ميلعتلا ةرازو
Ministry of Education
نارنج ةعماج
Najran University
ةرورشب بادلآا و مولعلا ةيلك
Faculty of Science and Arts, Sharourah
تايضايرلا مسق
Mathematics Department
1
Program Name: Bachelor of Science & Education In Mathematics Contents of Mathematics Courses
Pre-requisite Credit Hours
Course Code Course Title
3 none Math 101
Calculus (1)
Course Content: Real Numbers, Inequalities, Functions, One – one Function and its Inverse, Limit Def., Continuity, Properties of Continuous Fun's., Derivative and its Rules, Critical Points, Local and absolute Extreme Values, Mean Value theorem, Increasing & Decreasing, First Derivative Test, Second Derivative Test, Concavity, Inflection Points, asymptotes , Curve Sketch, Extreme Value Problems, Related Rates Problems.
Pre-requisite Credit Hours
Course Code Course Title
Math 101 3
Math 121 Calculus (2)
Course Content: Integral Def. by Riemaan's Sums, Definite Integral Properties, Integral Mean Value Theorem, Fundamental of Calculus, Original Function and Indefinite Integral, Integration by substitution, Logarithmic and Exponential Fun's., Hyperbolic Functions and their Inverses, Integration Methods : Integration by Parts, Integration by Trigonometric Substitution, Integration by Complete Square, Rational Fun's Integration, Approximation method of Definite integration (Trapezoid Method), l'Hopital's Rule, Improper Integral, Areas and Volumes of Revolution Solids, Calculation of the Length Arc of a Curve, Polar Coordinates, Sketch curves in Polar Coordinates, Calculation of Areas Using Polar Coordinates.
Pre-requisite Credit Hours
Course Code Course Title
3 none Math 145
Principles of logic and
Modern Algebra
ميلعتلا ةرازو
Ministry of Education
نارنج ةعماج
Najran University
ةرورشب بادلآا و مولعلا ةيلك
Faculty of Science and Arts, Sharourah
تايضايرلا مسق
Mathematics Department
2
Course Content: Sets, Numbers sets and their Properties, Algebra of Sets, Propositions and Connectives, Proof Methods, Binary Operations, Relations, Equivalence Relations, Equivalence Classes, Partitions of Sets, Set of Integers modulo n, Mappings, Composition of Mappings, Mean Theorem of Mappings, Permutations, Binary Operations and Algebraic Structures (Groups, Rings, Fields, …..).
Pre-requisite Credit Hours
Course Code Course Title
Math 101 3
Math 161 Analytic Geometry
Course Content: Cartesian Coordinates, General Equation of Straight Line, Different Types of Straight Line Equations, Circle, Conics, Classification of Second Order Equation of Two Variables, Polar Coordinates.
Pre-requisite Credit Hours
Course Code Course Title
Math 101 3
Math 171 Statics
Course Content: Vectors, Force Resultants, Condition for the Equilibrium of Coplanar Forces, Vacuum Statics, Centered of Gravity, Moments of Inertia, Hypothetical Work, Fluid Statics.
Pre-requisite Credit Hours
Course Code Course Title
Math 241 3 Matrix Algebra
Course Content: Scalars, Matrices on real Numbers Field, Operations on Matrices, Types of Matrices, Elementary Operation & Echelon Forum, The Inverse of a Square Matrix, Systems of Linear Equations and their Solution, Determinants.
Pre-requisite Credit Hours
Course Code Course Title
3 Stat 101
Principles of Statistics and
Probability
ميلعتلا ةرازو
Ministry of Education
نارنج ةعماج
Najran University
ةرورشب بادلآا و مولعلا ةيلك
Faculty of Science and Arts, Sharourah
تايضايرلا مسق
Mathematics Department
3
Course Content: Introduction to Statistics, Organization and presentation of statistical data, Measures of central tendency, Measures of dispersion, Simple Linear Regression and Correlation, Basics of Probability.
Pre-requisite Credit Hours
Course Code Course Title
Math 171 3
Math 212 Dynamics 1
Course Content: Plane Motion of a Particle on Cartesian Coordinate, Projectiles, Simple Harmonic Motion,
Impulsive Forces and Collisions, Pulleys, Motion of a Particle of variable mass, Plane Motion of a Particle on Polar Coordinate, Motion in a circle, Central Paths.
Pre-requisite Credit Hours
Course Code Course Title
Math 161 2
Math 262 Solid Analytic Geometry
Course Content: Vectors In Three Dimensions Space, Straight Line, Plane, Conicoid, Sphere, Classification of Second Order Equation of Three Variables, Cylindrical and Spherical Coordinates.
