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:

  • professors – 3
  • associate professors – 4
  • lecturers – 35
  • assistant lecturers and – 19
  • tutors – 10

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.

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

Dr Kay Thi Tin Professor

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Dr Aung Kyaw Professor

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Dr. Kyaw Zaw Associate Professor

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Dr. Yin Yin Su Win Associate Professor

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Dr Thin Thin Mar Associate Professor

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Dr May Thida Htun Lecturer

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U Kyi Htin Paw Lecturer

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Dr Saw Mar Lar Aung Associate Professor

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Dr Soe Soe Moe Lecturer

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Dr Thiri Thinzar Aung Assistant Lecturer

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Daw Thu Zar Lin Assistant Lecturer

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Daw Thu Zar Win Maung Assistant Lecturer

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U Win Thant Zaw Assistant Lecturer

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Daw Kyawt Thuzar Khine Tutor

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Daw Myint Myint May Assistant Lecturer

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Daw Yee Yee Lwin Assistant Lecturer

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Daw Aye Zarni Zaw Tutor

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Daw Khin Myo Swe Lecturer

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Daw Khin Nyein Aye Lecturer

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Daw Khin San Moe Lecturer

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Daw Khin Swe Win Lecturer

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Daw Khine Wah Win Lecturer

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Daw Khin Win Maw Lecturer

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Daw Kyawt Kyawt Aye Lecturer

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Daw Mya Thu Zar Lecturer

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Daw Nan Aye Latt Lecturer

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Daw Ngu Wah Assistant Lecturer

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Daw Sa Pai Myint Lecturer

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Daw Saw Saw Than Lecturer

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Daw Sein Htay Lecturer

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Daw Su Myat Yi Lecturer

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Daw Than Than Nyunt Lecturer

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Daw Cho Mar Hlaing Lecturer

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Daw Su Su Lecturer

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Dr. Theinge Hlaing Lecturer

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Daw Thida Oo Lecturer

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Dr thin Thin Si Lecturer

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Daw Saw Yu Mon Assistant Lecturer

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Daw Win Win Phyo Assistant Lecturer

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Daw Zin Thwe Aye Assistant Lecturer

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Daw Nilar Lwin Tutor

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Curriculum

FIRST SEMESTER

Math   1101   Algebra and Analytic Geometry

Algebra: logic and sets, polynomial functions, permutations, combinations, binomial theorem, mathematical induction.

Analytic Geometry: lines, circles, conic sections, translation of coordinate axes, rotation of coordinate axes.

Texts:

[1] Lipschutz, S. (1981), Set Theory and Related Topics, SOS, McGraw-Hill.

(Chapter 14     Algebra of Propositions

Chapter 15     Quantifiers)

 

[2]             Vance, E. P. (1983), Modern Algebra and Trigonometry, Addison-Wesley.

(Chapter 9       Polynomial Functions

Chapter 11     Permutations, Combinations and the Binomial Theorem

Chapter 12     Mathematical Induction)

 

[3]             Anton, H (1995), Calculus with Analytic Geometry, 5th Edition, John Wiley & Sons.
(Chapter 1       Coordinates, Graphs, Lines

Section 1.4 Lines

Section 1.5      Distances; Circles; Equations of the Form

Chapter 12     Topics in Analytic Geometry

Section 12.1    Introduction to the Conic Sections

Section 12.2    The Parabola; Translation of Coordinate Axes                                                                                 Section 12.3     The Ellipse

Section 12.4    The Hyperbola

Section 12.5    Rotation of Axes; Second-Degree Equations)

Math   1102   Trigonometry and Differential Calculus

Trigonometry: inverse trigonometric functions.

Calculus: limits, continuity, exponential, logarithmic, hyperbolic functions and their inverses, differentiation of inverse trigonometric functions, differentiation of exponential, logarithmic, hyperbolic functions and their inverse, L’Hopital’s rule, Taylor series.

 

Text:   Thomas, G. B. (2009), Calculus, 12th Edition, Addison-Wesley.

(Chapter 2  Limits and Continuity

Section 2.1      Rates of Change and Tangents to Curves

Section 2.2      Limit of a Function and Limit Laws

Section 2.3      The Precise Definition of a Limit

Section 2.4      One-Sided Limits

Section 2.5      Continuity

Section 2.6      Limits Involving Infinity; Asymptotes of Graphs

 

Chapter 7   Transcendental Functions

Section 7.1      Inverse Functions and Their Derivatives

Section 7.2      Natural Logarithms                 [Except Integration]

Section 7.3      Exponential Functions            [Except Integration]

Section 7.5      Indeterminate Forms and L’Hospital’s Rule

Section 7.6      Inverse Trigonometric Functions                 [Except Integration]

Section 7.7      Hyperbolic Functions             [Except Integration]

 

Chapter 10 Infinite Sequences and Series

Section            10.8    Taylor and Maclaurin Series)

Math   1001   Mathematics I (For Science Students)

permutations, combinations, binomial theorem, mathematical inductions;

lines, circles, conic sections;

limits, continuity, inverse trigonometric functions, exponential, logarithmic, hyperbolic functions and their inverse functions, L’Hopital’s rule, differentiation of inverse trigonometric functions.

Texts:

  [1]     Vance, E. P. (1983), Modern Algebra and Trigonometry, Addison-Wesley.

(Chapter 11  Permutations, Combinations and the Binomial Theorem

Chapter 12    Mathematical Induction)

  [2]     Anton, H (1995), Calculus with Analytic Geometry, 5th Edition, John Wiley & Sons.
(Chapter 1      Coordinates, Graphs, Lines

Section 1.4 Lines

Section 1.5      Distances; Circles; Equations of the Form

Chapter 12   Topics in Analytic Geometry

Section 12.1    Introduction to the Conic Sections

Section 12.2    The Parabola; Translation of Coordinate Axes                                                                                 Section 12.3     The Ellipse

Section 12.4    The Hyperbola

Section 12.5    Rotation of Axes; Second-Degree Equations)

[3]    Thomas, G. B. (2009), Calculus, 12th Edition, Addison-Wesley.

