Mathematics Department is located in right wing of the Science Building and near University of Yangon library. Head of the department of Mathematics is Professor Dr. Cho Win. His research works are in Qualitative theory of Differential Equations. Our department is very proud for working with Professor Dr. Aung Kyaw. He is specialize in Graph Theory, Combinatorial Mathematics.
Our department has conducted the programs with following number of faculties:
We offers the following programs.
* Bachelor of Science in Mathematics (BSc)
* Bachelor of Honours in Mathematics (BSc Honours)
* Master of Science in Mathematics (MSc)
* Master of Research in Mathematics (MRes)
* Doctor of Philosophy in Mathematics (PhD)
Our department collaborates with Graduate School of Mathematics, Nagoya University, Japan. Two of our students are now making research in Nagoya University. Professors from Nagoya University came to conduct lectures this year.
1. Analysis
2. Algebra
3. Ordinary Differential Equation
4. Partial Differential Equation
5. Graph Theory
6. Combinatorics and Number Theory
Curriculum for B. Sc. Degree (Mathematics Specialization)
First Year First Semester
Module No.  Name of Module  Credit
units 
Hours per week  
Lecture  Tutorial/ Practical  
Ma 1001  Myanmar  3  2  2 
Eng 1001  English  3  2  2 
Math 1101  Algebra and Analytic Geometry  4  3  2 
Math 1102  Trigonometry and Differential Calculus  4  3  2 
Elective  *  3  2  2 
AM 1001  Aspects of Myanmar  3  2  2 
Total  20  14  12 
*A student can choose any 1 of 4 elective courses offered by the departments of physics, chemistry, philosophy, geology to fulfill a total of 20 credit units.
Foundation Courses
Ma 1001 Myanmar
Eng 1001 English
Core Courses
Math 1101 Algebra and Analytic Geometry
Math 1102 Trigonometry and Differential Calculus
Elective Courses
Phys 1001 Physics
Chem 1001 Chemistry
Phil 1005 Mathematical Logic I
Geol 1001 General Geology I
First Year Second Semester
Module No.  Name of Module  Credit
units 
Hours per week  
Lecture  Tutorial/ Practical  
Ma 1002  Myanmar  3  2  2 
Eng 1002  English  3  2  2 
Math 1103  Algebra and Analytical Solid Geometry  4  3  2 
Math 1104  Differential and Integral Calculus  4  3  2 
Elective  *  3  2  2 
AM 1002  Aspects of Myanmar  3  2  2 
Total  20  14  12 
*A student can choose any 1 of 4 elective courses offered by the departments of physics, chemistry, philosophy, geology to fulfill a total of 20 credit units.
Foundation Courses
Ma 1002 Myanmar
Eng 1002 English
Core Courses
Math 1103 Algebra and Analytical Solid Geometry
Math 1104 Differential and Integral Calculus
Elective Courses
Phys 1002 Physics
Chem 1002 Chemistry
Phil 1006 Mathematical Logic II
Geol 1003 General Geology II
Second Year First Semester
Module No.  Name of Module  Credit
units 
Hours per week  
Lecture  Tutorial/ Practical  
Eng 2001  English  3  2  2 
Math 2101  Complex Variables I  4  3  2 
Math 2102  Calculus of Several Variables  4  3  2 
Math 2103  Vector Algebra and Statics  4  3  2 
Elective (1)  *  3  2  2 
Elective (2)  *  3  2  2 
Total  21  15  12 
*A student can choose any 2 of 4 elective courses offered by the department of mathematics and physics to fulfill a total of 21 credit units.
Foundation Courses
Eng 2001 English
Core Courses
Math 2101 Complex Variables I
Math 2102 Calculus of Several Variables
Math 2103 Vector Algebra and Statics
Elective Courses
Phys 2003 Physics
Math 2104 Discrete Mathematics I
Math 2105 Theory of Sets I
Math 2106 Spherical Trigonometry and Its Applications
Second Year Second Semester
Module No.  Name of Module  Credit
units 
Hours per week  
Lecture  Tutorial/ Practical  
Eng 2002  English  3  2  2 
Math 2107  Linear Algebra I  4  3  2 
Math 2108  Ordinary Differential Equations  4  3  2 
Math 2109  Vector Calculus and Dynamics  4  3  2 
Elective (1)  *  3  2  2 
Elective (2)  *  3  2  2 
Total  21  15  12 
*A student can choose any 2 of 4 elective courses offered by the department of mathematics and Physics to fulfill a total of 21 credit units.
