# Department of Mathematics

## Yangon University of Economics

## Department of Mathematics

# Head of Department

**Professor Dr. Myint Wai**

Daw Khin Sabai Soe

Daw Kyi Kyi Pe

Daw Naing Naing Myint

Daw Than Than Myint

Dr. Yin Yin Nu

Dr. Zar Zar Oo

Daw Nandar Su Hlaing

Daw Cho Nwe Wai

Daw Zin Pa Pa Phyo

Daw Zin Myo Win

U Aung Thet Lwin

U Hein Ko Ko Zaw

Daw Aye Nandar Htet

**Curriculum**

**Assessment System**

**First Year**

Mathematical Logic - Statements and Logical Operators, Logical Equivalence, Tautologies, Contradictions, and Arguments ; Set and Counting – The Addition and Multiplication, Permutations and Combinations; Functions and Linear Models – Function and Models, Linear Functions and Models; Nonlinear Functions and Models – Quadratic Functions and Models, Exponential Functions and Models, Logarithmic Functions and Models; Introduction to the Derivative – Average Rate of Change, Derivatives: Numerical and Graphical Viewpoints, Algebraic Viewpoints; Techniques of Differentiation with Application – A First Application: Marginal Analysis, The Product and Quotient Rules, The Chain Rule; Further Application of the Derivative – Application of Maxima and Minima, The Second Derivative Test for Relative Extrema.

** Second Year**

Matrix Algebra and Applications – Matrix Addition and Scalar Multiplication, Matrix Multiplication, Matrix Inversion, Input- Output Model; The Integral – The Indefinite Integral, Substitution, The Definite Integral: Algebraic Approach and the Fundamental Theorem of Calculus, Further Integration Techniques and Applications of the Integral, Integration by Parts, Area Between Two Curves and Applications, Differential Equations and Application; Functions of Several Variables – Partial Derivatives; Trigonometric Models – Trigonometric Functions, Models and Regression, Integrals of Trigonometric Functions and Applications.

** Third Year & First Year Honours
**

Complex number and Analytic Functions; Complex Integrals; Linear Mappings; Series Solutions of ODEs; Fourier Analysis; Partial Differential Equations – Solution by Separating Variables Used of Fourier Series; D’Alembert Solution of the Wave Equations.

**Fourth Year & Second Year Honours**

Sets and Mapping – Sets, Mapping, Natural Number and Induction, Denumerable Sets; Fourier Analysis(Continued) – Fourier Integral, Fourier Cosine and Sine Transforms, Discrete and Fast Fourier Transforms, Tables of Transforms; System of Differential Equation - A Simple Mass-Spring System, Coupled Mass-Spring System, Systems of First Order Equations, Vector-Matrix Notation for Systems, The Need for a Theory, Existence, Uniqueness and Continuity, The Gronwall Inequality; Basic Properties of Linear Programs – Examples of Linear Programming Problems, Basic Solutions, The Fundametal Theorem of Linear Programming, Relations to Convexity; The Simplex Method – Pivots, Adjacent Extreme Points, Determining a Minimum Feasible Solution, Computational Procedure-Simplex Method, Artifical Variables, Matrix Form of the Simplex Method, The Revised Simplex Method, LU Decomposition; Determinant; Eigen Value, Eigen Vector.

**Third Year Honours & M.Com (Q) **

Euclidean Vector Spaces – Vector in 2-Spanace, 3-Spanace and n-Spanace, Norm, Dot Product and Distance in R^{n}, Orthogonality, The Geometry of Linear System, Cross Product; General Vector Spaces – Real Vector Space, Subspace, Linear Independence, Coordinates and Bases, Dimension, Change of Basis, Row Space, Colum Space and Null Space, Rank Nullity and the Fundamental Matrix Spaces, Basic Matrix Transformation in R^{2} and R^{3}, Properties of Matrix Transformation, Geometry of Matrix Operators on R^{2}; Inner Product Spaces – Inner Products, Angel and Orthogonality in Inner Product Spaces, Gram-Schmidth Process, Q-R, Q-R Decomposition, Best Approximation: Least Squares, Mathematical Modeling Using Least Squares, Function Approximation: Fourier Series; Diagonalization and Quadratic Forms – Orthogonal Matrices, Optimization Using Quadratic Forms, Quadratic Forms, Hermitian, Unitary and Normal Matrices; Set and Relation; Functions; Cardinality Order.

**M. Econ( Economics) I**

Laws of Algebra of Sets; Set Operations; Product Sets; Compositions of Relations; Equivalence Relations; Algebra of Real Value Functions; Equivalent Sets; Denumeriable Sets; Cardinality, Ordered Sets and Subsets; Applications of Zorn’s Lemma; Linear Programming – Simplex Method; Power of a Square Matrix, the Characteristics Equation, Cayley – Hamilton Theorem; Computation of e^{At}; Solution of Linear Differential Equations with Constant Coefficients by Matrix Method.

**M. Econ( Statistics) I**

Riemann Integration; Riemann Integral as a Limit of a Sum; Improper Riemann Integral ; The Lebesgue Integral for Bounded Functions; The Lebesgue Integral Defined on a Bounded Measurable Sets; Power of a Square Matrix, the Characteristics Equation, Cayley – Hamilton Theorem; Computation of e^{At}; Solution of Linear Differential Equations with Constant Coefficients by Matrix Method; Numerical Methods – Modified Euler Methods, Runnge – Kutta Method; Adams – Bashforth – Moulton Method; Eigen Value Problem; Sturm –Liouville Problems.