(Chapter 2  Limits and Continuity

Section 2.1      Rates of Change and Tangents to Curves

Section 2.2      Limit of a Function and Limit Laws

Section 2.3      The Precise Definition of a Limit

Section 2.4      One-Sided Limits

Section 2.5      Continuity

Section 2.6      Limits Involving Infinity; Asymptotes of Graphs

Chapter 7  Transcendental Functions

Section 7.1      Inverse Functions and Their Derivatives

Section 7.2      Natural Logarithms                 [Except Integration]

Section 7.3      Exponential Functions            [Except Integration]

Section 7.5      Indeterminate Forms and L’Hospital’s Rule

Section 7.6      Inverse Trigonometric Functions                 [Except Integration]

Section 7.7      Hyperbolic Functions             [Except Integration]

Math   1002   Mathematics I (For Arts Students)

permutations, combinations, binomial theorem, variables and graphs, frequency distributions, mean, median, mode and other measures of central tendency, standard deviation and other measures of dispersion, elementary probability theory.

Texts:

  [1] Vance, E. P. (1983), Modern Algebra and Trigonometry, Addison-Wesley.

(Chapter 11   Permutations, Combinations and the Binomial Theorem)

  [2]   Spiegel. M. R. (1961), Statistics, SOS, McGraw-Hill.

(Chapter 1    Variables and Graphs       Chapter 2  Frequency Distributions

Chapter 3    Mean, Median, Mode and Other Measures of Central Tendency

Chapter 4    The Standard Deviation   Chapter 6  Elementary probability theory)

 

SECOND SEMESTER

Math   1103   Algebra and Analytical Solid Geometry

Algebra: determinants, matrices, complex numbers.

Polar Coordinates System: polar coordinates, graphing in polar coordinates, areas and lengths in polar coordinates.

Analytical Solid Geometry: three dimensional Cartesian coordinate system, lines, planes, quadric surfaces.

Texts:

[1]    Kolman, B. (1988), Introductory Linear Algebra with Applications, Macmillan.

(Chapter 1       Linear Equations and Matrices

Chapter 2       Determinants)

 

[2]    Brown, J. W. and Churchill, R. V. (2009), Complex Variables and Applications, McGraw-Hill.

(Chapter 1       Complex Numbers)

 

[3] Thomas, G. B. (2009), Calculus, 12th Edition, Addison-Wesley.

(Chapter 11     Parametric Equations and Polar Coordinates

Section 11.3    Polar Coordinates

Section 11.4    Graphing in Polar Coordinates

Section 11.5    Areas and Lengths in Polar Coordinates

 

Chapter 12     Vectors and the Geometry of Space

Section 12.6    Cylinders and Quadric Surfaces)

 

[4]    Narayan, S. (1999), Analytical Solid Geometry, S. Chand.

(Chapter 1       Coordinates

Chapter 2         The Plane

Chapter 3        Right Line)

Math   1104   Differential and Integral Calculus

extreme values of functions, the mean value theorem, monotonic functions and the first derivatives test, methods of integration, improper integrals, applications of integration, partial differentiation, ordinary differential equation of first order.

Texts:

[1]   Thomas, G. B. (2009), Calculus, 12th Edition, Addison-Wesley.

(Chapter 4             Applications of derivatives

Section 4.1      Extreme Values of Functions

Section 4.2      The Mean Value Theorem

Section 4.3      Monotonic Functions and the First Derivatives Test

 

Chapter 5             Integration

 

Chapter 6             Applications of the definite integrals

Section 6.1      Volumes Using Cross-Sections

Section 6.2      Volumes Using Cylindrical Shells

Section 6.3      Arc Length

Section 6.4      Areas of Surfaces of Revolution

 

Chapter 8             Techniques of Integration

Section 8.1      Integration by Parts

Section            8.2      Trigonometric Integrals

Section 8.3      Trigonometric Substitutions

Section 8.4      Integration of Rational Functions by Partial Fractions

Section 8.7      Improper Integrals

 

Chapter 9             First-order differential equations

 

[2]       Thomas, G. B. (1977), Calculus and Analytic Geometry, 4th Edition, Addison-Wesley.

                  (Chapter 15           Partial Differentiation

Section 15.1, 15.2, 15.3

Chapter 20      Section 20.6

Math   1003   Mathematics II          (For Science Students)

Algebra: determinants, matrices, complex numbers;

Polar Coordinates System: polar coordinates, graphing in polar coordinates, areas and lengths in polar coordinates;

methods of integration, improper integrals, partial differentiation, ordinary differential equation of first order.

Texts:

[1]   Kolman, B. (1988), Introductory Linear Algebra with Applications, Macmillan.

(Chapter 1     Linear Equations and Matrices

Chapter 2       Determinants)

 

[2]   Brown, J. W. and Churchill, R. V. (2009), Complex Variables and Applications, McGraw-Hill.

(Chapter 1      Complex Numbers)

 

[3]   Thomas, G. B. (2009), Calculus, 12th Edition, Addison-Wesley.

(Chapter 5  Integration

 

Chapter 8  Techniques of Integration

Section 8.1      Integration by Parts

Section 8.2      Trigonometric Integrals

Section 8.4      Integration of Rational Functions by Partial Fractions

Section 8.7      Improper Integrals

 

Chapter 9       First-order differential equations

 

Chapter 11     Parametric Equations and Polar Coordinates

Section 11.3    Polar Coordinates

Section 11.4    Graphing in Polar Coordinates

Section 11.5    Areas and Lengths in Polar Coordinates)

[4]       Thomas, G. B. (1977), Calculus and Analytic Geometry, 4th Edition, Addison-Wesley.

                  (Chapter 15           Partial Differentiation

Section 15.1, 15.2, 15.3

Chapter 20   Section 20.6)

Math   1004   Mathematics II (For Arts Students)

inverse trigonometric functions and their derivatives, determinants, matrices, solving system of linear equations, lines, circles, conic sections.

Texts:

[1]    Kolman, B. (1988), Introductory Linear Algebra with Applications, Macmillan.

(Chapter 1         Linear Equations and Matrices

Chapter 2       Determinants)

 

[2]   Thomas, G. B. (2009), Calculus, 12th Edition, Addison-Wesley.

