Mathematical Foundations of Computer Science (CS 270/CS 680)

Course Description

Emphasizes analytic problem-solving and introduction of mathematical material necessary for later courses in algorithms, compiler theory, and artificial intelligence. Includes topics such as logic, theorem-proving, language operations, context-free grammars and languages, recurrence relations, and analysis of algorithms.

Course Goals

To provide students with the mathematical tools and techniques necessary for describing and analyzing algorithms, programs, and software systems. Material in this course should be helpful in other Computer Science topics and courses such as algorithms and data structures, programming languages and compilers, computer architecture, artificial intelligence, concurrent programming, and software engineering.

Course Objectives

• To provide recursive definitions of patterns and data structures.
• To use induction and other proof techniques to prove properties of algorithms, data structures, programs, and software systems.
• To use regular expressions and grammars to describe patterns and languages.
• To construct and use a finite state machines to accept patterns described by a regular expression and to design a parser to read a language described by a grammar.
• To use logic to describe the state of systems and to use logical deduction to prove properties of systems.
To be able

Audience

This is a required sophomore level course for Computer Science and Software Engineering students. A graduate version of the course is available as a pre-core course for those students who have not had a previous course in the mathematical foundations of Computer Science.

Prerequisites

Students should have some programming experience (CS 172 or equivalent)

Instructor

Jeremy Johnson

Office: 100 University Crossings
phone: (215) 895-2669
e-mail: jjohnson@cs.drexel.edu
office hours: Monday 4-6, T 4-6, W 1-2. Additional hours by appointment.

TAs

Riddhi Dattani

Office: 147 Univ. Crossings (CS Student Resource Center)
e-mail: riddhi@drexel.edu
office hours: R 10:30-12:30.

Xu Xu

Office: 147 Univ. Crossings (CS Student Resource Center)
e-mail: xx27@drexel.edu
office hours: T 3:00-4:00.

Meeting Time

T 6:00-9:00 in Curtis 353

Course Mailing List

cs-foundations@cs.drexel.edu

Please use this list for questions and discussions related to the course. If you know the answer to someone's question, please feel free to jump in, as long as well it is not an answer to a homework problem. I will moderate the list so that frivolous mail and spam is not forwarded.

Textbook

Alfred V. Aho and Jeffrey D. Ullman, Foundations of Computer Science - C Edition, W. H. Freeman and Company, 1995.

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Topics

1. Recursion, Recursive Definitions and Induction
2. Iteration, Loop Invariants, and Induction
3. Introduction to the Analysis of Algorithms
4. Divide and Conquer Algorithms and Recurrence Relations
5. Finite State Machines and Regular Expressions
6. Grammars and Recursive Description of Patterns
7. Elements of Set Theory
8. Logic (Propositional and Predicate) and Deduction
9. Applications of Logic to Program Specification and Verification
10. Applications of Logic to Digital Circuits

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Grading

1. Weekly homework assignments (40%)
2. Class participation (10%)
3. Midterm Exams (two exams worth 15% each) (30%)
4. Final Exam (20%)

Homework problems will be assigned every week, except those weeks with exams. Assignments will be discussed in class when they are due. Students are expected to participate in the discussion of the problems and will have to present their solutions atleast once in the term. No late assignments will be accepted.

Assignments and exams will be returned on a regular basis to provide feedback to students. All students must do their own work. Any violation of this will result in a zero grade for the assignment. A second violation may lead to an F for the course.

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Resources

Reference Books

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Web Pages

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Look Here for Important Announcements

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Lectures

1. Week 1
1. Sept. 28, 2004 (Recursion and Induction)
2. Week 2
1. Oct. 5, 2004 (Divide and Conquer)
3. Week 3
1. Oct. 12, 2004 (Big Oh and Growth Rates)
4. Week 4
1. Oct. 19, 2004 (Recursive Data Structures)
5. Week 5
1. Oct. 26, 2004 (First Midterm)
6. Week 6
1. Nov. 2, 2004 (Grammars and Languages)
7. Week 7
1. Nov. 9, 2004 (Parsers)
8. Week 8
1. Nov. 16, 2004 (Regular Expressions and Finite State Automata)
9. Week 9
1. Nov. 23, 2004 (Second Midterm and Introduction to Logic)
10. Week 10
1. Nov. 30, 2004 (Propositional Calculus)
11. Week 11
1. Dec. 7, 2004 (Predicate Calculus)

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Programs and Worksheets

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Assignments

• Submitting Assignments
• Assignment 1 - Due by start of class on Tuesday Oct. 5.
• Assignment 2 - Due by start of class on Tuesday Oct. 12.
• Assignment 3 - Due by start of class on Tuesday Oct. 19.
• Midterm 1 - In class on Tuesday Oct. 26 (week 5).
• Assignment 4 - Due by start of class on Tuesday Nov. 9.
• Assignment 4 (extra credit) - Due by start of class on Tuesday Nov. 16.
• Assignment 5 - Due by start of class on Monday Nov. 22 by 10 am.
• Midterm 2 - Due in class on Tuesday Nov. 23 (week 9).
• Assignment 6 - Due in class on Tuesday Dec. 7 (week 11).
• Assignment 7 (extra credit) - Due Monday Dec. 13 by 10am (finals week).
• Optional Project (extra credit) - Due Monday Dec. 13 by midnight (finals week).
• Final Exam - In class on Tuesday Dec. 14 (finals week).

Solutions

• Not posted on the website.