DISCRETE MATHEMATICS: MTH 2110

Welcome to Discrete Math!

Welcome to DM! There are lots of new and exciting things going on in the course this year, so you picked a good year to take this class!. All of the best aspects of my previous offerings of the course have been kept, but I think the new changes, mostly driven by prior student feedback, will make this a fun and enriching class for all of us. I hope you grow to love the world of all things discrete as much as I do!

On the linked "Calendar" page, you will find the daily schedule, including all assignments. It will be updated often, so always check online for the latest changes. Below, you will find information about the course - please read it carefully as you are responsible for making yourself familiar with all expectations.

Course Information

Instructor Information
Professor Sarah Spence Adams
Office: MH 258
Office Phone: 781.292.2536
Email: sarah.adams AT olin.edu
Meeting Times/Location:  M, Th 10:50AM – 12:30PM, AC328
Office Hours: Mon after class in AC326, Weds 3:15-4:15 in MH258, and by appointment.
Course Assistants: Philip Loh  and Poorva Singal - Help Hours TBA in location TBA, including Thurs immediately after class in AC326.

Discrete Mathematics is a course that will introduce you to advanced counting techniques and discrete structures such as graphs, trees, codes, and designs.  It will also make you a better problem solver, mathematical ‘prover,’ and technical writer.  You will learn to argue logically, flawlessly, and convincingly.  You will improve at working hard problems in groups and individually.  Like a gift that keeps on giving, with high probability, you will see some of the structures that you meet here at some later point in your career, and with probability 1, you will use the skills you gain in problem solving, critical thinking, logical reasoning, and teamwork for the rest of your natural born lives.   What a bargain!

Learning Objectives

1. Solve problems and organize precise solutions for a variety of topics in discrete mathematics. Topics include:
1. sets and functions
2. counting techniques including permutations, combinations, the pigeonhole principle, and inclusion/exclusion and interpreting the meaning of such counting problems in a variety of contexts
3. analyzing graphs, including theory-based properties and how graphs model real-world situations
4. recurrence relations
2. Understand and be able to construct elementary proofs, including proofs by induction, involving various discrete mathematics topics
3. Improve teamwork skills through collaboratively solving/discussing problems and through collaboratively writing precise solutions/proofs
4. Self-direct a group project on a specialized topic in discrete math
5. Discuss several applications of discrete math
6. Improve oral and written communication skills through projects, class participation, homework, and tests

Text
Discrete Mathematics and its Applications, Kenneth H. Rosen, 5th edition, McGraw Hill, 0-07-242434-6.  

Attendance
Class meetings will vary from day to day.  Sometimes, we will cover material in your book, but with different examples or applications.  Sometimes we will cover material not covered in your book.  Often you will be working problems in groups at your desks or at the boards.  Sometimes you will be taking quizzes.  Usually you will be handing in homework.   I expect you to be there to participate and engage in conversation with your peers and me.  If you do miss a class, it is your responsibility to seek out one of your peers to find out what you missed, including any announcements or handouts. As your class participation plays a role in your final grade (not to mention your personal learning and enrichment!), it is in your best interest not to miss any classes.  

Homework

• Pre-class Reading Problems:  These problems will help focus your reading, and they are due at the start of each class period.  Based on prior student feedback, these problems have changed in a variety of ways.  First, they are now all (or almost all) odd-numbered problems from the book so that you can easily check your answers after trying them. Second, they now include problems that should be very straightforward after reading the text and its examples as well as a couple of problems that will probably make you think for a couple of extra minutes (yes, students really did ask for harder pre-class problems!).  Third, you do not have to hand in all of these problems to be graded; instead, you will hand in as many as you deem appropriate, including at least one problem that you felt was instructive, interesting, confusing, or hard. (None fit the bill? Well, you still need to pick at least one to turn in - you must be able to find at least one that you think could help someone else understand some concept, or at least one that made you think about some other concept you have seen somewhere else, or...) Indicate why you aren't handing in the others (e.g., “I quickly did #3 in my head and got it right."). These problems will enable you to participate in class, and they will give you practice at the oft-mentioned skill of life-long learning – you are going to need to be able to learn from a book in the future, so you might as well practice now! Please try to solve these problems independently before seeking help, and cite help if you do seek it. These will be graded using a 0 (did not pass in on time or clearly did not put any effort in), 1 (did something), 2 (put in extra effort) scale. Although they don’t  “count” much in your grade directly, they will allow you to get much more out of class than if you skip them! This will then help you succeed in the other aspects of the course. As part of my holistic approach to grading, your grades on these problems also contribute to your participation and engagement grade - more specifically, lots of 2s will bump up your participation and engagement grade.  
• Group Problem Sets:  These problem sets will be more challenging, and they will be done in pre-assigned groups.  You are required to try each problem on your own before meeting with your group, bringing your attempts and ideas to your group meeting. You are encouraged to solve these problems only with your team-mates.  Any collaboration with other students outside your group (or anyone else or with any other resources) must be cited.  Your group will hand in one solution set, and all group members will receive the same grade.  Group compositions will likely change once during the semester.   
• Practice Problems:  These problems will help you self-check your progress.  They are not collected or graded, but you may ask me (or anyone!) questions about them at any time.  The answers are in the back of the book, and more detailed solutions are in the Student Solutions Manual (search online). 

