My key skills Pre 2009

Concepts

Mathematics, Numerical analysis, Probabilities, Operations research, Algorithms, Data structures.

Programming Languages

VISUAL BASIC, FORTRAN, MATLAB, C, C++

Web

HTML

Database

Microsoft Access, SQL

Tools

FrontPage, Visual Basic 6.0, Microsoft Office 2003-2007, Visual Studio .NET 2005

Operating Systems

Windows 95, Windows 98, Windows 2000, Windows millennium, Windows XP, Symbian, Series 40, Linux Redhat 

Mathematics: Calculus Topics

 

- Differential Calculus- حساب التفاضل

*Functions and Graphs

*Limits of functions

*Continuity

*Derivatives

*Differentiation Functions of several variables

*Partial derivatives

*Application of Derivatives

- Integral Calculus - حساب التكامل

*Integration and Approximating areas

*Definite and Indefinite integral

*Line and surface integral

*Techniques of Integration

*Numerical integration

*Improper integrals

*Multiple integration

*Applications of Integration

- Differential Equations - المعادلات التفاضلية

*Formation of ordinary differential equations(ODE’S)

*First order Differential Equations

*Linear Second order Differential Equations

*Higher-order Linear Differential Equations

*Laplace Transforms

*Partial differential equations

*Applications of Differential Equations

Mathematics: Trigonometry Topics

 

- Trigonometry

*Angles and their measure

*The Unit circle

*Trigonometric Functions

*Trigonometric Identities

*Graphs of Trigonometric Functions

*The Inverse Trigonometric Functions

*Trigonometric Equations and Inequalities

*Applications of Trigonometry

Mathematics: Geometry Topics

        - Elementry

*Lines, angles, and triangles 

*Lines in the plane

*Congruent triangles 

*Quadrilaterals

*Similar triangles 

*Trigonometry of the right triangle

*Area and Perimeter 

*Regular Polygons and circles

- Lines and circles in general forms

- Geometric transformations in the plane

- Lines and Planes in the Space

- Coordinate systems in the plane

*Rectangular cartesian coordinates

*Polar coordinates

- Coordinate systems in the space

*Cylindrical coordinates

*Sperical coordinates system

- Conic sections

*Hyperbola

*Parbola

*Ellipse

- Quadrics Surfaces

*Hyperbolid

*Parabolaid

*Ellipsoid

- Ruled Surfaces

- The Sphere

Applied Mathematics: Operations Research Topics

 

- Operations Research Modeling approach

- Linear Programming

- The Simplex Method

- Other Algorithms for Linear Programming

*Dual Simplex Method

*Parametric Linear Programming

*The Upper Bound Technique

*Interior-Point Algorithm

*Goal Programming

- Duality Theory and Sensitivity Analysis

- Transportation and Assignment Problems

- Network Optimization Models

- Dynamic Programming

- Integer Programming

- Non-linear Programming

- Heuristic Programming

- Game Theory

- Decision Analysis

- Queuing Theory

- Inventory Theory

- Simulation Modeling

Applied Mathematics: Numerical Analysis Topics

 

- Errors in Numerical Computations

- Solutions of Equations in One Variable

- Solving Linear Systems of Equations

*Direct Methods

*Iterative Methods

- Solutions of Non-leanear Equations

- Interpolation

- Approximation Theory

- Approximating Eigenvalues

- Numerical Differentiation

- Numerical Integration

- Numerical methods to Ordinary Differential Equations

*Initial value problems

*Systems of Ordinary Differential Equations

*Boundary value problems

- Numerical methods to Partial Differential Equations

- Optimization

Mathematics: Algebra Topics

- Algebra Essentials

*Numbers and Arithmetics

*Mathematical Induction

*sequences and series

*Exponents and Notations

*Radicals and Rational Exponents

*Polynomails

*The binomial Theorem

*Rational Expressions

*Permutations and combinations

- Equations and Inequalities

*Linear Equations

*Complex numbers

*Quadratic Equations

*Other Types of Equations

*Linear Inequalities and Absolute Value Inequalities

- Functions

*Function Notation

*Domain and Range

*Composition of Functions

*Transformation of Functions

*Absolute Value Functions

*Inverses and radical Functions

*Exponential function

*Linear Functions

*Polynomail Functions

*Rational Functions

*Quadratic Functions

*Exponential Functions 

*Logarithmic Functions

*Periodic Functions

*Trigonometric Functions

- System of Equations and Inequalities

*System of Linear Equations

*System of NonLinear Equations and Inequalities

*Partial Fraction

*Matrices

*Determinants

*Solving System of Equations

Paradigm of Mathematics Courses

Paradigm of Mathematics Courses

• Algebra
• Differential Calculus I
• Mechanics I, Statics
• Analytic Geometry
• Integral Calculus I
• Mechanics I, Dynamics
• Linear Algebra
• Differential Calculus II
• Mechanics II, Dynamics of Particle
• Solid Geometry
• Integral Calculus II
• Mechanics II, Dynamics of Solid Bodies
• Differential Equations
• Numerical Analysis I & II
• Operations Research I & II
• Probabilities and Statistics

