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Algebraic Foundations of Computer Science

Spring 2026

Course Information

Discipline Sheet: FLT_AFCS_RO, FLT_AFCS_EN

Course Goal: Algebraic Foundations of Computer Science (AFCS) is designed for undergraduate students, especially first-year students. The course presents the basic elements of algebra necessary to understand fundamental areas of computer science. Concrete applications follow each course chapter in one or more fields, such as variable-length codes, data compression, error detection and correction codes, cryptography, and information security.

Students interested in deepening their AFCS for a career in coding theory, cryptography, or related areas can contact me directly. Our department offers a master’s program in Information Security, whose director is the instructor for this course. There is also the option to pursue doctoral studies in cryptography and information security (please see the Students section on this site).

Prerequisites: No special prior math knowledge is required, except for that acquired in high school.

Textbook: The course is based entirely on

F.L. Țiplea: Algebraic Foundations of Computer Science, second edition, “Alexandru Ioan Cuza” University Publishing House, 605 pages, 2021.

Each lecture has explicit references to textbook pages or additional reading recommendations. It is highly recommended that you purchase the textbook from the “Alexandru Ioan Cuza” University Publishing House in Iasi (no shipping fees).

Student Resources:

Lectures, office hours, exam sessions:

  • Teaching weeks: Feb 16 – April 12 and April 20 – May 31, 2026.
  • Partial evaluation week: April 6 – 12, 2026.
  • Lectures: Monday, 10:00 – 12:00 (series A) in C2, and 8:00 – 10:00 (series EN) in C309.
  • Office hours: Monday, 12:00 – 14:00 in C301.
  • Examination session: June 1 – June 21, 2026.
  • Re-examination session: June 22 – June 28, 2026.

Grading:

  • The final grade is based on the scores obtained in the ongoing evaluation and the final exam.
  • The ongoing evaluation consists of one written test in the 8th week of the didactic activity. Its score is measured on a scale from 0 to 100.
  • The final exam takes place in the examination session. Its score is measured on a scale from 0 to 100.
  • The course is passed if the scores from the ongoing evaluation and the final exam are each at least 45. If this requirement is met, the final score is computed as the average of the two scores. The final grade is then obtained by converting the final score (division by 10 and usual rounding).

Course Staff

Course Holder and Instructor: Prof. Dr. Ferucio Laurențiu ȚIPLEA, Department of Computer Science, “Alexandru Ioan Cuza” University of Iași, Romania, e-mail: ferucio dot tiplea at uaic dot ro or fltiplea at gmail dot com.

Course assistants: Lect. Dr. Sorin Iftene, Lect. Dr. Cătălin Bîrjoveanu, Lect.Dr. Anca-Maria Nica.

Syllabus

Closures

Closures
Lesson 1 of 1 within section Closures. You must enroll in this course to access course content.

Computational introduction to number theory 

Part I: Divisibility, congruences
Lesson 1 of 4 within section Computational introduction to number theory . You must enroll in this course to access course content.
Part II: Congruential equations, Chinese remainder theorem, quadratic residues 
Lesson 2 of 4 within section Computational introduction to number theory . You must enroll in this course to access course content.
Part III: Asymptotic notation, complexity of the basic arithmetic operations 
Lesson 3 of 4 within section Computational introduction to number theory . You must enroll in this course to access course content.
Application in cryptography
Lesson 4 of 4 within section Computational introduction to number theory . You must enroll in this course to access course content.

Semigroups and monoids

Semigroups and monoids: definitions and basic properties
Lesson 1 of 3 within section Semigroups and monoids. You must enroll in this course to access course content.
Variable-length codes
Lesson 2 of 3 within section Semigroups and monoids. You must enroll in this course to access course content.
Applications to data compression: Huffman codes
Lesson 3 of 3 within section Semigroups and monoids. You must enroll in this course to access course content.

Groups

Groups: definitions and basic properties
Lesson 1 of 3 within section Groups. You must enroll in this course to access course content.
Order of an element, primitive roots, discrete log problem
Lesson 2 of 3 within section Groups. You must enroll in this course to access course content.
Applications in cryptography: digital signature standard
Lesson 3 of 3 within section Groups. You must enroll in this course to access course content.

Rings and fields

Rings and fields: definitions and basic properties
Lesson 1 of 3 within section Rings and fields. You must enroll in this course to access course content.
Finite fields
Lesson 2 of 3 within section Rings and fields. You must enroll in this course to access course content.
Applications in cryptography: advanced encryption standard
Lesson 3 of 3 within section Rings and fields. You must enroll in this course to access course content.

Vector spaces

Vector spaces: definitions and basic properties
Lesson 1 of 5 within section Vector spaces. You must enroll in this course to access course content.
Basis and dimension
Lesson 2 of 5 within section Vector spaces. You must enroll in this course to access course content.
Linear maps
Lesson 3 of 5 within section Vector spaces. You must enroll in this course to access course content.
Inner product and orthogonality
Lesson 4 of 5 within section Vector spaces. You must enroll in this course to access course content.
Applications in linear codes
Lesson 5 of 5 within section Vector spaces. You must enroll in this course to access course content.

Seminar guide

Seminar guide to AFCS
Lesson 1 of 1 within section Seminar guide. You must enroll in this course to access course content.

Assessment of student performance

Results
Lesson 1 of 1 within section Assessment of student performance. You must enroll in this course to access course content.
  • Enrollment in this course closed on July 13, 2025.