Upcoming coursework

• Module theory: Jan-March 2026 (tentative)

(Associated with Hochschild homology)

• Differential geometry: May-July 2026 (tba)

(Associated with differential manifolds)

Ongoing coursework

General topology

Oct - Dec 2025

Course instructor: Sreykeopichmesa KIM

Course advisor: Vanny DOEM

Nature of lecture:

• Aim at understanding the basic topology and realizing its connection with advanced topology 

• Online mode, every Sunday, 8:00 - 9:30 pm CST

• Google meeting: Click here

Schedule & Syllabuses: 

Date 12.10_L01: Metric & topological spaces

Date 19.10_L02: Continuity I

Date 26.10_L03: Continuity II

Date 02.11_L04: Bases & subspaces

Date 09.11_L05: Closed sets & limit points

Date 16.11_L06: New spaces from old

Date 23.11_L07: Compactness I

Date 30.11_L08: Compactness II

Date 07.12_L09: Connectedness I

Date 14.12_L10: Connectedness II

Date 21.12_L11: Algebraic topology I

Date 28.12_L12: Algebraic topology II

References

• Armstrong. Basic topology. Springer, 1983

• Munkres. Topology. 2nd ed., Prentice Hall, 2000

• Hatcher. Algebraic topology. Cambridge uni., 2002

All lecture notes: tba

Annual courses from 2020-2024

First Semester (March - July)

Calculus I + II

Lecturer: Monyrattanak SENG

TA: Kimsan CHEA

REF:

• Real Number system [PDF]

• James Stewart. Calculus: Early Transcendentals. Eighth edition, Cengage Learning, 2012
• Michael Spivak. Calculus. Fourth edition, Publish or Perish, Inc., 2008

Linear Algebra

Lecturer: Vanny D.

TA: Makara THA

REF:

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

• Textbook: Third edition
  This textbook has its 4th edition, but we prefer the 3rd edition since it is more readable and gives students chances to work on examples on their own. 

• Video lecture series: Sheldon Axler
  One should see his lectures before each class happens. 

• Assignments: See them in the following Document
  Each set of problems will be divided into groups. 

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

• Textbook: Fourth edition

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

1. The first week is for the theoretical framework: the lecturer will describe the broader lens through the researcher's views of the topic and guide students to the (more or less) overall understanding and approach in each context. 
2. The second week is for the proof presentation: each student will have to do a presentation that includes the proofs of some important lemmas, theorems, corollaries, propositions, or examples. 
3. The third week is for the tutorial: each group of students will have to solve a certain set of problems and this will be guided by a TA.  

Documents:

• Assignments: Ch 01 - Ch 02 - Ch 03 - Ch 04 - Ch 05 - Ch 06 - Ch 07

• Edited textbook: Sheldon Axler

• Slide presentations: Slide 01 -

• Summary: (separated site) - list all useful concepts/ questions in LA

Assignments

• Ch 01: 1, 2, 9, 10, 20, 25, 27, 28 - 3, 4, 7, 8, 15, 16, 21, 22 - 5, 6, 11, 12, 23, 24, 31, 32 - 13, 14, 17, 18, 19, 26, 29, 30

• Ch 02: 1, 2, 3, 4, 5, 6, 15, 16, 42, 45, 59, 60 - 20, 21, 22, 8, 9, 17, 18, 46, 48 - 23, 24, 33, 34, 11, 12, 25, 27, 28, 51, 52, 53 - 35, 36, 37, 38, 13, 14, 32, 39, 40, 55, 56, 57

• Ch 03:
  Theoretical Part I: 5, 6, 7, 8 - 9, 12, 15, 16, 17 - 10, 11, 18, 19 - 1, 2, 3, 4, 21, 22
  Computational Part I: 1, 5, 6, 14, 15, 44, 47, 58 - 3, 14, 15, 39, 51, 52 - 4, 11, 24, 28, 29, 30, 31, 50 - 7, 13, 19, 48, 57
  Theoretical Part II: 1, 2, 3, 4 - 5, 7, 8 - 9, 10, 11, 12 - 15, 16

• Ch 04: All problems

• Ch 05: 1, 2, 3, 4, 15, 16, 18, 19, 26, 27, 33, 36, 38, 39 (All of them belong to the Computational Part only)

• Ch 06: 1, 2, 3, 4, 5, 14, 15, 16, 17, 18, 20, 22, 23, 24, 25, 26, 29, 37 (All of them belong to the Computational Part only)

• Ch 07: 1, 3, 4, 7, 10, 12, 19, 25, 29, 34, 35 (All of them belong to the Computational Part only)

Note: The assignment is expected to be submitted within two weeks, by June 15. Submit your assigned work in a PDF form to: mac.kh.cam@gmail.com 

Presentation

• Ch 06: Inner Product Spaces
  Sina - Kimsin

• Ch 07: Operators on Inner Product Spaces
  Vattanak - Seaver

• Ch 08: Operators on Complex Vector Spaces
  Rachnyt - Nalin - Kealay

• Ch 09: Operators on Real Vector Spaces
  Mesa - Rachana - Kunthea

• Ch 10: Trace and Determinant
  Kay - Pheany - Chantong

Nature of our talks:

• All talks are in latex slides

• Each talk is expected to finish within 30 minutes

• Cover all important parts of the chapter

• Try to include proofs of some main results

Note: All these chapters follow our main reference, a textbook by Sheldon Axler. We plan to do it on August 01 - 02, 2024. Prepare well for it. 

Second Semester (August - December)

Real Analysis

Lecturer: Monyrattanak SENG

TA: Kimsan CHEA

REF:

• Canuto & Tabacco. Mathematical analysis I. Second edition, Springer, 2015. 

• Thomson & Bruckners. Elementary real analysis. Prentice-Hall, Inc., 2001. 

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

Abstract Algebra

Lecturer: Vanny D.

TA: Makara THA

REF:

• Dummit-Foote, Abstract algebra. Third edition, John Wiley & Sons, 2004.
• Thomas Hungerford. Algebra. First edition, Springer, 1974.
• Joseph Gallian. Contemporary abstract algebra. Ninth edition, Cengage Learning, 2017.

• Textbook: Dummit-Foote - AA

• Lecture notes

Group theory (GT)
L01: Groups

L02: Subgroups

L03: Isomorphisms

L04: Stabilizers, Normalizers, Centralizers

L05: Quotient groups

L06: Lagrange's theorem

L07: Isomorphism theorems

L08: Group actions & Sylow's theorem

Ring theory (RT)
L09: Rings and examples

L10: Quotient rings

L11: Ideals 

L12: ED, PID, UFD

L13: Polynomial rings

L14: Irreducibility criteria

Assignments

Group and Ring Theory (to be submitted by December 31, 2024)

• Field extensions

• Algebraic extensions

• Splitting fields and algebraic closures

• Separable and inseparable extensions

Rules & Regulations:

• Missed three classes consecutively without permission will be removed. 

• Each has to be responsible for their homework, no exception. 

• Respect and follow the guidance of the lecturer and TA.

• Always be prepared for the coming classes. 

• Always be punctual and if late, drop a permission message in the learning group.