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

Outline What is CS 2420? Mathematical Preliminaries

Part 1 What is CS2420 is about?

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?

Textbook Author: Mark Weiss Title: Data Structures and Algorithm Analysis in C++, Third Edition Publisher: Addison Wesley ISBN: X

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

Homework Submission All coding problems should be submitted at You must register for this class on the Eagle server. All analytical problems will be pencil and paper.

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 %

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

Part 2 Mathematical Prelims (Chapter 1: Section 1.2)

Floors and Ceilings

Exponents

Logarithms

Arithmetic Series

Geometric Series

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

Factorials

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).

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

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.

Direct Proof: Example

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.