This degree is offered by ( Al-Muthanna University) at the college of (Science). The typical length of study is four years. During these years, the students have to complete the following courses:

**Advance Calculus I ( First )**

- Introduction
- Function of Two and More independent Variable
- Limits
- Continuity
- Partial Derivatives - Definition
- Differentiable
- Direction Derivatives
- Extrema of Functions
- Multiple Integrals Definition
- Double Integrals on rectangular regions
- Double Integrals on nonrectangular regions
- Area Calculated as a Double integral
- Double Integrals in Polar Coordinates
- Triple Integrals

**C++ language**

- Introduction to C++
- variables
- Statements
- Order evaluation and math libraries
- Selection Statements
- If-then-else statement
- for ) statement)
- While-do while Statement)
- Breaking statement
- Array of One Dimension
- Array of Two Dimension
- Examples of array
- Functions
- Types of Functions
- Examples of function

**C++ language ( Experiments Assignments)**

- variables
- Starting with c++
- Example of order evaluation
- Selection Statements
- If-then-else statement
- for) statement)
- While-do while Statement
- Example of breaking statement
- Array of One Dimension
- Array of Two Dimension
- Examples of array
- Functions
- Types of Functions
- Examples of function

**Calculus I**

Course Description (Definition of function, domain and range of a function, graph of functions in the plane, definition of limit, continuity and derivative of a function)

- Coordinates, distance formula, the slope and equation of a straight line.
- Definition of functions, domain and co-domain of functions, graph & types of functions with examples.
- Definition of limits, continuity of functions with examples.
- Derivatives of algebraic functions with examples.
- Polynomial functions and their derivatives with examples.
- Derivatives of rational and inverse functions with examples.
- The increment of function, composite functions and their derivatives with examples.
- Increasing and decreasing functions, curve plotting with examples.
- Maxima and minima problems, Rolle’s theorem with examples & applications.

**Calculus I**

Course Description (Real function and their graph ,theorems ,limits ,continuous ,trigonometric function )

- Definition of real function and their graph with example
- Definitions\theorems
- Using definition of the limit
- Definition,with examples
- Theorem about continuity
- Definition,theorems and some application
- Trigonometric function with inverse
- Hyperbolic function with inverse
- Exponential qnot algorithm
- Functions with application

**Calculus I (Lab. Experiment Assignments)**

- Functions 1
- Functions 2
- Limits 1
- Limits 2
- Continuous 1
- Continuous 2
- differentiation
- Transcendental function 1
- Transcendental function 2
- Transcendental function 3
- Transcendental function 4

**Complex analysis**

Course Description (Introduction , real and complex numbers , complex plan , roots form a complex plan , , functions of complex variable , analytic functions ,Cauchy – Riemaaan equation, harmonic functions, elementary function , complex integration ,Cauchy integral formulas)

- real and complex numbers and geometric representation 1
- real and complex numbers and geometric representation 2
- roots form a complex plan field of complex numbers as metric space 1
- roots form a complex plan field of complex numbers as metric space 2
- Complex numbers as complete space , open sets and closed sets in complex plan. 1
- Complex numbers as complete space , open sets and closed sets in complex plan 2
- Connected sets , complex functions 1
- Connected sets , complex functions 2
- Differential complex functions and analytic functions 1
- Differential complex functions and analytic functions 2
- Cauchy – Riemaaan equations and harmonic functions 1
- Cauchy – Riemaaan equations and harmonic functions 2
- complex integration 1
- complex integration 2
- Cauchy integral formula

**Foundation of Mathematics**

**Course Description (**Set theory- the Logic- Countable Sets**)**

- Set theory 1
- Set theory 2
- The Logic
- The Relations 1
- The Relations 2
- Equivalent Relations
- Order relations
- The Functions 1
- The Functions 2
- Examples +Theorems
- Equivalent Sets 1
- Equivalent Sets 2
- Examples +Theorems
- The Numbers
- Examples +Theorems
- Countable Sets

**Functional analysis (15 weeks)**

- Vector spaces
- Balanced set ,absorbs set
- subspace
- Dependent and independent , direct some
- Basis and dimension
- Normed spaces
- Multiplication of Normed spaces
- Equivalent Norms
- Concepts of metric in normed space , convergence in normed spaces
- Banach spaces , convexity
- Continuous linear functions , bounded linear functions
- Quotient space
- The spaces of linear functions , The spaces of bounded linear functions
- Hahn Banach theorems
- Isomorphic of normed spaces

**general mathematics (10 weeks)**

- Linear systems are consistent inconsistent and it is solutions
- matrices and some types and algebraic operations on them
- Transported matrix, equivalent arrays, symmetry matrices and their properties, algebraic properties of operations on matrix
- Reduced class format , Class equivalence, Writing linear systems in matrices format
- Solution of linear systems using Gauss's method
- Abnormal and irregular matrices for matrices and how to find determinants and properties
- Use the transaction posting method to find the value of the parameter, the associated matrix
- Grammar method to solve the linear system
- Introduction to nodal numbers and their properties
- The roots and properties of nodal nodules, the relationship of polynomials to their roots

