Current Students
Mathematics (M.Sc. & Ph.D.)
Master Program
Master of Science Program in Mathematics (M.Sc.)
Plan A : Coursework and Thesis
| Plan | Total credits required |
|---|---|
| Plan A(1) | 42 credits |
| Plan A(2) | 42 credits |
Study Duration 2 years
| Curriculum Structure | Plan A(1) | Plan A(2) |
|---|---|---|
| Total Credit Units throughout the Program Not less than | 42 | 42 |
| Number of Credit Units for Courses | – | 24 |
| – Compulsory Courses | – | – |
| – Compulsory Elective Courses | – | 9 |
| – Elective Courses | – | 15 |
| Number of Thesis Credit Units | 42 | 18 |
Note: Students enrolled in Plan A, Plan A(1), if deemed to have insufficient knowledge foundation, the curriculum management committee may require them to take additional courses or participate in other academic activities without credit counting.
| Plan A(1) | ||
| 1) Compulsory course (Students are required to enroll in the following courses without credit and with S/U grading.) | ||
| 2301560 | Computer Tools in Mathematics | 2(1-2-5) |
| 2301698 | Comprehensive Examination in Mathematics | 0(0-0-0) |
| 2301701 | Seminar | 1(1-0-3) |
| 2301704 | Research in Mathematics I | 3(3-0-9) |
| 2301705 | Research in Mathematics II | 3(3-0-9) |
| 2) Dissertation | ||
| 2301817 | Thesis | 42 credit |
| Plan A(2) | ||
| 1) Compulsory course (Students are required to enroll in the following courses without credit and with S/U grading.) | ||
| 2301560 | Computer Tools in Mathematics | 2(1-2-5) |
| 2301701 | Seminar | 1(1-0-3) |
| 2301704 | Research in Mathematics I | 3(3-0-9) |
| 2) Required elective course | 9 credit | |
| You must choose at least 2 subject groups from the following groups. | ||
| Algebra Group | ||
| 2301610 | Linear and Multilinear Algebra | 3(3-0-9) |
| 2301613 | Abstract Algebra I | 3(3-0-9) |
| 2301614 | Abstract Algebra II | 3(3-0-9) |
| Analysis Group | ||
| 2301620 | Mathematical Analysis | 3(3-0-9) |
| 2301621 | Real Analysis I | 3(3-0-9) |
| 2301622 | Real Analysis II | 3(3-0-9) |
| 2301623 | Complex Analysis | 3(3-0-9) |
| Topology and Geometry Group | ||
| 2301631 | Topology | 3(3-0-9) |
| 2301632 | Algebraic Topology | 3(3-0-9) |
| 2301635 | Differentiable Manifold | 3(3-0-9) |
| Applied Mathematics Group | ||
| 2301640 | Fundamentals of Mathematical Programming | 3(3-0-9) |
| 2301641 | Methods of Applied Mathematics I | 3(3-0-9) |
| 2301650 | Partial Differential Equations I | 3(3-0-9) |
| 2301653 | Numerical Analysis I | 3(3-0-9) |
| 2301676 | Stochastic Models | 3(3-0-9) |
| 3) Elective courses | 15 credit | |
| Please select from the list of courses below. | ||
| 2301601 | Recursion Theory | 3(3-0-9) |
| 2301602 | Model Theory | 3(3-0-9) |
| 2301603 | Set Theory | 3(3-0-9) |
| 2301608 | Mathematical Foundations of Cryptography | 3(3-0-9) |
| 2301609 | Analytic Number Theory I | 3(3-0-9) |
| 2301612 | Representation Theory I | 3(3-0-9) |
| 2301616 | Algebraic Semigroup Theory | 3(3-0-9) |
| 2301617 | Lie Algebras I | 3(3-0-9) |
| 2301618 | Combinatorial Theory | 3(3-0-9) |
| 2301619 | Algebraic Number Theory I | 3(3-0-9) |
| 2301629 | Functional Analysis | 3(3-0-9) |
| 2301634 | Convex and Discrete Geometry | 3(3-0-9) |
| 2301646 | Nonlinear Programming Theory | 3(3-0-9) |
| 2301649 | Combinatorial Design Theory | 3(3-0-9) |
