CS 270 Mathematical Foundations in CS - Syllabus

Term and Credits

Summer 2019
3 Credits

Room and Time

Tuesday/Thursday 3:30pm-5:20pm 3675 Market Street 1052


Mark Boady
Electronic Mail Address: mwb33@drexel.edu
Office: 3675 Market Street Room 1058 (near snack machine)
Extention: 215-895-2347
Office Hours: Tuesday 11-12PM, Wednesay 2-4PM Thursday 11-12PM

Teaching Assistant(s)

Steve Earth
Electronic Mail Address: se435@drexel.edu
Office: Drexel CLC 3675 Market St Room 1066
Office Hours:Monday 6-8PM, Thursday 6-8PM

Course Description

Introduces formal logic and its connections to Computer Science. Students learn to translate statements about the behavior of computer programs into logical claims and to prove such assertions using both traditional techniques and automated tools. Considers approaches to proving termination, correctness, and safety for programs. Discusses propositional and predicate logic, logical inference, recursion and recursively defined sets, mathematical induction, and structural induction.

Course Objective and Goals

  1. To use recursion and divide and conquer to solve problems
  2. To provide recursive definitions of patterns and data structures
  3. To formally specify the input/output requirements of programs
  4. To use induction and other proof techniques to prove properties of algorithms, data structures, programs, and computer systems
  5. To use logic to describe the state of systems and to use logical deduction (by hand and using tools) to prove properties of systems
  6. To understand the power and limitations of formal logic.


  1. Functional Programming
  2. Recursion, Recursive Definitions and Induction
  3. Propositional and Predicate Logic
  4. Formal Proof using Natural Deduction
  5. Applications of Logic to Computer Science
  6. Divide and Conquer Algorithms and Recurrence Relations
  7. Program Specification and Verification
  8. Automated Reasoning
  9. Termination Analysis
  10. Test Case and Counter Example Generation

Audience and Purpose within Plan of Study

This is a required course for all Computer Science and Software Engineering students. It should also be of interest to Computer Engineering, Mathematics students and students with an interest in logic and computation.


CS 172 Minimum Grade: D or CS 176 Minimum Grade: D or CS 265 Minimum Grade: D or SE 103 Minimum Grade: D or ECEC 301 Minimum Grade: D or ECEC 201 Minimum Grade: D

What Students Should Know Prior to this Course

  1. Ability to read and understand code.
  2. Basic understanding of program execution.
  3. Ability to write simple recursive programs.

What Students will be able to do upon Successfully Completing this Course:

  1. Use Proofs by Deduction to Justify Logical Statements
  2. Be able to write and analyze Recursive Functions
  3. Be able to implement and use a SAT solver.
  4. Use Inductive Proofs to Justify the correctness of programs and statements.
  5. Use logic to describe the state of systems.


We will use free resources for this class.

Book of Proof (Second Edition)
Richard Hammack
Paperback: ISBN 978-0-9894721-0-4
Hardcover: ISBN 978-0-9894721-1-1
Available for Free online at: http://www.people.vcu.edu/~rhammack/BookOfProof/

The Racket Guide
Matthew Flatt, Robert Bruce Findler and PLT

Grading and Policies

Final grades will be determined by your total points weighted according to this distribution. Grades may be curved but are generally computed via the formula below. It may be modified at the instructor's sole discretion, but letter grades will generally not be lower than those shown here.

Course Material

Programming Language

Late Policy

Academic Honesty Policy

The CCI Academic Honesty policy is in effect for this course. Please see the policy at http://drexel.edu/cci/resources/current-students/undergraduate/policies/cs-academic-integrity/.

Academic Honesty Violations will be reported to the University. Punishment will be determined by the severity of the incident. Punishments include, but are not limited to,





Slack Channel

Computer/Software Help
iCommons: http://drexel.edu/cci/about/our-facilities/rush-building/iCommons/

University Policies
In addition to the course policies listed on this syllabus, course assignments or course website, the following University policies are in effect:

Tentative Course Schedule

Please see the appropriate assignment webpages for a detailed description of course deliverables.

Week Topic Reading Homework
(1) June 24, 2019 Introduction to Racket Quick: An Introduction to Racket with Pictures
So You Want to be a Functional Programmer (Part 1)
Lab 1 and Lab 2
Homework 1 - Due July 1, 2019 at 11:59PM
(2) July 1, 2019 List Processing and Numbers
Thursday No Class. Complete Lab on your own and bring to class July 9
List, Iteration, and Recursion
High-order list operations (Ignore Haskell Part)
Peano Axioms
Lab 3 and Lab 4
Homework 2 - Due July 8, 2019 at 11:59PM
(3) July 8, 2019 Boolean Expressions Chapter 2.1-2.6 from Book fo Proof Lab 5 and Lab 6
Homework 3 - Due July 15, 2019 at 11:59PM
Quiz 1 Thursday (Covers HW1 and HW2 Material)
(4) July 15, 2019 Predicate Logic Chapter 2.6-2.12 from Book fo Proof Lab 7 and Lab 8
Homework 4 - Due July 22, 2019 at 11:59PM
(5) July 22, 2019 Normal Forms and SAT Solvers MiniSat in Browser
Boolean Satisfiability Problems
Lab 9 and Lab 10
Quiz 2 Thursday (Covers HW3 and HW4 Material)
(6) July 29, 2019 Tuesday - Midterm Review
Thursday - Midterm in Class
(7) August 5, 2019 Natural Deduction Chapter 4 from Book of Proof
Deduction Proof Checker
Pages 142 to 164 of Symbolic Logic: A First Course
Lab 11 and 12
Homework 5 - Due August 12, 2019 at 11:59PM
(8) August 12, 2019 Proofs by Contradiction Chapter 6 from Book of Proof
Deduction Proof Checker
Pages 164 to 183 of Symbolic Logic: A First Course
Lab 13 and Lab 14
Homework 6 - Due August 19, 2019 at 11:59PM
Quiz 3 Thursday (Covers HW5 Material)
(9) August 19, 2019 Mathematical Induction Chapter 10 from Book of Proof
Lab 15 and Lab 16
Homework 7 - Due August 26, 2019 at 11:59PM
(10) August 26, 2019 Structural Induction   Lab 17 and Lab 18
Homework 8 - Due September 2, 2019 at 11:59PM
Quiz 4 Thursday (Covers HW6 and HW7 Material)
(11) September 2, 2019 Final Exam - Time and Location TBD