Essential Discrete Mathematics for Computer Science

For freshman/sophomore one-semester introductory courses in discrete math that include intermediate programming for computer science and mathematics students.

This brief introduction to the mathematics of computer science prepares students for the math they will encounter in later courses. With applications that are specific to computer science, this text helps students develop reasoning skills and provides them with an early introduction to fundamental mathematics necessary for future math and computer science courses.

• Topics have been chosen with CS in mind, both with regard to mathematical concepts and their applicability to CS.
• Allows students to see immediate CS applications of what they are learning.
• Exercises, including programming assignments that promote immediate use of the topics.
• Helps students gain a deeper understanding of the mathematics by asking them to design programs that implement the concepts. Helps students enhance their programming skills using exercises that have both conceptual and practical components.
• Exercises progress from easy to difficult.
• Allows students to start with easy problems that build their confidence and understanding and then move on to more challenging exercises that build their problem solving abilities.
• "Reader Checks" throughout the text-These are short questions that students should stop and answer to be sure that they are ready to continue.
• Encourages students to read carefully and to reread materials they did not understand before continuing; provides instructors with topics for discussion in the classroom.
• Brevity-The text can be covered in a semester.
• Prevents students from becoming intimidated by the level or volume of topics.
• Focus on the acquisition of skills necessary for reading mathematics.
• Helps students gain better reading and programming skills by learning to reason about what they are reading and the algorithms they are designing.

Contents

1. Notes on Proofs
2. Sets
3. Functions and Relations
4. Boolean Algebra
5. Natural Numbers and Induction
6. Number Theory
7. Recursion
8. Solving Recurrences
9. Counting
10. Matrices
11. Graphs