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Math 330 Syllabus for Section 1 - CRN:12080
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Lecture: Mon Wed Fri 8:00 - 9:30 AM in WH 100B
General Course Info / Math 330 Section 1 Web Site:
This syllabus is only a part of an entire course website for Math 330 Section 1.
Here is the
link to the home page
of that the Math 330 Section 1 web site.
The red boxes that come next have been written according to a provided Harpur template.
they are followed by additional information that is not part of the template.
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Bulletin Course Description
(A detailed course Description can be found further down):
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Careful discussion of
the real numbers, the rational numbers and the integers,
including a thorough study of induction and recursion.
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The methodology of mathematics:
basic logic, the use of quantifiers, equivalence relations, sets and functions.
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Methods of proof in mathematics.
Training in how to discover and write proofs.
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Student Learning Outcomes:
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By the end of this course, students should have acquired the mathematical sophistication
and tool kit to attend any 300 and 400 level course in mathematics and statistics that
does not directly build on a prior course.
(Of course, the student must have taken, for example,
a Modern Algebra I to be successful in a Modern Algebra II).
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Contact Hours:
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This is a 4-credit course, which means that,
in addition to the scheduled meeting times,
students are expected to do at least 9.5 hours of course-related work
outside of class each week during the semester.
This includes time spent completing assigned readings,
studying for tests and examinations, preparing written assignments,
and other course-related tasks.
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Prerequisites:
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C or better in MATH 227 or MATH 230, or consent of instructor.
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Course Schedule:
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See the
Schedule
page of the Math 330, Section 1 website.
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Course materials:
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- This instructor's lecture notes: Math 330 - Lecture Notes.
We abbreviate this as MF or the MF doc.
(Required)
A downloadable PDF of this document and additional background material
can be found on the
Course material
page of the Math 330, Section 1 website.
- The Art of Proof: Basic Training for Deeper Mathematics
by Matthias Beck and Ross Geoghegan (Springer, 2010).
We abbreviate this as B/G or AoP.
(Optional, but strongly recommended)
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Assignments:
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Exams:
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There will be two midterm exams and one final exam.
No notes, books, cell phones, or laptops are allowed for tests.
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Exam dates can be found on the course home page and schedule page.
Make all arrangements necessary to take the tests at those dates
as it is extremely unlikely that they will be changed.
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Each midterm will last 60 minutes and is worth 100 points.
Make an effort to show up 10 minutes early for those exams
so they can start on time.
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The final exam counts for 200 points and it will last two hours.
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I have published the date for the final exam on my home and schedule pages.
That is for your convenience only.
You are advised to double-check with the official schedule.
Makeup Exams:
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You can request a makeup final if you have another final at the same time
(direct conflict) or you have three final exams scheduled within 24 hours.
To request a makeup final,
please contact me by email no later than Monday, Nov 25.
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Quizzes:
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There will be approximately 10 quizzes. The sum of points will be adjusted to 200.
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The number of quizzes depends on how the class is doing in knowing the axioms,
definitions, main propositions and theorems as checking for this
will be the main purpose of the quizzes.
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Additional quizzes will be given if the class needs to do better.
Quizzes will often not be announced.
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Homework:
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Homework counts for 40% of the grade and will be graded in iterations:
You will have a total of up to 3 iterations (i.e., a total of 4 submissions)
for most of those assignments.
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The final submission date will be noted on the homework assignment.
It usually is two weeks after the date when the homework is posted.
You will have less than two full weeks during the last two weeks of the semester
` and you may get additional time when holidays fall into that period.
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Especially at the beginning, I will grade your homework according to
the "red line" method:
I stop grading when I see a major flaw and I'll mark that spot with a red line.
Sometimes I'll comment on the nature of the problem,
at others you will have to figure it out on your own.
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You will learn from the course material and from my presentations how to write a proof,
but here are some purely technical requirements you should be clear about
from the start:
- Write your proofs very neatly.
Use lined paper so that your text is written in straight lines.
I may allow you to used unlined paper if you can show evidence that
you can write in straight lines on plain paper.
- Leave margins of at least 1/2 inch to the left
and at least 1 1/2 inches to the right.
- Write your homework double-spaced so you and I can insert
corrections in a neat and orderly fashion.
- Write legibly! I'll be spending a lot of time
looking at your homework and I won't have extra time
to carefully deliberate whether your variable was,
e.g., a "u" or a "v".
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You are allowed, even encouraged, to work in groups on your homework.
However, each student must turn in his or her own work, not a copied solution.
You must note on your assignment with whom you collaborated.