(Chapter 7       Transcendental Functions

Section 7.1      Inverse Functions and Their Derivatives

Section 7.6      Inverse Trigonometric Functions     [Except Integration]

 

[3]    Anton, H (1995), Calculus with Analytic Geometry, 5th Edition, John Wiley & Sons.
(Chapter 1       Coordinates, Graphs, Lines

Section 1.4 Lines

Section 1.5      Distances; Circles; Equations of the Form

 

Chapter 12    Topics in Analytic Geometry

Section 12.1    Introduction to the Conic Sections

Section 12.2    The Parabola; Translation of Coordinate Axes                                                                                 Section 12.3     The Ellipse

Section 12.4    The Hyperbola

Section 12.5    Rotation of Axes; Second-Degree Equations)

FIRST SEMESTER

Math 2101 Complex Variables I
analytic functions, elementary functions, integrals, residues and poles.
Text: Brown, J. W. and Churchill, R. V. (2009), Complex Variables and Applications,
8th edition, McGraw-Hill.
(Chapter 2 Analytic Functions
Chapter 3 Elementary Functions
Chapter 4 Integrals
` Chapter 6 Residues and Poles)

Math 2102 Calculus of Several Variables
Functions of two or more variables, partial derivatives, directional derivatives, chain rule for partial derivatives, total differential, maxima and minima, exact differentials, derivatives of integrals, double integrals in Cartesian coordinates and polar coordinates, triple integrals in cartesian coordinates, cylindrical coordinates and spherical coordinates, applications of multiple integrals.
Text: Thomas, G. B. (2009), Calculus, 12th Edition, Addison-Wesley.
(Chapter 14 Partial Derivatives
Chapter 15 Multiple Integrals)

Math 2103 Vector Algebra and Statics
Vector Algebra: dot products, cross products, triple scalar products, triple vector products.
Statics: statics of a particle, tension of a string, friction, moment and couples, centre of gravity, statics of a rigid body in a plane, jointed rods, virtual works, stability.
Texts: [1] Chorlton, L.(1967), Textbook of Fluid Dynamics, Van Nostrand.
(Chapter 1 Vector Analysis [Sections 1.1 to 1.7])
[2] Humphery, D. (1964), Statics, Longmans.
(Chapter 1 Statics of a Particle
Chapter 2 Statics of a Rigid Body–Parallel Forces–Monents–Couples
Chapter 3 Forces in a Plane Acting on a Rigid Body
Chapter 5 Friction
Chapter 7 Center of Gravity
Chapter 9 Virtual Work–Stability–Miscellaneous Examples)
Math 2104 Discrete Mathematics I
Counting Methods and the Pigeonhole Principle: basic principle, permutations and combinations, algorithms for generating permutations and combinations, generalized permutations and combinations, binomial coefficients and combinatorial identities, the pigeonhole principle.
Recurrence Relations: introduction, solving recurrence relations, applications to the analysis of algorithms.
Text: Johnsonbaugh, R. (1990), Discrete Mathematics, Macmillan.
(Chapter 4 Counting Methods and the Pigeonhole Principle
Chapter 5 Recurrence Relations)

Math 2105 Theory of Sets I
cardinal numbers, partially and totally ordered sets.
Text: Lipschutz, S. (1981), Set Theory and Related Topics, SOS, McGraw-Hill.
(Chapter 9 Cardinal Numbers
Chapter 10 Partially and Totally Ordered Sets)

Math 2106 Spherical Trigonometry and Its Applications
Spherical Trigonometry: the spherical triangle, length of small circle arc, terrestrial latitude and longitude, the fundamental formula of spherical trigonometry, the sine formula, formula C, the four parts formula, the trigonometrical ratios for small angles.
Celestial Sphere: altitude and azimuth, declination and hour angle, diagram for the southern hemisphere, circumpolar stars, the standard or geocentric celestial sphere, right ascension and declination, the earth’s orbit, celestial latitude and longitude, sidereal time, mean solar time, hour angle of a heavenly body, rising and setting, Twilight.
Text: Smart, W. M & Greene, R. (1986) , Text-Book on Spherical Astronomy, Cambridge University Press.
(Chapter 1 Spherical Trigonometry [Sections 1 to 8, 15]
Chapter 2 Celestial Sphere)
Math 2001 Mathematics I (For Science Students)
coordinates, the plane, partial derivatives, the chain rule for partial derivatives, the total differential, maxima and minima, double integrals, area by double integration, triple integrals Volume, the dot and cross product.

Statistics: a quick review on mean, median, mode and other measures of central tendency, standard deviation and other measures of dispersion.

Probability: introduction to probability, finite sample spaces, conditional probability and independence, one-dimensional random variables.

Texts:
[1] Narayan, S. (1999), Analytical Solid Geometry, S. Chand & Co., LTD.
(Chapter 1 Coordinates
Chapter 2 The Plane)

[2] Spiegel, M.R.(1963), Vector Analysis, SOS, McGraw-Hill.
(Chapter 2 The dot and cross product)
[3] Thomas, G. B. (2009), Calculus, 12th Edition, Addison-Wesley.
(Chapter 14 Partial Derivatives
Section 14.3 Partial Derivatives
Section 14.4 The Chain Rule
Section 14.6 Tangent Planes and Differentials
Section 14.7 Extreme Values and Saddle Points
Chapter 15 Multiple Integrals
Section 15.1 Double and Iterated Integrals over Rectangles
Section 15.3 Area by Double Integration
Section 15.5 Triple Integrals in Rectangular Coordinates

[4] Spiegel, M.R., (1961) Statistics, SOS, McGraw-Hill.
(Chapter 1 Variables and Graphs,
Chapter 2 Frequency Distributions
Chapter 3 Mean, Median, Mode and Other Measures of Central
Tendency
Chapter 4 The Standard deviation)

[5] Francis, A., (1979) Advanced Level Statistics, Stanley Thrones Ltd., London.
(Chapter 4 Probability [Sections: 4.3, 4.4]
Chapter 5 Random variables and Probability Distributions [Section: 5.3])
Math 2002 Mathematics I (For Arts Students)
methods of integration, binomial distribution, normal distribution, Poisson distribution, method of least square, regression.