Pre-requisite Credit Hours
Course Code Course Title
Math 101 3
Math 281 Real Analysis1
Course Content: Basic Properties of Real Numbers Field, Completion Axiom, Countable Sets, Sequences &
Convergence, Monotonic Sequences, Bolzano – Weierstrass Theorem, Cauchy Criterion, Basic Topological Properties of Real Numbers, Limits of Functions, Continuous Functions and their Properties, Uniform Continuity, Compact Sets and Continuity, Heine – Borel Theorem, Derivative and Derivative Properties, Mean Value Theorem, l'Hopital's Rule, Taylor's Theorem.
Pre-requisite Credit Hours
Course Code Course Title
Math 145 3
Math 341 Group Theory
Course Content: Binary Operation, Definition of Group, Basic Algebraic Properties of a Group, Abelian Group, Cyclic Group, Permutation Group, Direct Product Group, Subgroups and their Theorems, Order of an Element,
ميلعتلا ةرازو
Ministry of Education
نارنج ةعماج
Najran University
ةرورشب بادلآا و مولعلا ةيلك
Faculty of Science and Arts, Sharourah
تايضايرلا مسق
Mathematics Department
4
Lagrange's Theorem of finite Groups, Cosets, Normal Subgroups, Factor Groups, Group Homomorphism, Kernel of a Homomorphism, Mean Theorem of Group Homomorphism, Cayley Theorem.
Pre-requisite Credit Hours
Course Code Course Title
Math 121 3
Math 221 Calculus 3
Course Content: Sequences and Infinite Series, Cartesian, Cylindrical and Spherical Coordinates, Functions of Two
& Three Variables, Lagrang's Factors, Double Integral in Polar Coordinates, Triple Integral and its Applications, Triple Integral in Cylindrical and Spherical Coordinates, Convergence Tests, Expansion of Functions By Power Series, Taylor and Maclaurin Series, General Binomial Theorem.
Pre-requisite Credit Hours
Course Code Course Title
Math 121 3
Math 280
Introduction to ProgrammingCourse Content: Preparing mathematical Problems for Computer work, The definition of languages used in programming, programming in a computer language (Fortran, C ++, Pascal, Visual Basic ...)
Pre-requisite Credit Hours
Course Code Course Title
Math 121 3
Math 222
Introduction to OrdinaryDifferential Equations
Course Content: Definition of Differential Equations, Formation of Differential Equation, Classification of Differential Equations, First Order and First Degree Differential Equations ( Separable, Homogeneous, Linear, Exact), Solutions of First Order and First Degree Differential Equations, Equations Reduced to (Homogeneous, Exact) Equations, Equations Reduced to Linear Equation ( Bernoulli Equation, Ricatti Equation), Second OrderHomogeneous Linear Differential Equation with Constant Coefficients,Differential Operator, Linear Dependence and Independence of Functions, Wronski Determinant, General Solution of Homogeneous Linear Differential Equationwith Constant Coefficients, Solutions of Non Homogeneous Linear Differential Equation by
ميلعتلا ةرازو
Ministry of Education
نارنج ةعماج
Najran University
ةرورشب بادلآا و مولعلا ةيلك
Faculty of Science and Arts, Sharourah
تايضايرلا مسق
Mathematics Department
5
(UndeterminedCoefficients, Variation of Parameters), Solutions of Linear Differential Equation by Reducing Order, Laplace Transforms, Using Laplace Transforms to solve Initial Value Problems.
Pre-requisite Credit Hours
Course Code Course Title
Math 145 3
Math342 Linear Algebra
Course Content: Vector Spaces, Subspaces, Linear Combinations and Spanning Sets, Linear Dependence and Linear Independence, Basis and Dimension, Coordinates and change of Basis, Row Space and Column Space, Rank of Matrix, Inner Product Space, Orthogonality, Orthonormal Basis, Gram – Schmidt Algorithm, Linear Transformations, Kernel and Image of Linear Transformation, Matrix of Linear Transformation, Eigen Values and Eigen Vectors, Diagonalization.
Pre-requisite Credit Hours
Course Code Course Title
Math 101 3
Stat 241 Probability Theory
Course Content: Basics of probability: Revision , Probability and Counting Techniques, Random variables, Expectation and Moments, Discrete Probability Distributions, Continuous Probability Distributions.