Algebra and Geometry

• Mathematical Induction
• Partial Fraction
• Series
• Determinant and Matrix
• Linear equations
• Nonlinear equations
• Coordinate system
• Conic sections
• Euclidean vector
• Surfaces and Quadric Surfaces
• Ruled Surface

Differential and Integral calculus

• Function of one real variable
• Limits of functions
• Continuity
• Derivative
• Taylor series
• Indefinite integral
• Definite integral
• Improper integral
• Numerical integration

Newtonian Mechanics

• Statics in plane
• Application on equilibrium of 2D Force Systems
• Statics in space
• Friction
• Center of gravity and centroid
• Virtual work
• Kinematic of a particle in a straight line
• Kinematic of a particle in a plane
• Relative motion in plane
• Kinetics of a particle
• Simple harmonic motion
• Projectile motion
• Dynamics of rigid body in a plane

Analytical Mechanics

• Dynamics of a particles in 3D Dimensions
• Rotating Axes
• Component of velocity and acceleration in different coordinate systems
• Foucault’s pendulum
• Dynamic of rigid body in three dimensions
• Eulerian angles
• Moment on inertia
• Equation of motion of rigid body
• Euler equations
• Generalized coordinate
• Lagrange Equations
• Hamilton functions
• Routh Equations
• Sturm–Louwville equation
• Invariants
• Hamilton–Jacobi equation

Linear algebra and Solid geometry

• Vector Spaces
• Linear Transformations
• Eigenvalues and Eigenvectors
• Inner product spaces
• Bilinear and quadratic forms
• Applications in Geometry

Advanced Calculus

• Functions of several real variables
• Partial derivatives
• Maxima and minima
• Multiple integrals
• Line and surface integral
• Using MATLAB Program

Differential Equations

• Formation of ordinary differential equations(ODE’S)
• ODE’S of first order and first degree
• ODE’S of first order and higher degrees
• Applications
• Linear ODE’S of higher orders with constant coefficients and its applications
• Linear ODE’S of higher orders with variant coefficients
• Partial differential equations

Probabilities and Statistics

• Sample Space
• Random Variables
• Some Discrete distributions
• Some Continuous distributions
• Bivariate and multivariate random variables
• Some special Bivariate distributions
• Mathematical Expectation
• Least squared concept
• Correlation and regression
• Statistical tests most useful to software engineering
• T-test, ANOVA and chi-squared
• Design of experiments and testing of hypotheses
• Statistical analysis of data from a variety of sources.
• Applications of statistics to performance analysis
• reliability engineering
• Usability engineering
• Cost estimation

Discrete mathematics

• Sets
• Relations
• Functions
• Mathematical logic
• Group Theory
• Counting Theory
• Probability
• Mathematical Induction
• Recurrence Relations
• Graph Theory
• Trees
• Boolean Algebra

Operations Research

• Linear Programming
• Non-linear programming
• Geometric Programming
• Dynamic Programming
• Integer Programming
• Game Theory
• Decision Analysis
• Queuing Theory
• Inventory Theory

Numerical Analysis

• Errors in Numerical Computations
• Solutions of Non-Linear equations
• Direct Methods for solving linear systems
• Iterative Methods for solving linear systems
• Interpolation Approximations
• Polynomial Approximations
• Numerical differential
• Numerical Integration
• Numerical methods for differential equations
• Approximation theory

Mathematical and statistical Packages

• Using Mathematica
• Using MATLAB
• Using in Matrices
• Using in Functions
• Using in Graphics
• Using in Data Fitting
• Applied statistics

University/College Computer Science Program

Mathematics

• Algebra
• Differential Calculus I
• Mechanics I, Statics
• Analytic Geometry
• Integral Calculus I
• Mechanics I, Dynamics
• Linear Algebra
• Differential Calculus II
• Mechanics II, Dynamics of Particle
• Solid Geometry
• Integral Calculus II
• Mechanics II, Dynamics of Solid Bodies
• Differential Equations
• Numerical Analysis I & II
• Operations Research I & II
• Probabilities and Statistics