| 2301661 | Probability Theory | 3(3-0-9) |
| 2301665 | Mathematical Statistics | 3(3-0-9) |
| 2301670 | Graph Theory and Applications | 3(3-0-9) |
| 2301690 | Special Topics in Advanced Mathematics | 3(3-0-9) |
| 2301691 | Special Topics in Algebra | 3(3-0-9) |
| 2301692 | Special Topics in Analysis | 3(3-0-9) |
| 2301693 | Special Topics in Geometry | 3(3-0-9) |
| 2301694 | Special Topics in Applied Mathematics | 3(3-0-9) |
| 2301711 | Algebraic Geometry | 3(3-0-9) |
| 2301717 | Lie Algebras II | 3(3-0-9) |
| 2301719 | Algebraic Number Theory II | 3(3-0-9) |
| 2301721 | Advanced Analysis I | 3(3-0-9) |
| 2301783 | Advanced Topics in Algebra | 3(3-0-9) |
| 2301784 | Advanced Topics in Analysis | 3(3-0-9) |
| 2301785 | Advanced Topics in Geometry | 3(3-0-9) |
| 2301791 | Selected Topics in Mathematics I | 3(3-0-9) |
| 2301792 | Selected Topics in Mathematics II | 3(3-0-9) |
| 2301796 | Individual Study I | 3(3-0-9) |
| 2301797 | Individual Study II | 3(3-0-9) |
| New elective courses may be added each year and will be announced accordingly. Students can also choose to take required electives or graduate-level courses as electives, with the approval of the curriculum committee. | ||
| 4) Dissertation | ||
| 2301813 | Thesis | 18 credit |
New graduate students in the Master’s program in Mathematics who are interested in participating in the Double-Degree Master’s Program in Mathematics with the Graduate School of Natural Science and Technology, Kanazawa University, Japan, can review the attached DDP Program document and/or submit their application/inquire about the program during the orientation day or contact the program chair at email: yotsanan.m@chula.ac.th
Guidelines for Applicants (For New Students Enrolling in the First Semester of Each Academic Year) on website: http://cmpsci.w3.kanazawa-u.ac.jp/DDP/
- Application Period: August of each year
- Interview: August
- Location: To be announced via email.
For more information, please refer to the document titled “GUIDELINES FOR APPLICANTS“
Study Plan : [DDP Program]
Doctoral Program
Doctor of Philosophy Program in Mathematics (Ph.D)
Plan 1: Thesis Emphasis
| Plan 1.1 | For students with a Master’s degree | |
| Total credits required | 60 credits | |
| Plan 1.2 | For students with a Bachelor’s degree | |
| Total credits required | 72 credits |
Plan 2: Coursework and Thesis
| Plan 2.1 | For students with a Master’s degree | |
| Total credits required | 60 credits | |
| Plan 2.2 | For students with a Bachelor’s degree | |
| Total credits required | 72 credits |
Study Duration 3 years for students with a Master’s degree and 4 years for students with a Bachelor’s degree
| Curriculum Structure | Plan 1 | Plan 2 | ||
|---|---|---|---|---|
| Plan 1.1 | Plan 1.2 | Plan 2.1 | Plan 2.2 | |
| Total Credit Units throughout the Program Not less than | 60 | 72 | 60 | 72 |
| Number of Credit Units for Courses | – | – | 12 | 24 |
| – Compulsory Courses | – | – | – | – |
| – Compulsory Elective Courses | – | – | – | 9 |
| – Elective Courses | – | – | 12 | 15 |
| Number of Thesis Credit Units | 60 | 72 | 48 | 48 |
Note:
- All students must register for the course 2301894 Doctoral Dissertation Seminar every semester until the completion of their studies, with no credit counted, and graded as S/U.