**Mathematical Analysis I**

**Course Description (**The main subjects of the course are: Ordered set and ordered Field, Infinite Sequences and infinite Series, Metric spaces, Topological spaces, complete metric spaces, Compact spaces)

- Real numbers and rational numbers
- The relation between the field of rational numbers and the Field of real numbers.
- The density of rational and irrational numbers
- Metric space
- Basic principles in Topology
- Convergence sequence in a metric space
- Complete metric space
- Compact metric space
- Continuity(Definition and Examples)
- Uniformly continuous
- Intermediate value
- The sequence and series of functions
- Uniformly convergence and point wise Convergence 1
- Uniformly convergence and point wise Convergence 2
- Power series

**Mathematical Analysis I ( Experiments Assignments)**

- Inclusion concepts, Equal sets, Subsets
- Proper subset, Empty set, Universal set
- Union, Intersection, Disjoint set, Symmetric difference
- Definition and Examples
- Equivalence relation,
- Partition of the set
- Partially ordered set
- Domain and Co-domain of the function 1
- Domain and Co-domain of the function 2
- Definition and Examples 1
- Definition and Examples 2
- Property and application
- Definition and Examples
- Property and examples 1
- Property and examples 2
- Interval of convergence of power series

**Mathematical statistics I**

Course Description (Definition of random variable, find the probability density function, distributions and their properties)

- Random variable, Discrete random variables, Continuous variables.
- The probability density function, The cumulative Distribution function.
- Mathematical Expectation, properties of Expectation.
- Expectation Laws, Examples.
- Chebyshev inequality, Examples.
- The moment generating function.
- Properties of the moment generating function.
- Discrete Distribution.
- Bernoulli Distribution.
- Binomial Distribution.
- Poisson Distribution.
- Continuous Distribution, Uniform Distribution.
- Gamma Distribution.
- Beta Distribution.
- Normal Distribution.

**Multivariate1 (First course, 15 weeks)**

- Matrix concepts
- Linearity
- Vector inner product
- Quadratic forms
- Problems
- Differentiation with matrices
- Characteristic roots
- correlation
- Simple linear regression
- The residuals analysis
- Regression parameter calculation
- Multiple regression
- Correlation coefficient matrix
- Some important issues in multivariate normal distribution
- Hypotheses testing with MND
- Applications

**Numerical analysis - First semester (15 weeks)**

- Errors
- Numerical solutions of eq.s by graph
- Bisection method
- False position method with secant method
- Fixed point and convergence
- Newton-Raphson method and convergence
- Numerical solution of linear system eq.s
- Numerical solution of linear system eq.s
- Interpolation 1
- Interpolation 2
- Lagrange’s interpolation
- Finite difference 1
- Finite difference 2
- Finite difference 3
- Numerical differentiation

**Numerical analysis ( Experiment Assignments)**

- Method of errors calculating
- Find the root graphically
- Example with theorem
- To solve eq. f(x)=0
- To solve eq. f(x)=0
- To solve eq. f(x)=0
- Jaccopi with example
- Gauss-Seidal with example
- Definition with example
- Linear and quadratic interpolation
- Theorem and example
- Newton’s forward interpolation
- Newton’s backward interpolation
- Central interpolation formula
- Differentiation with example

**Methods for solving partial differential equations I**

**Course Description (**Classifications partial differential equations, partial differential equations of higher order and solving methods, canonical forms, Cauchy problem, Fourier series)

- Introduction of partial differential equations of order one
- Classifications of partial differential equations of order one with constant coefficients and solving methods 1
- Classifications of partial differential equations of order one with constant coefficients and solving methods 2
- Methods of find the general solution of partial differential equations 1
- Methods of find the general solution of partial differential equations 2
- Methods of find the general solution of partial differential equations 3
- Canonical forms of partial differential equations
- Types of partial differential equations, Cauchy problems 1
- Types of partial differential equations, Cauchy problems 2
- Types of partial differential equations, Cauchy problems 3
- Partial differential equations of order n 1
- Partial differential equations of order n 2
- Partial differential equations of order n 3
- Fourier series 1
- Fourier series 2

**Probability & Statics 1 (First course, 15 weeks)**

- Basic review
- Probability function
- Some operations
- Combination
- Permutation
- Some problems
- Special theorems
- Independent and pair wise independent
- Probability Laws
- The conditional probability
- Bayes Law and Bayes theorem
- Some applications
- Random variables
- d.f and P.m.f
- D.F

**Rings Theory**

- The concept of a ring with examples.
- Types of rings with examples.
- Subrings with theorems and examples.
- Integral domains.
- The zero divisor elements.
- The ring homomorphism with theorems and exercises.
- The homomorphism kernel with examples.
- The fundamental theorems of ring homomorphism.
- Ideals.
- The external direct sum of rings with examples. 1
- The internal direct sum of rings with examples. 2
- Types of ideals.
- The Jacobian’s root of a ring with examples.
- The primal’s root of a ring with examples.
- Homomorphism on Jacobian’s and primal’s roots.

