Science College – Math Dept

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:

  1. 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
  1. 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
  1. 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
  1. 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.
  1. 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
  1. 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
  1. 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
  1. 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
  1. 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
  1. 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
  1. 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
  1. 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
  1. 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.
  1. 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
  1. 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
  1. 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
  1. 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
  1. 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
  1. 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.
  1. 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
  1. 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.
  1. Ordinary Differential Equations.

Course Description (Definitions of differential equations, 1st 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.
  1. 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
  1. 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
  1. 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
  1. 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
  1. 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
  1. 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