- Students enrolled in Plan 1.1 and Plan 1.2 may be required by the curriculum management committee to take additional courses or participate in other academic activities without credit counting.
| Plan 1.1 | for applicants with a master’s degree. | |
| 1) Compulsory course (evaluated as S/U and non-credit) | ||
| 2301704 | Research in Mathematics I | 3(3-0-9) |
| 2301705 | Research in Mathematics II | 3(3-0-9) |
| 2301706 | Research in Mathematics III | 3(3-0-9) |
| 2301707 | Research in Mathematics IV | 3(3-0-9) |
| 2301894 | Doctoral Dissertation Seminar | non-credit |
| 2301897 | Qualifying Examination | non-credit |
| 2) Dissertation | ||
| 2301829 | Dissertation | 60 credit |
| Plan 1.2 | for applicants with a bachelor’s degree. | |
| 1) Compulsory course (evaluated as S/U and non-credit) | ||
| 2301560 | Computer Tools in Mathematics | 2(1-2-5) |
| 2301704 | Research in Mathematics I | 3(3-0-9) |
| 2301705 | Research in Mathematics II | 3(3-0-9) |
| 2301706 | Research in Mathematics III | 3(3-0-9) |
| 2301707 | Research in Mathematics IV | 3(3-0-9) |
| 2301708 | Research in Mathematics V | 3(3-0-9) |
| 2301709 | Research in Mathematics VI | 3(3-0-9) |
| 2301894 | Doctoral Dissertation Seminar | non-credit |
| 2301897 | Qualifying Examination | non-credit |
| 2) Dissertation | ||
| 2301830 | Dissertation | 72 credit |
| Plan 2.1 | for applicants with a master’s degree. | |
| 1) Compulsory course (evaluated as S/U and non-credit) | ||
| 2301704 | Research in Mathematics I | 3(3-0-9) |
| 2301705 | Research in Mathematics II | 3(3-0-9) |
| 2301894 | Doctoral Dissertation Seminar | non-credit |
| 2301897 | Qualifying Examination | non-credit |
| 2) Required elective course | — | |
| 3) Elective courses | 12 credit | |
| Please select from the list of courses below. | ||
| 2301601 | Recursion Theory | 3(3-0-9) |
| 2301602 | Model Theory | 3(3-0-9) |
| 2301603 | Set Theory | 3(3-0-9) |
| 2301608 | Mathematical Foundations of Cryptography | 3(3-0-9) |
| 2301609 | Analytic Number Theory I | 3(3-0-9) |
| 2301610 | Linear and Multilinear Algebra | 3(3-0-9) |
| 2301612 | Representation Theory I | 3(3-0-9) |
| 2301613 | Abstract Algebra I | 3(3-0-9) |
| 2301614 | Abstract Algebra II | 3(3-0-9) |
| 2301616 | Algebraic Semigroup Theory | 3(3-0-9) |
| 2301617 | Lie Algebras I | 3(3-0-9) |
| 2301618 | Combinatorial Theory | 3(3-0-9) |
| 2301619 | Algebraic Number Theory I | 3(3-0-9) |
| 2301620 | Mathematical Analysis | 3(3-0-9) |
| 2301621 | Real Analysis I | 3(3-0-9) |
| 2301622 | Real Analysis II | 3(3-0-9) |
| 2301623 | Complex Analysis | 3(3-0-9) |
| 2301629 | Functional Analysis | 3(3-0-9) |
| 2301631 | Topology | 3(3-0-9) |
| 2301632 | Algebraic Topology | 3(3-0-9) |
| 2301634 | Convex and Discrete Geometry | 3(3-0-9) |
| 2301635 | Differentiable Manifold | 3(3-0-9) |
| 2301640 | Fundamentals of Mathematical Programming | 3(3-0-9) |
| 2301641 | Methods of Applied Mathematics I | 3(3-0-9) |
| 2301646 | Nonlinear Programming Theory | 3(3-0-9) |
| 2301649 | Combinatorial Design Theory | 3(3-0-9) |
| 2301650 | Partial Differential Equations I | 3(3-0-9) |
| 2301653 | Numerical Analysis I | 3(3-0-9) |
| 2301661 | Probability Theory | 3(3-0-9) |
| 2301665 | Mathematical Statistics | 3(3-0-9) |
| 2301670 | Graph Theory and Applications | 3(3-0-9) |
| 2301675 | Mathematical Modeling | 3(3-0-9) |
| 2301676 | Stochastic Models | 3(3-0-9) |
| 2301690 | Special Topics in Advanced Mathematics | 3(3-0-9) |
| 2301691 | Special Topics in Algebra | 3(3-0-9) |
| 2301692 | Special Topics in Analysis | 3(3-0-9) |