Texts:
[1] Spiegel. M. R. (1961), Statistics, SOS, McGraw-Hill.
(Chapter 7 The Binomial, Normal and Poisson Distributions
Chapter 13 Curve Fitting and the Method of Least Squares)
[2] Thomas, G. B. (2009), Calculus, 12th Edition, Addison-Wesley.
(Chapter 5 Integration
Chapter 8 Techniques of Integration
Section 8.1 Integration by Parts
Section 8.4 Integration of Rational Functions by Partial Fractions

Math 2003 Mathematics I (For Industrial Chemistry Students)
three-dimensional cartesian coordinate system, lines, planes, quadric surfaces, partial derivatives, chain rule, total differentials, maxima and minima, multiple integrals.

Statistics: a quick review on mean, median, mode and other measures of central tendency, standard deviation and other measures of dispersion.

Probability: introduction to probability, finite sample spaces, conditional probability and independence, one-dimensional random variables.
Texts:
[1] Thomas, G. B. (2009), Calculus, 12th Edition, Addison-Wesley.
(Chapter 14 Partial Derivatives
Section 14.3 Partial Derivatives
Section 14.4 The Chain Rule
Section 14.6 Tangent Planes and Differentials
Section 14.7 Extreme Values and Saddle Points
Chapter 15 Multiple Integrals
Section 15.1 Double and Iterated Integrals over Rectangles
Section 15.3 Area by Double Integration
Section 15.5 Triple Integrals in Rectangular Coordinates

[2] Narayan, S., (1999), Analytical Solid Geometry, S. Chand.
(Chapter 1 Coordinates, Chapter 2 The Plane, Chapter 3 Right Line)

[3] Francis, A., (1979) Advanced Level Statistics ,Stanley Thornes Ltd., London.
(Chapter 4 Probability [Sections: 4.3, 4.4]
Chapter 5 Random variables and Probability Distributions [Section: 5.3])

[4] Spiegel, M.R., (1961) Statistics, SOS, McGraw-Hill.
(Chapter 1 Variables and Graphs,
Chapter 2 Frequency Distributions
Chapter 3 Mean, Median, Mode and Other Measures of Central Tendency
Chapter 4 The Standard deviation)
SECOND SEMESTER

Math 2107 Linear Algebra I
vector spaces, subspaces, bases and dimensions, sums and direct sums, linear mapping, kernel and image of linear map and their dimension, compositions of linear mapping.
Text: Lang, S. (2004), Linear Algebra, Third Edition, Springer.
(Chapter 1 Vector Spaces
Chapter 2 Matrices
Chapter 3 Linear Mappings)

Math 2108 Ordinary Differential Equations
second-order linear differential equations, higher-order linear differential equations, system of differential equations.
Text: Kreyszig, E (2011), Advanced Engineering Mathematics, Tenth Edition, John Wiley.
(Chapter 2 Second-Order Linear Differential Equations
Chapter 3 Higher-Order Linear Differential Equations
Chapter 4 System of Differential Equations. Phase Plane, Stability
[Sections 4.1, 4.2, 4.3, 4.6])

Math 2109 Vector Calculus and Dynamics
Vector Calculus: gradient, divergence, curl, line integrals, green’s theorem, divergence theorem, Stoke’s theorem.
Dynamics: kinematics of a particle, relative velocity, mass, momentum and force, Newton’s law of motion, work, power and energy, simple harmonic motions, kinematics of a particle in two dimensions, kinetic of a particle in two dimensions.
Texts: [1] Chorlton, L.(1967), Textbook of Fluid Dynamics, Van Nostrand.
(Chapter 1 Vector Analysis [Sections 1.8 to 1.19])
[2] Humphery, D. and Topping, J. (1964), Intermediate Mechanics, Vol I.
(Dynamics), Longmans.
(Chapter 1 Speed and velocity [Section: Relative velocity]
Chapter 3 Force, momentum, laws of motion
[Sections: mass, momentum, Newton’s law of motion]
Chapter 4 Work, power and energy
Chapter 8 Simple harmonic motions
Chapter 9 Motion of a particle in two dimensions)

Math 2110 Discrete Mathematics II
Graph Theory: introduction, paths and cycles, hamiltonian cycles and the traveling salesperson problem, a shortest path algorithm, representations of graphs, isomorphism of graphs, planar graphs.
Trees: introduction, terminology and characterizations of trees, Spanning trees, minimal spanning trees, binary trees.
Text: Johnsonbaugh, R. (1990), Discrete Mathematics, Macmillan.
(Chapter 6 Graph Theory, Chapter 7 Trees)

Math 2111 Theory of Sets II
well-ordered sets, ordinal numbers, axiom of choice, Zorn’s lemma, well-ordering theorem
Text: S. Lipschutz, (1981) Set Theory and Related Topics, SOS, McGraw-Hill.
(Chapter 11 Well-ordered sets. Ordinal Numbers
Chapter 12 Axiom of Choice, Zorn’s Lemma, Well-ordering Theorem)
Math 2112 Astronomy
Planetary Motions: Kepler’s three laws, Newton’s law of gravitation, the masses of the planets, the dynamical principles of orbital motion, the equation of the orbit, velocity of a planet in its orbit, components of the linear velocity perpendicular to radius vector and to the major axis, the true and eccentric anomaly expressed as a series in terms of e and the eccentric anomaly, the equation of the centre, the orbit in the space, the orbital and synodic periods of a planet, the earth’s orbit, the sun’s orbit, the moon’s orbit.
Time: sidereal time, the mean sun, the sidereal year and the tropical year, relation between mean and sidereal time, the calendar, the Julian date, the equation of time, the seasons.
Text: Smart, W. M. & Greene, R. (1986), Text-Book on Spherical Astronomy, Cambridge University Press.
(Chapter 5 Planetary Motions)

Math 2004 Mathematics II (For Science Students)
right line, second order linear differential equations, higher order linear differential equations, power series method, vector differentiation, gradient, divergence, curl.
Texts:
[1] Kreyszig, E (2011), Advanced Engineering Mathematics, Tenth Edition, John
Wiley.
(Chapter 2 Second-Order Linear Differential Equations
Chapter 3 Higher-Order Linear Differential Equations
Chapter 5 Series Solutions of ODEs)
[2] Narayhan, S. (1999), Analytical Solid Geometry, S. Chand & Co., Ltd.
(Chapter 3 Right Line)
[3] Spiegel, M.R.(1963), Vector Analysis, SOS, McGraw-Hill.
(Chapter 3 Vector Differentiation
Chapter 4 Gradient, Divergence, Curl)

