General Information

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 field 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. Four faculty members - two from the Mathematics and Statistics (MA) Department and two from the Computer Science (CS) Department - will team-teach this course. Each faculty member will present roughly a quarter of the lectures. 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

Instructors:

The four faculty instructors for the Fall 2010 offering are Azer Bestavros (CS), Richard Hall (MA), Eric Kolaczyk (MA), and Leo Reyzin (CS). Contact information and office hours are listed below:

Teaching Fellows:

There are two teaching fellows (TFs) for this course, one from Computer Science (Ray Sweha) and one from Mathematics and Statistics (TBA).  Contact information and office hours are listed below, noting that TF office hours will be held in the CS Undergraduate Lab, located on the third floor of the EMA building (730 Commonwealth Avenue).

Course Modules and Topics

Mathematics Module

• Mathematical Proof (4 lectures)
  Introduction to careful mathematical argument; basic proof techniques; critical analysis of "logical" arguments and "proofs".

• Functions (2 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.)

Computer Science Module

• Digitization (3 lectures)
  Representing storing, computing, and transmitting information as bits.

• What Digitization Means (2 lectures)
  Social and technical implications. Limits of Computation.

• Graphs as Models (2 lectures)
  Graphs as powerful models for various real applications, systems, and phenomena.

• Algorithms and Complexity (3 lectures)
  How long computation takes and why it matters: algorithms and running times.

• Beyond Computation (3 lectures)
  Computer science beyond just computing. Cryptography, security, and privacy.

Statistics Module

• 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 (3 lectures)
  Quantifying association between variables. Testing for associations in data.

Capstone Module

• Building complex artifacts through the process of layering abstractions (2 lectures)
  Using well-understood layers of functionality to build seemingly complex systems -- the Internet.

• Understanding the world through modeling (4 lectures)
  Using models to explain seemingly 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), and perform quantitative evaluations (e.g., quantify the relative importance of a set of web pages or a set of characters in a Shakespeare play).

Course Materials

Reading Materials:

Due to its unique nature, there is no single textbook that covers the entire content of this course (which makes coming to lecture/discussion even more important!). Instead, the materials covered in this course will be available through a collection of notes compiled by the course instructors, as well as periodic readings and on-line materials, which will be made available on-line through the course web site.

Web-based Resources:

The website for the course is at http://mcs109.bu.edu. To distribute class materials (e.g., homework assignments and solutions, etc.) and to facilitate on-line discussion of course topics, we will make use of the on-line course management system called Moodle. Each student should go to http://mcs109.bu.edu/moodle and click on MA/CS-109 to create a new account there. Please see the accompanying handout on Moodle for more details.

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. Most assignments will be turned in electronically via Moodle. 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.

Students are allowed to work together on homework assignments (after a suitable amount of effort on their own beforehand), but subject to important restrictions and guidelines. All students should consult the course website for a detailed description of the homework collaboration policy for this course.

Students are responsible for knowing, and abiding by, the provisions of the CAS Academic Conduct Code, (see http://www.bu.edu/cas/academics/programs/conductcode.html).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 five labs during the semester. Labs will be held in the Computer Science Computer Laboratory 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.

Exams:

There will be a midterm exam and final exam for this course. The midterm exam is scheduled on Fri October 22, and the final exam is scheduled on Mon, December 20, 12:30-2:30pm. 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

• 20% on Midterm Exam

• 30% on Final Exam

Course Lectures

Lectures (and exams) are held Mon/Wed/Fri from 1-2pm in room SCI-115, in the Metcalf Science Center. The following is a tentative schedule of lectures.

Discussion and Lab Sessions

Each student must be registered for one of the four sections listed below:

The following is a tentative list of planned weekly discussion or laboratory sessions. 

Last Updated on 09/03/2010