2016 Fundamentals of Computing

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Academic unit or major
Undergraduate major in Computer Science
Murata Tsuyoshi  Nishizaki Shin-Ya 
Course component(s)
Lecture / Exercise     
Day/Period(Room No.)
Tue7-8(W934)  Fri1-4(W934)  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
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Course description and aims

This course covers the mathematical concepts and theories related to computer science, which are based on the fundamentals learnt in Foundations of Computer Science.
The principle of computing and computing models are viewed from various angles to reveal the essence of calculation.

Student learning outcomes

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

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

As a general rule, two 90-minute lecture sessions followed by one 90-minute exercise will be given.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Turing Machine 1 : Introduction to Turing machine After each lesson, review what you learnt. Use the exercise problems in the textbook.
Class 2 Turing Machine 2 : Binary coding
Class 3 Turing Machine 3 : Programming technique
Class 4 Execercise
Class 5 Turing machine 4 : Universal Turing machine
Class 6 Turing machine 5 : Computability
Class 7 Execercise
Class 8 Recursive function 1 : Introduction to recursive function
Class 9 Recursive function 2: Programming technique
Class 10 Execercise
Class 11 Summary of the first half
Class 12 Assessment of the students' level of understanding on what has been taught so far
Class 13 Recursive function 3 : Data expression using Gödel number
Class 14 Recursive function 4 : Computability of recersive function
Class 15 Execercise
Class 16 Recursive function 5 : Equivalence between recersive function and computability
Class 17 Lambda calculus 1 : Introduction to lambda calculus
Class 18 Execercise
Class 19 Lambda calculus 2 : Data expression using lambda term
Class 20 Lambda calculus 3 : Computability of lambda calculus
Class 21 Execercise
Class 22 Summary of the latter half
Class 23 Execercise


Osamu Watanabe, Naoki Yonezaki. "Introduction to Theory of Computing". Nippon Hyoron Sha Co. Ltd. (Japanese)

Reference books, course materials, etc.


Assessment criteria and methods

Students' course scores are based on midterm exam (50%) and final exam (50%).

Related courses

  • GRE.C101 : Foundations of Computer Science I
  • GRE.C102 : Foundations of Computer Science II

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Students must have successfully completed Foundations of Computer Science I and II, or have equivalent knowledge.

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