Monyrattanak SENG, PhD

General Topology - 3 Lectures

• Preliminaries: Functions, relations, axiom of choice, Euclidean spaces

• Topological Spaces: Topological spaces, the basis for a topology, creating new topological spaces

• Continuity: Continuous functions, homeomorphisms

• Connectedness:  Connected spaces, components & local connectedness, path connected, the intermediate value theorem

• Compactness: Compact spaces, limit point compactness, one-point compactification, local compactness, the extreme value theorem

References

1. James Munkres, Topology. Second edition, McGraw-Hill, 2000.

2. Mark Armstrong. Basic topology. First edition, Springer, 1983.

3. Colin Adams - Robert Franzosa. Introduction to topology: pure and applied. First edition, Pearson, 2008.

Veasna KIM, PhD

Real Analysis - 4 Lectures

• Real Number Systems: Real number system, algebraic structure, ordered structure, the real field

• Sequences & Series: Convergent sequences, subsequences, Cauchy sequences, upper and lower limits, series, the root and ratio tests, power series

• Continuity: Limits, properties of limits, limit superior & inferior, continuity, uniform continuity

• Differentiation: Derivatives, properties of derivatives, Mean Value theorem, the continuity of derivatives, derivatives of higher order, Taylor's theorem

• Integration: Cauchy's methods, properties of integral, the Riemann integral, properties of Riemann integral, the improper Riemann integral

References

1. Thomson - Bruckners. Elementary real analysis. Prentice-Hall, 2001.

2. Stephen Abbott. Understanding analysis. Second edition, Springer, 2015.

3. Walter Rudin. Principles of mathematical analysis. McGraw-Hill, 1976. 

Sothea HAS, PhD

Linear Algebra - 3 Lectures

• Vector Spaces: Vector spaces, subspaces, span, linear independence, bases, dimension, real-world examples

• Linear Transformations: Linear maps, null spaces & ranges, the Fundamental Theorem of linear maps, invertibility, isomorphisms, its applications in data science

• Determinants: Determinant of an operator, determinant of a matrix, its applications in data science

• Diagonalization: Eigenvalues, eigenvectors, diagonalizability, its applications in data science

References

1. Sheldon Axler. Linear Algebra - Done Right. Third edition, Springer, 2015.

2. Friedberg, Insel, Spence. Linear Algebra. Fourth edition, Person, 2003.

3. Serge Lang. Linear Algebra. Third edition, Springer, 1987.

Schedules

Day 01 - Nov. 09

Morning sessions

L00: 07:20 - 07:30 am - Introduction

L01: 07:30 - 09:00 am - VK

L02: 09:15 - 10:45 am - MS

L03: 11:00 - 12:00 pm - SH

[Lunch time: 12: 15 pm]

Afternoon sessions

L04: 01:00 - 02:30 pm - VK

L05: 02:45 - 04:15 pm - MS

L06: 04:30 - 05:30 pm - SH

[Dinner time: 5: 45 pm]

Day 02 - Nov. 10

Morning sessions

L01: 07:30 - 09:00 am - VK

L02: 09:15 - 10:45 am - VK

L03: 11:00 - 12:00 pm - SH

[Lunch time: 12: 15 pm]

Afternoon sessions

L04: 01:00 - 02:30 pm - MS

NL01: 02:45 - 04:15 pm - Talk show

NL02: 05:00 - 06:30 pm - Boat tour+Special dinner

Notation

MS = Monyrattanak SENG - VK = Veasna KIM - SH = Sothea HAS

L = Lecture - NL = Non Lecture