This course covers the mathematical concepts and theories related to computer science, which are based on the fundamentals learned in Foundations of Computer Science.
The principle of computing and computing models are viewed from various angles to reveal the essence of calculation.
At the end of this course, students will be able to deal with Turing Machine, the recursive function, the lambda calculus, and the computability theory.
Turing Machine, recursive function, lambda calculus, computability theory
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Based on lecture sessions followed by mid-term and final exams.
Course schedule | Required learning | |
---|---|---|
Class 1 | Turing Machine 1 : Introduction to Turing machine | After each lesson, review what you learned. Use the exercise problems in the textbook. |
Class 2 | Turing Machine 2 : Binary coding | Specified in the class. |
Class 3 | Turing machine 3 : Universal Turing machine | Specified in the class. |
Class 4 | Turing machine 4 : Computability | Specified in the class. |
Class 5 | Recursive function 1 : Introduction to recursive function | Specified in the class. |
Class 6 | Recursive function 2 : Data expression using Gödel number | Specified in the class. |
Class 7 | Mid-term exam | Specified in the class. |
Class 8 | Recursive function 3 : Computability of recursive function | Specified in the class. |
Class 9 | Recursive function 4: Equivalence between recursive function and computability | Specified in the class. |
Class 10 | Lambda calculus 1 : Introduction to lambda calculus | Specified in the class. |
Class 11 | Lambda calculus 2 : Data expression using lambda term | Specified in the class. |
Class 12 | Lambda calculus 3 : Computability of lambda calculus | Specified in the class. |
Class 13 | Summary | Specified in the class. |
Class 14 | Final exam | Specified in the class. |
Osamu Watanabe, Naoki Yonezaki. "Introduction to Theory of Computing". Nippon Hyoron Sha Co. Ltd. (Japanese)
None
Students' course scores are based on assignments (50%), history of video watching (25%) and mid-term/final exams (25%). Depending on the situation of COVID-19, the exams might be canceled.
Students must have successfully completed Foundations of Computer Science I and II, or have equivalent knowledge.
On-demand classes will be offered by T2SCHOLA. For more information, please refer to the following site.
http://www.net.c.titech.ac.jp/lecture/comp/