Foundation Courses
Eng 2002 English
Core Courses
Math 2107 Linear Algebra I
Math 2108 Ordinary Differential Equations
Math 2109 Vector Calculus and Dynamics
Elective Courses
Phys 2004 Physics
Math 2110 Discrete Mathematics II
Math 2111 Theory of Sets II
Math 2112 Astronomy
Third Year First Semester
Module No.  Name of Module  Credit
units 
Hours per week  
Lecture  Tutorial/ Practical  
Eng 3001  English  3  2  2 
Math 3101  Analysis I  4  3  2 
Math 3102  Linear Algebra II  4  3  2 
Math 3103  Differential Equations  4  3  2 
Math 3104  Differential Geometry  4  3  2 
Elective (1)  *  3  2  2 
Total  22  16  12 
*A student can choose any 1 of 2 elective courses offered by the department of mathematics to fulfill a total of 22 credit units.
Foundation Courses
Eng 3001 English
Core Courses
Math 3101 Analysis I
Math 3102 Linear Algebra II
Math 3103 Differential Equations
Math 3104 Differential Geometry
Elective Courses
Math 3105 Tensor Analysis
Math 3106 Number Theory I
Third Year Second Semester
Module No.  Name of Module  Credit
units 
Hours per week  
Lecture  Tutorial/ Practical  
Eng 3002  English  3  2  2 
Math 3107  Analysis II  4  3  2 
Math 3108  Linear Algebra III  4  3  2 
Math 3109  Mechanics  4  3  2 
Math 3110  Probability and Statistics  4  3  2 
Elective (1)  *  3  2  2 
Total  22  16  12 
*A student can choose any 1 of 2 elective courses offered by the department of mathematics to fulfill a total of 22 credit units.
Foundation Courses
Eng 3002 English
Core Courses
Math 3107 Analysis II
Math 3108 Linear Algebra III
Math 3109 Mechanics
Math 3110 Probability and Statistics
Elective Courses
Math 3111 Complex Variables II
Math 3112 Number Theory II
Fourth Year First Semester
Module No.  Name of Module  Credit
units 
Hours per week  
Lecture  Tutorial/ Practical  
Eng 4001  English  3  2  2 
Math 4101  Analysis III  4  3  2 
Math 4102  Numerical Analysis I  4  3  2 
Math 4103  Linear Programming  4  3  2 
Math 4104  Partial Differential Equations  4  3  2 
Elective (1)  *  3  2  2 
Total  22  16  12 
*A student can choose any 1 of 2 elective courses offered by the department of mathematics to fulfill a total of 22 credit units.
Foundation Courses
Eng 4001 English
Core Courses
Math 4101 Analysis III
Math 4102 Numerical Analysis I
Math 4103 Linear Programming
Math 4104 Partial Differential Equations
Elective Courses
Math 4105 Stochastic Process I
Math 4106 Fundamentals of Algorithms and Computer Programming
Fourth Year Second Semester
Module No.  Name of Module  Credit
units 
Hours per week  
Lecture  Tutorial/ Practical  
Eng 4002  English  3  2  2 
Math 4107  Analysis IV  4  3  2 
Math 4108  General Topology I  4  3  2 
Math 4109  Abstract Algebra I  4  3  2 
Math 4110  Hydromechanics  4  3  2 
Elective (1)  *  3  2  2 
Total  22  16  12 
*A student can choose any 1 of 2 elective courses offered by the department of mathematics to fulfill a total of 22 credit units.
Foundation Courses
Eng 4002 English
Core Courses
Math 4107 Analysis IV
Math 4108 General Topology I
Math 4109 Abstract Algebra I
Math 4110 Hydromechanics
Elective Courses
Math 4111 Stochastic Process II
Math 4112 Integer Programming
Curriculum for B. Sc. ( Hons ) Degree (Mathematics Specialization)
First Year Honours First Semester
Module No.  Name of Module  Credit
units 
Hours per week  
Lecture  Tutorial/ Practical  
Eng 3001  English  3  2  2 
Math 3201  Analysis I  4  3  2 
Math 3202  Linear Algebra II  4  3  2 
Math 3203  Differential Equations  4  3  2 
Math 3204  Differential Geometry  4  3  2 
Elective (1)  *  3  2  2 
Total  22  16  12 
*A student can choose any 1 of 2 elective courses offered by the department of mathematics to fulfill a total of 22 credit units.
