Spring 2017

No Textbook for this Course

Prerequisites: This is an advanced, theory-based course.  Math 3460 is a required prerequisite; Math 2010 is strongly recommended but not required.

Purpose: This course is intended to provide advanced undergraduates with additional experience in proof techniques while also giving them extensive exposure to groups.  Topics covered include basic properties of groups,  subgroups,  group homomorphisms, quotient groups, and direct products.

OBJECTIVES: Upon completion of this course, students will have developed an understanding of: 
1. operations and equivalence relations, 
2. basic properties of groups, 
3. special classes of groups, 
4. homomorphisms and isomorphisms,
5. normal subgroups, 
6. quotient groups. 

REQUIREMENTS: In general, you are expected to 
1. attend class lectures and work with your assigned small group, 
2. read and study class assignments and solve assigned problems, 
3. ask questions in class when unsure of any concept or unclear on any assigned problem; 
4. take all announced exams (including the final) on the day they are scheduled
5. present assigned homework problems regularly in class. 

Grading:  This is an inquiry-oriented class that uses the "constructivist" approach to learning.  Among other things, this means many class meetings will involve you working in small groups to help you understand the fundamental concepts of group theory.  It is your responsibility as a member of this learning team to be actively participating, rather than merely taking notes.  You will be frequently working in a small group, and your group leader will be assessing the degree to which you are participating in moving the group forward.  Groups will be randomly selected each day, and everyone will have multiple chances to serve as group leader.

The course will consist of eleven investigations.  Each investigation presents you with of set of in-class problems that you will work on in small groups.  I will frequently ask you to explain your thinking on parts of a problem or to present a completed problem along with your group.  Your efforts in this regard will be part of your participation grade.

Investigations can be found on my webpage.

Ten percent of your grade will come from your participation in these groups.   The group leader will assess your participation in your group each day and assign you zero to four participation points.   Participation points relate to the following questions:

I will hand out a blank group roster each day.  You will sign it (for roll taking purposes) and your group leader will place your participation points next to your signature.

Each investigation includes a set of homework problems.  You are required to submit hardcopies of your solutions to these problems by the assigned deadlines.  You are encouraged to work with your classmates or use other outside resources to help complete your homework.  However, you must credit all individuals or outside sources that you used as part of your submitted homework.  Typically, one homework assignment will be due each week.  Late assignments will not be accepted unless you have contacted me in advance to make arrangements for turning in the assignment late.

A word of caution:  Never draw upon ideas or concepts from outside of class if you cannot explain them.  If you use notation or concepts that have not been developed in class, then I and everyone else in the class reserve the right to question you about their meaning.  Your ability to explain  these outside ideas and connect them to class content will be part of your participation grade or homework grade.

Fifteen percent of your grade will come from your submitted homework.  

There will be regular definitions and concept quizzes.  Most of these will be announced a class day in advance, and there will be roughly one per week starting in the second or third week.  All quizzes will be about twenty minutes long and cannot be made up, unless you have made prior arrangements with me.

Fifteen percent of your grade will come from these quizzes.

There will be two closed-book in-class exams, each lasting a full class period.  The first exam will be given near midterm and will cover the material in Investigations 1 - 6.  The second exam will be given at the end of the semester and will cover the material in Investigations 7 - 11.  Graduate students will also have a take-home portion of each exam that focuses exclusively on proofs.

Graduate students will also be expected to write a short paper (five to ten typed pages) that addresses some group theory topic or application.  This paper must include the statement and detailed proof of at least one result not discussed in class.  The paper will serve as a third exam grade.  

Fifty percent of your grade will come from these exams.

There will be a two-hour, closed-book, comprehensive final exam.

Ten percent of your grade will come from the final exam.  

A standard grading scale will be used on all graded work: 90-100 --- A, 80 - 89.5 --- B, etc. Particular grades are not curved; there will be an end-of-semester curve on exams based upon class performance.  (The curve is separate for graduate and undergraduate students.)

