MAS 323 Spring 2021
Introduction to Modern Algebra and Geometry
Course Syllabus

last update: 2021-02-20

Course policies and calendar are subject to change, at the discretion of the instructor. See the Syllabus Update Log.


  

Table of Contents

1 Basics
  1.1 Instructor
  1.2 Class Meetings, Office Hours
  1.3 Course Calendar
  1.4 Exam Dates (Tentative)
  1.5 Prerequisites
  1.6 Requirements Met
  1.7 Required Text(s) and Materials

2 Course Content
  2.1 Course Description
  2.2 Reading and Problem List
  2.3 Course Goals, Objectives, and Learning Outcomes

3 Grades
  3.1 Graded Work
  3.2 Daily Participation
  3.3 Writing Assignments
  3.4 Exams
  3.5 Makeup Assignments, Makeup Exams, and Extra Credit
  3.6 Letter Grades

4 Policies
  4.1 Attendance
  4.2 Class Engagement
  4.3 Collaboration versus Plagiarism
  4.4 Honor Policy

5 Learning and Study
  5.1 Learning
  5.2 Study Strategies
  5.3 Sample Vocabulary Notecards
  5.4 Sample Written Solutions

6 LVC Official Syllabus Material
  6.1 LVC Policies and Statements

1 Basics

1.1 Instructor

  David W. Lyons, Professor
  Department of Mathematical Sciences
  Lebanon Valley College
  Email: lyons (at) lvc.edu
  Phone: (717) 867-6081
  Office: LYN 283H

1.2 Class Meetings, Office Hours

Meeting times for classes and office hours will be kept up to date on the Instructor's Schedule.

As of 1/25/2021, all class meetings for the first two weeks of the semester, 2/1/2021 to 2/12/2021, will be online for all students.

Office hours will be held online until further notice.

Zoom links for online class meetings and office hours will be posted on the Canvas course homepage.

1.3 Course Calendar

The course calendar is maintained on Canvas. It includes class meetings, graded homework assignments, and exams. All dates are subject to change.

1.4 Exam Dates (Tentative)

Subject to change, exams are scheduled on the following dates.
  Thu 2/18 Exam Ch 1
  Thu 4/1  Exam Ch 2
  Thu 5/13 Exam Ch 3
  Tue 5/18 at 8:30  Final Exam Section 2 (3pm class)

1.5 Prerequisites

MAS 202 and MAS 222

1.6 Requirements Met

  Credit Hours: 3

1.7 Required Text(s) and Materials

The textbook is free online.

2 Course Content

2.1 Course Description

This course is an introduction to group theory combined with an introduction to modern geometries. Group theory topics include properties of groups and homomorphisms and actions of groups on sets. Geometry topics include the basic theory of Möbius, hyperbolic, elliptic, and projective geometries.

2.2 Reading and Problem List

The reading list is Chapters 1, 2, and 3 of the textbook. The problem
list is all the problems in each section of the textbook.

2.3 Course Goals, Objectives, and Learning Outcomes

The primary goal of the course is mathematical intellectual growth through the understanding and mastery of mathematical concepts. Student learning objectives are strength and fluency in reading, in analysis and problem solving, and in clear, concise communication. Achievement of goals and learning objectives requires desire for learning, willingness to work hard, time commitment (at least two hours on homework outside of class for each hour in class), and persistence.

Learning Outcomes Summary. Through the medium of the mathematical concepts of this course, a student who achieves the course learning objectives will:

3 Grades

3.1 Graded Work

Your cumulative average is determined by graded work in the categories listed below with the indicated weights. Details and instructions are given in the sections that follow.
  Daily Participation    10%
  Written Assignments    35%
  Exams (non-final)      35%
  Final exam             20%

3.2 Daily Participation

Daily participation consists of presenting solutions to problems and participating in discussion of presentations made by other students and the instructor. Presentations will be graded for effort and completeness, but not for correctness. Because the list of problems and the roster rotation is known in advance, students will usually be able to plan ahead and coordinate who will present which problem. In the case that one's pre-prepared problem is already "taken", the presenter will display a positive spirit and make an honest attempt at improvising a solution to a new problem. Here is the grading rubric.

Daily presentations
Category Description
Complete Presentations are fully prepared in a way that shows a good faith effort to thoroughly complete the assignment. In case of a last-minute problem change, the presenter makes an honest attempt and improvises in a positive spirit.
Partially complete A presentation that should have been thoroughly prepared is not fully complete or shows little effort.
No credit Presentations are not prepared.

3.3 Writing Assignments

Writing assignments must be typed and must use appropriate mathematical symbols and typesetting conventions. Handwritten solutions will not be accepted. Your writing assignment will be graded for correctness in the following ways: for correct use of vocabulary and notation; for correct logical flow in your argument; and for the correct final conclusion(s). The grading rubric for each written solution is the same as for the "Exam Grading Rubric" (below) with the addition of the following in the description of the top category called "complete and correct".
The written solution is typed and uses appropriate mathematical symbols and typesetting conventions.