Pre-requisite Credit Hours
Course Code Course Title
Math 281 3
Math 381 Real Analysis 2
Course Content: Definition of Riemann Integral, Darboux Theorem, Mean theorem of Integration, Uniform Convergence of Sequences and Series of Functions, Power Series, Measure, Segma Algebra, Borel Algebra, Outer Measure, Lebesgue Measurable Sets, Lebesgue Measure and its Properties, Lebesgue Integral, Simple Functions, Measurable Functions, Monotonic Convergence Theorem, Dominated Convergence Theorem, Relation Between Riemann and Lebesgue Integral.
Pre-requisite Credit Hours
Course Code
Course Title
ميلعتلا ةرازو
Ministry of Education
نارنج ةعماج
Najran University
ةرورشب بادلآا و مولعلا ةيلك
Faculty of Science and Arts, Sharourah
تايضايرلا مسق
Mathematics Department
6
Math 121 3
Math 452 Numerical Analysis 1
Course Content:Errors, Approximations, Numerical Differentiation, Solutions of Simultaneous Linear Equations, Rots of Nonlinear Equations.
Pre-requisite Credit Hours
Course Code Course Title
Math 281 3
Math 471 General Topology
Course Content: Topology of Euclidian Space, Topology of Metric Space, Topological Space (open and closed Sets, Neighborhood, accumulation Points, Cluster Points, Interior Points), Continuity of Functions and Homeomorphisms, Topological Property, Form a topology on a set (Relative, Quotient, Product, Base, Subbase, Neighborhood System), Separation Axioms, Compactness, Connectedness.
Pre-requisite Credit Hours
Course Code Course Title
Math 222 3
Math 321 Differential Equations1
Course Content: Second Order Linear Differential Equations with Variant Coefficients( Solution of Homogenous Cauchy – Euler Equation, Solution of Nonhomogenous Cauchy – Euler Equation by Variation of Parameters, Solution of Second Order Linear Differential Equations with Variant Coefficients which are not in Cauchy – Euler Form by (Abel Form, Transformation to Equation with Constant Coefficients, Variation of Parameters), Solution of Second Order Linear Differential Equations with Variant Coefficients by Power Series about Ordinary Point, Frobenious Method to solve Second Order Linear Differential Equations with Variant Coefficients by Power Series about Uniform Singular Point, Solution of Bessel Equation, Solution of Legendre Equation, Hypergeometric Functions.
Pre-requisite Credit Hours
Course Code Course Title
Math 281 3
Math 383 Theory of Complex variable
Course Content:Complex Numbers, Algebraic properties of complex number, Argand Diagram, Polar and Exponential Forms of complex number, DeMoivre's Theorem, Power and roots of complex number, Complex
ميلعتلا ةرازو
Ministry of Education
نارنج ةعماج
Najran University
ةرورشب بادلآا و مولعلا ةيلك
Faculty of Science and Arts, Sharourah
تايضايرلا مسق
Mathematics Department
7
Functions, Limits and Continuity, Analytic Functions, Cauchy-Riemann Equations, Harmonic Functions, Exponential and Logarithmic Functions, Complex Powers, Trigonometric and Hyperbolic Functions, Complex Integration, Line Integral, Cauchy-Goarsat Theorem, Independence of path, Cauchy Integral Theorem, Representation of Analytic functions by Series, Zeros and Singular Points, Residue Theorem.
Pre-requisite Credit Hours
Course Code Course Title
Math 341 3
Math 441 Rings and Fields
Course Content: Ring Definition, Basic Algebraic of rings, Zero Divisors, Integral Domains, Fields, Quotient (Factor) Ring, principals Theorems of Finite Rings, Direct Product of Rings, Subrings, Ideals, Prime and Maximal Ideals, Ring Homomorphism and its Theorems, Characteristic of a Ring, Field of Divisors of an Integral Domain, Euclidean Rings, Polynomials Ring, Roots of Polynomials in a Field, Extension of Fields, Algebraic Closure of a Field .
Pre-requisite Credit Hours
Course Code Course Title
Math 381 3
Math 483 Functional Analysis
Course Content: Metric Spaces, Complete Metric Space, Normed Space, Banach Space, Hilbert Space, Linear Functionals , Linear Operators, Spectrum of Linear Operators.
Pre-requisite Credit Hours
Course Code Course Title
Math 471 1
Math 498 Graduate project
Course Content:The course includes writing an article in one of subjects, which are presented by the course coordinator after Department approving. At the end of the student gives a presentation about his article that is evaluated by a committee chosen by the department council.
