| Announcements |
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- Welcome to MATH 267. Our first meeting is Monday, August 24. There is no reading to do beforehand.
- Your first reading reflection is due Tuesday, August 25 at 11:59pm, on Chapter 2. You will write it in your own Overleaf project — an invitation has been sent to your Towson email address. Read the Reading Reflections Guide before you start; it explains the format, walks through a complete example, and covers setting up Overleaf.
- Quiz 1 is Monday, August 31. Quizzes are given in class, generally on Mondays, and cover the practice problems. The lowest quiz score is dropped.
- Sign up for two class meetings on the Course Notes Sign-Up sheet. On each of your dates you will type up that day's lecture notes in LaTeX and submit them; they are posted on the Schedule page for the whole class to use.
| Important Links |
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- Reading Reflections Guide — format, worked example, grading rubric, and Overleaf setup. Read this first.
- Overleaf — where you write and submit your reading reflections.
- Course Notes Sign-Up — claim two class meetings to type up for the class.
- Course Notes Template (.tex source) — the format to use when you write up your two class meetings. A copy is already in your Overleaf project under Course Notes.
- Schedule — what we cover each day, and what to read before it.
- Written Assignments — collected proof write-ups, listed at the top of the homework page.
- Practice Problems — not collected, but the best predictor of your quiz and exam scores.
- Math Tutoring Schedule — drop-in and online tutoring hours at the Spence Mathematics Tutoring Lab, including MATH 267.
| Instructor and Meeting Times |
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Email: nmcnew@towson.edu
Office hours: Mondays 2:30-3:30 and Fridays 11:00-12:00, or by appointment.
Office: YR 229
Lecture: Mondays and Wednesdays, 12:00-1:50 p.m., YR 219
Note that you do not need an appointment to attend regularly-scheduled office hours. If you have a conflict you may make an appointment to meet outside those times.
| Course Description and Objectives |
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Sets, mappings, relations, logic, mathematical induction, properties of the integers, Fundamental Theorem of Arithmetic, polynomials, and elementary analytic concepts. Not open to those who successfully completed MATH 361 or MATH 467. Prerequisites: MATH 273 and MATH 265, or consent of the instructor.
In practice, MATH 267 is the course where you stop computing answers and start proving statements. It is the bridge between the calculus and linear algebra you have already taken and every upper-level mathematics course you will take afterward. The central skill is writing an argument that another mathematician will accept as correct, and reading someone else's argument closely enough to tell whether it is. A week-by-week list of topics is on the schedule page.
Course objectives:
- Develop proficiency in understanding, writing, and verifying mathematical proofs.
- Master fundamental concepts in set theory, logic, and mathematical reasoning.
- Understand functions, relations, and equivalence relations with rigorous definitions.
- Apply mathematical induction and other proof techniques to solve problems.
- Prepare for advanced mathematics courses through practice with abstract mathematical concepts.
| Textbook |
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| Homework |
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Problems will be assigned regularly on the homeworks tab of this page. Students are expected to work through these problems to practice the material, and are encouraged to ask questions in office hours regarding any difficulties they encounter. These will not be collected, however these problems or problems similar to them are likely to appear on quizzes.
Occasional written assignments will also be given, which will be listed on the schedule tab of this page. These assignments will explore concepts more in depth, including applications and use of technology. Solutions to these assignments must be written up carefully. These written solutions must be turned in at the beginning of class to receive full credit.
Students will be asked to participate in class, by presenting solutions to homework problems and asking/answering questions.
Expect to spend a substantial amount of time studying, working on homework and preparing for the course. The general rule is two to three hours outside class for each hour inside; this translates to about 6-9 hours of homework and personal study per week.
Additionally, each student is responsible for writing up notes describing what was covered during two lectures during the term. These notes should be written up clearly using latex and submitted to the instructor within a week of the class period. Students are also encouraged to include additional examples/explanation. Notes will be posted for use by the rest of the class. Claim your two class periods on the Course Notes Sign-Up sheet. Use the Course Notes Template — a copy is in your Overleaf project under Course Notes. Note: these notes will count as one written assignment.
