Math 20630 – Introduction to Math Reasoning – Spring 20
Math 20630 – Introduction to Math Reasoning – Spring 20
Schedule (this will updated on a weekly basis)
NOTE: all course policies announced here are subject to change up to the first day of semester!
As with all writing, mathematics should be presented in grammatically correct sentences and paragraphs. The difference with other fields is that any conclusions are not opinions based on convincing evidence, but are supposed to be irrefutable given our accepted rules of logical reasoning. For this to be possible we must make absolutely clear what exactly is being said, and therefore mathematical essays usually start with precise definitions. Then, in the reasoning which follows, each sentence must have a clear, unambiguous meaning, and any statements must be logically justified. In practice this means taking extreme care with quantifiers and the structure of sentences, and so we’ll spend lots of time on this.
Once you become familiar with mathematical writing, you’ll find that it is useful for far more than carefully justifying things you already know. The process involved in writing a careful proof is the same as that required to think about and solve a problem. We will learn to express problems precisely and then manipulate them, think about them in different ways, and finally derive (irrefutable!) solutions.
Here is a link to the course outline.
Meeting times: Monday, Wednesday, Friday, 11.30am to 12.20pm, DeBartolo Hall 210, January 14 to April 29.
Instructor: Abdul Basit, 248 Hayes-Healy (abasit@nd.edu).
Note that while Sakai offers a “contact the instructor” option, you will have no success getting in touch with me through that, as I don’t check it with any regularity. I do, however, respond quickly to email sent to my nd.edu address.
(Updated) Office hours:
Mondays, 3.00pm — 5.00pm
Fridays, 3.00pm — 5.00pm
Mathematical Thinking: Problem-Solving and Proofs (2nd Edition) by D’Angelo and West.
I’ll aim to cover roughly Chapters 1 – 8 and 13 – 15 but this can be adjusted as the semester progresses. This list of chapters covers mathematical writing and proofs together with a brief introduction to abstract algebra and analysis.
Your final grade in this class will be based on a combination of homework, quiz, midterm and final exam scores.
Here is the updated grading scheme.
Homework: 150 out of 500 points (was 100/500)
Quizzes: 75 out of 500 (was 50/500)
One midterms: 100 out of 500 (Changed from two exams to one)
Final: 175 out of 500 (was 150/500)
Scores will be recorded on Sakai. This is the only use I will make of Sakai; all other information about the course will be communicated either through email or through this website.
An average of 94% will earn you an A; of 90% an A-; 85% a B+; 80% a B; 75% a B-; 70% a C+; 65% a C; and 60% a C-.
Grading disputes: If you have any issue with the grading of your weekly assignments or with your midterm exams, you must let me know (in writing; email is fine) within seven days of receiving the work back; otherwise I can’t promise that I can consider the issue.
Homework will be announced Fridays and posted on this website. It will be due at the beginning of class the following Friday. Detailed homework policies will be announced with the first homework.
Homework 1. (due Friday, Jan 24th)
Solutions are here.
Homework 2. (due Friday, Jan 31st)
Solutions are here.
Homework 3. (due Friday, February 7th)
Solutions are here.
Homework 4. (due Friday, February 14th)
Solutions are here.
Homework 5. (due Friday, February 21st)
Solutions are here.
Homework 6. (due Monday, March 2nd)
Solutions are here.
Homework 7. (due Monday March 30th)
Solutions are here.
Homework 8. (due Monday April 6th)
Solutions are here.
Homework 9. (due Tuesday April 14th)
Solutions are here.
Homework 10. (due April 20th)
Solutions are here.
Homework 11. (due April 29th)
Solutions are here.
Credit back policy for quizzes: For the quizzes, you can get credit back. To do this, you will have to submit corrections by the deadline (announced with each quiz). However, you’re now allowed to look up or discuss solutions with anyone but me. If you wish to set up a time to do this, you can email me.
Here is the updated Quiz policy: There will be a quiz every Wednesday from now on (which means 5 more quizzes). The quizzes will be based on material from lectures the previous week (next week’s quiz will be based on this weeks lectures).
The quizzes will be “in-class”. This will mean that you are now *required* to attend the zoom session on Wednesdays to give the quiz. I will email out the quiz handout at the beginning of the lecture. You will have 25 minutes to do the quiz, and email me a scan of your solutions.
The credit back policy still applies. You will have an opportunity to get 75% of the credit back on each quiz. I’ll announce the due date with each quiz.
All homework must be done by the due date to receive credit, and all quizzes and exams must be taken at the assigned times.
I will not consider requests for homework extensions — the online homework system gives ample time after each section has been covered to complete each assignment, so if you have to be off-campus, I expect that you manage your travel time in such a way that you can complete your assignments in a timely manner, and if you have computer problems I expect you to go to a computer cluster on campus to complete your online homework.
I will not consider requests for make-up quizzes and/or exams, except in the case of legitimate, university-sanctioned conflicts. It is your responsibility to let me know the full details of these conflicts before they cause you to miss an assignment! Excepting university-sanctioned conflicts, it is your responsibility to be in class for all scheduled lectures and mid-semester exams; in particular, you should not plan travel on the morning of any of the Thursdays on which mid-semester exams are scheduled.
There will be two in-class midterm exams, tentatively scheduled for:
Midterm 1: Friday, February 28.
This will cover everything up to and including Chapter 5. See the Schedule link for details on what to expect.
Here is a list of what we have covered, and what you are expected to know for the exam.
Here are some practice questions. Solutions are here.
Here are solutions to the actual exam.
Midterm 2: There will no longer be an Exam 2. The points for Exam 2 will be distributed among the Homeworks, Quizzes and Final.
Specific exam policies (such as format, which sections will be covered, et cetera) will be announced in class closer to the date.
There will also be a (cumulative) final exam:
Final exam: Tuesday, May 5, 1.45pm — 3.45pm.
Here are solutions to the actual exam.
The exam will be “take home”, with a time limit of 2 hours. Here is how things would work: When you’re ready to take the exam, you should send me an email, and I will send you the exam. Once I’ve sent you the exam, you’ll have 2.5 hours to send me your solutions (the additional half an hour should help in case of logistic problems).
Here is a list of topis we have covered.
Here are some practice problems that deal with limits. Here are solutions.
Mathematics, like all the other sciences, is not a solitary discipline. It is a collaborative, communicative affair. Your mathematical skills will thrive by practicing talking mathematics. I encourage you to take every advantage of the opportunities available to you to do this. In particular, please contribute in class, and please come to office hours when you need to. I encourage you also to talk to each other. Share knowledge, share concerns, share questions.
Mathematics is also a cumulative subject. What we see for the first time one week, we will be building on the next week. It’s important to keep up with new material, because if you let one topic slide, you run the risk of not following any subsequent topic. I encourage you to bring up in office hours any difficulties you encounter, soon after you encounter them.
Tutoring is available in the Math Library. Please check the schedule for times focused on proof-based classes. If you feel you need help beyond this, Judy in the math office has list of private tutors available for hire.
Honor code: You have all taken the Honor Code pledge, to not participate in or tolerate academic dishonesty. For this course, that means that although you may discuss homework assignments with your colleagues, you must complete each WebAssign assignment yourself, all work that you present in quizzes and exams must be your own, and you will adhere to all announced exam policies.
Class conduct: The lecture room should be a place where you should feel free to engage in lively discussion about the course topic; don’t be shy! But non course related interruptions should be kept to a minimum. In particular, you should turn off or switch to silent all phones, etc., before the start of class. If for some good reason you need to have your phone on during class, please mention it to me in advance.