← Lucas Buzaglo

MATH 109 | Fall 2026

Course Overview

Section 2

Time TBD
Location TBD

Instructor

Lucas Buzaglo
AP&M 6442

Resources

Office Hours

  • TBD Time TBD
  • TBD Time TBD
All office hours are held in AP&M 6442.

Discussions

Section number Time Location TA
TBD TBD TBD TBD
TBD TBD TBD TBD

Course calendar

Fall 2026

Note: The numbers in each lecture block correspond to the associated chapters in the course textbook.

Week Monday Wednesday Friday Homework
0 Introduction
1 The language of mathematics
1 2 Implications 2 Implications 3 Proofs
2 4 Proof by contradiction 4 Proof by contradiction 5 The induction principle HW1
3 5 The induction principle 6 The language of set theory 6 The language of set theory HW2
4 Review lecture Midterm 1 7 Quantifiers
Last day to drop without W
5 7 Quantifiers 8 Functions 8 Functions HW3
6 8 Functions 9 Injections, surjections, bijections 9 Injections, surjections, bijections
Last day to drop without F
HW4
7 10 Counting Veterans Day Holiday 10 Counting HW5
8 Review lecture Midterm 2 11 Properties of finite sets
9 12 Counting functions and subsets 14 Counting infinite sets Thanksgiving Holiday HW6
10 15 The division theorem 15 The division theorem Catch-up/Review HW7
Finals Week Final Examination Time & Location TBD

Homework

These assignments are to be turned in through Gradescope. The course Gradescope can be accessed through Canvas. Homework must be uploaded onto Gradescope by 11:59pm on the due date (Tuesdays). Please make sure to upload your homework well ahead of the deadline to avoid any technical issues.

Late homework will be accepted up to 24 hours after the deadline, with a 10% penalty. Lowest homework score will be dropped.

As a main focus of this course is proof writing, your solutions must be written in complete English sentences, including punctuation. Discussing homework with others is OK, but it is expected that everyone writes in their own words the homework solutions. No points will be given to solutions that are not readable.

You must select the appropriate page(s) for each question when submitting your work on Gradescope. Points will be taken off if you fail to do this. If you do not know how to use Gradescope, have a look at this Gradescope guide.

The homework assignments can be found below.

Note, this page is subject to revision during the term. Please check regularly for updates.

Assignment Deadline
Homework 1 October 7
Homework 2 October 14
Homework 3 October 28
Midterm 1 covers Homework 1-3.
Homework 4 November 4
Homework 5 November 12
Homework 6 November 25
Midterm 2 covers Homework 4-6.
Homework 7 December 2
The final exam is cumulative.

Syllabus

Course Information

Course

MATH 109

Title

Mathematical Reasoning

Credit Hours

4

Prerequisites: MATH 18 or MATH 20F or MATH 31AH, and MATH 20C, or consent of instructor.

Course description: This course uses a variety of topics in mathematics to introduce students to rigorous mathematical proof, emphasizing quantifiers, induction, negation, proof by contradiction, naive set theory, equivalence relations, and epsilon-delta proofs. Required of all departmental majors.

Grading

The higher score between Version 1 and Version 2 is automatically awarded.

Component Version 1 Version 2
Homework 20% 20%
Midterm 1 20% 20%
(Best)
Midterm 2 20%
Final Exam 40% 60%

Textbooks

Main textbook: An Introduction to Mathematical Reasoning by Peter J. Eccles.

Other recommended textbooks:

  • Mathematical Proofs by G. Chartrand, A. Polimeni, and P. Zhang.
  • Reading, Writing, and Proving by U. Daepp and P. Gorkin.
  • Foundations of Higher Mathematics by P. Fletcher and C. Patty.
  • A Concise Introduction to Pure Mathematics by M. Liebeck.

Piazza: This quarter we will be using Piazza for class discussion. The system is highly catered to getting you help fast and efficiently from classmates, the TA, and myself. Rather than emailing questions to the teaching staff, I encourage you to post your questions on Piazza.

Email policies

I get many emails every day. As such, it helps a lot if you can keep your emails short and to the point. If you do this, I will likely reply much more quickly.

Please refrain from using ChatGPT (or another LLM) to write your emails, as they tend to write very lengthy and wordy emails. As a result, if you write me an email that was clearly written by ChatGPT, I will likely take much longer to reply.

Grading policies

Weekly assignments will be posted on Gradescope.

  • Submit your work on Gradescope.
  • Typed-up solutions or photographed/scanned copies are both accepted.
  • You must select the appropriate page(s) for each question when submitting your work on Gradescope. Points will be taken off if you fail to do this. If you do not know how to use Gradescope, have a look at this Gradescope guide.
  • DO NOT email me your homework.
  • Late homework will be accepted up to 24 hours after the deadline, with a 10% point penalty.