Every class meeting opens with a short warm-up, handed out on paper and worked in pairs for about ten minutes. Warm-ups are collected before the lecture begins and are graded for completion rather than correctness: the goal is to have you thinking about the day's ideas, and being wrong on a warm-up costs you nothing. Both partners put their names on the sheet.
Before most class meetings you will submit a short reading reflection on the assigned section of the textbook. These are what make it possible to spend class time on proofs rather than on definitions you could have read yourself. Full details, including the format and the grading rubric, are in the Reading Reflections Guide.
Regular quizzes will be given in class, generally on Mondays, beginning the second week of the term. These quizzes will cover material from the homework assignments. The lowest quiz score (including one missed for any reason, excused or unexcused) will be dropped.
| Exams |
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There will be two midterm exams and a final exam covering the material presented in lectures, readings and on homework assignments. The schedule for the midterm exams is tentative.
| Midterm 1 | Midterm 2 | Final Exam |
|---|---|---|
| Wednesday, October 7 | Wednesday, November 18 | Friday, December 11 12:30-2:30 p.m. |
| Evaluation |
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Grades will be assigned based on written work, in-class participation, quizzes and exams, weighted in your final grade as follows:
| Component | Contribution |
| Written assignments and typed course notes | 10% |
| Warm-ups and in-class participation | 10% |
| Reading reflections | 10% |
| Quizzes | 15% |
| Midterms (each) | 15% |
| Final Exam | 25% |
| Getting Help |
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This course asks you to do something you have probably never been asked to do before: write mathematics rather than compute it. Almost everyone finds the first few weeks disorienting. That is normal, and there is help available.
Office hours are Mondays 2:30-3:30 and Fridays 11:00-12:00 in YR 229. You do not need an appointment. If both times conflict with your schedule, email me and we will find another time. Bringing a partial attempt at a proof and asking "why doesn't this work?" is one of the most efficient things you can do in this course.
The Spence Mathematics Tutoring Lab (7800 York Road, Room YR310) now offers drop-in tutoring for MATH 267 as well as the calculus and linear algebra sequence; see the Fall 2026 Math Tutoring Schedule for current hours and room locations. For questions specifically about proofs, office hours are still the best place to come. Forming a study group with two or three classmates is also unusually valuable in this course, because reading someone else's proof and saying honestly whether you believe it is the skill we are practicing.
If you are struggling with circumstances outside of class - illness, housing, food security, family emergencies - Student Outreach and Support can help, and the TU Counseling Center provides confidential mental health services. Please also let me know if something is affecting your work in the course.
| Academic Integrity Policy |
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Per Towson University's Academic Integrity Policy, faculty members will reasonably assess that student work submitted for academic credit is authentic as well as consistent with established academic standards. Therefore, academic evaluation includes a judgment that the student's work is free from academic dishonesty of any type. Students are expected to be familiar with the policy, especially the sections that define plagiarism, cheating and complicity (II.B-II.E) and describe the possible grade penalties (V.C).
On quizzes and exams: No assistance may be given or received, except that you may ask the instructor for clarification of a problem. Quizzes and exams are closed book; the use of notes, the textbook, calculators, or any other external resource is prohibited.
On warm-ups: Warm-ups are done in class with an assigned partner and both names go on the sheet. Discussion with your partner is the point of the exercise.
On homework and written assignments: You are permitted and encouraged to collaborate with other students. However, after discussing the problems, you must write up the final solutions in your own words, and you must list your collaborators at the top of the assignment. You may consult your class notes and the text. It is not permitted for someone to provide the answers for you, and it is not permitted to submit answers found on the internet as your own work. If you are unsure whether a particular kind of help crosses the line, ask me before you submit; the answer is almost always easy to give in advance and awkward to give afterward.
Use of AI tools: Generative AI tools (ChatGPT, Claude, Copilot, Gemini, and the like) may not be used to produce any work you submit in this course. This includes proofs, written assignments, typed course notes, and reading reflections. You may use AI tools to ask for an explanation of a concept or for help with LaTeX formatting. You may not ask them to write, complete, check, or repair a proof for you.
