Course description

This course presents mathematical material necessary for the Computer Science student to approach the study of many advanced topics in Theoretical Computer Science at the graduate level. The course will cover the textbook Concrete Mathematics (A foundation for Computer Science) by R. Graham, D. Knuth, O. Patashnik.

The course includes recursions, sums, integer functions, elementary number theory, binomial coefficients, special numbers, generating functions, discrete probability, asymptotic.

Course goal(s)

To provide students with mathematical tools for the study of recurrence equations and their applications to relevant to computing and information technology.

Course objectives:

Course objectives include:

• To understand basic mathematical principles (proving, counting, understanding discrete objects).
• To learn main analytic methods through concrete examples from enumerative combinatorics, number theory and discrete mathematics, probability.
• To analyze different mathematical methods.
• To solve concrete problems using different enumeration methods.
• To develop mathematical abilities in writing programs by computers.

Skills & Competences

• Basic school mathematical knowledge
• Ability to construct examples and counterexamples
• Working with discrete objects

In the class, we do not explain the course textbook, but teach how to use knowledge you learned through exercises. To maximize the efficiency of the class, be sure to peruse the course textbook.

Course Learning Outcomes:

At the end of the course, the successful students:

• become familiar with different mathematical methods in combinatorics, number theory, discrete mathematics, and statistics.
• acquire the mathematical technique used to analyze the algorithm;
• understand the usage and meaning of basic formula in discrete mathematics.
• understand concrete problems as a unifying abstraction of natural and computing systems;
• are enabled and motivated to begin independent project / research work in discrete mathematics and computation.