This class follows a rotating "B-week" schedule:               The first week's lectures (Aug 26 and Aug 28) will be online, the second week's lectures will be in UU 206, and then we keep alternating: odd-numbered week's lectures online, even-numbered week's lectures UU 206.

COVID-19:

Even if you happen to be a transfer student and this is your first semester at BU you will be painfully aware that things are going to be very different not only from last year's fall semester but also from this year's spring semester. I will not repeat here where on the Binghamton University website you find the information pertaining to the pandemic, but I make one major exception.

Here is the link to the COVID-19 Campus Re-Opening, Fall 2020S: Student Acknowledgement of Rights and Responsibilities PDF Which each one of you must sign by September first. I cannot tell you how and where to submit that acknowledgement, but since it concerns the entire semester and not only this class I assume you will to submit this to Harpur College in some way. Be sure to also read carefully the info in the links provided on the Restarting Binghamton webpage.
   

If a student does not comply with the requirements and refuses to wear their face mask properly so that it covers the nose and mouth tightly, to leave the classroom when directed, or to follow instructions for reseating when directed by the instructor, the instructor will immediately cancel the remainder of the class session and inform the dean’s office, which will work with the Student Records office to issue a failing grade ('F') for the course regardless of when in the semester the incident occurs. The dean’s office will also inform the Office of Student Conduct.

If the above which we instructors have been asked to include into the syllabus seems harsh, consider: If you violate the safety instructions and a student in my class becomes severely ill with COVID 19 then I will have to live with it, legally and emotionally. Whether that student actually got the virus in my class or somewhere else may never be known, but that is only of minor importance. On a personal note, I am in the second half of my sixties and I am not willing to take any unnecessAry risk due to a student's lack of consideration.

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.

We may not be able to progress that far if online teaching this course slows us down.

General course info / Math 330 section 6 web site:

There is a course website for Math 330 section 6, and this syllabus is published both as part of that site, but also as a standalone version on the Mycourses (Blackboard) site. You can link to my Math 330 site from my instructor's home page. Here is a direct link to the home page of the Math 330 section 6 web site.

Prerequisites:    

Math 223-227 (single variable calculus) on a C- level or permission of the instructor. If you did not pass each one of those courses with a grade better than D then this does not automatically disqualify you, but you must see me asap! You need some calculus background in the second half of the course and you may have to catch up on some topics to follow the course. You will be dropped from this course unless you can convince me that you have knowledge or are able to learn quickly about limits, continuity, power series, derivatives as limits of difference quotients and integrals as limits of Riemann sums.

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.

Course material:    

• 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. (Required)
• This instructor's lecture notes: Math 330 - Additional Material. 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 website.

Lectures:

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 assignments constitute a complete record of the material that was taught then. There will always be changes, but those reading assignments reflect to a large extent what I will teach during this semester.

Blackboard:

Grades will be recorded in the Blackboard online gradebook. Stay on top of your grades! If your grade is incorrect you must contact me immediately.

Record keeping:

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.

Quizzes & Homework:

Quizzes:

There will be approximately 10 quizzes. The sum of points will be adjusted to 200. 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. Additional quizzes will be given if the class needs to do better. Quizzes will often not be announced. They will very likely be administered via Blackboard.

Homework:

Homework counts for 40% of the grade. It comes in two flavors:

• Most of the assignments will be graded in iterations: You will usually have a total of up to 2 iterations (i.e., a total of 3 submissions) for most of those assignments. The final submission date will be noted on the homework assignment, and it will usually be 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.
• There may also be one or more assignments which will be graded only once. They are less about proofs and more about checking that you have learned the material. For many of the problems you will just be asked to provide the correct result.

Usually each problem is worth one point. You will see for example that homework #1 consists of four problems, so you can earn up to 4 points on this assignment.

• Partial credit will be given.
• If the homework set has several iterations (default = 2 iterations) you have the chance to improve your scores with each iteration.
• At the end of the semester the homework points will be scaled to 400 points (=40%). An example: Assume that a total of 50 problems was given during the semester. Then each homework point is worth 400/50 = 8.0 points. Assume further that you got a total of 35.0 points for your homework. Then your homework will be worth a total of 35.0 * 8.0 = 280.0 grade points.
• Partial credit will be given.