| 2301693 | Special Topics in Geometry | 3(3-0-9) |
| 2301694 | Special Topics in Applied Mathematics | 3(3-0-9) |
| 2301711 | Algebraic Geometry | 3(3-0-9) |
| 2301717 | Lie Algebras II | 3(3-0-9) |
| 2301719 | Algebraic Number Theory II | 3(3-0-9) |
| 2301721 | Advanced Analysis I | 3(3-0-9) |
| 2301783 | Advanced Topics in Algebra | 3(3-0-9) |
| 2301784 | Advanced Topics in Analysis | 3(3-0-9) |
| 2301785 | Advanced Topics in Geometry | 3(3-0-9) |
| 2301791 | Selected Topics in Mathematics I | 3(3-0-9) |
| 2301792 | Selected Topics in Mathematics II | 3(3-0-9) |
| 2301796 | Individual Study I | 3(3-0-9) |
| 2301797 | Individual Study II | 3(3-0-9) |
| Furthermore, new elective courses may be introduced annually, and the specific offerings will be announced each academic year. Additionally, students may, subject to the approval of the Curriculum Management Committee, elect to take required elective courses under Plan2.2 or graduate-level courses within the department as elective courses. | ||
| 4) Dissertation | ||
| 2301828 | Dissertation | 48 credit |
| Plan 2.2 | for applicants with a bachelor’s degree. | |
| 1) Compulsory course (evaluated as S/U and non-credit) | ||
| 2301560 | Computer Tools in Mathematics | 2(1-2-5) |
| 2301704 | Research in Mathematics I | 3(3-0-9) |
| 2301705 | Research in Mathematics II | 3(3-0-9) |
| 2301894 | Doctoral Dissertation Seminar | non-credit |
| 2301897 | Qualifying Examination | non-credit |
| 2) Required elective course | 9 credit | |
| You must choose at least 2 subject groups from the following groups. | ||
| Algebra Group | ||
| 2301610 | Linear and Multilinear Algebra | 3(3-0-9) |
| 2301613 | Abstract Algebra I | 3(3-0-9) |
| 2301614 | Abstract Algebra II | 3(3-0-9) |
| Analysis Group | ||
| 2301620 | Mathematical Analysis | 3(3-0-9) |
| 2301621 | Real Analysis I | 3(3-0-9) |
| 2301622 | Real Analysis II | 3(3-0-9) |
| 2301623 | Complex Analysis | 3(3-0-9) |
| Topology and Geometry Group | ||
| 2301631 | Topology | 3(3-0-9) |
| 2301632 | Algebraic Topology | 3(3-0-9) |
| 2301635 | Differentiable Manifold | 3(3-0-9) |
| Applied Mathematics Group | ||
| 2301640 | Fundamentals of Mathematical Programming | 3(3-0-9) |
| 2301641 | Methods of Applied Mathematics I | 3(3-0-9) |
| 2301650 | Partial Differential Equations I | 3(3-0-9) |
| 2301653 | Numerical Analysis I | 3(3-0-9) |
| 2301676 | Stochastic Models | 3(3-0-9) |
| 3) Elective courses | 15 credit | |
| Please select from the list of courses below. | ||
| 2301601 | Recursion Theory | 3(3-0-9) |
| 2301602 | Model Theory | 3(3-0-9) |
| 2301603 | Set Theory | 3(3-0-9) |
| 2301608 | Mathematical Foundations of Cryptography | 3(3-0-9) |
| 2301609 | Analytic Number Theory I | 3(3-0-9) |
| 2301612 | Representation Theory I | 3(3-0-9) |
| 2301616 | Algebraic Semigroup Theory | 3(3-0-9) |
| 2301617 | Lie Algebras I | 3(3-0-9) |
| 2301618 | Combinatorial Theory | 3(3-0-9) |
| 2301619 | Algebraic Number Theory I | 3(3-0-9) |
| 2301629 | Functional Analysis | 3(3-0-9) |
| 2301634 | Convex and Discrete Geometry | 3(3-0-9) |
| 2301646 | Nonlinear Programming Theory | 3(3-0-9) |
| 2301649 | Combinatorial Design Theory | 3(3-0-9) |
| 2301661 | Probability Theory | 3(3-0-9) |
| 2301665 | Mathematical Statistics | 3(3-0-9) |
| 2301670 | Graph Theory and Applications | 3(3-0-9) |
| 2301690 | Special Topics in Advanced Mathematics | 3(3-0-9) |
| 2301691 | Special Topics in Algebra | 3(3-0-9) |
| 2301692 | Special Topics in Analysis | 3(3-0-9) |
| 2301693 | Special Topics in Geometry | 3(3-0-9) |