Math 2005 Mathematics II (For Arts Students)
three-dimensional cartesian coordinate system, lines, planes, quadric surfaces, spherical trigonometry.
Texts: [1] Narayhan Math 2005 Mathematics II (For Arts Students)
three-dimensional cartesian coordinate system, lines, planes, quadric surfaces, spherical trigonometry.
Texts: [1] Narayhan, S. (1999), Analytical Solid Geometry, S. Chand & Co., Ltd.
(Chapter 1 Co-ordinates
Chapter 2 The Plane
Chapter 3 Right Line)

[2] Thomas, G. B. (2009), Calculus, 12th Edition, Addison-Wesley.
(Chapter 12 Vectors and the Geometry of Space
Section 12.6 Cylinders and Quadric Surfaces)

[3] Smart, W. M & Greene, R. (1986) Text-Book on Spherical Astronomy, Cambridge University Press.
(Chapter 1 Spherical Trigonometry [Sections 1 to 8, 15])
Math 2006 Mathematics II (For Industrial Chemistry Students)
dot products, cross products, triple scalar products, triple vector products, complex functions, complex integrals, higher order linear ordinary differential equations.
linear programming: general discussion, mathematical background, the general linear programming problem, the simplex computational procedure.

Texts:
[1] Spiegel, M.R.(1974), Vector Analysis, SOS, McGraw-Hill.
(Chapter 2)
[2] Brown, J. W. and Churchill, R. V. (2009), Complex Variables and Applications,
8th edition, McGraw-Hill.
(Chapter 2 Analytic Functions
Chapter 4 Integrals)
[3] Kreyszig, E (2011), Advanced Engineering Mathematics, Tenth Edition, John Wiley.
(Chapter 2 Second-Order Linear Differential Equations
Chapter 3 Higher-Order Linear Differential Equations)
[4] Gass, S.I., (1964) Linear Programming, Third Edition, McGraw-Hill.
(Chapter 1 General Discussion
Chapter 2 Mathematical Background
Chapter 3 The General Linear-programming Problem
Chapter 4 The Simplex Computational Procedure)

FIRST SEMESTER

Math 3101 Analysis I
elements of set theory, numerical sequences and series.
Text: Rudin, W. (1976), Principle of Mathematical Analysis, McGraw-Hill.
(Chapter 2 Basic Topology
Chapter 3 Numerical Sequences and Series)

Math 3102 Linear Algebra II
linear maps and matrices, determinants.
Text: Lang, S. (2004), Linear Algebra, Third Edition, Springer.
(Chapter 4 Linear Maps and Matrices
Chapter 6 Determinants)

Math 3103 Differential Equations
series solutions of differential equations, special functions, laplace transforms.
Text: Kreyszig, E (2011), Advanced Engineering Mathematics, Tenth Edition, John Wiley.
(Chapter 5 Series Solutions of ODEs. Special Functions
Chapter 6 Laplace Transforms)

Math 3104 Differential Geometry
concept of a curve, curvature and torsion, the theory of curves, concept of a surface.
Text: Lipschutz, M. M. (1969), Differential Geometry, SOS, McGraw-Hill.
(Chapter 3 Concept of a Curve
Chapter 4 Curvature and Torsion
Chapter 5 The Theory of Curves
Chapter 8 Concept of a Surface)

Math 3105 Tensor Analysis
curvilinear coordinates, tensor analysis
Text: Spiegel, M. R. (1974), Vector Analysis, SOS, McGraw-Hill.
(Chapter 7 Curvilinear Coordinates
Chapter 8 Tensor Analysis)

Math 3106 Number Theory I
divisibility theory, congruences, Fermat’s little theorem, Euler’s generalization of FLT, Wilson’s theorem, Eulers-function.
Text: Malik, S. B. (1995), Basic Number Theory. Vikas Publishing House PVT Ltd.
(Chapter 2 Divisibility Theory
Chapter 3 Congruences
Chapter 4 Some Special Congruences and Euler’s φ-Functions)
SECOND SEMESTER
Math 3107 Analysis II
continuity, differentiation
Text: Rudin, W. (1976), Principle of Mathematical Analysis, McGraw-Hill.
(Chapter 4 Continuity, Chapter 5 Differentiation)

Math 3108 Linear Algebra III
scalar products and orthogonality, matrices and bilinear maps.
Text: Lang, S. (2004), Linear Algebra, Third Edition, Springer.
(Chapter 5 Scalar Products and Orthogonality
Chapter 7 Symmetric, Hermitian and Unitary Operators)

Math 3109 Mechanics
Impulsive Forces, central force motion, kinematics of plane rigid bodies, kinetics of plane rigid bodies, impact, dynamics of a particle in three dimensions, dynamics of system of particles, moment of inertia, polar coordinates, orbits.
Texts: [1] Humphery, D. and Topping, J. (1964), Intermediate Mechanics, Vol I.
(Dynamics), Longmans.
(Chapter 5 Impulsive Forces
Chapter 10 Dynamics of a rigid body)
[2] Ramsey, A.S., (2009) Dynamics, Digitally printed version 2009, Cambridge
University. (Chapter 12 Polar Coordinates. Orbits )

Math 3110 Probability and Statistics
introduction to probability theory, random variables, mean, median, mode, standard deviation, correlation, regression.
Texts: [1] Ross. S. M. (2010), Introduction to Probability Models, Tenth Edition,
Elsevier.
(Chapter 1 Introduction to Probability Theory,
Chapter 2 Random Variables)
[2] Spiegel. M. R. (1961), Statistics, SOS, McGraw-Hill.
(Chapter 3 Mean. Median. Mode
Chapter 4 The Standard Deviation, Chapter 14 Correlation Theory)

Math 3111 Complex Variables II
conformal mapping, application of conformal mapping.
Text: Brown, J. W. and Churchill, R. V. (2009), Complex Variables and Applications,
8th edition, McGraw-Hill.
(Chapter 9 Conformal Mapping, Chapter 10 Application of Conformal Mapping)

