Unit 2

Topics to be addressed:

• Algorithms and abstraction
• Connections between Mathematics and Computer Science
• Societal impacts of computing

Topic Description:

This unit provides students with opportunities to become “computational thinkers” by applying a variety of problem-solving techniques as they create solutions to problems that are situated in a variety of contexts. The range of contexts motivates the need for students to think abstractly and apply known algorithms where appropriate, but also create new algorithms. Analysis of various solutions and algorithms will highlight problems that are not easily solved by computer and for which there are no known solutions. This unit also focuses on the connections between mathematics and computer science. Students will be introduced to selected topics in discrete mathematics including Boolean logic, functions, graphs and the binary number system. Students are also introduced to searching and sorting algorithms and graphs.

Objectives:

The student will be able to:

• Name and explain the steps they use in solving a problem.
• Solve a problem by applying appropriate problem-solving techniques.
• Express a solution using standard design tools.
• Determine if a given algorithm successfully solves a stated problem.
• Create algorithms that meet specified objectives.
• Explain the connections between binary numbers and computers.
• Summarize the behavior of an algorithm.
• Compare the tradeoffs between different algorithms for solving the same problem.
• Explain the characteristics of problems that cannot be solved by an algorithm.