Spring 2010 MAS480A Topics in Mathematics: Matroid Theory
This course will introduce the notion of matroids, a common generalization of vector spaces and graphs. We will start with learning several equivalent definitions of matroids and then study various aspects of matroids, including duality and minors, matroid intersection and union theorems, representable matroids and graphic matroids, and branch-width of matroids.
It is recommended to have some prior knowledge on elementary linear algebra as well as graph theory.
For an introduction to matroids, read What is a matroid? written by J. Oxley.
- Lecture: TTh 2:30PM-3:45PM, Room 2413, Bldg #E6-1 (Natural Science Bldg 자연과학동)
- Office Hour: Tuesday 4PM (tentative)
- Textbook: D. Král’ and O. Pangrác, Introduction to Matroid Theory (Lecture notes), ITI Series 2009-430, Charles University, Prague, Czech Republic. (It will be provided to students in class.)
For the reference, read the book: J. Oxley, matroid theory, Oxford university press.
- Course website: http://moodle.kaist.ac.kr
- Syllabus
Last Updated on Saturday, 28 November 2009 18:39
Spring 2010 MAS101F Calculus 1
In the view that the first semester of calculus deals with differentiation and integration of functions of a single variable, it might be an extension of mathematics taught in high school but the treatment will be more precise and new subjects will be introduced. Using mathematically precise definitions of limits, derivatives, and definite integrals, we will be able to provide proofs for important results such as Mean Value Theorem and Fundamental Theorem of Calculus, which was impossible in high school. The list of new materials we will learn in this semester includes inverse trigonometric functions, hyperbolic functions and their inverses, integral technique using these functions, improper integrals, convergence of infinite series, power series, and Taylor’s series.
- Lecture: TTh 9AM-10:15AM, E6-4409
- Office Hours: Tuesday 5:30PM-6:30PM (tentative)
- Textbook: University Calculus: Elements with Early Transcendentals-1st ed., by J. Hass, M.D. Weir, and G.B. Thomas, Jr, Pearson Addison Wesley, 2009.
- Course website: to be built on http://moodle.kaist.ac.kr
Last Updated on Saturday, 28 November 2009 18:45
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Fall 2009 MAS477 Introduction to Graph Theory
Course website: http://moodle.kaist.ac.kr/course/view.php?id=118
This course is an introduction to some of the major topics of graph theory. They include graph connectivity, matchings, planar graphs, graph coloring, and nowhere-zero flows.
Basic notions and theorems covered in Discrete Mathematics (MAS275) will be assumed; but we will review them in the first week.
Last Updated on Monday, 30 November 2009 09:56
Spring 2009 MAS101E Calculus I
Course website
- Lecture: TTh 2:30PM-3:45PM, E11-410
- Office Hours: Tuesdasy 4:30PM-6PM (tentative)
- Textbook: University Calculus: Elements with Early Transcendentals-1st ed., by J. Hass, M.D. Weir, and G.B. Thomas, Jr, Pearson Addison Wesley, 2009.
In the view that the first semester of calculus deals with differentiation and integration of functions of a single variable, it might be an extension of mathematics taught in high school but the treatment will be more precise and new subjects will be introduced. Using mathematically precise definitions of limits, derivatives, and definite integrals, we will be able to provide proofs for important results such as Mean Value Theorem and Fundamental Theorem of Calculus, which was impossible in high school. The list of new materials we will learn in this semester includes inverse trigonometric functions, hyperbolic functions and their inverses, integral technique using these functions, improper integrals, convergence of infinite series, power series, and Taylor’s series.
Last Updated on Sunday, 29 November 2009 11:33
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Spring 2009 MAS575 Combinatorics
Course website (Ask the enrollment key to me)
- Lecture: TTh 9:00AM-10:15AM, E6-1(Natural Science Bldg 자연과학동), 2413
- Office Hours: Tuesdasy 4:30PM-6PM (tentative)
Textbook: None.
This is a graduate-level course on Combinatorics. Since the area of Combinatorics is so wide, we will study various theorems as well as useful methods for approaching combinatorial problems. It is strongly recommended that you have certain knowledge of materials covered in Discrete Mathematics (MAS275). Some elementary knowledge of graph theory and probability theory will be helpful.
The following topics are currently being considered to be included in this course:
- Extremal Set Theory
- Ramsey Theory
- Probabilistic Method
- Linear Algebra Method
Last Updated on Monday, 30 November 2009 09:58
Fall 2008 MAS477 Introduction to Graph Theory
Course website: http://mathsci.kaist.ac.kr/~sangil/fall08mas477/
This course is an introduction to some of the major topics of graph theory. They include graph connectivity, matchings, planar graphs, graph coloring, and nowhere-zero flows.
Basic notions and theorems covered in Discrete Mathematics (MAS275) will be assumed; but we will review them in the first week.
Last Updated on Monday, 30 November 2009 09:57
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