1. CS2420: Lecture 1 Vladimir Kulyukin Computer Science Department Utah State University

2. Outline What is CS 2420? Mathematical Preliminaries

3. Part 1 What is CS2420 is about?

4. Four Basic Questions for the Computer Scientist I have implemented an algorithm. How do I know how fast it runs? How can I prioritize tasks? How can I store/organize data efficiently? How can I retrieve/search data efficiently?

5. Textbook Author: Mark Weiss Title: Data Structures and Algorithm Analysis in C++, Third Edition Publisher: Addison Wesley ISBN: 0-321-44146-X

6. Workload There will be regular assignments. Assignments will require reading, coding and/or analysis. Times allocated for assignments will vary (1 – 3 weeks).

7. Homework Submission All coding problems should be submitted at http://eagle.cs.usu.edu. http://eagle.cs.usu.edu You must register for this class on the Eagle server. All analytical problems will be pencil and paper.

8. Final Grade Homework – 20 % Midterm Exam (March 5 th, in class, 1:30 – 2:20) – 30 % Final Exam (April 28 th, in class, 11:30 – 1:20) – 50 %

9. Class Attendance Attendance of regular classes is optional. Attendance of exams is mandatory (unless you want to get an F).

10. Part 2 Mathematical Prelims (Chapter 1: Section 1.2)

11. Floors and Ceilings

13. Exponents

14. Logarithms

17. Arithmetic Series

18. Geometric Series

19. Polynomials Let d be a positive integer, then a polynomial in n of degree d is a function p(n) defined as

20. Factorials

21. Proofs A mathematical proof system consists of axioms, definitions, and terms Axioms are statements that are assumed to be true. Terms are elementary units that are not defined (dots, numbers). Definitions define new concepts through terms or existing definitions (lines, even numbers, odd numbers).

22. Useful Proof Techniques Direct proof Proof by contradiction Proof by counterexample Proof by induction

23. Direct Proof Need to Show: If P, then Q. (P  Q). Assume that P is true and use the axioms, definitions, and previous theorems to show that Q is true.

24. Direct Proof: Example

25. Proof By Contradiction Need to Show: If P, then Q. Assume that P is true and Q is false and find a contradiction, i.e., a statement that contradicts another true statement.