Math 21-127 Syllabus (2024)

Subject Material:This course will focus on the basic building blocks of mathematical reasoning and proof. Our goal is to build a foundation of understanding about what a mathematical proof looks like, and how to write one. We will discuss fundamental concepts, as well as elementary proof techniques.Our structure will look as follows. We will start by understanding the fundamental ideas about how to write formal proofs, and to use propositional logic. We will then apply these ideas to explore basic, tangible objects, like numbers, sets, and functions. We'll introduce a hugely important proof technique, called Mathematical Induction, and use these basic objects and induction to help develop some fluency with logic and proof. We'll be able to use this technique to prove that there are different sizes of infinite sets (!!), showing that there are strictly more irrational numbers than there are rational numbers.Next, we'll learn to count! We shall discuss some elementary tools in combinatorics, and how sophisticated counting techniques can help us do mathematics. Finally, we will end the course with a look at basic number theory, division, and how to count like a clock.Depending on how much time is left in the course, we will add additional topics at the end. Those will be discussed as a class later on.

Lecture: Attending the lecture is a fundamental part of the course; you will be responsible for all material presented in lecture.

Classroom Conduct: In the classroom, a certain level of respect and attentiveness is expected. Please do not use phones or computers, play games, or talk to friends during lecture. This can be distracting to other students and the instructor.

Calculators: A calculator is not required for this course. The use of any calculators or other electronic equipment will NOT be permitted on exams.

Homework: Homework problems will be assigned on the course homework page, and should be completed and turned in by the beginning of class on the indicated due date. You should make every effort to complete the homework assignments and seek help with problems you have been unable to solve. You may turn in one assignment late (no later than one class period) without permission. A 3% bonus on each assignment will be given for sending the assignment in typeset with LaTeX.

Exams: There will be two exams given during the regular lecture hour. Please see the course calendar for the specific dates. More information will be provided within 1 week of the exam. These exams will not be cumulative. See exam policies below.

Final Exam: There will be a cumulative final exam. The exam will be Friday, 10 May, from 5:30-8:30pm.
Exam Policies: No calculators or other electronic devices will be allowed during the exams. Unless you have a very serious, well documented, and compelling reason to miss an exam, there will be no makeup exams, for any reason. Regrades on exams will be subject to the regrade policy below.

Regrade Policy: If you wish to have a problem rescored on an exam, you must first hand back the exam to the person who handed it back to you the same day it was handed back. This person will then deliver the exam to the professor, and you must either make an appointment or come in during office hours to discuss your request in person within one week.

Grading: Your final course grade will be based on the following weighted average:

• 30% Homework
• 20% each of your midterm exams
• 30% Final Exam

• Scores above 90%: A
• Scores above 80%: At least B
• Scores above 70%: At least C
• Scores above 60%: At least D

Academic Honesty: Academic dishonesty is a serious offense, carrying serious administrative sanctions. Any instance of dishonesty will be pursued by the instructor. It is in your best interest to follow all policies laid out here and elsewhere on the website, and familiarize yourself with the university guidelines for academic honesty. Please help maintain both your own integrity and the integrity of Carnegie Mellon University.