Florida Atlantic University • Fall 2024• Markus Schmidmeier

Welcome to Modern Algebra! We meet MWF 1:00 - 1:50 p.m. in Sanson Life Science 178. ## Modern Algebra

Why Abstract Algebra?As scientists, when we capture facts, we never try to reproduce them in full, but only that side which is important or relevant in a particular context. This process of

selecting what is relevantis the very essence of abstraction.We therefore will not study, say, the integers as one subject, the complex numbers as another, and matrices as a third subject. Rather, particular aspects will be isolated, put in axiomatic form, and studied without reference to any specific objects. The other side is that each aspect is shared by many traditional systems.

One of the most basic and ubiquitous structures in mathematics is the concept of groups, of which we will study both theoretical aspects and many applications: As you know, the integers form a group, but also the functions on the real line, the letters in a code word, the symmetries in a wallpaper pattern...

Textbook and topicsCharles C. Pinter,

A book of abstract algebra,2nd edition, Dover, ISBN-13: 978-0-486-47417-5. I plan to cover in particular the following sections.

Groups 2: Operations; 3: Definition of groups; 4: Elementary properties; Subgroups 5: Cayley diagrams, introduction to coding theory Examples 6: Functions, 7: permutations, 8: dihedral groups Symmetry Some examples of symmetry groups, say of three-dimensional objects or from music theory Comparing groups & New groups 9: Isomorphisms, 12: Cosets, 13: Lagrange's Theorem, 14: Homomorphimsm (as time permits)

Course Objectives

- Work with examples.
- Apply mathematical statements.
- Recognize mathematical structures in applications.
- Discuss axioms and definitions.
- Establish results about abstract mathematical structures, working from the axioms.
- Present in writing sequences of logical steps which demonstrate the validity of mathematical statements.
- Contribute to classroom discussion, in particular by presenting the solution of an algebra problem.

PrerequisiteDiscrete Mathematics with a minimum grade of C.

TutoringThe Math Learning Center in GS 211 offers in-person tutoring M-R 10-5 and F 10-4. Also, small group tutoring is available. For details please visit MLC or e-mail mlc@sci.fau.edu.

For online tutoring via zoom, please see ONLINE for available days and times.

Credit

I will assign homework problems every week, they will be posted on CANVAS. The problems will not be graded, but some may show up on a quiz.Homework:We will have a quiz every week onQuizzes:Friday.The quiz is based on the homework assignments. The best twelve quizzes count for50 %of the grade.Three presentations during class, each about a problem from our textbook. The best two will count forPresentation:10 %of the grade. The first (second, third) presentation needs to be given before September 13 (October 11, November 8). Unless there are volunteers, I will assign presentations for the next class meeting at random among all registered students.The final exam is comprehensive and will count forFinal Exam:40 %of your grade. It is scheduled for Monday, December 9, 10:30 a.m. - 1:00 p.m. in our classroom. Please bring a picture id (Owl card or drivers licence)!

Further InformationFor the Disability Policy, the Make-Up Policy, the Code of Academic Integrity, Religious Accommodation, my Grading Scale, the FAU Attendance Policy Statement, Financial Assistance Opportunities and the FAU Covid Statement please visit Infos for all my courses.

Contact Me

MW 10:00 - 11:20 a.m. in SE 272.Office hours:561-297-0275 (office)Phone:E-mail:mschmidm@fau.eduMarkusWeb Site:

Last modified:by Markus Schmidmeier