Class meetings, Fall 2017: Tuesday and Thursday 9:30am – 10:45am in Hanes 120
Prerequisites: Mathematics 110
Registration: Enrollment and registration for the course is handled online. Students who wish to be put on the wait list for the class should go here.
Instructor: Andrew B. Nobel
Office: Hanes 308 Phone: 919-962-1352.
Office Hours: Mondays 2-3:15pm and Fridays 1-2pm.
Instructional Assistant: Wei Liu
Office: Hanes B48 Email: liuwei1@live.unc.edu
Teaching Assistant: Matt Jones Email: mattbbll@live.unc.edu
Office Hours: Mondays 10-11:30am and Fridays 10-11am
Location: Hanes 115 (STOR Computer Lab)
Audience and Goals: STOR 215 is an intermediate undergraduate level course that provides an introduction to mathematical reasoning for students seeking a minor or major in the STOR Statistics and Analytics program. The course may also be appropriate for students in mathematically oriented disciplines such as Physics, Quantitive Psychology, Mathematics, and Computer Science.
The objective of the course is to teach students the basics of rigorous mathematical reasoning, so that they are able to understand and execute elementary mathematical arguments and proofs. The course will provide a proof-based introduction to several subjects that are important to decision sciences, including elementary number theory, elementary combinatorics, discrete probability, and graphs.
Text: The primary text for the class is “Discrete Mathematics” 7th edition, by Kenneth Rosen.
Homework policy: Homework problems will be assigned regularly throughout the semester, usually every week, and will be posted on the class web page. Each homework assignment will be graded: late/missed homeworks will receive a grade of zero. In computing a student’s overall homework score for the course, their two lowest homework scores will be dropped. This provision is meant to cover exceptional situations in which a student is unable to turn in an assignment due to circumstances beyond his/her control: under ordinary circumstances, students are expected to turn in every homework assignment.
To receive full credit on the homework assignments, you must clearly label each problem, neatly show all your work (including your mathematical arguments), and staple together the pages of each assignment in the correct order. You should give a clear account of your reasoning in English, and use full sentences where appropriate. Please write your name or initials on each page.
Students are welcome to discuss the homework problems with other members of the class, but should prepare their final answers on their own. Copying of homework is not allowed. If you have any questions concerning the grading of homework, please speak first with the TA. If you are absent from class when an assignment is returned, you can get your homework from the TA during their office hours.
Class attendance and protocol: Students are expected to attend all lectures. If you are unable to attend a lecture, please let the instructor know and make plans to get the notes from another student in the class. Please arrive on time, as late arrivals disturb other students. Reading of newspapers and the use of laptops, tablets, and cell-phones is not allowed in class. If you use a tablet to take notes, please see the instructor to discuss this.
Exams: There will be two in-class midterm exams and a comprehensive final examination, which will also be in-class. All exams will be closed book and closed notes, and without calculators. The final exam will be given at the time and date specified by the UNC Final Exam Schedule.
| Midterm 1 | September 26 |
| Midterm 2 | November 7 |
| Final | See Official UNC Schedule |
Grading: Grading will be based on homework, two in-class midterms, and an in-class final exam, using the weights below.
| Homework | 11% |
| Midterm 1 | 24% |
| Midterm 2 | 24% |
| Final | 41% |
When Midterms 1 and 2 are returned, a rough correspondence between numerical scores and letter grades for that exam will be provided. If you receive a D or an F you should come to the instructor’s office hours to discuss your exam.
Honor Code: Students are expected to adhere to the UNC honor code at all times.
Syllabus (subject to change): The first part of the course is devoted to an overview of elementary logic, sets, and functions, and a variety of proof strategies. Topics include propositional logic with quantifiers, direct proofs, proof by contradiction, and induction. We then illustrate, develop, and apply these ideas in the study of several subjects where proofs and proof techniques are common, including elementary number theory, basic combinatorics, discrete probability, and graphs.
- Propositional logic, basic logical operations
- Quantifiers
- Direct and indirect proofs
- Sets and basic set operations
- Functions
- Sequences and summations
- Elementary number theory
- Divisibility, modularity, and primes
- Weak and strong induction
- Elementary combinatorics: basics of counting
- Permutations, combinations, binomial coefficients
- Discrete probability: model of a random experiment
- Conditional probability and Bayes Theorem
- Expected value and variance
- Graphs: basic terminology and applications
- Adjacency matrices
- Connectivity, Euler and Hamilton paths
Study tips:
1. Keep up with the reading and homework assignments. If the reading assignment is long, break it up into smaller pieces (perhaps one section or subsection at a time). Keep a pencil and scratch paper on hand as you read the book, and use these to work out the details of any argument that is not clear to you.
2. Look over the notes from the lecture k before attending lecture k+1. This will help keep you on top of the course material. Ideas from one lecture often carry over to the next: you will get much more out of the material if you can maintain a sense of continuity and keep the “big picture” in mind.
3. Read the book carefully *before* doing the homework. Trying to find the right section, formula, or paragraph for a particular problem often takes as much time, and it can create more confusion than it resolves. Each chapter of the book contains many examples illustrating the ideas presented there. When you first read the chapter, don’t feel as if you need to read through every example: focus first on the shorter, simpler examples, and then look at the longer, more complicated examples afterwards.
4. It is important to know what you know, but it’s especially important to know what you don’t know. As you read over new material in the text or your notes, ask yourself if you (really) understand it. Keep careful track of any concepts and ideas that are not clear to you, and make efforts to master these in a timely fashion, using the class notes, the text, office hours, study groups, and outside reading if necessary.
5. One good way to see if you understand an idea or concept is to write down the associated definitions and basic facts, without the book or your notes, in full, grammatical sentences. It’s also helpful to state the definitions and basic facts out loud — the same grammatical criteria apply here. Translating ideas from mathematics to complete English sentences, and back again, is an important component of the course, and important component of mathematical research.
6. Homework plays two important roles in the course. First, it provides an opportunity to actively think about, engage with, and learn the course material. In addition, homework provides feedback on your understanding of the material. Carefully look over your corrected homework assignments. Most students do well on the homework: even if you received a good score, make sure to note and understand or correct any mistakes you made on the problems.
7. Begin studying for exams at least one week before they are given. Look over your notes, homework, and the text. Write up a study guide containing the main concepts and definitions being covered, and use this to get a clear picture of the overall landscape of the material. A study guide for each midterm will be posted online. For every topic on the study guide, you should know the relevant definitions, motivating ideas, and at least one or two examples.