MAS 323 Spring 2023
Introduction to Modern Algebra and Geometry
Course Syllabus
last update: 2023-05-05
Course policies and calendar are subject to change, at the
discretion of the instructor.
Table of Contents
Basics
1 Instructor
2 Class Meetings, Office Hours
3 Course Calendar
4 Exam Dates (Tentative)
5 Prerequisites
6 Requirements Met
7 Required Text(s) and Materials
Course Content
8 Course Description
9 Reading and Problem List
10 Course Goals, Objectives, and Learning Outcomes
Grades
11 Graded Work
12 Daily Participation
13 Writing Assignments
14 Exams
15 Makeup Assignments, Makeup Exams, and Extra Credit
16 Letter Grades
Policies
17 Attendance
18 Class Engagement
19 Collaboration versus Plagiarism
20 Honor Policy
Learning and Study
21 Learning
22 Study Strategies
23 Sample Study Aids
24 Portfolio
LVC Official Syllabus Material
25 LVC Policies and Statements
Basics
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
2 Class Meetings, Office Hours
Meeting times and locations for classes and office hours will be kept up to date on the
Instructor's
Schedule.
Bring your portfolio (see the "Portfolio"
section below) when you come to office hours.
3 Course Calendar
The course calendar is maintained on Canvas. All dates are subject to change.
4 Exam Dates (Tentative)
Subject to change, exams are scheduled on the following dates.
Thu 2/2 Exam Ch 1
Thu 3/23 Exam Ch 2
Thu 5/4 Exam Ch 3
Tue 5/9 8:30--11:00 Final Exam
5 Prerequisites
MAS 202 and MAS 222
6 Requirements Met
Credit Hours: 3
7 Required Text(s) and Materials
The textbook is free online.
Course Content
8 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.
9 Reading and Problem List
Reading Problems
------- --------
1.1 all
1.2 all
1.3 all
1.4 all
2.1 all
2.2 all
2.3 all
2.4 all
2.5 all
3.1 all
3.2 all
3.3 all
3.4 all
3.5 all
10 Course Goals, Objectives, and Learning Outcomes
The primary goal of the course is understanding and proficiency
in the use of mathematical concepts. Student learning objectives are
proficiency in reading, analysis and problem solving,
and clear, concise communication. Achievement of goals and
objectives requires desire for learning, willingness to work hard,
time commitment (two hours outside of class for every one hour in
class), and persistence.
Learning Outcomes Summary. Understanding and using the mathematical
concepts of this course, a student who achieves the course learning objectives will:
- demonstrate proficiency in reading skills
- demonstrate proficiency in analysis and problem solving skills
- demonstrate proficiency in clear, concise communication skills
Grades
11 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 20%
Written Assignments 40%
Exams 40%
12 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. |
13 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.
14 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, 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. Solutions must be
written in narrative form, using 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.
No music listening devices or electronics with wireless or network capabilities
(computers, phones, etc.) are allowed during exams. No hats
with brims are allowed during quizzes or exams. If you need to leave the
classroom during an exam, you must leave your cell phone at the
instructor's desk in the front of the room.
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. |
15 Makeup Assignments, Makeup Exams, and Extra Credit
There are no makeup assignments, makeup exams, or extra credit
assignments.
16 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 proficiency with 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.
Policies
17 Attendance
Class attendance is expected, but it is understood that sometimes there
are reasonable circumstances for absence. For most students, there is no
grade for attendance or participation (see the exception for "chronic
absenteeism" below), but it is expected that each student will exercise
good judgment for choosing to miss a class.
Absence from an exam may be excused, at the discretion of the instructor, for
certain events planned in advance or for emergency or illness. (If you
are quarantined, you make take the exam online.) 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. Except for extreme circumstances, your email
notice is due by 5pm on the day of the missed exam. Collect
documentation (doctor's notes, etc)
and send them to the instructor by email.
Absence does not change the due date for any graded work.
Policy for chronic absenteeism: Chronic unexcused absence has a
negative impact on classroom learning. The instructor may elect to
impose a grade deduction for each unexcused absence beyond the
third. Communication will be made by email when this policy is in
effect.
18 Class Engagement
The purpose of class meetings is to pursue understanding and proficiency
with 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.
- No food is allowed during class.
- 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, social media browsing, 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.
19 Collaboration versus Plagiarism
You are encouraged to collaborate with classmates and ask questions of
the instructor or consult any source for homework. 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.
20 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.
Learning and Study
21 Learning
The process of reading, learning vocabulary, 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 there is no substitute for study
that you do yourself.
The time expectation for out-of-class work is two hours outside of class for
every one 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 study time guarantees lack of success in the course;
consistent high quality studying guarantees a positive learning
experience. Here is an outline of the work flow for each section in the text(s).
- BEFORE class discussion
- Read the text material indicated on
the course calendar.
- Write vocabulary study cards (or study lists) for
terminology, facts, and formulas from the new text
section.
- Solve at least a few of the 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 class discussion
- Reread text material from previous
class meetings.
- Revise your vocabulary and
fact note cards; make sure your vocabulary list is complete.
- Solve and check solutions to all of the problems listed in
the "Reading and Problem List" in the
syllabus. Prepare complete written solutions, using
complete sentences. Compare your solutions to the
answer keys in the text(s) and solutions manual(s).
- BEFORE the quiz
- Assess your progress and proficiency. Have
you addressed all the questions and difficulties
noted previously?
- Rehearse vocabulary using the cards or
lists you have prepared.
- Practice solving problems using a timer.
- Follow up on any questions or gaps
that remain.
- AFTER the quiz
- Assess (again!) your progress and
proficiency. Rework and check solutions to all quiz
problems for which you received less than full
credit.
- Follow up (again!) on any questions or gaps
that remain.
22 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 (see the Portfolio section below). 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.
23 Sample Study Aids
24 Portfolio
Keep your work organized. Use electronic or hard copy media, whatever
works best for you. Whatever method you use, it should be designed to
facilitate sorting, searching, planning, and tracking. A complete
portfolio includes:
- Progress tracking sheets
- Vocabulary notecards or study sheets
- Reading and class notes
- Solved problems
The portfolio is an essential tool for learning; it is also an essential
instrument for diagnosis and improvement. Bring your portfolio to office
hours visits.
There is no specific portfolio grade. However, a consistent, thorough,
and complete portfolio will influence the letter grade assignment for a
cumulative average near a grade cutoff borderline (see
the Letter Grades section below). For
example, if two students both have an 86% cumulative average, the
student who has shown a consistently thorough portfolio during office
hours might receive a B+, while the other student might receive a B.
LVC Official Syllabus Material
25 LVC Policies and Statements