Course Syllabus
The syllabuses on both this page and the NTU online course information are synchronized.
Course Information
| Item | Content |
| Course title | Graph Theory (Ⅱ) |
| Semester | 112-2 |
| Designated for | GRADUATE INSTITUTE OF MATHEMATICS |
| Instructor | SHAGNIK DAS |
| Curriculum No. | MATH 7704 |
| Curriculum Id No. | 221 U3460 |
| Class | |
| Credit | 3 |
| Full/Half Yr. | Half |
| Required/Elective | Required |
| Time | Tuesday 8,9(15:30~17:20)Friday 5(12:20~13:10) |
| Place | 天數102 |
| Remarks | The course is conducted in English。 |
Course Syllabus
| Item | Content |
| Course Description | This course will introduce students to the problems and methods of extremal combinatorics. The fundamental extremal problem asks how large a structure can be without containing a forbidden substructure. This very flexible problem arises in many different settings and enjoys several applications. A variety of methods have been developed to tackle them, and this course will pay special attention to the probabilistic, linear algebraic and (briefly) topological methods. |
| Course Objective | The first half of the course will continue from the previous semester’s Graph Theory course, taking a deeper look into Ramsey and Turán Theory. The second half will cover problems from extremal set theory, including the central theorems of Erdős-Ko- Rado and Sperner. Alongside the important results, equal attention will be paid to the development of methods used to prove them. |
| Course Requirement | Successful completion of Graph Theory I (or an equivalent course) Familiarity with linear algebra and (discrete) probability Some knowledge of topology would be a bonus, but is not required |
| Student Workload (expected study time outside of class per week) | 4-6 hours |
| References | Sources for supplemental reading: - “The probabilistic method” (Alon-Spencer) - “Extremal Combinatorics” (Jukna) - “A Course in Combinatorics” (Van Lint-Wilson) - "Graph Theory” (Diestel) - “Linear Algebra Methods in Combinatorics” (Babai-Frankl) |
| Designated Reading | The course will be self-contained, with notes provided online |
Progress
| Week | Date | Topic |
Grading
| NO | Item | Pc | Explanations for the conditions |
| 1 | Homework | 30% | Homework assignments, roughly every two weeks, covering the recent topics from the course |
| 2 | Midterm | 30% | A midterm exam administered during the halfway point of the course |
| 3 | Final | 40% | The final exam at the end of the course, covering all of the material taught |
Adjustment methods for students
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Office Hour
| Remarks | Feel free to schedule office hours by asking before/after lectures or sending an e-mail. You should also post any questions in the NTU COOL Discussions forum. |