Physics

• Properties of Matter
• Electricity and Magnetism
• Heat and Thermodynamics
• Geometric Optics and Acoustics
• Electricity and AC Current
• Physical Optics
• Physics of Vibrations and Waves
• Principles of Modern Physics
• Introduction to Physical Electronics
• Physics of Semiconductors and Applications
• Digital Logic Circuits
• Physical Measurements Using Computer

Computer Science

• Principles of Computer Science
• Fundamentals of Programming Languages
• Scientific Computation I & II
• Theoretical Foundation of Computer Science
• Formal Language and Automata
• Computer Systems and Architecture
• Microprocessors and Communication Circuits
• Operating Systems
• File Structures
• Computer Networks
• Data Communications
• Compilers
• Systems Simulations
• Algorithms
• Data Structure and Databases
• Data Mining
• Artificial Intelligence
• Distributed Computing
• Object-Oriented Programming and C++

Others

• History of Science
• Business Management
• Scientific Thinking
• English 

Mathematics: Linear Algebra Topics

- Linear Algebra

*Systems of Linear equations

*Matrices

*Determinants

*Vector Spaces

*Linear maps between spaces

*Inner product spaces

*Linear Transformations 

*Eigenvalues and Eigenvectors

*Linear and quadratic forms

Computer Science: Data Structures Topics

- Software Engineering Principles

*The Software Process

*Program Design

*Verification of Software Correctness

*C++ Programming Language

- Data Design and Implementation

*Different Views of data

*Data Abstraction

*Object-Oriented Programming

*Constructs for Program Verification

- Abstract Data Type (ADTs)

*Unsorted List and Sorted List

*Stack and Queue

*Lists

- Linked Structure

- Linked Lists

- Programming with Recursion

- Binary Search Trees

- Heaps and Graphs

Software Engineering Principles

Software engineering

The discipline devoted to the design, production and maintenance of computer programs that are developed on time and within cost estimates using tools that help to manage the size and complexing of the resulting software product.

Software process

A standard integrated set of software engineering tools and techniques used on a project or by organization.
Software process activities:

• Problem analysis
• Requirements elicitation
• Requirements definition
• High and low-level design
• Implementation of the design
• Testing and verification
• Delivery
• Operation
• Maintenance

Software engineering tools

• Hardware
• Software
• Idea ware

Software specification

A detailed description of the function, inputs, output and special requirements of a software product, it provides the information needed to design and implement the program
Goals of quality software:

• It works
• It can be modified
• It is reusable
• It is completed on time

Program design tools

• Abstraction
• Information hiding
• Stepwise refinement: Top down – Bottom up – Functional decomposition – round- trip gestalt design
• Visual tools: UML – Class -Responsibilities and collaboration cards (CRC).

Design approaches

• Top down design
• Object oriented design (OOP)

Verification of software correctness

• Testing
• Debugging
• Acceptance test
• Regression testing
• Program verification (fulfills its specification)
• Program validation (fulfills its intended purpose)

Errors

• Specification and design errors
• Compile time errors
• Run time errors

Robustness

• The ability of program to recover following an error
• The ability of a program to continue to operate within its environment.

Designing for correctness

• Assertion: logical preposition that can be true or false.
• Preconditions and post conditions.
• Design review activities: Desk checking – walk through – inspection

Exceptions

An unusual generally unpredictable event detectable by software or hardware, that requires special processing, the event may or may not be erroneous

Program Testing

• Unit testing: test a module of function by itself.
• Functional domain: the set of valid input data for a program or function.

Black-box Testing

• Testing a program or function based on the possible input values.
• Treating the code as a black box.
• Testing based on data coverage.

Clear(White) box testing

• Testing a program or function based on covering all the statements, branches or paths of the code.
• Statement coverage: every statement in the program is executed at least one.
• Branch: a code segment that is not always executed (switch)
• Path: a combination of branches that might be traversed when the program or function is executed.
• Path testing: a testing technique whereby the tester tries to execute all possible paths in the program or function.

Metric-based testing

• Testing based on measurable factors.
• Test plan: a document showing the test cases planned for a program or module, their purposes, input, expected outputs and criteria for success.
• Implementing a test plan: Running the program with the test cases listed in the test plan.
• Test driver: a program that setup the testing environment by declaring and assigning initial values to variables, then calls the sub program to be tested.

Integration Testing

• Testing performed to integrate program modules that have already been independently unit tested.
• Stub: a special function that can be used in top-down testing to stand in for a lower-level function.

References Book: C++ Plus Data Structures, Nell Dale