Math 3112 Number Theory II
primitive roots, quadratic congruence and quadratic reciprocity law, perfect numbers and Fermat’s numbers, representation of integers as sum of squares.
Text: Malik, S. B.(1995), Basic Number Theory. Vikas Publishing House PVT Ltd.
(Chapter 6 Primitive Roots
Chapter 7 Quadratic Congruences and Quadratic Reciprocity Law
Chapter 8 Perfect Numbers and Fermat’s Numbers
Chapter 10 Representation of Integers as Sum of Squares)

FIRST SEMESTER

Math 4101 Analysis III
methods of mathematical research, the Riemann-Stieltjes integral.
Text: [Zaw Win (2011), Some Strategies of Mathematical Research, Math
Department, Yangon University.]
Rudin, W., (1976), Principle of Mathematical Analysis, McGraw-Hill.
(Chapter 6 The Riemann-Stieltjes Integral )

Math 4102 Numerical Analysis I
numerical methods in general, numerical methods in linear algebra.
Text: Kreyszig, E (2011), Advanced Engineering Mathematics, Tenth Edition, John Wiley.
(Chapter 19 Numerics in General
Chapter 20 Numeric Linear Algebra
[Sections 20.1, 20.2, 20.3, 20.4])
Math 4103 Linear Programming
basic properties of linear programs, the simplex method, duality, dual simplex method and primal dual algorithms,
Text: Luenberger, D. G.(1971), Linear and Nonlinear Programming,
Addison-Wesley.
(Chapter 2 Basic Properties of Linear Programs
Chapter 3 The Simplex Method
Chapter 4 Duality)

Math 4104 Partial Differential Equations
fourier series, integrals, and transforms, partial differential equations.
Text: Kreyszig, E (2011), Advanced Engineering Mathematics, Tenth Edition, John Wiley.
(Chapter 11 Fourier Analysis
Chapter 12 Partial Differential Equations)

Math 4105 Stochastic Process I
conditional probability and conditional expectation, Markov chains .
Text: Ross. S. M. (2010), Introduction to Probability Models, Tenth Edition,
Elsevier.
(Chapter 3 Conditional Probability and Conditional Expectation
Chapter 4 Markov Chains [Sections 4.1 to 4.4])

Math 4106 Fundamentals of Algorithms and Computer Programming
the idea of an algorithm, pseudo code descriptions of algorithms, efficiency of algorithms, algorithms for arithmetic and algebra, coding and implementations of algorithms in some programming languages
Text: Grossman J.W, (1990), Discrete Mathematics, Macmillan.
(Chapter 4 Algorithms)
SECOND SEMESTER
Math 4107 Analysis IV
sequences and series of functions
Text: Rudin, W. (1976), Principle of Mathematical Analysis. McGraw-Hill.
(Chapter 7 Sequences and Series of Functions)

Math 4108 General Topology I
topology of the line and plane, topological spaces, bases and subbases.
Text: Lipschutz. S. (1965), Theory and Problems of General Topology, SOS,
McGraw-Hill.
(Chapter 4 Topology of the Line and Plane
Chapter 5 Topological Spaces, Chapter 6 Bases and Subbases)

Math 4109 Abstract Algebra I
semigroups, monoids and groups, homomorphisms and subgroups, cyclic groups, cosets and counting, normality, quotient groups, and homomorphisms.
Text: Herstein, I.N. (1996), Abstract Algebra (3rd Edition). Prentice-Hall.
(Chapter 2 Groups [Sections 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7])

Math 4110 Hydromechanics
density and specific gravity, theorems on fluid-pressure under gravity, pressure of heavy fluids, thrusts on curved surfaces and floating bodies, stability of floating bodies, equation of continuity, equation of motion, some three dimensional flows.
Texts: [1] Chorlton, F. (1967), Textbook of Fluid Dynamics, Van Nostrand.
(Chapter 2 Kinematics of Fluids in Motion
Chapter 3 Equations of Motion of a Fluid
Chapter 4 Three Dimensional Flows Sections 4.1 to 4.4)
[2] Ray, M. and Sharma, H.S. (1961), A Text Book of Hydrostatics, Premier
Publishing.
(Chapter 2 Density and Specific Gravity
Chapter 3 Theorems on Fluid-Pressure under Gravity
Chapter 4 Pressures on Plane Surfaces
Chapter 5 Center of Pressure
Chapter 6 Thrusts on Curved Surfaces
Chapter 7 Floating Bodies
Chapter 9 Stability of Floating Bodies)

Math 4111 Stochastic Process II
Markov chains, the exponential distribution and the Poisson process.
Text: Ross. S. M. (2010), Introduction to Probability Models, Tenth Edition,
Elsevier.
(Chapter 4 Markov Chains [Sections 4.5 to 4.11]
Chapter 5 The Exponential Distribution and the Poisson Process)

Math 4112 Integer Programming
formulations of integer programming, branch and bound algorithms, cutting plane methods.
Texts: [1] Bronson, R. (1983), Theory and Problems of Operations
Research, SOS, McGraw-Hill.
[2] Wolsey, L. (1998), Integer Programming, John Wiley.
(Chapter 1 Formulations)

FIRST SEMESTER

Math 3201 Analysis I
elements of set theory, numerical sequences and series.
Text: Rudin, W. (1976), Principle of Mathematical Analysis, McGraw-Hill.
(Chapter 2 Basic Topology
Chapter 3 Numerical Sequences and Series)

Math 3202 Linear Algebra II
linear maps and matrices, determinants.
Text: Lang, S. (2004), Linear Algebra, Third Edition, Springer.
(Chapter 4 Linear Maps and Matrices
Chapter 6 Determinants)

Math 3203 Differential Equations
series solutions of differential equations, special functions, laplace transforms.
Text: Kreyszig, E (2011), Advanced Engineering Mathematics, Tenth Edition, John Wiley.
(Chapter 5 Series Solutions of ODEs. Special Functions
Chapter 6 Laplace Transforms)

