Introduction to Abstract Mathematics

Fall 2023

The main goal of the course is to provide basic training in rigorous mathematical reasoning. To pass the course, you will need to learn how to understand mathematical arguments and how to express your own arguments in a clear and mathematically correct way.

You will learn problem-solving techniques as well as basics of mathematical logic and proof methods. Those will be applied to study basic mathematical objects, such as sets, functions, sequences, and natural numbers.

More often than not, mathematics is a collaborative activity. Mathematicians rely on their peers to review their work to see if there are any gaps in the arguments. For you, working with other students is also an efficient way to learn proofs. You are encouraged to work in groups in this class.

The textbook is available electronically through Cook Library. This access has one important limitation: only 3 people can access the book at the same time.

The textbook, like most mathematical literature, starts with the more fundamental topics and builds on them to develop the more advanced ones. This approach makes perfect sense in the abstract and works well for most mathematical books. However, if this course were to follow the chapters of textbook in order, you would likely think that it lacks focus and find it more abstract than it actually is. To prevent this from happening, we will rearrange the material and focus on proving a handful of theorems. We will cover the necessary background as we need it for their proofs.

You are encouraged to use the typesetting system LaTeX to type up your solution. This is not a requirement, but it will make revisions for the more difficult exercises easier. There are multiple options to get started with LaTeX, the easiest one is by getting a free account on Overleaf.

There will be reading assignments, including "read ahead" ones. For each of the reading assignments, there will be a formally collected reading check and in-class discussion.

If your reading checks and participation in discussions are consistently good (feel free to ask me for feedback if you are not sure), I will add a third of a letter grade to your final grade. At worst (if you are not ready or miss the class half the time), I will subtract one full letter grade from your final grade.

Office Hours. I encourage you to come to my office hours, which are Mondays and Wednesdays right after our class, from 4pm to 5pm, in YR 230, with questions you have in the course. If you are not able to come during these hours, I am available by appointment (just talk to me after the class or send an email).

Prime time. The Math Tutoring Center does not have tutors for our class. The Math Department has established peer-led sessions, called Prime Time, that will be happening daily in YR 307 from 12noon to 2pm.

You are welcome and encouraged to ask me for help with course material during the office hours or by making an appointment.

You should expect to spend a considerable amount of time working on this course outside of class. At the same time, try to be efficient. If you are spending a lot of time on homework without making much progress, talk to me.

You are expected to be familiar with TU's University's Academic Integrity Policy, especially the sections that define plagiarism, cheating and complicity (II.B-II.E) and describe the possible grade penalties (V.C). You are encouraged to work with other students in the course on homework assignments, but each student must submit their own version of the solutions. Tests and quizzes are to be written strictly individually.

Normally, no make-up tests will be given; if for some reason you are not able to take a test, please, let me know as soon as possible.

Everyone participating in this course is expected to be respectful of each other without regard to race, class, linguistic background, religion, political beliefs, sex, gender identity or expression, sexual orientation, ethnicity, age, veteran's status, or physical ability. If you feel these expectations have not been met, please feel free to discuss it with me or with the designated diversity liaison Dr. Elizabeth Goode.

This course is in compliance with Towson University policies for students with disabilities. Students with disabilities are encouraged to register with TU ADS.

If you have questions or concerns about the course, be sure to discuss them with me during my office hours or by appointment.