse function ,Second Term Exam

13.

Solution of equations with discontinuous forcing terms

14.

Revision

15.

Final Exam

College:

Faculty of Science

Department:

Mathematics

Course Title:

Real Analysis1

Course Code:

Math 311

Credit Hours:

3

Prerequisite:

Fundamentals of integral calculus (Math 200), Basics of Mathematics Math 251

Text Books:

1.

Elements of Real Analysis,2nd Edition. John Wiley and Sons,Inc. New York, 1976- R. G. Bartle

2.

Basic  elements of Real Analysis - Murrary H.Protter

3.

Introduction to Real Analysis, 2nd edition, by Manfred Stoll

Course Description:

This course concerns itself with the concepts of limit and continuity, which are the basis of mathematical analysis and the calculus from which it evolved.  We focus on limits of sequences and of functions, and continuity of functions and the the concept of differentiability.  While the main context is the real numbers, i.e. limits of sequences of real numbers, continuity of functions from the real numbers to the real numbers,... Existence of global extrema and the Intermediate Value Theorem are studied…

Learning Objectives:

To develop and generalize techniques studied in Calculus 1 in IR and to master theoretical subtleties such as uniform convergence and uniform continuity…

At the completion of this course, the successful student will have demonstrated these abilities:

·         The ability to understand both abstract and concrete mathematical reasoning.

·         The ability to differentiate between sound mathematical reasoning, flawed reasoning, and non-rigorous reasoning.

·         The ability to use the basic tools and methods of proof seen in analysis, in particular set theory and epsilon-delta and epsilon-n arguments.

·         The ability to formulate and prove theorems that arise from the definitions and concepts of the course content, and the ability to apply those theorems to specific examples.

·         The ability to write up, and occasionally present orally, one’s mathematical proofs and arguments in a clear and compelling manner.

Grading: 

No.

Assessment

Evaluation

1.

Med semester exam 1

25%

2.

Med Semester exam 2

25%

3.

Home works

5%

4.

Quizzes

5%

5.

Final Exam

40%

Total

100 %

Methods of Teaching: (Lectures, Laboratory, Individual exercises, In-class discussion, Selection of Readings,…)

1.

Lectures

2.

Tutorials

3.

Homework

4.

Quizzes

Course Outline:

Week

Lecture Topics

1.

Real numbers – Algebraic properties

2.

Completeness- arrangement properties

3.

Open sets- closed sets

4.

limit points–  Compact sets

5.

Heine-Borel Theorem and Weirstrass Theorem

6.

Continuity

7.

Uniform Continuity

8.

Differentiation

9.

Mean value Theorem –L’Hˆopital’s rule 

10.

Convergent sequences

11.

Limits - Theorem of limits

12.

upper and lower of limit sequences , Cauchy sequence

13.

Tests of convergence : Comparison test – root test ratio – Abel's Test – Alternating series test…

14.

REVIEW FOR FINAL EXAM

15.

College:

Faculty of Science 

Department:

Statistics

Course Title:

Probability Theory

Course Code:

Stat. 311

Credit Hours:

3 hrs

Prerequisite:

General Statistics (Stat 201)

Text Books:

1.

Introduction to Probability and Mathematical Statistics, Second Edition

Author : Bain and Engelhardt

2.

Mathematical Statistics with Applications  (7th Edition)

Author : Dennis Wackerly, William Mendenhall, Richard L. Scheaffer

3.

Recommended Books and Reference Material (Journals, Reports, etc)

Course Description:

The course focuses on the importance and the efficiency of the random variables idea in statistical mechanism. The several types of discrete and continuous random variables in addition to Some applications of random variables beside the mathematical illustration of several issues related to random variables and statistical distributions.

Learning Objectives:

-The course aims to enable students to apply the fundamentals of probability theory.

-The course Provide students with the required knowledge of random variables (Discrete and continuous), bivariate and multivariate random variables in addition to the applications of moment generating function and its use

  - The course aims to teach  students the meaning of the continuous probability distributions and their applications as well as derivations of their means and variances

Grading: 

No.