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How the Assignments Determine Your Grade:
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You can earn a total of 1,000 points in this course:
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| Final Exam |
200 pts |
200 pts |
| 2 Midterm Exams |
100 pts each |
200 pts |
| About 10 Quizzes |
Points may vary and will add up to a total of 200 points |
200 pts |
| About 20 Homeworks |
Points are varying
and will be scaled to a total of 400 points |
400 pts |
| Total: |
1,000 pts |
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TENTATIVE
Grading Scale
(unlikely to be adjusted):
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850 - 899 pts → A- |
900 - 1000 pts → A |
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700 - 749 pts → B- |
750 - 799 pts → B |
800 - 849 pts → B+ |
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550 - 599 pts → C- |
600 - 649 pts → C |
650 - 699 pts → C+ |
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500 - 549 pts → D |
Below 500 pts → F |
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Detailed Course Description:
You will learn in this course how to think like a mathematician:
- Understand the nature of a rigorous mathematically proof
- Learn to write such proofs
- Generalize familiar mathematical concepts to abstract
settings
To reach this goal you will acquire knowledge in the following areas:
- logic: direct proofs vs proofs by contradiction, logical quantifiers
- the difference between axioms, definitions and theorems
- sets, functions and relations
- recursive definitions and proofs by induction
- proofs that use Zorn's Lemma
The specific subject matter used to teach you this will be
primarily taken from number systems and real analysis:
- an axiomatic approach to the properties of natural numbers, integers,
fractions and real numbers will be presented.
- You will learn how to compare the sizes of infinite sets (cardinality).
- Convergence and continuity will be explored with mathematical rigor
in the context of real numbers.
- Convergence, continuity and other concepts involving closeness and distance
will be generalized to metric and topological spaces.
The
Homework page
of the course website contains a link to the complete set of homework assignments that
were given out during the previous semester.
The reading assignments of those homework sets constitute a complete record of
the material that was taught during that semester.
There will always be changes, but those reading assignments reflect to a large extent
what I will teach during this semester.
Not a Prerequisite, but helpful:
Basics of linear algebra:
vector spaces and subspaces,
linear independence, (linear) span, basis,
and Euclidean space Rn as a vector space.
See the bottom of the
Course material
page of the Math 330 website for more.
Lectures during campus wide class cancellations:
BU admin leaves it at the discretion of the instructor whether or not
lectures will be held in case of a cancellation due to inclement weather or other
circumstances that transportation to/from campus is suspended.
My policy for this situation, should it occur, is as follows.
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I will hold lecture via Zoom.
I will create a separate session for each such meeting
and publish the link for the meeting via email.
This may happen on short notice, so check your email for an announcement
in case there is a campus wide cancellation of classes.
- I plan to record those sessions and publish the links on the course materials page.
- If a midterm or quiz is scheduled during such a date, then it will be administered
during the next in-class lecture date.
MyCourses (Brightspace):
I do NOT plan to use Brightspace. Instead I will assign to each one of you a course internal ID
which is known only to you and me.
I will periodically email a spreadsheet of everyone's grades to-date, one row per student,
and each row will contain that internal ID.
That way your grades will remain anonymous.
Record keeping:
Stay on top of your grades!
If your grade is incorrect you must contact me immediately.
You must retain all returned papers in case of any discrepancy with your course grade.
I cannot correct mistakes in grading or recording of scores
without the original document.
I won't review disputed points after the final.
All grading issues must be settled within one week of the return of the paper.
Students With Disabilities:
Students requesting disability-related accommodations should register with
the Services for Students with Disabilities office (SSD).
They are the appropriate entity on campus to determine and authorize
disability-related accommodations.
For more info please
click here.
Once you are registered with SSD you should approach me during office hours or after lecture
so that you and I can discuss the implementation of your accommodations.
Success:
See the
Advice
page of the Math 330 website.
Attendance Policy and Make-up Policy:
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Attendance will not be taken, but you are advised not to skip lecture:
If you cannot spare the time to go to lecture then you should
consider dropping/withdrawing from the course before
your GPA is messed up.
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Make-up exams and quizzes will only be given in response to an excused absence.
Excused absences include illness, religious holidays, a major tragedy in the family,
and participation in official BU athletic events.
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I very seldom give a make-up quiz and instead, I will count the next quiz double.
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To be excused, absences must be properly documented.
The document should be issued to you at the day of the test.
The makeup will be scheduled within 3 or 4 days after the missed exam.
You must request a make-up in writing by sending an email.
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Except in very exceptional circumstances such as a prolongued illness,
you will NOT be given the opportunity to complete old assignments at the end of the
semester to improve your grades.
When you receive a grade, whether on MyCourses or in class,
you will have one week to discuss that grade before it becomes FINAL.
Academic Honesty:
Incidents of academic dishonesty will be dealt with severely.
There is precedent for giving an "F" for the course to a student who attempts to advance
his/her grade illegally.
Dishonesty includes, but is not limited to:
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Copying another student's work
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Letting someone copy your work
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lying to or intentionally misleading an instructor
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Signing someone else's name to a document
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Homework assignments only:
only having your name on the PDF but not understanding the proofs.
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I will make spot checks
of exams, quizzes and homework
to ascertain that the student obtained the correct answers on her/his own.
To eliminate suspicion, only writing/erasing utensils will be permitted
on desks during an in-class exam.
Best wishes for a successful semester!
Michael Fochler
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