# Math 280 Modern Algebra I

### Course Information

Meeting Times: Monday, Wednesday, and Friday, 9:00 - 9:50 am

Location: Hirt 213

Office Hours: Monday 1-1:50, Tuesday 9:30-11 and 3:30-4, Wednesday 1-1:50, Thursday 9-10, Friday 1-1:50

Prerequisite: Math 150, Math 265

Location: Hirt 213

Office Hours: Monday 1-1:50, Tuesday 9:30-11 and 3:30-4, Wednesday 1-1:50, Thursday 9-10, Friday 1-1:50

Prerequisite: Math 150, Math 265

### Course Description

This is the first semester of a year long sequence on the study of algebraic structures. Course topics include the properties of numbers, equivalence relations, groups, rings, fields, direct products, homomorphisms and isomorphisms, and the natural development of various number systems.

### Objectives

On successful completion of the course, students will be able to:

- provide the definitions of algebraic objects, and know some examples of each.
- develop abstract and critical reasoning by studying and writing mathematical proofs.
- understand the connection between modern algebra and other branches of mathematics.
- relate the material learned in this course to prerequisite courses.
- recognize algebraic structures and objects in everyday situations.
- learn about the historical development of modern algebra.

### Required Materials

We will be using

The book may be available as an inexpensive rental. If you plan to take Modern Algebra II (Math 281), it is highly recommended that you purchase the text, as you will need it for both semesters.

**Contemporary Abstract Algebra**, 8th Edition, by Joseph A. Gallian. An older edition of the text would be fine. No other texts or materials are required. You will not be required to bring the text to class, so an electronic version is acceptable.The book may be available as an inexpensive rental. If you plan to take Modern Algebra II (Math 281), it is highly recommended that you purchase the text, as you will need it for both semesters.

### Homework

You will have several assignment due throughout the semester (generally every Friday). You should expect to spend a fair amount of time on each assignment - don't wait until the night before it's due to get started! You are free to work together on your assignments, but everyone must submit their own work, in their own words. Late homework will be accepted with a 10% per day penalty, until the graded assignments are returned.

Along with each assignment, you will be given a list of suggested problems from the textbook. These are often more computational in nature, and will not be collected. However, these questions may appear on an exam, so please try them and ask questions.

Along with each assignment, you will be given a list of suggested problems from the textbook. These are often more computational in nature, and will not be collected. However, these questions may appear on an exam, so please try them and ask questions.

### Exams

We will have two midterm exams and a final exam. The final exam will be cumulative, while the midterm exams will focus on more recent material. Both exams will be based on homework problems and the suggested textbook problems that do not need to be turned in.

Midterm Exam: Friday, October 6

Midterm Exam: Wednesday, November 15

Final Exam: Friday, December 15, 8 - 10 am.

**Exam Dates:**Midterm Exam: Friday, October 6

Midterm Exam: Wednesday, November 15

Final Exam: Friday, December 15, 8 - 10 am.

### Final Grades

Your final grade will be calculated as follows:

**Midterm Exam Average:**40%**Assignments:**35%**Final Exam:**25%

F | D | D+ | C | C+ | B | B+ | A |

0-59 | 60-66 | 67-69 | 70-76 | 77-79 | 80-86 | 87-89 | 90-100 |

### Learning Differences

In keeping with college policy, any student with a disability who needs academic accommodations must call Learning Differences Program secretary at 824-3017, to arrange a confidential appointment with the director of the Learning Differences Program during the first week of classes.

### Mercy Mission

This course supports the mission of Mercyhurst University by creating students who are intellectually creative. Students will foster this creativity by: applying critical thinking and qualitative reasoning techniques to new disciplines; developing, analyzing, and synthesizing scientific ideas; and engaging in innovative problem solving strategies.

### Links and Resources

**Joseph Gallian's Abstract Algebra Website**

Website of our textbook's author, including some useful links and information.

**MIT OpenCourseWare Abstract Algebra by Michael Artin**

Full online course in abstract algebra, as presented by Dr. Michael Artin. Includes notes, videos, problems, and study material. If you're planning to continue in mathematics, I'd also highly recommend purchasing a copy of Artin's

*Algebra*, a graduate level textbook.

*Algebra: Abstract and Concrete*, Frederick M. GoodmanFree abstract algebra textbook, along with accompanying Mathematica programs and demos from the University of Iowa. Great introduction to symmetry.

*Abstract Algebra: Theory & Applications*, Thomas Judson"...an open-source textbook written by Tom Judson that is designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Its strengths include a wide range of exercises, both computational and theoretical, plus many nontrivial applications."

**Harvard Extension School's Abstract Algebra Course**

Resources for an abstract algebra course, including videos, audio files, and problem sets covering most of the topics we'll be learning. Also includes a section on linear algebra.

*Book of Proof*, Richard HammackFree textbook offering a good review of the structure and language of proofs. Also includes a section on relations, functions, and cardinality.

*Linear Algebra*, Jim HefferonLinear algebra textbook, if you need a refresher on systems of equations, vector spaces, etc.

#### Free Software

**Wolfram Alpha**(Web Application)

Use it to check your work and visualize graphs. From the makers of Mathematica. A (modestly priced) upgrade is available, but the free version allows unlimited computations without an account.

**GAP**(Unix, Mac OS, or Windows)

"GAP is a system for computational discrete algebra, with particular emphasis on Computational Group Theory. GAP provides a programming language, a library of thousands of functions implementing algebraic algorithms written in the GAP language as well as large data libraries of algebraic objects. See also the overview and the description of the mathematical capabilities. GAP is used in research and teaching for studying groups and their representations, rings, vector spaces, algebras, combinatorial structures, and more. The system, including source, is distributed freely. You can study and easily modify or extend it for your special use."

**Sage**(Unix or Mac OS)

An open source mathematics software system. Runs natively on Linux and Mac, but you can also run it within your browser. Plenty of documentation to help offset the learning curve. Based on Python with plenty of useful packages, and you can contribute!

## Schedule

The exact topic covered on a particular date is subject to change. Exams and quizzes will be given on the day they are scheduled, though the sections appearing on a quiz may differ. Announcements will be made in class regarding any schedule changes.

Date | Topic | Notes |