### Course Description:

Buying music on-line, making phone calls, predicting the weather, or controlling disease outbreaks would be impossible without mathematics, statistics, and computer science. This class focuses on methods of reasoning common to these disciplines, and how they enable the modern world. The primary goal of this course is to instill the skills of precise, rigorous logical thinking, modeling, and abstraction. It features an integrated subset of some of the basic elements of mathematics, statistics, and computer science, presented in such a way as both to reveal their inherent depth and beauty and to relate them more immediately to the students' chosen fields of study.

### Prerequisites:

None (beyond basic K-12 math and willingness to use it!)

### Administrative Information:

This course satisfies the Mathematics Competency and Divisional Studies requirements for CAS students (students from other colleges are encouraged to consult their advising offices to confirm what requirements are satisfied by the course). Four faculty members—two from the Mathematics and Statistics (MA) Department and two from the Computer Science (CS) Department—developed this course. Two of them will team-teach it this semester. Students are required to register for the main course lectures, as well as for one of the discussion sections. The latter will be used to facilitate a more interactive and deeper exploration of topics covered in the lectures through smaller group discussions or laboratory work. Please note that MA-109 A1 is the same as CS-109 A1, so it does not matter for which one you are registered.

### Course Staff

The two faculty instructors for the Spring 2012 offering are Glen Hall (MA) and Leo Reyzin (CS). Contact information office hours

## Course Modules and Topics (Tentative)

### Mathematics Module (Prof. Hall)

- Mathematical Proofs (4 lectures)

Introduction to careful mathematical argument; basic proof techniques; critical analysis of logical arguments and proofs. - Functions (3 lectures)

A zoo of functions. Linear, polynomial, exponential and logarithmic growth and related function notation. - Modeling Growth and Decay (3 lectures)

Exponential and logistic growth models. Comparison of models with actual systems (biological, physical, etc.)

### Statistics Module (Prof. Hall)

- Probability (3 lectures)

Being quantitatively precise about uncertainty. Foundations and interpretation; equally likely outcomes model; independence. - Estimation and Confidence (3 lectures)

Learning about a population from data. Population versus sample, opinion polls, sample-based estimates and margin-of-error. - Discovering Associations (4 lectures)

Quantifying association between variables. Testing for associations in data.

### Computer Science Module (Prof. Reyzin)

- Digitization (3 lectures)

Representing, storing, and transmitting information and programs as bits. - What Digitization Means (4 lectures)

Computation: bits operating on bits. Social and technical implications. Limits of Computation. - Algorithms and Complexity (3 lectures)

How long computation takes and why it matters.

### Capstone Module (Prof. Reyzin)

- Graphs as Models (2 lectures)

Graphs as powerful models for various real applications, systems, and phenomena. - Building complex artifacts through the process of layering abstractions (2 lectures)

Using well-understood layers of functionality to build seemingly complex systems on the example of the Internet. - Mathematics, Statistics, and Computer Science on the Internet (5 lectures)

Using modeling techniques learned up to this point to explain complicated phenomena (e.g., structure of social networks), answer questions about complex systems (e.g., is physical distance a good explainer of Internet delays), predict the future (e.g., evolution of social networks), perform quantitative evaluations (e.g., quantify the relative importance of a set of web pages or a set of characters in a Shakespeare play), and understand security and privacy on the Internet.

## Course Materials and Website: Moodle

Due to the unique nature of the course, there is no single textbook that covers its entire content (which makes coming to lecture/discussion even more important!). The course material will be distributed on-line through the on-line course management system called Moodle. Emails to the class list will also be sent through Moodle. Moodle will also host our discussion boards (where you can ask and answer questions) and will be used to assign and distribute homework. Each student should create a new Moodle account as soon as possible. Please add a few words about yourself in the "Description" field and upload a picture (but crop it to a square first—else Moodle may cut off your head).

## Course Requirements and Evaluation

### Homework Assignments:

Understanding of weekly material will be developed and assessed through seven homework assignments. Homework assignments and solutions will be available for download and printing through Moodle. Some assignments will be turned in electronically via Moodle; others on paper. Detailed instructions on how to do this will be made available on-line.

As a general rule, late homework assignments will not be accepted. However, students will be allowed to drop the lowest assignment score, with the scores on the remaining assignments re-weighted accordingly. This policy is intended to cover absences due to illnesses and family emergencies---so plan accordingly and do not use up your dropped assignment for no good reason.

Limited collaboration on the homework is allowed, subject to important conditions, described in the course collaboration policy in Moodle. Students are responsible for knowing and abiding by this policy and the provisions of the BU Academic Conduct Code. Violations of the code of conduct are punishable by sanctions, including expulsion from the University.

### Module Projects:

Students will complete a set of three projects, one for each of the mathematics, statistics, and computer science modules. To help break up the workload into manageable pieces, each module project will consist of a sequence of tasks. Some of the tasks will be assigned as part of regular homework. The end result of each module project will be a short report, to be handed in at the end of the corresponding module or shortly thereafter (due dates to be announced).

### Laboratory Assignments:

"Learning by doing" is no less true in mathematics, statistics, and computer science than in any other endeavor. To facilitate learning in this manner, there will be about five labs during the semester. Labs will be held in the Computer Science Computer Laboratory (730 Commonwealth Ave, EMA 304) during regularly scheduled discussion sections. Lab write-ups are to be completed by the end of the discussion period and turned in to be graded.

### Pop Quizzes:

There will be occasional unannounced quizzes at the beginning of lecture; they will check attendance (so be on-time to class!) and may test important course topics. Your lowest pop-quiz score will be dropped. Make-ups for pop quizzes will not be given.

### Exams

There will be a midterm exam and (a cumulative) final exam. The midterm exam is scheduled for Wednesday, March 7 (Wednesday before spring break), in class, and the final exam is scheduled for Friday, May 11 (the last day of exams), 3-5pm. The final exam date/time is scheduled by the Registrar and cannot be adjusted. Please plan accordingly!

### Course Grade:

The course grade is broken down as follows:

- 20% on Homework Assignments (excluding the one with the lowest/missing grade)
- 20% on Module Projects
- 10% on Lab Assignments and Pop Quizzes
- 20% on Midterm Exam
- 30% on Final Exam