| 2301694 | Special Topics in Applied Mathematics | 3(3-0-9) |
| 2301711 | Algebraic Geometry | 3(3-0-9) |
| 2301717 | Lie Algebras II | 3(3-0-9) |
| 2301719 | Algebraic Number Theory II | 3(3-0-9) |
| 2301721 | Advanced Analysis I | 3(3-0-9) |
| 2301783 | Advanced Topics in Algebra | 3(3-0-9) |
| 2301784 | Advanced Topics in Analysis | 3(3-0-9) |
| 2301785 | Advanced Topics in Geometry | 3(3-0-9) |
| 2301791 | Selected Topics in Mathematics I | 3(3-0-9) |
| 2301792 | Selected Topics in Mathematics II | 3(3-0-9) |
| 2301796 | Individual Study I | 3(3-0-9) |
| 2301797 | Individual Study II | 3(3-0-9) |
| Furthermore, new elective courses may be introduced from time to time, and the specific offerings will be announced annually. Additionally, students may, subject to the approval of the Curriculum Management Committee, elect to take required elective courses or graduate-level courses within the department as elective courses. | ||
| 4) Dissertation | ||
| 2301828 | Dissertation | 48 credit |
Qualifying Exam
Qualifying Examination for Doctoral Candidates
The Qualifying Examination is designed to assess a student’s fundamental knowledge, analytical skills, and independent research capabilities. It serves as a benchmark to evaluate a student’s readiness for doctoral studies.
Specific requirements for the Qualifying Examination are as follows:
-
Eligibility:
- A student may only take the Qualifying Examination upon receiving approval from the Program Committee.
- Students entering the program with a master’s degree or a bachelor’s degree with honors may register for the Qualifying Examination starting from the first semester of enrollment.
- Students entering the program with a bachelor’s degree without honors (specifically, Plan G and G2 students) must complete at least 9 credit hours (*) and maintain a cumulative GPA of 3.25 or higher to be eligible for the Qualifying Examination.
-
Examination Timeline:
- Students must register for and pass the Qualifying Examination with a grade of S (pass) within 4 semesters from the first semester of enrollment for master’s degree holders and within 5 semesters from the first semester of enrollment for bachelor’s degree holders (**).
-
Retaking the Examination:
- Students who receive a grade of U (fail) may retake the examination once. If they receive a grade of U twice, they will be dismissed from the program unless approved by the program to transfer to a master’s degree program.
-
Examination Format:
- The Qualifying Examination consists of a written examination.
-
Subject Areas:
- Students must pass examinations in two out of four subject areas: Algebra, Analysis, Topology+Geometry, and Applied Mathematics. For each subject area, students must select and pass two specific courses. A passing score is defined as obtaining at least 50% of the total points in each subject area.
-
Examination Schedule:
- Students may choose to take the examination in one or two subject areas per semester. If a student passes only one subject area, it is considered a pass for that subject area, and the student may take the remaining subject area in the following semester.
(*, **) For students who enrolled starting from the academic year 2018 onward.
The content of each branch covers the following subjects
2301610 Linear and Multilinear Algebra
– Basic concepts; linear maps; linear geometry; multilinear algebra; quadratic forms.
2301613 Abstract Algebra I
– Groups; group actions; Sylow theorems; rings; ideals; polynomial rings; unique factorization domains;
fields and field extensions.