3.4 Exams

Exam problems are based on, but not limited to, the assigned reading and exercises. Exam format, subject matter, and rules will be announced in advance. The final exam will be comprehensive, including material from the entire course. In keeping with College policy, the final exam can only be taken at the officially scheduled time during final exams week.

For full credit, quiz and exam solutions must show not just final results, but also demonstrate with appropriate supporting work and using appropriate vocabulary that you understand the reasoning involved. Each solution requires one or more complete sentences. Solutions will be graded not only for mathematical correctness, but for clarity of writing. Illegible work or a final answer given without supporting work shown receives no credit.

Here is the rubric for each exam problem solution. Exceptions will be announced in advance.

Exam Grading Rubric
Category Description
Complete and correct The solution is written using one or more complete sentences, shows appropriate work, and uses appropriate vocabulary. Calculations and logical reasoning are correct.
Substantive progress The solution shows understanding of facts, methods, and issues involved, but does not meet the description of "complete and correct".
Some progress The response shows plausible evidence that some aspect of the problem is grasped, but does not meet the description of "substantive progress".
No progress The response is blank, illegible, or shows no plausible evidence that some key aspect of the solution is grasped.

3.5 Makeup Assignments, Makeup Exams, and Extra Credit

There are no makeup assignments, makeup exams, or extra credit assignments.

3.6 Letter Grades

Meaning of letter grades

According to the College Catalog, letter grades have the following meanings.
   Letter Grade     Meaning
   ------------     ------
        A           excellent
        B           good
        C           satisfactory
        D           requirements and standards met at a minimum level
        F           course requirements not met
Standards for ``excellent'' and ``good'' (letter grades A and B) are high. In this course, your grade reflects your mastery of the material. A good grade is not guaranteed by class attendance and performing the motions of homework; to earn an A or a B, you must demonstrate understanding that transcends mere rote familiarity.

Determination of letter grade

At the end of the semester, your final cumulative average is used to assign a letter grade. The scale used to convert cumulative averages to letter grades is based on the ``standard 10 point scale'' (A-,A,A+ for 90 to 100 percent range, B-,B,B+ for percentages in the 80's, C-,C,C+ for the 70's, etc.), but the scale may be adjusted, at the discretion of the instructor, so that the meanings of the letter grades fit the descriptions given in the previous section. Pluses and minuses are used to distinguish between the low, middle and high achievers within each letter grade category.

Note on mid-term grades: Pluses and minuses are not used for midterm grades.

4 Policies

4.1 Attendance

Class attendance, both face-to-face and online, is expected, but it is understood that sometimes there are reasonable circumstances for absence. There is no grade for attendance or participation, but it is expected that each student will exercise good judgment for choosing to miss a class.

Except for exam days, excuses for absences are not required. Absence from an exam may be excused, at the discretion of the instructor, for certain events planned in advance or for emergency or illness. Here is the procedure to follow if you wish to have an exam absence excused.

Absence does not change the due date for any graded work.

4.2 Class Engagement

The purpose of class meetings is to pursue understanding and mastery of the course material. This requires mental presence, engagement with the subject, and participation. Class meetings presume respect, politeness, and kindness among all those in attendance. In consideration for the learning environment, please observe the following in the classroom.

4.3 Collaboration versus Plagiarism

You are encouraged to collaborate with classmates and ask questions of the instructor or consult any source for homework and out-of-class writing exercises. You must work hard to avoid plagiarism, which is presenting someone else's ideas or work as your own. The work you submit must be your own. Your writing must be your own voice and your own understanding. You must use proper academic citation for any material created by others. Plagiarism is a serious academic offense; penalties range from failing the course to expulsion from the college.

4.4 Honor Policy

It is expected that each student in this class will act with honesty and academic integrity. Instances of academic dishonesty will be pursued as described in the College Catalog and Student Handbook.

5 Learning and Study

5.1 Learning

Learning through study outside of class is the most important part of the course. The process of reading, thinking, solving problems, and writing is the only way to achieve real understanding and skills. No one else can read, think, or write for you. It can be very helpful to watch other people solve problems and explain ideas in class, in a video, in a study group, or in a tutoring session, but that is no substitute for study that you do yourself.

The time expectation for out-of-class study is two hours outside of class for every hour of class meeting time. Plan your study time in your weekly schedule.

The quality of your out-of-class study translates directly into success. Low effort or too little time spent studying guarantees lack of success in the course; consistent high quality studying guarantees a positive learning experience. Here is an outline of the studying process.

5.2 Study Strategies

5.3 Sample Vocabulary Notecards

Examples of notecards for study aids

5.4 Sample Written Solutions

Guidelines and examples for graded written work

6 LVC Official Syllabus Material

6.1 LVC Policies and Statements

LVC policies and statements required for all course syllabi, from the office of the Dean of the Faculty