Foundation Courses
Eng 3001 English
Core Courses
Math 3201 Analysis I
Math 3202 Linear Algebra II
Math 3203 Differential Equations
Math 3204 Differential Geometry
Elective Courses
Math 3205 Tensor Analysis
Math 3206 Number Theory I
First Year Honours Second Semester
Module No.  Name of Module  Credit
units 
Hours per week  
Lecture  Tutorial/ Practical  
Eng 3002  English  3  2  2 
Math 3207  Analysis II  4  3  2 
Math 3208  Linear Algebra III  4  3  2 
Math 3209  Mechanics  4  3  2 
Math 3210  Probability and Statistics  4  3  2 
Elective (1)  *  3  2  2 
Total  22  16  12 
*A student can choose any 1 of 2 elective courses offered by the department of mathematics to fulfill a total of 22 credit units.
Foundation Courses
Eng 3002 English
Core Courses
Math 3207 Analysis II
Math 3208 Linear Algebra III
Math 3209 Mechanics
Math 3210 Probability and Statistics
Elective Courses
Math 3211 Complex Variables II
Math 3212 Number Theory II
Second Year Honours First Semester
Module No.  Name of Module  Credit
units 
Hours per week  
Lecture  Tutorial/ Practical  
Eng 4001  English  3  2  2 
Math 4201  Analysis III  4  3  2 
Math 4202  Numerical Analysis I  4  3  2 
Math 4203  Linear Programming  4  3  2 
Math 4204  Partial Differential Equations  4  3  2 
Elective (1)  *  3  2  2 
Total  22  16  12 
*A student can choose any 1 of 2 elective courses offered by the department of mathematics to fulfill a total of 22 credit units.
Foundation Courses
Eng 4001 English
Core Courses
Math 4201 Analysis III
Math 4202 Numerical Analysis I
Math 4203 Linear Programming
Math 4204 Partial Differential Equations
Elective Courses
Math 4205 Stochastic Process I
Math 4206 Fundamentals of Algorithms and Computer Programming
Second Year Honours Second Semester
Module No.  Name of Module  Credit
units 
Hours per week  
Lecture  Tutorial/ Practical  
Eng 4002  English  3  2  2 
Math 4207  Analysis IV  4  3  2 
Math 4208  General Topology I  4  3  2 
Math 4209  Abstract Algebra I  4  3  2 
Math 4210  Hydromechanics  4  3  2 
Elective (1)  *  3  2  2 
Total  22  16  12 
*A student can choose any 1 of 2 elective courses offered by the department of mathematics to fulfill a total of 22 credit units.
Foundation Courses
Eng 4002 English
Core Courses
Math 4207 Analysis IV
Math 4208 General Topology I
Math 4209 Abstract Algebra I
Math 4210 Hydromechanics
Elective Courses
Math 4211 Stochastic Process II
Math 4212 Integer Programming
Third Year Honours First Semester
Module No.  Name of Module  Credit
units 
Hours per week  
Lecture  Tutorial/ Practical  
Math 5201  Analysis V  4  4  2 
Math 5202  General Topology II  4  4  2 
Math 5203  Abstract Algebra II  4  4  2 
Math 5204  Hydrodynamics I  4  4  2 
Math 5205  Numerical Analysis II  4  4  2 
Math 5206  Qualitative Theory of Ordinary Differential Equations I  4  4  2 
Total  24  24  12 
Third Year Honours Second Semester
Module No.  Name of Module  Credit
units 
Hours per week  
Lecture  Tutorial/ Practical  
Math 5207  Analysis VI  4  4  2 
Math 5208  General Topology III  4  4  2 
Math 5209  Abstract Algebra III  4  4  2 
Math 5210  Hydrodynamics II  4  4  2 
Math 5211  Graph Theory  4  4  2 
Math 5212  Qualitative Theory of Ordinary Differential Equations II  4  4  2 
Total  24  24  12 
Curriculum for M Sc. Degree (Mathematics Specialization)
M.Sc First Year First Semester
Module No.  Name of Module  Credit
units 
Hours per week  
Lecture  Tutorial/ Practical  
Math 611  Analysis I  4  4  2 
Math 612  Abstract Algebra  4  4  2 
Math 613  (a) Qualitative Theory of Ordinary Differential Equations(OR)
(b) Dynamical systems 
4  4  2 
Math 614  Discrete Mathematics

4  4  2 
Math 615  Numerical Analysis I
(OR) Solution of linear Systems of equations 
4  4  2 
Math 616  Physical Applied Mathematics I  4  4  2 
Math 617  Stochastics Process I  4  4  2 
Total  28  28  14 
M.Sc First Year Second Semester
Module No.  Name of Module  Credit
units 
Hours per week  
Lecture  Tutorial/ Practical  
Math 621  Analysis II  4  4  2 
Math 622  Linear Algebra  4  4  2 
Math 623  (a) Partial Differential Equations (OR)
(b) Differential Geometry 
4  4  2 
Math 624  Graph Theor  4  4  2 
Math 625  Numerical Analysis II  4  4  2 
Math 626  Physical Applied Mathematics II  4  4  2 
Math 627  Stochastics Process II  4  4  2 
Elective (1)  *  3  2  2 
Total  28  28  14 
*A student can choose any 1 of 2 elective courses offered by the department of mathematics to fulfill a total of 22 credit units.