This is not primarily a rule about honesty; it is a rule about what the course is for. The entire point of MATH 267 is to build the habit of deciding for yourself whether an argument is correct. A tool that hands you a plausible-looking proof removes exactly the difficulty you are here to learn to work through - and it is very good at producing arguments that look right and are not. You will be asked to write proofs by hand, without assistance, on the quizzes and exams, which together are 70% of your grade.
Reading reflections are graded on your personal engagement with the reading, and AI-generated text defeats their purpose entirely.
| Cellphones and Wearable Technology |
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To maintain academic integrity, protect privacy, and minimize distractions, the use of wearable technology and other electronic devices is restricted during class.
- Cellphones and other personal recording devices must be powered off and put away during class.
- Any wearable technology with communication, recording, or data retrieval capabilities, including smart watches, smart glasses, earpieces, or similar devices, must be removed and stored away during assessments.
- Capturing material from this course in any technology-based manner is prohibited unless explicitly approved by the instructor.
- Note that Maryland is a two-party consent state (Md. Code, Cts. & Jud. Proc. § 10-402), meaning it is illegal to record conversations without the consent of all parties involved.
Any use of unauthorized devices during class will be considered a violation of academic integrity policies and may also have legal consequences. Failure to comply with these guidelines will result in academic penalties in accordance with the Towson University academic integrity policy. If you require an accommodation that involves the use of technology, please discuss this with me in advance.
| Class Attendance and Absence Policy |
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Attendance expectations. Students are expected to attend all classes. Regular attendance helps students understand course material and meet expectations. This course meets only twice a week, and each meeting includes a graded in-class warm-up, so an absence costs more here than in a course that meets more often. If you are absent from class, it is your responsibility to get any missed information from your classmates.
Excusable absences.
- Health absences due to illness or injury when the student is unable to attend class. For repeated illness or long-term injury which prevents course completion, students may be advised to seek a medical withdrawal for that course. For illness-related absences, students are encouraged to contact the Student Outreach and Support office for additional assistance and resources.
- Wellness: Students may take one excused general wellness day to be excused from one class session per course. Students may not use a wellness day during the final exam period.
- Religious observance where the nature of the observance prevents the student from attending class. If you have a religious observance that conflicts with your participation in the course, please meet with me before the end of the second week of the term so we can arrange accommodations in advance.
- Participation in University activities at the request of University authorities (e.g., intercollegiate athletics, conferences, dance company, etc.).
- Compelling, verifiable circumstances beyond the control of the student.
Students should inform me about absences as early as possible. Documentation may be required for certain types of absences (e.g., participation in University activities), but generally, medical documentation for short-term illnesses is not needed. Please remember that misrepresenting the cause of an absence is a violation of academic integrity.
Any absence of a type not listed above is an unexcused absence. Assessments missed due to an unexcused absence will be given a grade of zero.
Support services. Students registered with Accessibility and Disability Services may be approved for an accommodation that provides some modifications to an attendance policy. The student's individualized letter of accommodation will specify the modifications.
| Make-Up Work |
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Because warm-ups and quizzes are done in class, they generally cannot be made up. Instead, each of these categories drops its lowest scores, which is intended to absorb an ordinary absence without any paperwork.
Warm-ups. Warm-ups are handed out at the start of class and collected before the lecture begins; they count toward the participation component of your grade. They cannot be made up. The two lowest warm-up scores, including any missed for any reason, will be dropped.
Quizzes. No make-up quizzes will be given. The lowest quiz score, including one missed for any reason, excused or unexcused, will be dropped. If you have an excused absence on a quiz day beyond that one, contact me and the quiz will be exempted, meaning it will simply not count toward your grade. You may be exempted from at most three quizzes in this manner; further missed quizzes will be given a grade of zero. If you find yourself in that situation, I encourage you to work with Student Outreach and Support to determine the best course of action.
Reading reflections and written assignments. Reading reflections are due before the class meeting they accompany and are not accepted late, since their whole function is to prepare you for that day's class. The two lowest reading reflection scores will be dropped. Written assignments turned in late will be accepted for reduced credit up to one week past the due date; after that they are not accepted. If an excused absence covers the entire window during which an assignment was open, you will be exempted from it.
