Harold P. Boas

Math 300
Section 903
Foundations of Mathematics
Spring 2021

Course Information

Course Data

Instructor Details

Course Description

This course introduces the fundamental concepts of abstract mathematical reasoning: logic, proofs, sets, functions, equivalence relations, mathematical induction, and the integers.

Course Prerequisite

The official prerequisite for this course is a grade of C or better in second-semester calculus, namely, one of the three courses Math 148, Math 152, and Math 172.

Special Course Designation

One of the requirements for an undergraduate degree is to pass two writing (W) courses in your major or one W course and one oral communication (C) course. Math 300 is a designated W course. Accordingly, you must pass the writing portion of Math 300 in order to earn a grade in the course.

Course Learning Outcomes

The main goal of Math 300 is to develop fluency in abstract mathematical reasoning through reading, understanding, and writing proofs. At the conclusion of this course, you will be able to

Textbook

The textbook is Version 3 of Mathematical Reasoning: Writing and Proof by Ted Sundstrom. A free pdf download is available at the author’s website.

At the same site, there are links to study guides and to YouTube videos associated with the book.

Grading Policy

Course letter grades are assigned using the standard scale (60% is passing, 70% or higher earns a C, 80% or higher earns a B, 90% or higher earns an A).

The categories contributing to the course grade have the following weights.

There are no major exams (no midterm exams and no final exam). Instead, grades are based on a variety of assignments distributed over the whole semester.

Late Work Policy

Effective learning requires dedicated effort extending over the entire semester. The syllabus is designed to encourage spaced practice on a regular schedule. Completing the assigned activities on time is important for success in the course.

The expectation is that you will meet announced deadlines for submission of assignments. I recognize that extraordinary circumstances may arise, so I will accept late work for partial credit. I have configured Canvas to apply a penalty of 10% per day for late submissions. (To handle partial days, Canvas uses the ceiling function ⌈·⌉, the smallest integer greater than or equal to the number, so the grade penalty for a submission n days late is ⌈n⌉ × 10%, capped at 100%.)

Work submitted to make up for an excused absence is not considered late and is exempted from the late work policy. See Student Rule 7.

Bring Your Own Device Policy

“As a result of the changing landscape in higher education, Texas A&M University now requires students to have access to an appropriate computer to complement course instruction,” according to the university’s page about Computer Requirements.

And of course you need internet access, since class meets via Zoom.

Revised Course Schedule (updated 21 February 2021)

You should read each section of the textbook before the class meeting in which that section is on the agenda. When you log in to class, be prepared to work problems, discuss the topics, and participate in class activities.

Week 1
Tuesday 19 January: §1.1, statements and conditional statements.
Thursday 21 January: §1.2, direct proofs; §1.3, Chapter 1 summary.
Week 2
Tuesday 26 January: §2.1, statements and logical operators; §2.2, logically equivalent statements.
Thursday 28 January: §2.3, open sentences and sets.
Week 3
Tuesday 2 February: §2.4, quantifiers and negations; §2.5, Chapter 2 summary.
Thursday 4 February: §3.1, direct proofs.
Week 4
Tuesday 9 February: §3.2, more methods of proof.
Thursday 11 February: §3.3, proof by contradiction.

Classes were canceled the week of February 15–19 because of a winter storm and rolling power outages. Accordingly, the remainder of the schedule has been adjusted to fit into the available 14 weeks instead of the originally planned 15 weeks.

Week 5
Tuesday 23 February: §3.4, using cases in proofs; §3.6, review of proof methods.
Thursday 25 February: §3.5, the division algorithm and congruence.
Week 6
Tuesday 2 March, Texas Independence Day, classes do not meet.
Thursday 4 March: §4.1, the principle of mathematical induction.
Week 7
Tuesday 9 March: §4.2, other forms of mathematical induction.
Thursday 11 March: §4.3, induction and recursion; §4.4, Chapter 4 summary; §3.7, Chapter 3 summary.
Week 8
Tuesday 16 March: §5.1, sets and operations on sets.
Thursday 18 March: redefined day — students attend their Friday classes.
Friday 19 March: Spring Break, classes do not meet.
Week 9
Tuesday 23 March: §5.2, proving set relationships.
Thursday 25 March: §5.3, properties of set operations; §5.4, Cartesian products.
Week 10
Tuesday 30 March: §6.1 and §6.2, functions.
Thursday 1 April: §6.3, injections, surjections, and bijections.
Friday 2 April: Reading day, classes do not meet.
Week 11
Tuesday 6 April: §6.4, composition of functions.
Thursday 8 April: §6.5, inverse functions.
Week 12
Tuesday 13 April: §6.6, functions acting on sets; §6.7, Chapter 6 summary.
Thursday 15 April: §7.1, relations; §7.2, equivalence relations.
Week 13
Tuesday 20 April: §7.3, equivalence classes.
Thursday 22 April: §7.4, modular arithmetic; §7.5, Chapter 7 summary.
Week 14
Tuesday 27 April: §8.1, the greatest common divisor.
Wednesday 28 April: Redefined day, students attend their Friday classes.
Thursday 29 April: §8.2, prime numbers and prime factorization.
Friday 30 April: Reading day, classes do not meet.

Additional Information

Math Learning Center

Help for many mathematics courses, including Math 300, is available at the Math Learning Center. Both online and face-to-face support are available through drop-in help sessions and tutoring by appointment. Additionally, the Math Learning Center hosts an archive of supplemental material, such as Python tutorial videos and recorded review sessions.

Writing Center

The following paragraph was contributed by the University Writing Center.