Core Courses
Math 621  Analysis II 
Math 622  Linear Algebra 
Math 623  (a) Partial Differential Equations
(OR) (b) Differential Geometry 
Math 624  Graph Theory 
Math 625  Numerical Analysis II 
Math 626  Physical Applied Mathematics II 
Math 627  Stochastics Process II 
Elective Courses
Math 628 PDE and Approximations
Math 629 Applied Probability and Satatistics
FIRST SEMESTER
Math 611 Analysis VII
Integration: concept of measurability, simple functions, elementary properties of measures, integration of positive functions, Lebesgue’s monotone convergence theorem, integration of complex functions, Lebesgue’s dominated convergence theorem.
Positive Borel Measures: Riesz representation theorem, regularity properties of Borel measures, Lebesgue measures, continulity properties of measurable functions
Lpspaces: convex functions and inequalities, the Lpspaces, approximation by continuous functions.
Texts
[1] Swe. K. M. (1995) Lectures on Functional Analysis, Mathematics Association,
University of Mawlamyine
[2] Rudin. W. (1966) Real and Complex Analysis, McGraw Hill, New York.
References
[1] Royden.H.L. (1968) Real Analysis. 2nd Printing, Macmillan.
[2] Friedmen .A. (1982) Foundations of Modern Analysis , Dover
Publications, Inc, New York.
[3] Taylor A.E, General Theory of Function and Integration.
Math 612 Abstract Algebra IV
Ring: Polynomial rings, polynomials over the rationals, field of quotients of an integral domain
Fields: Examples of fields, a brief excursion into vector spaces, field extensions
Text: Herstein, I. N. (1996), Abstract Algebra, PrenticeHall.
(Chapter 4 Ring Theory [Sections 4.5, 4.6, 4.7]
Chapter 5 Fields [Sections 5.1, 5.2, 5.3])
Math 613
(a) Qualitative Theory of Ordinary Differential Equations
Lyapunov’s second method, applications of ODE
Text: Brauer. F. and Nohel, J. A. (1969), The Qualitative Theory of Ordinary
Differential Equations: An Introduction, W. A. Benjamin, Inc.
(Chapter 5 Lyapunov’s Second Method
Chapter 6 Some Applications)
(OR)
(b) Dynamical Systems
1. Linear differential systems
Case of constant coefficients. Existence and uniqueness theorem in the general case, resolvent.
2. Nonlinear differential systems
Analytical aspects: existence and uniqueness theorem, maximal solutions, estimations of the time of existence, Gronwell lemma.
Geometric aspects: flow, phase portrait and qualitative study of differential systems, Poincare first return map, invariance submanifolds, PoincareBendixson theorem. Perturbations of a differential system.
3. Stability of invariant sets
First integrals and Lyapunov functions. Stability of fixed points. Stability of periodic orbits.
4. Local study in the neighborhood of a fixed point
Stable and unstable manifolds of a hyperbolic fixed point. HartmanGrobman theorem.
Text:
[1] Hirsch, Smale and R. L. Devancy. (2004), Differential equations, dynamical systems and an introduction to chaos, Elevesier.