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: You are not allowed to submit your homework in handwritten format. Instead you must use the Latex typesetting program. I intend to publish one or more samples before the start of the semester. This is all the help you will get from this instructor. You are expected to teach yourself the few things about Latex you truly need to know on your own. Here are some items that might help about this subject:

• I know of two major distributions: MikTex and Tex Live. I used MikTex for many years before switching to Tex Live.
• MikTex download and other info: https://miktex.org/download
• Tex Live download and other info: https://www.tug.org/texlive/acquire.html
• There are GUI environments for editing Latex documents Here you find a list: https://beebom.com/best-latex-editors/
• I have created a zip file with two sample tex files which you can examine.

You are allowed, even encouraged, to work in groups on your homework. Group size limit for homework is THREE persons. You must note on your assignment with whom you collaborated.

You will submit your homework by email. I expect the file name to be in the following format:

• NamesPortion-HWnn.tex
• The "NamesPortion" part gives the name(s) of the submitter(s). Your last name will suffice unless there is more than one person with the same last name enrolled in this class. In that case you have to APPEND the first letter of your first name to your last name. If you work in groups, please submit your names in alphabetical order.
• The "nn" part consists of two digits and denotes the number of the homework assignment. Please provide a leading zero if necessary. Write, e.g., 07 for the seventh assignment.
• An example: If the group consists of Ann Miller and Pedro Garcia and this is homework assignment #3 then NamesPortion = Garcia-Miller or GarciaP-MillerA and nn=03. Thus your latex file name should be Garcia-Miller-HW03.tex or GarciaP-MillerA-HW03.tex.

Exams:

There will be two midterm exams and one final exam. No notes, books, cell phones, or laptops are allowed for tests. Each standard exam will last 60 minutes and is worth 100 points.

Exam dates can be found on the course home page. Make all arrangements necessary to take the tests at those dates as it is extremely unlikely that they will be changed.

All exams are given online. They will consist of a free form portion and a multiple choices portion.

• The multiple choices portion will very likely be given as a Blackboard test.
• The free form portion is in hand-written format for problems like proofs. Use an app like CamScanner to create a PDF and email this PDF to me. I expect the file name to be in the following format:
  • NamesPortion-Exam1.tex (for midterm #1)     Example: ChenA-Exam1.tex
  • NamesPortion-Exam1.tex (for midterm #2)     Example: SmithD-Exam2.tex
  • NamesPortion-Final.tex (for the final exam)     Example: Togukawa-Final.tex
  The meaning of "NamesPortion" was explained in the Homework section.
• Make an effort to be on time: The free form questions will be emailed to you at the start of the exam, and you will be asked to submit a return receipt so I have proof of the exact time when you have received it.

The final exam counts for 200 points and it will last two hours. Date and time are not known at the time of writing of this syllabus and I will publish the info in the course home page once it becomes available.

Date and time for all finals are set by the office of records (registrar) and there is no flexibility. You can request a makeup final only if you have another final at the same time (direct conflict) or you have three final exams scheduled within 24 hours. The makeup will be given after the regular final, not before. If you want to request to take the alternate final then you must do so by Monday, November 9, by sending me an email.

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. If you are already registered with SSD you should send me asap an email. Please attach your SSD letter. You should approach me during office hours or after lecture so that you and I can discuss the implementation of your accommodations.

Your grade: See the home page of this website!

Success:

See the Advice page of the Math 330 website.

Attendance Policy and Make-up Policy:

• Attendance will not be taken. Even the in class lectures will be recorded, and links to those recordings will be posted on the Course Material page of the course website. You are advised not to skip lecture or the recordings. If you cannot spare the time to go to lecture or view the recordings then you should consider dropping/withdrawing from the course before your GPA is messed up.
• Make-up exams and quizzes will only be given in response to an excused absence. Excused absences include illness, religious holiday, a major tragedy in the family and participation in official BU athletic events.
• To be excused, absences must be properly documented. The document must cover 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.
• The rules for Doctor's notes have changed since the start of the pandemic: As of the time of this writing (August 10, 2020), If you are ill then you no longer need to provide a Doctor's note. To avoid abuse, I will make the makeup quiz/exam slightly harder than the original.
• If the Dean's Office should decide that instructors can/should request proof for an absence due to illness then I will change the above policy for Doctor's notes accordingly.
• 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 Blackboard 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:

• Copying another student's work
• Letting someone copy your work
• lying to or intentionally misleading an instructor
• Signing someone else's name to a document
• Homework assignments only: only having your name on the PDF but not understanding the proofs.
• I will make spot checks (one-on-one ZOOM interviews) for exams, quizzes and homework to ascertain that the student did not get to the correct answers on her/his own.

The following is meaningful only in the highly unlikely case that there are zero online students in this course and an exam can be given in class: 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