Harold P. Boas

Math 300
Sections 901 and 903
Foundations of Mathematics
Fall 2020

Course Information

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 in order to earn a grade in the course.

Course Learning Outcomes

The main goal of the course 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.

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.

Notice that 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, and completing the assigned activities on time is important for success in the course. Accordingly, work submitted after announced deadlines is generally not acceptable.

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 and the temporary addendum for fall 2020.

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 page about Computer Requirements. Note that Chromebooks do not support Zoom breakout rooms, a Zoom feature that we will be using in Math 300.

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

Course Schedule

Wednesday, August 19
§1.1, statements and conditional statements.
Friday, August 21
§1.2, constructing direct proofs.
Monday, August 24
§1.3, Chapter 1 summary.
Wednesday, August 26
§2.1, statements and logical operators.
Friday, August 28
§2.2, logically equivalent statements.
Monday, August 31
§2.3, open sentences and sets.
Wednesday, September 2
§2.4, quantifiers and negations.
Friday, September 4
§2.5, Chapter 2 summary.
Monday, September 7
§3.1, direct proofs.
Wednesday, September 9
§3.2, more methods of proof.
Friday, September 11
§3.3, proof by contradiction.
Monday, September 14
§3.4, using cases in proofs.
Wednesday, September 16
§3.5, the division algorithm and congruence.
Friday, September 18
§3.6, review of proof methods.
Monday, September 21
§3.7, Chapter 3 summary.
Wednesday, September 23
§4.1, the principle of mathematical induction.
Friday, September 25
§4.2, other forms of mathematical induction.
Monday, September 28
§4.3, induction and recursion.
Wednesday, September 30
§4.4, Chapter 4 summary.
Friday, October 2
§5.1, sets and operations on sets.
Monday, October 5
§5.2, proving set relationships.
Wednesday, October 7
§5.3, properties of set operations.
Friday, October 9
§5.4, Cartesian products.
Monday, October 12
§5.5, indexed families of sets.
Wednesday, October 14
§5.6, Chapter 5 summary.
Friday, October 16
§6.1, introduction to functions.
Monday, October 19
§6.2, more about functions.
Wednesday, October 21
§6.3, injections, surjections, and bijections.
Friday, October 23
§6.4, composition of functions.
Monday, October 26
§6.5, inverse functions.
Wednesday, October 28
§6.6, functions acting on sets.
Friday, October 30
§6.7, Chapter 6 summary.
Monday, November 2
§7.1, relations.
Wednesday, November 4
§7.2, equivalence relations.
Friday, November 6
§7.3, equivalence classes.
Monday, November 9
§7.4, modular arithmetic.
Wednesday, November 11
§7.5, Chapter 7 summary.
Friday, November 13
§8.1, the greatest common divisor.
Monday, November 16
§8.2, prime numbers and prime factorizations.
Wednesday, November 18
§8.3, linear Diophantine equations.
Friday, November 20
§8.4, Chapter 8 summary.
Monday, November 23

Additional Information

Help Sessions

The Math Learning Center offers help sessions for various mathematics courses, including Math 300. Visit that website for the schedule.

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.


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

Technology Support

University Policies

The following policy statements are reproduced essentially verbatim from university documents.

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 makeup work, and the timeframe for makeup 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, 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, and 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. Emergency 24-hour help is also available through the National Suicide Prevention Hotline (800-273-8255) or at suicidepreventionlifeline.org.

COVID-19 Temporary Amendment

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 Fall 2020 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 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. While Student Rule 7, Section, indicates a medical confirmation note from the student’s medical provider is preferred, for Fall 2020 only, students may use the Explanatory Statement for Absence from Class form in lieu of a medical confirmation. Students must submit the Explanatory Statement for Absence from Class within three business days after the last date of absence.

Operational Details for Fall 2020 Courses

For additional information, please review the FAQ on Fall 2020 courses at Texas A&M University.