[2] Arnold. V. I., (1992) Oridinary differential equations, third edition, Springer Verlag
Network models, a maximal flow algorithm, the max flow, min cut theorem, matching,
Reference:
[1] Verhulst, F. (1980) Nonlinear equations and Dynamical Systems. SpringerVerlag
[2] Teschl. G. Oridinary Differential Equations and Dynamical Systems
Math 614 Discrete Mathematics III
Network models, a maximal flow algorithm, the max flow, min cut theorem, matching,
combinatorial circuits, properties of combinatorial circuits, Boolean algebras, Boolean functions and synthesis of circuits, applications
Text: Johnsonbaugh, R. (1990), Discrete Mathematics, Macmillan.
(Chapter 8 Network Models
Chapter 9 Boolean Algebras and Combinatorial Circuits)
Math 615 Numerical Analysis III
Polynomial approximation, interpolation, quadrature formulas, solution of non linear equations, optimization
Text:
[1] Quarteoni, A. and Sacco, R. and Saleri, F. (2007) Numerical mathematics, SpringerVerlag
References:
[1] Ciarlet, P. G. (1989) Introduction to numerical linear algebra and optimization, Cambridge University Press
[2] Trefethen Lioyd N. (2013) Approximation theory and approximation practice, SIAM.
(OR)
Solution of linear systems of equations
Text: Plato. R. (2003), Concise Numerical Mathematics, AMS.
(Chapter 4 Solution of Linear Systems of Equations)
Math 616 Physical Applied Mathematics I
General theory of stress and strain: Definitions of stress, stress vector and components of stress tensor, state of stress at a point, symmetry of stress tensor, transformation of stress components, principal stresses and principal directions, principal direction of stress tensors.
Nature of strain, transformation of the rates of strain components, relation between stress and rate of strain in two dimensional case, the rate of strain quadratic, translation, rotation and deformation.
Viscous fluid: The NavierStokes equations of motion of a viscous fluid, the energy equation conservation of energy.
Text
[1] M.D.RAISINGHANIA(2010)
( Chapter 13, Chapter 14)
Math 617 Stochastics Process III
Foundations of probability of theory, limit theorems, probability distributions, probability measures and spaces
References:
[1] Cramer, H. & Leadbetter, M. R. (1946) Stationary and related stochastic
processes, Princeton University Press
[2] Feller, W. (1970) An Introduction to Probability Theory and Its Applications, 3rd
Edition, Vol I, John Wiley & Sons
[3] Feller, W. (1966) An Introduction to Probability Theory and Its Applications,
Vol II, John Wiley & Sons
[4] Hida, T. (1980) Brownian Motion, SpringerVerlag
[5] Hida, T. & Hitsuda, M. (1991) Gaussian Processes, AMS
SECOND SEMESTER
Math 621 Analysis VIII
Banach Spaces: Banach Spaces. Examples: c1 , c0 , C(X) Continuous Linear Transformation. Functionals. Dual Space N * of a Normed Space N. The Hahn Banach Theorem. Duals of Natural Imbedding of N in N ** . Reflexive Spaces. Weak Topology. Weak* topology. The Open Mapping Theorem. The Closed Graph Theorem. The Uniform Boundedness Theorem. The Conjugate of an Operator.
Hilbert Space: Inner Product Space. Hilbert Space. Examples: , l2 , L2. Schwarz Inequality. Orthogonal Complement, Orthonormal Sets. Bessel’s Inequality. Parscal’s Equation. The Conjugate Space H* of a Hilbert Space H. Representation of Functionals in H*. The Adjoint of an Operator. SelfAdjoint Operator. Normal and Unitary OperatorsProjectory.
Texts
[1] Swe, K. M. (1995) Lectures on Functional Analysis. University of Mawlamyine, Mathematics Association.
[2] Simmons, G.F. (1963) Introduction to Topology and Modern Analysis, McGrawHill, New York.
Reference
[1] Kreyszig, E.(1978) Introductory Functional Analysis with Applications, John Wiley
& Sons, New York.
Math 622 Linear Algebra IV
Eigenvectors and eigenvalues, polynomials and matrices, triangulations of matrices and linear maps
Text: Lang, S. (2004), Linear Algebra, Third Edition, Springer.