Assessment

Evaluation

1.

Quiz 1

05

2.

First midterm

25

3.

Quiz 2

05

4.

Second midterm

25

5.

Final Examination

40

Total

100 %

Methods of Teaching: (Lectures, Laboratory, Individual exercises, In-class discussion, Selection of Readings…)

1.

Lectures

2.

Tutorials

3.

Exercises

4.

Discussions

Course Outline:

Week

Lecture Topics

1.

Revision on Discrete and continuous random variables and Probability.

2.

Moment generating function method.

3.

Geometric distribution, Gamma distribution.

4.

Exponential distribution, Normal distribution, Mean.

5.

Joint discrete distributions, Multinomial distribution.

6.

Joint continuous distributions.

7.

Independent Random Variables, Conditional Distributions.

8.

Properties of the expected values.

9.

Correlation, Conditional expectation.

10.

Bivariate normal distribution

11.

Joint moment generating function

12.

The CDF technique

13.

Transformation methods

14.

Sum of random variables

15.

Moment generating function method

College:

Science

Department:

Mathematics

Course Title:

Abstract Algebra 1

Course Code:

Math 342

Credit Hours:

3

Prerequisite:

Basic of mathematics – Math  251

Text Books:

1.

A First Course in Abstract Algebra. 5th ed. 1999 John B. Fraleigh,  Addison-Wesly Pub. Co.

2.

Topics in Algebra, I. N.  Herstein, John wily & sons 1975

3.

Abstract Algebra: A first Course By Dan Saracino. 1980.

Course Description:

Sets, relations and Binary operation - Definition and basic properties of group - Solutions of equations in any group - power of element in a group The order of a group and the order of element - Definition of Cyclic group – generators of a Cyclic group – Definition, elementary properties and Theorems of a subgroups - Definition of function – one to one and onto function – definition of permutation–composition of permutation – cyclic notation – even and odd permutation Cosets of a subgroup - Lagrange's theorem and its corollaries – multiplication of two subgroups - Normal subgroup and Quotient group – Homomorphsim and The fundamental theorem of homomorphisms

Learning Objectives:

1- Let the student present the basic definitions in abstract algebra, Let the student study the algebraic structures with one binary operation (groups).

2- Let the student acquire the ability of the student to abstract and logic thinking, and Let the student  development the ability of the  student to dealing with the abstract proofs.

3- Let the student study  the proofs in abstract algebra and methods of solution, and they acquires cognitive skills through thinking and problem solving.

Grading: 

No.

Assessment

Evaluation

1.

Med semester exam 1

25%

2.

Med Semester exam 2

25%

3.

Home works

5%

4.

Quizzes

5%

5.

Final Exam

40%

Total

100 %

Methods of Teaching: (Lectures, Laboratory, Individual exercises, In-class discussion, Selection of Readings,…)

1.

Lectures

2.

Individual exercises

3.

In-class discussion

4.

Home works, Quizzes

Course Outline:

Week

Lecture Topics

1.

Sets  and Relations – Binary operation -

2.

Definition and basic properties of group - Examples - Theorems

3.

Solutions of equations in any group - power of element in a group - Quizzes 1

4.

The order of a group and the order of element – Examples

5.

Definition of Cyclic group – generators of a Cyclic group

6.

Midterm 1 - Definition and elementary properties – Theorems of a subgroups

7.

Definition of function–one to one and onto function – definition of permutation - Composition of permutation – cyclic notation – even and odd permutation

8.

Cosets of a subgroup – Examples

9.

Lagrange's theorem and its corollaries- multiplication of two subgroups

10.

Continue - Normal subgroup

11.

Midterm 2 -Quotient group

12.

Continue Homomorphsims

13.

The fundamental theorem of homomorphism- Quizzes 2

14.

Continue

15.

Review and Final exam