Exams. If you have an excused absence on the day of an exam, contact me as soon as possible - before the exam if at all possible - to arrange a make-up. All make-up exams must be completed within one week of the original date. Please note that a make-up exam will not be the same as the exam given in class and may be more difficult.
| Course Repeat Policy |
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Per Towson University's Course Repeat Policy, when a course is repeated, students will receive credit for the course only once. The higher of the two grades earned will be calculated in the GPA. The lower grade will remain on the record with a repeat excluded message. Students may not make a third or subsequent attempt of a course without prior approval of the Academic Standards Committee.
| Withdrawal Policy |
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Towson University's Withdrawal Policy acknowledges that students may need to withdraw from some or all courses for medical or personal reasons. Students may withdraw themselves prior to the University's withdrawal deadline (Monday, November 2) via their Towson Online Student Dashboard. This will result in the grade of W. Withdrawal requests after the withdrawal deadline require documentation of medical, mental health or personal hardship be submitted to Student Outreach and Support. Towson's goal is to help students understand the impact of withdrawals, assist them in addressing their needs, and enable them to return to classes following withdrawal.
| Students with Disabilities Policy |
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Per Towson University's Policy for Providing Reasonable Accommodations to Individuals with Disabilities, students with disabilities are encouraged to register with Accessibility and Disability Services. Students who suspect that they have a disability but do not have documentation are encouraged to contact ADS for advice on how to obtain appropriate evaluation. A memo from ADS authorizing your accommodation is needed before any accommodation can be provided.
Students with disabilities, including "invisible" disabilities such as chronic illness and learning disabilities, are encouraged to discuss appropriate accommodations with me, either after class or during office hours. Please do so early in the term so that arrangements can be in place before the first quiz.
| Title IX Policy |
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Per Towson University's Policy on Sexual Harassment and Other Sexual Misconduct, TU is committed to ensuring a safe, productive learning environment on our campus that does not tolerate sexual misconduct, including harassment, stalking, sexual assault, sexual exploitation, or intimate partner violence as outlined in the policy. It is important for you to know that there are resources available if you or someone you know needs assistance. You may speak to a member of the university administration, faculty, or staff, but keep in mind that they have an obligation to report the incident to the Title IX Coordinator. If you want to speak to someone who is permitted to keep your disclosure confidential, please seek assistance from the TU Counseling Center.
| Reporting Hate Crimes and Bias Incidents |
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Per Towson University's Policy and Procedures for the Reporting of Hate Crimes and Bias Incidents, TU prohibits all students, staff, and faculty from committing or engaging in any hate crimes as defined under state and federal law, or any acts of bias, hate, or prejudice exhibited in conduct that is in violation of another University policy on campus, on University property, at University sponsored events, or when engaged in University activities and business on or off campus.
The University must receive notice to respond effectively to alleged Hate Crimes or Bias Incidents in the University Community. Please report or file a complaint of a Hate Crime or Bias by:
Reporting to Towson University Police. Towson University's Police Department will determine if incidents are criminal in nature. In cases of hate crimes, individuals can be punished with fines and/or imprisonment. Felony offenses demonstrated to be motivated by bias are subject to enhanced penalties. TUPD's contact information is: Public Safety Building, 290 Towsontown Blvd. W. Emergency phone: 410-704-4444. Non-emergency phone: 410-704-2134. Administrative phone: 410-704-2505. Email: police@towson.edu.
Contacting the Office of Inclusion and Institutional Equity. The Office of Inclusion and Institutional Equity strives to foster a culture of integrity that values shared responsibility as a critical element of an inclusive, equitable, and diverse community. Administration Building, Suite 2210. Phone: 410-704-0203. Email: oiie@towson.edu.
| Statement on Classroom Climate |
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Towson University fosters a climate that is grounded in respect for all individuals, enriches the educational experience of students, supports positive classroom and workplace environments, promotes excellence, and cultivates the intellectual and personal growth of the entire university community. Should you feel that you are experiencing a negative classroom environment, please reach out to the Mathematics Department at math@towson.edu.
A word specific to this course: much of what we do in class involves reasoning out loud in front of other people, and being wrong in public is a routine and necessary part of learning to write proofs. Everyone in this room will produce a wrong argument at some point this semester, including me. Treat your classmates' attempts with the same generosity you would want for your own.