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2022　Exercises in Algebra A I

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Academic unit or major
Mathematics
Instructor(s)
Naito Satoshi  Suzuki Masatoshi  Minagawa Tatsuhiro 
Class Format
Exercise    (Face-to-face)
Media-enhanced courses
Day/Period(Room No.)
Thr5-8(W351)  Fri5-8(H103)  
Group
-
Course number
ZUA.A202
Credits
2
Academic year
2022
Offered quarter
1-2Q
Syllabus updated
2022/3/16
Lecture notes updated
-
Language used
Japanese
Access Index

Course description and aims

This course is an exercise session for the lecture ``Introduction to Algebra I'' (ZUA.A201). The materials for exercise are chosen from that course.

Student learning outcomes

To become familiar with important notions in algebra such as rings, subrings, fields, domains, ideals, residue rings, prime ideals, maximal ideals, ring homomorphisms, the fundamental theorem on ring homomorphisms, the Chinese remainder theorem, Euclidean domains, principal ideal domains, unique factorization domains.

To become able to prove by him/herself basic properties of these objects.

Keywords

ring, subring, field, domain, ideal, residue ring, prime ideal, maximal ideal, ring homomorphism, the fundamental theorem on ring homomorphims, the Chinese remainder theorem, Euclidean domain, principal ideal domain, unique factorization domain

Competencies that will be developed

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

Class flow

Students are given exercise problems related to what is taught in the course``Introduction to Algebra I'''.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Discussion session on the definition and typical examples of rings Details will be announced during each lecture.
Class 2 Discussion session on basic properties of rings Details will be announced during each lecture.
Class 3 Discussion session on the definition and typical examples of subrings Details will be announced during each lecture.
Class 4 Discussion session on invertible elements and nilpotent elements; that on fields and domains Details will be announced during each lecture.
Class 5 Discussion session on the definition and typical examples of ideals Details will be announced during each lecture.
Class 6 Discussion session on the definition and typical examples of residue rings Details will be announced during each lecture.
Class 7 Discussion session on prime ideals and maximal ideals Details will be announced during each lecture.
Class 8 evaluation of progress Details will be announced during each lecture.
Class 9 Discussion session on the definition and typical examples of ring homomorphisms Details will be announced during each lecture.
Class 10 Discussion session on the fundamental theorem on ring homomorphisms Details will be announced during each lecture.
Class 11 Discussion session on the Chinese remainder theorem and its applications Details will be announced during each lecture.
Class 12 Discussion session on the definition and typical examples of Euclidean domains Details will be announced during each lecture.
Class 13 Discussion session on the definition and typical examples of principal ideal domains Details will be announced during each lecture.
Class 14 Discussion session on the definition and basic properties of unique factorization domains Details will be announced during each lecture.

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.

Textbook(s)

Shoichi Nakajima : Basics of Algebra and Arithmetic, Kyoritsu Shuppan Co., Ltd., 2000.

Reference books, course materials, etc.

P.J. Cameron : Introduction to Algebra (second ed.), Oxford Univ. Press, 2008.
N. Jacobson : Basic Algebra I (second ed.), Dover，1985.
M. Artin : Algebra (second ed.), Addison-Wesley, 2011.
N. Herstein: Topics in algebra, John Wiley & Sons, 1975.
A. Weil: Number Theory for Beginners, Springer-Verlag, 1979.

Assessment criteria and methods

Brief exam and presentation for exercise problems. Details will be announced during a lecture.

Related courses

  • MTH.A201 ： Introduction to Algebra I
  • MTH.A202 ： Introduction to Algebra II
  • ZUA.A201 ： Introduction to Algebra I
  • ZUA.A203 ： Introduction to Algebra II
  • ZUA.A204 ： Exercises in Algebra A II

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

Students are supposed to have completed [Linear Algebra I / Recitation], [Linear Algebra II] and [Linear Algebra Recitation II].
Students are strongly recommended to take ZUA.A201: Introduction to Algebra I (if not passed yet) at the same time.

Other

Zoom URL for the online recitation classes is provided through the T2SCHOLA system.

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