Using resources on Homework
The following are strictly forbidden:  You may not use the Instructor’s Solutions Manual, you may not use past students’ work, and you may not use any other source of solutions (from other schools, on the web, etc) except for the Student Solutions Manual, which is permitted and available for purchase online.

Any other resources are permitted under the following two conditions:

• You must never simply copy a solution or hand in a solution that you do not fully understand.  By handing in a solution, you are certifying that you understand it completely and you can independently solve similar problems.
• You must always cite your source of help next to each problem.  Simple notes like “checked answers with Luisa,” “used back of book,”  “used solns manual,”  “used website X,” “used Book A,” “helped by Jenny” are perfectly fine.  Feel free to use obvious abbreviations – I don’t want citing to be a time burden.  Getting in the habit of always citing sources of help is good professional practice and it is in the spirit of learning and the Honor Code. 

If you do not use any sources or receive any help from friends, then please write “No Help” on the top of your paper.  If you have any questions about what resources are allowed or how to cite them, please just ask! 

Other HW requirements
It is essential that all turned-in homework be neatly written or typed.  On the upper right hand corner of the first page, please list your full name(s), DM,  the assignment (e.g. “Group HW #1”) and the due date for the assignment.  You must staple all pages together.  Each problem must be clearly labeled (e.g. Ch 5.4, #23) and done in order.   You must show your work, which means that steps must be clearly explained.  Neatness and clarity of explanation are essential; your exposition will be evaluated.   

No late work (including pre-class problems, group homework, tests, or any other assignments) will be accepted unless there is an OSL-approved emergency.  Please do not ask for an exception and please do not put your NINJAs in an uncomfortable situation by asking them for exceptions.

Quizzes
On almost every Thursday at 10:50AM, you will take a very short quiz.  The quizzes can include any material that has already been covered, normally whatever was covered the previous Monday or Thursday.

Tests
You will have two take-home tests. You will not be allowed to use any resources, so get in the habit of trying to do all problems without resources, and then only using resources when you are really stuck. This will maximize your learning.

Projects
In small groups, you will investigate discrete mathematics topics not covered in class.  Your group will give an in-class presentation and write a paper (including a first draft and a final draft).  You will assess classmates’ projects.

Grades
Group Homework: 20%
Group Project: 10%
Pre-class problems: 5%
Quizzes: 20%
Tests: 45%
Participation and engagement: Priceless…*

*What does priceless mean? It is a magical word that gives me the wiggle room I want to assign fair and holistic grades at the end of the semester. (Gifts and money in early December also do wonders….**) You may have heard about “starred” problems in this class in the past. Due to past student feedback and some other pedagogical changes in this course, I am discontinuing the starred problem policy. Instead, throughout the semester, there will be a variety of opportunities for you to work on extra problems in addition to the problems that are officially due and graded. There are practice problems listed on the website at the medium level, there are in-class worksheet problems at the medium and hard levels, and I’ll periodically give out some very hard problems. I encourage you to work on a variety of such problems and share your progress with me (and also with the entire class when appropriate). The more problems you do, the more you will learn, and the better you will get at technical communication. The more effort I see, the more generous I will be at the end of the semester.  Does this mean you can get an A by trying really hard but getting Bs or Cs on the tests? Sorry, but no. It is math after all, and the whole point of math is precision. Accuracy matters, but I also consider what you have learned through your efforts.

**For all you lawyers out there, there is a joke.

Laptops
I will sometimes want you to have your laptops in class.  Please refrain from talking on IM, doing email, or doing unrelated web surfing during class, as this is distracting to both me and your fellow students.  If you are that bored, please talk to me about it!  I will find a solution. Do I also need to include no phone browsing, texting, or whatever else you can do with your phones now?  Don’t do that stuff either.

Office Hours
Please come to office hours with questions big or small!  Or maybe you don’t even know what your questions are; I can probably still help.  Sometimes a few minutes in office hours can make a big difference.  If you need a special appointment, please ask.  Office hours are a great time to show off your valiant efforts at various problems.  You can also ask questions and show off your efforts to your NINJAs, who are both awesome at all things discrete.

Supplies
I recommend that you use a loose-leaf notebook.  This way, you can keep your class notes, various homework problems, various hand-outs (there will be a lot of these!), etc, all in order.  Please save all of your work until (at least) the end of the semester. 

Daily Schedule
The schedule and all assignments are subject to change as we go. You are responsible for knowing what is due when – be prepared! Check the calendar every day! http://faculty.olin.edu/~sadams/DM/Calendar.htm

Special Needs
Please discuss your needs with OSL and with me as soon as possible so that we can make appropriate accommodations to maximize your learning.

Honor Code
This professor regards the Honor Code as essential to the academic integrity of the College. Please express any concerns in a timely fashion.