# 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
• 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
• 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
• 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