The mission of the University Writing Center (UWC) is to help you develop and refine the communication skills vital to success in college and beyond. Currently, you can choose to work with a trained UWC peer consultant via web conference or email. You can schedule an appointment to discuss any kind of writing or speaking project, including research papers, lab reports, application essays, or creative writing. Consultants can work with you at any stage of your process, whether you’re deciding on a topic or reviewing your final draft. You can also get help with public speaking, presentations, and group projects. To schedule an appointment or to view handouts, videos, or interactive learning modules, visit writingcenter.tamu.edu. Questions? Call 979-458-1455 or email uwc@tamu.edu.

StudyHub

For general academic support, check out the list of resources at StudyHub, sponsored by the Academic Success Center.

TAMU Curated Lists of Resources

The university has compiled a list of academic resources and a list of university resources.

Technology Support

University Policies

This section contains university-level policies. The TAMU Faculty Senate established the wording of these policies.

Attendance Policy

The university views class attendance and participation as an individual student responsibility. Students are expected to attend class and to complete all assignments.

Please refer to Student Rule 7 in its entirety for information about excused absences, including definitions, and related documentation and timelines.

Makeup Work Policy

Students will be excused from attending class on the day of a graded activity or when attendance contributes to a student’s grade, for the reasons stated in Student Rule 7, or other reason deemed appropriate by the instructor.

Please refer to Student Rule 7 in its entirety for information about makeup work, including definitions, and related documentation and timelines.

“Absences related to Title IX of the Education Amendments of 1972 may necessitate a period of more than 30 days for make-up work, and the timeframe for make-up work should be agreed upon by the student and instructor” (Student Rule 7, Section 7.4.1).

“The instructor is under no obligation to provide an opportunity for the student to make up work missed because of an unexcused absence” (Student Rule 7, Section 7.4.2).

Students who request an excused absence are expected to uphold the Aggie Honor Code and Student Conduct Code. (See Student Rule 24.)

Academic Integrity Statement and Policy

“An Aggie does not lie, cheat or steal, or tolerate those who do.”

“Texas A&M University students are responsible for authenticating all work submitted to an instructor. If asked, students must be able to produce proof that the item submitted is indeed the work of that student. Students must keep appropriate records at all times. The inability to authenticate one’s work, should the instructor request it, may be sufficient grounds to initiate an academic misconduct case” (Section 20.1.2.3, Student Rule 20).

You can learn more about the Aggie Honor System Office Rules and Procedures, academic integrity, and your rights and responsibilities at aggiehonor.tamu.edu.

Americans with Disabilities Act (ADA) Policy

Texas A&M University is committed to providing equitable access to learning opportunities for all students. If you experience barriers to your education due to a disability or think you may have a disability, please contact Disability Resources in the Student Services Building or at (979) 845-1637 or visit disability.tamu.edu. Disabilities may include, but are not limited to attentional, learning, mental health, sensory, physical, or chronic health conditions. All students are encouraged to discuss their disability related needs with Disability Resources and their instructors as soon as possible.

Title IX and Statement on Limits to Confidentiality

Texas A&M University is committed to fostering a learning environment that is safe and productive for all. University policies and federal and state laws prohibit gender-based discrimination and sexual harassment, including sexual assault, sexual exploitation, domestic violence, dating violence, and stalking.

With the exception of some medical and mental health providers, all university employees (including full and part-time faculty, staff, paid graduate assistants, student workers, etc.) are Mandatory Reporters and must report to the Title IX Office if the employee experiences, observes, or becomes aware of an incident that meets the following conditions (see University Rule 08.01.01.M1):

Mandatory Reporters must file a report regardless of how the information comes to their attention – including but not limited to face-to-face conversations, a written class assignment or paper, class discussion, email, text, or social media post. Although Mandatory Reporters must file a report, in most instances, you will be able to control how the report is handled, including whether or not to pursue a formal investigation. The University’s goal is to make sure you are aware of the range of options available to you and to ensure access to the resources you need.

Students wishing to discuss concerns in a confidential setting are encouraged to make an appointment with Counseling and Psychological Services (CAPS).

Students can learn more about filing a report, accessing supportive resources, and navigating the Title IX investigation and resolution process on the University’s Title IX webpage.

Statement on Mental Health and Wellness

Texas A&M University recognizes that mental health and wellness are critical factors that influence a student’s academic success and overall well-being. Students are encouraged to engage in proper self-care by utilizing the resources and services available from Counseling & Psychological Services (CAPS). Students who need someone to talk to can call the TAMU Helpline (979-845-2700) from 4:00 p.m. to 8:00 a.m. weekdays and 24 hours on weekends. 24-hour emergency help is also available through the National Suicide Prevention Hotline (800-273-8255) or at suicidepreventionlifeline.org.

COVID-19 Temporary Addendum

The Faculty Senate temporarily added the following statements to the minimum syllabus requirements in Spring 2021 as part of the university’s COVID-19 response.

Campus Safety Measures

To promote public safety and protect students, faculty, and staff during the coronavirus pandemic, Texas A&M University has adopted policies and practices for the Spring 2021 academic term to limit virus transmission. Students must observe the following practices while participating in face-to-face courses and course-related activities (office hours, help sessions, transitioning to and between classes, study spaces, academic services, etc.):

Personal Illness and Quarantine

Students required to quarantine must participate in courses and course-related activities remotely, if that option is available, and must not attend face-to-face course activities. Students should notify their instructors of the quarantine requirement. Students under quarantine are expected to participate in courses and complete graded work unless they have symptoms that are too severe to participate in course activities.

Students experiencing personal injury or illness that is too severe for the student to attend class qualify for an excused absence. (See Student Rule 7, Section 7.2.2.) To receive an excused absence, students must comply with the documentation and notification guidelines outlined in Student Rule 7.