The Mathematics Department is located in the right wing of the Science Building near the University of Yangon library. Professor Dr. Cho Win is the Head of Department. His research is in Qualitative Theory of Differential Equations. Our department is proud to work with Professor Dr. Aung Kyaw. He specializes in Graph Theory and Combinatorial Mathematics.
We have the following academic staff in our department:

  • professors – 4
  • associate professors – 4
  • lecturers – 19
  • assistant lecturers – 16

We offer the following courses:

* 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)

Call for Papers (ICRINT2018)

International Conference on Recent Innovations

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David Taw Scholarship Announcement 2018

The Norwegian embassy in Yangon,

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1. Analysis
2. Algebra
3. Ordinary Differential Equation
4. Partial Differential Equation
5. Graph Theory
6. Combinatorics and Number Theory

UY Mathematics Department collaborates with the Graduate School of Mathematics, Nagoya University, Japan. Two of our students are currently doing research in Nagoya University. Visiting Professors from Nagoya University lectured at UY in 2018-19 AY.

Curriculum

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
Lp-spaces: convex functions and inequalities, the Lp-spaces, 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, Prentice-Hall.
(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, Poincare-Bendixson 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. Hartman-Grobman 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. Springer-Verlag
[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, Springer-Verlag

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 Navier-Stokes 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, Springer-Verlag
[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. Self-Adjoint Operator. Normal and Unitary Operators-Projectory.
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, McGraw-Hill, 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 quasi-linear 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 Quasi-Linear 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 one-step 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 One-Step 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 Hegen-Poiseuille flow, laminar steady flow of incompressible viscous fluid in tubes of cross-section 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, Springer-Verlag
[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, Springer-Verlag

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