**Topology**

**Course Description (**Topology-base and subbase-product topology and continuity**)**

- Concepts of top. spaces
- Base and Subbase
- Sets and points in top. space
- Inerior points
- Exterior and boundary points
- Product topology 1
- Product topology 2
- Continuous
- Open and closed function
- Homeomorphism
- Product topology by base and subbase 1
- Product topology by base and subbase 2
- Separation axioms 1
- Separation axioms 2
- Tichonov space
- Metric space

**Group Theory I**

**Course Description (**Definition of groups, subgroups, homomorphisms on groups theorems with their proofs , examples and applications)

- Binary operation,group with examples .
- Subgroups with examples.
- Semigroups ,cyclic group with theorems and examples.
- Normal subgroup
- Qoutient group
- Cosets, theorems, exercises.
- Simple group
- Homomorphisms and isomorphisms.
- Kernel and Image.
- Isomorphisms Theorems.
- Applications and examples.
- Derived subgroup.
- The commutator.
- Sylow’s theorems.
- Applications on Sylow’s theorems.

**Ordinary Differential Equations.**

**Course Description (**Definitions of differential equations, 1^{st} degree diff. eq., homogeneous and non-homogeneous diff. eq’s and linear diff. eq’s and their solution**)**

- Basic concepts in differential equations.
- eq’s. of the 1st order.
- The 1st degree diff. eq’s.
- Examples and applications.
- The equations of suppurated variables.
- Examples and applications.
- The homogeneous diff. eq’s.
- The non-homogeneous diff. eq’s.
- The exact diff.eq’s with examples.
- Bernoulli and Euler equation with examples.
- Reduce the order of diff. eq’s with examples.
- The ordinary linear diff. eq’s of order n with examples.
- The linear diff. eq’s of constant coefficients with examples.
- The linear diff. eq’s of variable coefficients with examples.
- Special equations and their solutions / revision.

**Data Base**

- What is data base-concept, definition, classification , design, model
- DB architecture-conceptual, external schema, internal schema
- File system- what is the file system, advantage, disadvantage, DB types-relational, distributed
- Relational data base , DB table key-super key, candidate key, primary key, foreign key
- DBMS- what is DBMS and RDBMS
- E/R diagram-multiplicity binary relationship
- Distributed data base-why distributedDB, DDB issues-design, concurrency control, reliability, query processing
- Fundamental principle of distributed DB
- Distributed data base design –fragmentation, replication, allocation
- Architecture of DBMS-components.
- Data base implementation-memory hierarchy.
- DBMS failure, commit
- Distributed one phase commit, distributed two phase commit, distributed three phase
- Dead lock in data base management system
- Recovery in distributed system

**Mathematics**

- Function
- Combining of function
- Shifting
- Limits
- Continuity
- Trigonomettic function
- The concept of limit
- differentiation, and diff. rules.
- Derivative of trigonomatric function
- Chain rule ,Implicit diff
- Applications of derivative
- Extreme values
- Absolut max and Absolut min
- Concave up concave down
- Inflection point

**Matlab**

- Matlab Definition, program FrontPage
- Basic operations definition ,titling during programming
- Matlab orders, Matrices, Operation on Matrices
- Vectors Operation on vectors
- Complex numbers
- 2D graphs
- Characteristics additive on matlab graphs
- Graphs on separated windows, axps titling
- 3D graph
- equations solving
- Zero Crossing
- Find the roots of polynomial
- Derivation and integration
- Functions
- Area under curve calculating

**Computer (First semester) ( Experiment Assignments)**

- Computer parts, Programs
- Laptop + quiz
- memories+ quiz
- The operating systems + quiz
- Windows system+ quiz
- Compering between the operating system+ quiz
- Icons , files and folders+ quiz
- The control panel
- Help and some of fames cases

**Computer (First semester) ( Experiment Assignments)**

- Identify of the program's interface and the basic ingredients
- Explain and apply the commands on the File tab+ quiz
- Explain and apply the commands on the Home tab+ quiz
- Explain and apply the commands on the Insert tab+ quiz
- Review past lectures
- Exercises
- Explain and apply the commands on the Design tab+ quiz
- Explain and apply the commands on the Transitions tab + quiz
- Explain and apply the commands on the Animations tab + quiz
- A review of the lectures for the examination of the second month
- Explain and apply the commands on the View tab
- Reviewing all lectures
- Exercises

**Human rights**

- The concept of human rights , human rights in ancient civilizations and heavenly laws
- human rights in medieval and modern
- human rights in thought and revolutions of modern legislation
- Contemporary international recognition of human rights
- Contemporary regional recognition of human rights
- international and regional recognition of human rights
- Exam the first month
- the emergence of nongovernmental organizations and their role in the fields of human rights
- human rights in the international and regional conventions
- human rights into national legislation
- Constitutional guarantees of human rights at the national level
- Judicial guarantees of human rights at the national level
- the role of the united nations
- the role of regional organizations
- Exam the second month