Final grade

At the end of the course, we will calculate both versions of your grade and give you the higher score. Letter grades will be assigned based on the following scale:

Letter grade Range
A+/A/A- 90-100
B+/B/B- 80-89
C+/C/C- 70-79

I might adjust the scale to be more lenient, but I can guarantee that the grade corresponding to a given percentage will not be lower than specified by the above scale. For example, if your score is 89, then your grade will be at least a B+.

Note: The weights displayed on Canvas are only for Version 1 of your grade. Version 2 of your grade is calculated separately.

Homework policies

  • As a main focus of this course is proof writing, your solutions must be written in complete English sentences, including punctuation.
  • Discussing homework with others is OK, but it is expected that everyone writes in their own words the homework solutions.
  • Homework must be uploaded onto Gradescope by 11:59pm on the due date (Tuesdays).
  • No points will be given to solutions that are not readable.
  • Late homework will be accepted up to 24 hours after the deadline, with a 10% penalty.
  • Lowest homework score will be dropped.
  • Note: There will be an assignment at the beginning of class for determining commencement of academic activity for financial aid purposes. This will not be part of your final score or grade.

Exam policies

The internet can be helpful when working through your homework. However, a computer should be used as an aid in the learning of concepts, not just as a means of computation. You should keep in mind that you will not be allowed access to any electronic devices during exams. Of course, this also means that you will not be asked to solve problems on exams that require the aid of an electronic device.

  • The use of electronic devices will not be permitted during exams.
  • Bring your student ID to the exams.
  • No make-up exams will be offered.

Midterms: We will have two 50-minute midterms, which will be held during class time on October 21 and November 18. There will be no make-up midterms under any circumstances.

Final exam: The final exam will take place on TBD.

  • It is your responsibility to ensure that you do not have a schedule conflict involving the final examination. You should not enroll in this class if you cannot sit for the final examination at its scheduled time.
  • There are no make-up exams for any reason. Nor do we allow alternate times for taking exams.
    • If you have a documented disability or must miss the exam for a university sponsored activity, then arrangements can be made using the standard procedures.
    • If you cannot attend one of the midterms, grading Version 2 (described above) will ensure fairness by taking such cases into account.
  • There may be different versions of exams involving different numbers and/or different orderings of questions.
  • Bring pen or pencil and your student ID.
  • You are allowed one letter size piece of paper of notes (front and back) for exams. The notes must be handwritten.
    • Notes written on an iPad/tablet are not acceptable.
    • If any part of your notes is typed or includes screenshots of my/other people's notes, they will be confiscated during the exam, and a point penalty may be applied.
  • No calculators or electronic devices of any kind will be allowed during the examinations.

Regrade policy

Your homework and your exams will be graded using Gradescope. You will be able to request a regrade via Gradescope for one week after the scores have been released. Be sure to make your request within one week; no regrade requests will be accepted after the deadline.

You cannot lose points for regrade requests, provided your request was legitimate. Frivolous regrade requests in exams (in other words, obvious attempts at fishing for points, without any clear justification) will not be tolerated, and points will be taken off for such violations. This includes, but is not limited to:

  • Asking for a regrade request for every question in an exam.
  • Getting ChatGPT to generate a regrade request for you.
  • Asking for extra points without any mathematical justification.
  • Overly long regrade requests will be ignored and points may be deducted.

As a result, when asking for regrade requests, you must do the following:

  • Only submit regrade requests if you believe there has been a mistake when grading a particular question.
    • Don't worry if it turns out that you simply misunderstood how your answer was graded. You will not lose any points if it's clear that you believe that there was a mistake and are not simply trying to fish for points.
  • You must include a brief justification (1-2 sentences is usually enough) for why you believe your answer deserves more points.
  • Do not submit regrade requests for every single question in an exam.

Doing the above will give you the best chance at a successful regrade request, and will also guarantee that you do not lose points.

Accommodations

Students requesting accommodations for this course due to a disability must provide a current Authorization for Accommodation (AFA) letter issued by the Office for Students with Disabilities. Students are required to discuss accommodation arrangements with instructors and OSD liaisons in the department in advance of any exams or assignments.

There may be different versions of exams given. All versions of any exam will cover the same topics and will be calibrated to the same level of difficulty. It is standard Math Department practice to utilize different versions of exams, both within each lecture's exam, and between lectures whose exams are at different times.

Information about incomplete grades

According to university-wide regulations, a student's work must be of "non-failing quality" to be eligible for an incomplete grade. In this class, work of "non-failing quality" is taken to mean:

  • At least 70% average homework score up to the day of the incomplete grade request.
  • At least 70% in either Midterm 1 or Midterm 2.

Both of the above must be true. For example, you are not eligible for an incomplete grade if you scored over 70% in one of the midterms but your homework score is below 70%.

Academic integrity

Cheating will not be tolerated. See this link for information on how to promote academic integrity and the consequences of cheating.