Math 3204 Differential Geometry
concept of a curve, curvature and torsion, the theory of curves, concept of a surface.
Text: Lipschutz, M. M. (1969), Differential Geometry, SOS, McGraw-Hill.
(Chapter 3 Concept of a Curve
Chapter 4 Curvature and Torsion
Chapter 5 The Theory of Curves
Chapter 8 Concept of a Surface)

Math 3205 Tensor Analysis
curvilinear coordinates, tensor analysis
Text: Spiegel, M. R. (1974), Vector Analysis, SOS, McGraw-Hill.
(Chapter 7 Curvilinear Coordinates
Chapter 8 Tensor Analysis)

Math 3206 Number Theory I
divisibility theory, congruences, Fermat’s little theorem, Euler’s generalization of FLT, Wilson’s theorem, Eulers-function.
Text: Malik, S. B. (1995), Basic Number Theory. Vikas Publishing House PVT Ltd.
(Chapter 2 Divisibility Theory
Chapter 3 Congruences
Chapter 4 Some Special Congruences and Euler’s φ-Functions)
SECOND SEMESTER

Math 3207 Analysis II
continuity, differentiation
Text: Rudin, W. (1976), Principle of Mathematical Analysis. McGraw-Hill.
(Chapter 4 Continuity, Chapter 5 Differentiation)

Math 3208 Linear Algebra III
scalar products and orthogonality, matrices and bilinear maps.
Text: Lang, S. (2004), Linear Algebra, Third Edition, Springer.
(Chapter 5 Scalar Products and Orthogonality
Chapter 7 Symmetric, Hermitian and Unitary Operators)

Math 3209 Mechanics
Impulsive Forces, central force motion, kinematics of plane rigid bodies, kinetics of plane rigid bodies, impact, dynamics of a particle in three dimensions, dynamics of system of particles, moment of inertia, polar coordinates, orbits.
Texts: [1] Humphery, D. and Topping, J. (1964), Intermediate Mechanics, Vol I.
(Dynamics), Longmans.
(Chapter 5 Impulsive Forces
Chapter 10 Dynamics of a rigid body)
[2] Ramsey, A.S., (2009) Dynamics, Digitally printed version 2009, Cambridge
University. (Chapter 12 Polar Coordinates. Orbits )

Math 3210 Probability and Statistics
introduction to probability theory, random variables, mean, median, mode, standard deviation, correlation, regression.
Texts: [1] Ross. S. M. (2010), Introduction to Probability Models, Tenth Edition,
Elsevier.
(Chapter 1 Introduction to Probability Theory,
Chapter 2 Random Variables)
[2] Spiegel. M. R. (1961), Statistics, SOS, McGraw-Hill.
(Chapter 3 Mean. Median. Mode
Chapter 4 The Standard Deviation, Chapter 14 Correlation Theory)

Math 3211 Complex Variables II
conformal mapping, application of conformal mapping.
Text: Brown, J. W. and Churchill, R. V. (2009), Complex Variables and Applications,
8th edition, McGraw-Hill.
(Chapter 9 Conformal Mapping, Chapter 10 Application of Conformal Mapping)

Math 3212 Number Theory II
primitive roots, quadratic congruence and quadratic reciprocity law, perfect numbers and Fermat’s numbers, representation of integers as sum of squares.
Text: Malik, S. B.(1995), Basic Number Theory. Vikas Publishing House PVT Ltd.
(Chapter 6 Primitive Roots
Chapter 7 Quadratic Congruences and Quadratic Reciprocity Law
Chapter 8 Perfect Numbers and Fermat’s Numbers
Chapter 10 Representation of Integers as Sum of Squares)

FIRST SEMESTER

Math 4201 Analysis III
methods of mathematical research, the Riemann-Stieltjes integral.
Text: [Zaw Win (2011), Some Strategies of Mathematical Research, Math
Department, Yangon University.]
Rudin, W., (1976), Principle of Mathematical Analysis, McGraw-Hill.
(Chapter 6 The Riemann-Stieltjes Integral )

Math 4202 Numerical Analysis I
numerical methods in general, numerical methods in linear algebra.
Text: Kreyszig, E (2011), Advanced Engineering Mathematics, Tenth Edition, John Wiley.
(Chapter 19 Numerics in General
Chapter 20 Numeric Linear Algebra
[Sections 20.1, 20.2, 20.3, 20.4])
Math 4203 Linear Programming
basic properties of linear programs, the simplex method, duality, dual simplex method and primal dual algorithms,
Text: Luenberger, D. G.(1971), Linear and Nonlinear Programming,
Addison-Wesley.
(Chapter 2 Basic Properties of Linear Programs
Chapter 3 The Simplex Method
Chapter 4 Duality)

Math 4204 Partial Differential Equations
fourier series, integrals, and transforms, partial differential equations.
Text: Kreyszig, E (2011), Advanced Engineering Mathematics, Tenth Edition, John Wiley.
(Chapter 11 Fourier Analysis
Chapter 12 Partial Differential Equations)

Math 4205 Stochastic Process I
conditional probability and conditional expectation, Markov chains .
Text: Ross. S. M. (2010), Introduction to Probability Models, Tenth Edition,
Elsevier.
(Chapter 3 Conditional Probability and Conditional Expectation
Chapter 4 Markov Chains [Sections 4.1 to 4.4])

Math 4206 Fundamentals of Algorithms and Computer Programming
the idea of an algorithm, pseudo code descriptions of algorithms, efficiency of algorithms, algorithms for arithmetic and algebra, coding and implementations of algorithms in some programming languages
Text: Grossman J.W, (1990), Discrete Mathematics, Macmillan.
(Chapter 4 Algorithms)
SECOND SEMESTER
Math 4207 Analysis IV
sequences and series of functions
Text: Rudin, W. (1976), Principle of Mathematical Analysis, McGraw-Hill.
(Chapter 7 Sequences and Series of Functions)

Math 4208 General Topology I
topology of the line and plane, topological spaces, bases and subbases.
Text: Lipschutz. S. (1965), Theory and Problems of General Topology, SOS,
McGraw-Hill
(Chapter 4 Topology of the Line and Plane
Chapter 5 Topological Spaces, Chapter 6 Bases and Subbases)

