MATH 4315 261: Abstract Algebra II

MATH 4315 - Abstract Algebra II

Spring 2025 Syllabus, Section 261, CRN 26853


Instructor Information

Mahanthesh Basavarajappa, PhD

Email: mbasavarajappa@tamiu.edu

Office: PLG 203C

Office Hours:
MW: 5 pm - 6 pm

Office Phone: 9563262594

Additional office hours are available by appointment.


Times and Location

MW 6pm-7:20pm in Bullock Hall 219


Course Description


Additional Course Information

AI Policy: AI programs may be used for idea generation and brainstorming, but be aware of potential inaccuracies in AI-generated content. AI tools are strictly prohibited during all assessments. To develop crucial writing, analytical, and critical thinking skills, students must prepare all assignments independently. These skills are vital for workplace competitiveness. Unauthorized AI use in assessments constitutes academic misconduct.

Attendance Policy: Students are responsible for attending every class and signing the attendance sheet. Active participation is essential for academic success.

Student Learning Outcomes

Upon successful completion of this course, the student will be able to: 

  • recognize and describe various examples of groups, including groups of numbers, permutations, matrices, and transformations. Students will also be able to recognize and describe examples of subgroups and quotient groups of such groups, and examples of homomorphisms and isomorphisms between them; 
  • derive basic properties of groups, subgroups, quotient groups, homomorphisms, and isomorphisms from their definitions;
  • recognize and describe various examples of rings, and as special cases of rings, of integral domains and fields. Students will also be able to recognize and describe examples of subrings, ideals, and quotient rings of such rings, and examples of homomorphisms and isomorphisms between them;
  • derive basic properties of rings, integral domains and fields from their definitions.
  • discuss and prove the unique factorization property of the ring of polynomials over a field, and perform related operations on polynomials such as Euclidean algorithm, irreducibility tests and factorization;
  • recognize and describe the process of construction of field extensions. In particular, students will be able to construct (i) the field extension obtained by adjoining elements to the base field, and (ii) the splitting field of a polynomial over the base field; and
  • describe the intermediate fields of a given field extension, and in the case of Galois extension, be able to describe the Galois group and Galois correspondence. 

Important Dates

Visit the Academic Calendar (tamiu.edu) page to view the term's important dates.

Textbooks

Group Title Author ISBN
Required Contemporary Abstract Algebra Joseph A. Gallian 978-1-305-65796-0
Optional Elementary Abstract Algebra: Examples and Applications Justin Hill, Chris Thron 978-0-359-04211-1

Grading Criteria

Grading Criteria: Semester grades will be based on two exams (40%)-20% each, Classwork assignments plus class participation (20%), Quizzes (10%), and a Final exam (30%). The final exam will be a comprehensive exam covering material from the entire course. The grading criteria are as follows:

Assessment tool                                        Weightage

Classwork assignments                              20%

Quizzes                                                         10%

Midterm-1                                                      20%

Midterm -2                                                     20%

Comprehensive Final Exam                         30%

Make-up Exams: There will be NO make-up exams except for an official university absence (you should have a good excuse).

E-mail: Students are required to have a TAMIU e-mail address. To get a TAMIU e-mail, visit TAMIU -mail for Life for Students and Alumni (http:// students.tamiu.edu/) to set up your account now. I will respond to emails within 24-48 hours, except on weekends. 

Grade Scale:

GRADE PERCENTAGE
A 91-100
B 80-90.9
C 70-79.9
D 60-69.9
F Below 60

Schedule of Topics and Assignments

Week of Agenda/Topic Reading(s) Due
1/22 Introduction, and Review Homework
1/27 Topics in group theory Contemporary Abstract Algebra 9th Ed by Joseph A Gallian. Homework
2/3 Topics in group theory Contemporary Abstract Algebra 9th Ed by Joseph A Gallian. Homework
2/10 Topics in group theory Contemporary Abstract Algebra 9th Ed by Joseph A Gallian. Homework
2/17 Topics in group theory Contemporary Abstract Algebra 9th Ed by Joseph A Gallian. Quiz 1
2/24 Topics in group theory Contemporary Abstract Algebra 9th Ed by Joseph A Gallian. Homework
3/3 Topics in Ring Theory Contemporary Abstract Algebra 9th Ed by Joseph A Gallian. Midterm 1
3/10 Spring Break Homework
3/17 Topics in Ring Theory Contemporary Abstract Algebra 9th Ed by Joseph A Gallian. Homework
3/24 Topics in Ring Theory Contemporary Abstract Algebra 9th Ed by Joseph A Gallian. Quiz 2
3/31 Topics in Ring Theory Contemporary Abstract Algebra 9th Ed by Joseph A Gallian. Homework
4/7 Topics in Ring Theory Contemporary Abstract Algebra 9th Ed by Joseph A Gallian. Midterm 2
4/14 Topics in Field theory Contemporary Abstract Algebra 9th Ed by Joseph A Gallian. Homework
4/21 Topics in Field theory Contemporary Abstract Algebra 9th Ed by Joseph A Gallian. Homwork
4/28 Topics in Field theory Contemporary Abstract Algebra 9th Ed by Joseph A Gallian. Quiz 3
5/5 Topics in Field theory
Review
5/12 Final exam at 6 p.m.

University/College Policies

Please see the University Policies below.