(Chapter 8 Eigenvectors and Eigenvalues
Chapter 9 Polynomials and Matrices
Chapter 10 Triangulations of Matrices and Linear Maps)
Math 623
(a) Partial Differential Equations
Integral curves and surfaces of vector fields, theory and applications of quasilinear and linear equations of first order, series solutions, linear partial differential equations, equations of mathematical Physics
Text: Zachmanoglou, E. C. and Thoe, D. W. (1976), Introduction to Partial
Differential Equations with Applications, Dover Publications, Inc.
(Chapter 2 Integral Curves and Surfaces of Vector Fields
Chapter 3 Theory and Applications of QuasiLinear and Linear Equations of
First Order
Chapter 4 Series Solutions
Chapter 5 Linear Partial Differential Equations
Chapter 6 Equations of Mathematical Physics)
(OR)
(b) Differential Geometry
The course of differential geometry is an introduction of methods of differential calculus on submanifolds. We address the following points: Inverse function theorem. Implicit function theorem. Local normal forms for maps of constant rank. Definition of submanifolds. Examples. Tangent bundle. Vector fields. Lie bracket. Lie groups. Local geometry of a hypersurface in the Euclidian soace. First and second fundmental form. Gauss curvature. Egregium theorem.
Text:
[1] M. P. Do Carmo, Differential Geometry of curves and surfaces
Math 624 Graph Theory II
Connectivity, Euler tours and Hamilton cycles
Text: Bondy, J. A., and Murty, U. S. R (1984), Graph Theory with Applications,
Springer Verlag.
(Chapter 3 Connectivity
Chapter 4 Euler Tours and Hamilton Cycles)
Math 625 Numerical Analysis IV
Nonlinear system of equations, explicit onestep methods for initial value problems in ordinary differential equations
Text: Plato. R. (2003), Concise Numerical Mathematics, AMS
(Chapter 5 Nonlinear System of Equations
Chapter 7 Explict OneStep Methods for Initial Value Problems in Ordinary
Differential Equations)
Math 626 Physical Applied Mathematics II
Viscous fluid: Diffusion of vorticity, equations for vorticity and circulation, dissipation of energy, vorticity equation of a vortex filament.
Laminar flow of viscous incompressible fluids: Plane coquette flow, generalized plane Couette flow, plane Poiseuille flow, the HegenPoiseuille flow, laminar steady flow of incompressible viscous fluid in tubes of crosssection other than circular.
Text
[1] M.D.RAISINGHANIA(2010)
( Chapter 15, Chapter 16)
Math 627 Stochastics Process IV
Higher dimensional distributions and infinite dimensional distributions, stochastic processes: Principle classes, Canonical representations of Gaussian process, multiple Markov Gaussian processes
References:
[1] Cramer, H. & Leadbetter, M. R. (1946) Stationary and related stochastic
processes, Princeton University Press
[2] Feller, W. (1970) An Introduction to Probability Theory and Its Applications, 3rd
Edition, Vol I, John Wiley & Sons
[3] Feller, W. (1966) An Introduction to Probability Theory and Its Applications,
Vol II, John Wiley & Sons
[4] Hida, T. (1980) Brownian Motion, SpringerVerlag
[5] Hida, T. & Hitsuda, M. (1991) Gaussian Processes, AMS
Math 628 PDE and Approximations
Introduction to the study of elliptic boundary value problems (modeling, mathematical analysis in the 1D case), of parabolic (heat equation) and hyperbolic (wave equation) problems. Introduction to the finite difference method for these 3 (model) problems and numerical simulations
Text:
[1] Le Dret H,m Lucquin B. (2016) Partial differential equations: modeling, analysis and numerical approximation, Birkhauser
References:
[1] Atkinson, K. E. and Han, W. (2009) Theoretical numerical analysis, Springer
[2] Quarteoni, A. and Sacco, R. and Saleri, F. (2007) Numerical mathematics, SpringerVerlag
Math 629 Applied Probability and Statistics 2
Markov chains, the random counterpart of the recursive sequences, and Martingales which are the mathematical tradition of the notion of equitable dynamics in economics. The aim of the course is to introduce the main concepts of the theory but also to furnish quantitative methods to use these models for concrete applications.
Text:
[1] A. N. Sirjaev. (1984) Probability, Springer
Reference:
[1] Williams, D. (1991) Probability with martingales