Applied Mathematics: Probabilities and Statistics Topics

 

- Probability and Random Variables

*Events and their probabilities

*Rules of Probability

*Combinatorics

*Conditional probability and independence

- Discrete Random Variables and Their Distributions

- Continuous Distributions

- Stochastic Processes

- Queuing Systems

- Introduction to Statistics

*Population and sample,parameters and statistics

*Simple descriptive statistics

*Graphical statistics

- Statistical Inference

*Parameter estimation

*Confidence intervals

*Unknown standard deviation

*Hypothesis testing

*Inference about variances

*Chi-square tests

*Nonparametric statistics

*Bootstrap

*Bayesian inference

- Regression

*Least squares estimation

*Analysis of variance,prediction,and further inference

*Multivariate regression

*Model building

Mathematics Topics - الرياضيات العامة

Algebra Topics - الجبر

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

Trigonometry Topics - حساب المثلثات

*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

Geometry Topics - الهندسة الرياضية

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

Differential Calculus Topics- حساب التفاضل

*Functions and Graphs

*Limits of functions

*Continuity

*Derivatives

*Differentiation Functions of several variables

*Partial derivatives

*Application of Derivatives

Integral Calculus Topics- 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 Topics - 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: 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

Discrete Mathematics Topics

 

- Introduction

*Mathematical Reasoning

*Combinatorial Analysis

*Discrete Structures

*Algorithmic Thinking

*Applications and Modeling

- Logic and Proofs

- Basic Structures

*Sets

*Functions

*Sequences

*Sums

*Matrics

- Number Theory

- Induction and Recursion

- Counting

- Discrete Probability

- Relations

- Graphs

- Trees

- Modeling Computation

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

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