Math 4209 Abstract Algebra I
semigroups, monoids and groups, homomorphisms and subgroups, cyclic groups, cosets and counting, normality, quotient groups, and homomorphisms.
Text: Herstein, I.N. (1996), Abstract Algebra (3rd Edition). Prentice-Hall.
(Chapter 2 Groups [Sections 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7])

Math 4210 Hydromechanics
density and specific gravity, theorems on fluid-pressure under gravity, pressure of heavy fluids, thrusts on curved surfaces and floating bodies, stability of floating bodies, equation of continuity, equation of motion, some three dimensional flows.
Texts: [1] Chorlton, F. (1967), Textbook of Fluid Dynamics, Van Nostrand.
(Chapter 2 Kinematics of Fluids in Motion
Chapter 3 Equations of Motion of a Fluid
Chapter 4 Three Dimensional Flows Sections 4.1 to 4.4)
[2] Ray, M. and Sharma, H.S. (1961), A Text Book of Hydrostatics, Premier
Publishing.
(Chapter 2 Density and Specific Gravity
Chapter 3 Theorems on Fluid-Pressure under Gravity
Chapter 4 Pressures on Plane Surfaces
Chapter 5 Center of Pressure
Chapter 6 Thrusts on Curved Surfaces
Chapter 7 Floating Bodies
Chapter 9 Stability of Floating Bodies)

Math 4211 Stochastic Process II
Markov chains, the exponential distribution and the Poisson process.
Text: Ross. S. M. (2010), Introduction to Probability Models, Tenth Edition,
Elsevier.
(Chapter 4 Markov Chains [Sections 4.5 to 4.11]
Chapter 5 The Exponential Distribution and the Poisson Process)

Math 4212 Integer Programming
formulations of integer programming, branch and bound algorithms, cutting plane methods.
Texts: [1] Bronson, R. (1983), Theory and Problems of Operations
Research, SOS, McGraw-Hill.
[2] Wolsey, L. (1998), Integer Programming, John Wiley.
(Chapter 1 Formulations)

FIRST SEMESTER

Math 5201 Analysis V
power series, the exponential and logarithmic functions, the trigonometric functions,
fourier series
Text: Rudin, W. (1976), Principle of Mathematical Analysis. McGraw-Hill.
(Chapter Some Special Functions)

Math 5202 General Topology II
continuity and topological equivalence, metric and normed spaces
Text: Lipschutz, S. (1965), Theory and Problems of General Topology, SOS.
(Chapter 7 Continuity and Topological Equivalence
Chapter 8 Metric and Normed Spaces)

Math 5203 Abstract Algebra II
symmetric, alternating, and dihedral groups, categories, products, coproducts, and free objects, direct products and direct sums, free groups, free products, generators and relations.
Text: Herstein, I.N. (1996), Abstract Algebra (3rd Edition). Prentice-Hall.
(Chapter 2 Groups [Sections 2.8, 2.9, 2.10, 2.11]
Chapter 3 The Symmetric Groups [Sections 3.1, 3.2, 3.3])

Math 5204 Hydrodynamics I
axisymmetric flow, Stoke’s stream function, some two-dimensional flows, general motion of cylinder
Text: Chorlton, F. (1967), Textbook of Fluid Dynamics, Van Nostrand.
(Chapter 4 Three Dimensional Flows [Section 4.5]
Chapter 5 Some Two-Dimensional Flows)

Math 5205 Numerical Analysis II
numerical methods in linear algebra, numerical methods for differential equations.
Text: Kreyszig, E (2011), Advanced Engineering Mathematics, Tenth Edition, John Wiley.
(Chapter 20 Numeric in Linear Algebra
[Sections 20.5, 20.6, 20.7, 20.8, 20.9]
Chapter 21 Numerics for ODEs and PDEs)

Math 5206 Qualitative Theory of Ordinary Differential Equations I
systems of differential equations, linear systems with an introduction to phase space analysis.
Text: Brauer.F.and Nohel, J. A.(1969), The Qualitative Theory of Ordinary Differential
Equations: An Introduction, W. A. Benjamin, Inc.
(Chapter 1 System of Differential Equations
Chapter 2 Linear Systems with an Introduction to Phase Space Analysis)
SECOND SEMESTER

Math 5207 Analysis VI
continuous transformations of metric spaces, euclidean spaces, continuous functions of several real variables, partial derivatives, linear transformations and determinants, the inverse function theorem, the implicit function theorem, functional dependence.
Text: Rudin, W. (1974), Principle of Mathematical Analysis, McGraw-Hill.
(Chapter 9 Functions of Several Variables)

Math 5208 General Topology III
separation axioms, compactness, concept of product topology and examples.
Text: Lipschutz. S. (1965), Theory and Problems of General Topology, SOS,
McGraw-Hill.
(Chapter 10 Separation Axioms
Chapter 11 Compactness
Chapter 12 Product Spaces Section: Product topology)

Math 5209 Abstract Algebra III
free abelian groups, finitely generated abelian groups, the Krull-Schmidt theorem, the action of a group on a set, the Sylow theorems.
Text: Herstein, I.N. (1996), Abstract Algebra (3rd Edition). Prentice-Hall.
(Chapter 3 Ring Theory [Sections 4.1, 4.2, 4.3, 4.4])

Math 5210 Hydrodynamics II
two-dimensional vortex motion, water waves
Texts: [1] Acheson, D. J. (1990), Elementary Fluid Dynamics, Oxford University
Press.
[2] O’Neill, M. E., Chorlton, F. (1986), Ideal and Incompressible Fluid Dynamics, Ellis, Harwood Ltd.
(Chapter 8)

Math 5211 Graph Theory
graphs and subgraphs, trees
Text: Bondy, J. A., and Murtyh, U. S. R (1984), Graph Theory with Applications,
Springer- Verlag.
(Chapter 1 Graphs and Subgraphs
Chapter 2 Trees)

Math 5212 Qualitative Theory of Ordinary Differential Equations II
existence theory, stability of linear and almost linear systems
Text: Brauer. F. and Nohel, J. A. (1969), The Qualitative Theory of Ordinary
Differential Equations: An Introduction, W. A. Benjamin, Inc.
(Chapter 3 Existence Theory
Chapter 4 Stability of Linear and Almost Linear Systems)

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