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2016　Algebra

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Academic unit or major
Undergraduate major in Mathematical and Computing Science
Instructor(s)
Kojima Sadayoshi  Umehara Masaaki  Nishibata Shinya  Terashima Yuji  Murofushi Toshiaki  Takasawa Mitsuhiko  Suzuki Masahiro  Suzuki Masahiro 
Class Format
Lecture / Exercise     
Media-enhanced courses
Day/Period(Room No.)
Mon5-8(W833)  Thr5-6(W833)  
Group
-
Course number
MCS.T231
Credits
3
Academic year
2016
Offered quarter
4Q
Syllabus updated
2017/1/11
Lecture notes updated
-
Language used
Japanese
Access Index

Course description and aims

The algebraic structure plays an important role in mathematical and computing sciences. The objectives of this course are to provide the fundamentals of algebra, particularly on congruence, group, subgroup, homomorphism, quotient group, homomorphism theorem, ring, ideal, finite fields and so on, and also for the students to built backgrounds to apply algebra in mathematical and computing sciences.

Student learning outcomes

The students are expected to understand the fundamentals of mathematical methods to handle algebraic structures appeared in mathematical and computing sciences and also to be able to apply them to practical problems.

Keywords

algebra, group, ring, field

Competencies that will be developed

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

Class flow

The lectures provide the fundamentals of algebra with recitation sessions.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Congruence Understand the contents covered by the lecture.
Class 2 Multiplicative Group Understand the contents covered by the lecture.
Class 3 Exercises regarding the contents covered up to the 2nd lecture Cultivate more practical understanding by doing exercises.
Class 4 Group Understand the contents covered by the lecture.
Class 5 Examples Understand the contents covered by the lecture.
Class 6 Exercises regarding the contents covered up to the 5th lecture Cultivate more practical understanding by doing exercises.
Class 7 Homomorphim Understand the contents covered by the lecture.
Class 8 Subgroup, Kernel and Image Understand the contents covered by the lecture.
Class 9 Exercises regarding the contents covered up to the 8th lecture Cultivate more practical understanding by doing exercises.
Class 10 Quotient Group and Isomorphism Theorem Understand the contents covered by the lecture.
Class 11 Ring Understand the contents covered by the lecture.
Class 12 Exercises regarding the contents covered up to the 11th lecture Cultivate more practical understanding by doing exercises.
Class 13 Examples Understand the contents covered by the lecture.
Class 14 Ideal Understand the contents covered by the lecture.
Class 15 Exercises regarding the contents covered up to the 14th lecture Cultivate more practical understanding by doing exercises.
Class 16 Quotient Ring and Isomorphism Theorem Understand the contents covered by the lecture.
Class 17 Fnite Field Understand the contents covered by the lecture.
Class 18 Exercises regarding the contents covered up to the 17th lecture Cultivate more practical understanding by doing exercises.
Class 19 Vector Space over Finite Field, Polynomial Understand the contents covered by the lecture.
Class 20 Quadratic Field Understand the contents covered by the lecture.
Class 21 Exercises regarding the contents covered up to the 20th lecture Cultivate more practical understanding by doing exercises.
Class 22 Algebraic Number Theory Understand the contents covered by the lecture.

Textbook(s)

Not specified in particular.

Reference books, course materials, etc.

References are provided in the lectures.

Assessment criteria and methods

By scores of examinations and recitation sessions.

Related courses

  • MCS.T203 ： Linear Algebra and Its Applications
  • MCS.T201 ： Set and Topology I

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

None

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