ATTENDANCE:  Attendance is expected and vital for this class.  Absences are not excuses for missing a graded in-class activity or turning in an assignment late.  Late assignments will not be accepted and makeup exams will not be given unless you have made prior arrangements with me.  With the exception of dire family emergency, you must contact me no later than the due day to get approval for late work.  

Except for medical or family emergencies, the scheduled makeup time cannot be more than two weekdays after the due date. 

I usually return an exam or quiz no more than two class days after it is given.  It is your responsibility to monitor your progress in the course.  I strongly recommend you actively ask questions in class or come to my office regularly to discuss your progress.  I will be happy to suggest strategies for helping you succeed, but no strategy provides a quick-fix. Do not wait until the last few weeks of class to try improving your grade. 


IMPORTANT:  It is Department policy not to grant withdrawals after the withdrawal deadline has passed, unless circumstances have arisen which make it impossible for you to complete the course.  Late withdrawals must be approved by the Department Chair and often require documentation for the extenuating circumstances.

No one will be exempt from the final.

LOTTERY STATEMENT:   To retain the Tennessee Education Lottery Scholarship eligibility, you must earn a cumulative TELS GPA of 2.75 after 24 and 48 attempted hours and a cumulative TELS GPA of 3.0 thereafter.  A grade of C, D, F, FA, or I in this class may negatively impact TELS eligibility. If you drop this class, withdraw, or if you stop attending this class you may lose eligibility for your lottery scholarship, and you will not be able to regain eligibility at a later time.For additional Lottery rules, please refer to your Lottery Statement of Understanding form ( or contact your MT One Stop Enrollment Counselor (

INCOMPLETES:  An incomplete will be given only in accordance with the University Policy.  If you have a disability that may require assistance or accommodation, or you have questions related to any accommodations  for testing, note takers, readers, etc., please speak with me as soon as possible. Students may also contact the  Office of Disabled Students Services (898-2783) with questions about such services.  

ACADEMIC MISCONDUCT:  Middle Tennessee State University takes a strong stance against academic misconduct.  Academic Misconduct includes, but is not limited to, plagiarism, cheating, and fabrication.  Plagiarism, cheating, fabrication, or facilitating any such act.  For purposes of this section, the following definitions apply:

(1) Plagiarism:  The adoption or reproduction of ideas, words, statements, images, or works of another person as one’s own without proper attribution. This includes self-plagiarism, which occurs when an author submits material or research from a previous academic exercise to satisfy the requirements of another exercise and uses it without proper citation of its reuse.

(2) Cheating:  Using or attempting to use unauthorized materials, information, or study aids in any academic exercise.  This includes unapproved collaboration, which occurs when a student works with others on an academic exercise without the express permission of the professor.  The term academic exercise includes all forms of work submitted for credit or hours.

 (3) Fabrication:  Unauthorized falsification or invention of any information or citation in an academic exercise.

Going online and taking information without proper citations, copying parts of other student’s work, creating information for the purposes of making your paper seem more official, or anything involving taking someone else’s thoughts or ideas without proper attribution is academic misconduct.  If you work together on an assignment when it is not allowed, it is academic misconduct.  If you have a question about an assignment, please come see me to clarify.  Any cases of academic misconduct will be reported to the Office of Academic Affairs for violating the academic honesty requirements in the student handbook.  They will also result in failure for the course.  Remember – ignorance is NOT a defense.   

Students with Disabilities:  Middle Tennessee State University is committed to campus access in accordance with Title II of the Americans with Disabilities Act and Section 504 of the Vocational Rehabilitation Act of 1973.  Any student interested in reasonable accommodations can consult the Disability & Access Center (DAC) website and/or contact the DAC for assistance at 615-898-2783 or

This syllabus is only a guide for your convenience; I reserve the right to make changes as class needs dictate.


Important dates:                                  

January 30 --- Last day to drop without a grade              March 26 --- Last day to drop with a "W"

March 6 - 11 --- Spring Break                                            April 27 --- Study Day (No Classes)                        

April 28 - May 4 --- Finals Week

 FINAL EXAM    ---    Thursday May 4       10:00  AM - 12:00 PM