MAS 323 Spring 2021
Introduction to Modern Algebra and Geometry
Course Syllabus
last update: 2021-04-19
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:
- have increased strength and fluency in reading skills
- have increased strength and fluency in analysis and problem solving skills
- have increased strength and fluency in clear, concise communication skills
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.
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.
- Send the instructor email notice of your exam absence as far as
possible in advance of the missed exam, with a complete
explanation for the purpose of your conflicting event.
- In the case of illness or emergency where advance notice
is not possible, send an email message as soon as it is practically possible. Collect
documentation (doctor's notes, etc) to present to the instructor
when you return to class. Except for extreme circumstances, your
email notice is due by 5pm on the
day of the missed exam.
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.
- No food during class (face-to-face or online attendance).
- Use electronic devices only for engaging with the course
material. For example, note-taking, calculating, and looking up facts
related to the class discussion are positive activities; text
messaging and web surfing are rude behaviors that distract everyone
from focusing.
- Except for emergencies, please do not leave the class meeting once class
begins. If you need to leave before the end of class, please inform
the instructor before class begins.
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.
- BEFORE each class meeting
- Read the text section(s) indicated on
the course calendar.
- Write vocabulary and facts from the new text
section. Make vocabulary study cards.
- Solve at least a few of the low numbered problems
from the new text section.
- Note your questions, problems, and
difficulties. In the reading, where, precisely, do you
have trouble understanding? With the problems, what,
precisely, is obstructing you from completing a
solution?
- AFTER each class meeting
- Reread text sections listed for previous
class meetings.
- Solve more problems. Complete the list of
homework problems from text sections for previous
class days. Prepare complete written solutions,
using complete sentences.
- Revise and update your vocabulary and
fact note cards after a second round with
each section of text.
- EVERY WEEK
- Assess your progress and mastery. Have
you addressed all the questions and difficulties
noted previously?
- Follow up on any questions or gaps
that remain.
5.2 Study Strategies
- Plan for two hours of study outside of class for each hour of class.
- Keep an organized paper binder or electronic notebook with reading notes, homework solutions, and
class notes. Mark your questions clearly with sticky notes or some
other device and follow up every question, either in class
or in office hours, until you gain understanding.
- After reading, summarize the material in your own words.
- Use flash cards or lists to learn
vocabulary. Write each term on one side of a card. Write a definition
(using complete sentences, not sentence fragments) and an example on
the back of the card.
- To prepare for quizzes and exams, do the following, beginning some
days to a week in advance.
- Make an outline of course topics and problem types.
- Memorize vocabulary, including examples.
- Work and check solutions to problems from previous quizzes, exams,
and homework.
- If clock management during exams is an issue, practice working a few
exam style problems once a week with a timer running.
- If test anxiety has a negative effect on your performance, here
is some advice.
- Do not become sleep deprived. Trading sleep for study time is
counterproductive.
- Eat a healthy diet and exercise every day. Eating poorly and
lack of physical activity reduce your mental abilities.
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