The main topic of this course is "discrete structures". We will deal with the basic concepts and applications of discrete structures through discussions, group work, lectures, and exercises. By providing students with definitions, examples, and analysis methods for "graphs", "combinatorial analysis", "algebraic systems", "formal languages", "ordered sets", "propositional calculus", and "Boolean algebra", students will hone the skills to mathematically represent and analyze discrete structures.
The purpose of this course is for students to hone the skills to select the appropriate discrete structure for representing and analyzing a given object, to represent the object as a discrete structure, to analyze the discrete structure to derive results, and to concisely communicate to others the results of analyzing discrete structures.
Upon completion of this course, students should be able to:
1) State the definitions of discrete structures using examples of objects described by discrete structures;
2) Apply analysis methods to examples of objects described by discrete structures, and explain the analysis results to others;
3) Select an appropriate discrete structure and describe a focal object; and
4) Apply analysis methods to an object described by a discrete structure, and explain the analysis results to others.
graphs, combinatorial analysis, algebraic systems, formal language, ordered sets, propositional calculus, Boolean algebra
|Intercultural skills||Communication skills||Specialist skills||Critical thinking skills||Practical and/or problem-solving skills|
One class deals with one discrete structure.
The students examine examples of objects which can be described by a discrete structure, first individually, second in pairs, then in groups of four, and finally with the class as a whole. Then a lecture on the discrete structure is presented, and the students work on exercise problems. At the end of the class, each student writes and submits a “summary report” on what he/she learned through individual observation, other students’ ideas, the lecture, and exercise problems.
|Course schedule||Required learning|
|Class 1||Planar graphs, coloring and trees||State the definitions of planar graphs, coloring and trees|
|Class 2||Directed graphs and finite automata||State the definitions of directed graphs and finite automata|
|Class 3||Signed graphs and balanced-ness||State the definitions of signed graphs and balanced-ness|
|Class 4||Combinatorial analysis||State the definition of combinatorial analysis|
|Class 5||Algebraic systems||State the definitions of algebraic systems|
|Class 6||Formal languages||State the definitions of algebraic systems|
|Class 7||Ordered sets and lattices||State the definitions of ordered sets and lattices|
|Class 8||Propositional calculus and Boolean algebra||State the definitions of propositional calculus and Boolean algebra|
Seymour Lipschutz and Marc Lipson, “2000 Solved Problems in Discrete Mathematics, ” The McGraw-Hill Companies, Inc., 1992 (ISBN-10: 0070380317, ISBN-13: 978-0070380318)
Course materials are posted on OCW-i and/or provided during the classes.
Assessment will be based on “summary reports” written during each class (50% in total) and the final examination (50%).
Students must have successfully completed “Trans-disciplinary Exercise in Social and Human Sciences S1A (Basics of Logic and Set Theory)” and “Trans-disciplinary Exercise in Social and Human Sciences S1B (Basics of Metric, Convergence and Continuity)” or have equivalent knowledge.
Takehiro Inohara, inostaff[at]shs.ens.titech.ac.jp
Instructor’s office: Rm. 813, 8 Fl., West Bldg. 9. Contact by e-mail in advance to schedule an appointment.
This course consists of the content of science.