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Math 127 Spring 2018
Textbook: We will use the book An infinite descent into pure mathematics by Clive Newstead. Most of the topics we will discuss are also easily found in many other places (like the internet!), so please don't hesitate to Google liberally.
Concepts of Mathematics
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 exploring 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 discrete probability theory, and how sophisticated counting techniques can help us do mathematics.
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 material presented in lecture regardless of whether it is discussed in the textbook.
Reading: Reading the assigned items corresponding to the class lectures and homework exercises is considered part of the homework assignment; you will be responsible for material in the assigned readings regardless of whether it is discussed in lecture. You are expected to read the assigned material in advance of the 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.
Exams: There will be three 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. Date and time TBA.
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. Any grade disputes on midterm exams must be submitted in writing to your TA within 24 hours of the exam being returned.
Grading: Your final course grade will be based on the following weighted average:
A curve may be applied to final scores or individual examinations at the instructor's discretion. Regardless of the curve, I will maintain the following minimum threshholds:
- 22% Homework
- 16% 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.
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