Harold P. Boas

Math 300
Section 906
Foundations of Mathematics
Fall 2023

Course Information

Course Data

Instructor Details

Course Description

This course explores fundamental concepts of abstract mathematical reasoning, including 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


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.


This course uses multiple technologies, all of which are available at no cost to registered students.

Artificial Intelligence (AI) Policy

Limited use of artificial intelligence assistants (chatbots), such as ChatGPT and Google Bard, is allowed in this course. Here are some guidelines about the parameters of acceptable use.

The general principle is that you may use a chatbot as a tool to improve your writing skills (just as you may in the past have used a spell checker). But submitting work entirely generated by AI is considered to be plagiarism, a major academic violation. You should familiarize yourself with Honor System Rule, according to which plagiarism includes the failure to acknowledge “electronic resources if they are utilized … in an academic exercise.”

You should create a draft of written work by yourself, based on your own ideas and knowledge. Then you may use AI to help edit the draft. Be aware that AI can produce nonsense that sounds authoritative, and you are responsible for verifying the accuracy of the end product.

When you write a research paper, you include a bibliography to credit the sources that you consulted. In the same spirit, when you get help from an AI assistant in this course, you should include a statement about what prompts you used and how they were helpful in completing the assignment.

Please consult your instructor if you have questions about appropriate use of AI in this course.

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 \(\lceil \cdot \rceil\), the smallest integer greater than or equal to the number, so the grade penalty for a submission \(x\) days late is \(\lceil x \rceil \times{}\) 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.

Course Schedule

You should complete the reading assignment for each section before the class meeting in which that section is on the agenda. The following schedule is subject to revision if circumstances change.

Week 1
Tuesday, August 22: § 1.1, statements and conditional statements.
Thursday, August 24: § 1.2, direct proofs.
Week 2
Tuesday, August 29: § 2.1, statements and logical operators; § 2.2, logically equivalent statements.
Thursday, August 31: § 2.3, open sentences and sets.
Week 3
Tuesday, September 5: § 2.4, quantifiers and negations.
Thursday, September 7: § 3.1, direct proofs.
Week 4
Tuesday, September 12: § 3.2, more methods of proof.
Thursday, September 14: § 3.3, proof by contradiction.
Week 5
Tuesday, September 19: § 3.4, using cases in proofs.
Thursday, September 21: § 3.5, the division algorithm and congruence.
Week 6
Tuesday, September 26: § 4.1, the principle of mathematical induction.
Thursday, September 28: § 4.2, other forms of mathematical induction.
Week 7
Tuesday, October 3: § 4.3, induction and recursion.
Thursday, October 5: § 5.1, sets and operations on sets.
Week 8
Tuesday, October 10: Fall Break, no classes.
Thursday, October 12: § 5.2, proving set relationships.
Week 9
Tuesday, October 17: § 5.3, properties of set operations; § 5.4, Cartesian products.
Thursday, October 19: § 5.5, indexed families of sets.
Week 10
Tuesday, October 24: § 6.1 and § 6.2, functions.
Thursday, October 26: § 6.3, injections, surjections, and bijections.
Week 11
Tuesday, October 31: § 6.4, composition of functions.
Thursday, November 2: § 6.5, inverse functions.
Week 12
Tuesday, November 7: § 6.6, functions acting on sets.
Thursday, November 9: § 7.1, relations; § 7.2, equivalence relations.
Week 13
Tuesday, November 14: § 7.3, equivalence classes.
Thursday, November 16: § 7.4, modular arithmetic.
Week 14
Tuesday, November 21: § 8.1, the greatest common divisor.
Thursday, November 23: Thanksgiving Holiday, no classes.
Week 15
Tuesday, November 28: § 8.2, prime numbers and prime factorization.
Thursday, November 30: § 8.3, linear Diophantine equations.

Additional Information

Math Learning Center

Help for many mathematics courses is available at the Math Learning Center. There are drop-in help sessions and tutoring by appointment. The Virtual Math Learning Center hosts an archive of tutorial videos.

Writing Center

The University Writing Center contributed the following paragraph.

The University Writing Center (UWC) has trained peer consultants available to work with you on any kind of writing or speaking project, including research papers, lab reports, application essays, or creative writing, and 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. We can work with you in person at our Evans or BLCC locations or via Zoom or email. To schedule an appointment or to view our handouts, videos, or interactive learning modules, visit writingcenter.tamu.edu. If you have questions, need help making an appointment, or encounter difficulty accessing our services, call 979-458-1455 or email uwc@tamu.edu.


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

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 (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, 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 office. 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.

Disability Resources is located in the Student Services Building or at (979) 845-1637 or visit disability.tamu.edu.

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, a person who is subjected to the alleged conduct 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 wellbeing. Students are encouraged to engage in proper self-care by utilizing available 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. Emergency help is also available 24 hours through the national 988 Suicide & Crisis Lifeline or at https://988lifeline.org.