2301614 Abstract Algebra II
– Jordan-Holder theorem; solvable groups; free groups; classification of extension fields; Galois theory;
Noetherian ring; modules.
2301620 Mathematical Analysis
– The real number system; metric spaces; sequences and series of real numbers; continuity;
differentiation; the Riemann integral; uniform convergence; the Arzela-Ascoli theorem; the Stone-
Weierstrass theorem.
2301621 Real Analysis I
– Measures; integration; normed linear spaces; – spaces; Hilbert spaces.
2301622 Real Analysis II
– Product measures; signed and complex measures; differentiation; Banach spaces.
2301623 Complex Analysis
– Holomorphic functions; complex power series; complex line integrals; Cauchy theorem, Cauchy integral
formula and applications; calculus of residues; maximum modulus principle; conformal mappings,
normal families, Riemann mapping theorem; harmonic functions.
2301631 Topology
– Topological spaces; complete metric spaces; product spaces; quotient spaces; countability axioms;
separation axioms; connectedmess; compactness; compactifications; net convergence; function
spaces.
2301632 Algebraic Topology
– Homotopy; fundamental groups; covering spaces; van Kampen’s theorem; simplicial homology; singular
homology CW-complexes; cellular homology; Eilenberg-Steenrod axioms.
2301635 Differentiable Manifolds
– Differentiable manifolds, tangent spaces; vector fields and flows; immersions and submersions;
Frobenius’ theorem; integration on manifols, differential forms, Stokes’theorem; introduction to Lie
groups and Lie algebras.
บังคับสอบรายวิชา 2301653 Numerical Analysis
– Solutions of systems of linear and non-linear equations, numerical methods for ordinary
differential equations, finite difference methods for two-point boundary value problems and finite
difference methods for partial differential equations.
และเลือกสอบอีก 1 รายวิชาจาก 3 รายวิชาต่อไปนี้
2301641 Method of Applied Mathematics I
– Theory of distribution, Green’s functions, operator theory, perturbation method.
2301650 Partial Differential Equations
– First-order equations; linear second-order PDEs; representation of solutions; introduction to Hamilton-
Jacobi equations; other ways to represent solutions.
2301676 Stochastic Models
– Stochastic programming models, probabilistic dynamic programming models, Markov chain, waiting line
models, birth-death process.
Qualifying Examination Application Form
Please submit this form by July for Fall Semester and by December for Spring Semester.
Proposal Examination
Thesis outline examination It is a test to measure students’ knowledge and understanding of issues related to issues. Research methods Methods and techniques used in solving research problems Examination of dissertation proposals in the Doctor of Philosophy degree program. There must be an examination of the basic knowledge and in-depth knowledge necessary to complete the thesis. To ensure that students have sufficient necessary knowledge to conduct research.
- For students in the Master’s degree program Project approval must be received within 2 academic years from the first semester of study.
- For Ph.D. students The outline must be approved within 3 academic years from the first semester of study. Except for continuous management courses Students can take the thesis outline examination at any time. But not less than 60 days before the thesis examination.
Thesis/Dissertation Defense
Thesis examination It is a test to measure students’ knowledge and understanding of issues related to issues. Research methods Methods and techniques used to solve research problems The thesis examination must include a test of basic knowledge and in-depth knowledge used in the thesis to assess whether the student has knowledge and understanding of the research.
Students will be able to take the thesis examination. Only if the following criteria are met.
- Register for all courses as specified in the curriculum.
- Receive approval of the thesis outline from the Faculty Executive Committee for a period of not less than 60 days before the date of the thesis examination. In the event that the thesis outline does not have any significant amendments. and the Faculty Executive Committee approves the thesis examination before the period specified in paragraph one. The said period shall begin counting from the day the Curriculum Executive Committee approves the thesis outline.
- There is evidence showing that Submitted a research article as part of a thesis to an academic journal for consideration for publication. or has been accepted to present work to an academic conference in accordance with the criteria set forth in university regulations or announcements.
- Pass the English language test criteria as specified by the university/program. (For students from academic year 2018 onwards)
Announcement
Announcement on the deadline of complete thesis/dissertation and independent study submission for Graduate Students, Academic Year 2024