CS 270 Mathematical Foundations in CS - Syllabus

Term and Credits

Fall 2020-2021
3 Credits

Room and Time

Section Days Room Instructor
002 Monday/Wednesday Online Only Mark Boady
801 Monday/Wednesday Online Only Mark Boady
805 Tuesday/Thursday Online Only Galen K Long
806 Tuesday/Thursday Online Only Galen K Long


Professor Mark Boady
Electronic Mail Address: mwb33@drexel.edu
Office: 3675 Market Street Room 1058 (near snack machine)
Extention: 215-895-2347 [Not Available During COVID]
Office Hours: Monday 1-5PM, Wednesday 1-5PM

Professor Galen Long
Electronic Mail Address: nkl43@drexel.edu
Office: 3675 Market Street Room 1153
Extention: 215-895-2474 [Not Available During COVID]
Office Hours: Tuesday 1-5PM, Thursday 1-5PM

Teaching Assistant(s)

Hoang Nam Le
Electronic Mail Address: hl662@drexel.edu
Office: Live In Slack Space
Office Hours: Friday 12PM-2PM and 2-4PM
CLC Information: https://www.cs.drexel.edu/clc

Quang Luong
Electronic Mail Address: qdl24@drexel.edu
Office: Live In Slack Space
Office Hours: Tuesday 6-8PM
CLC Information: https://www.cs.drexel.edu/clc

Andrew Senin
Electronic Mail Address: ams975@drexel.edu
Office: Live In Slack Space
Office Hours: Thursday 11AM-1PM
CLC Information: https://www.cs.drexel.edu/clc

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


If you want to learn more about functional programming.
The Little Schemer - 4th Edition
Daniel P. Friedman and Matthias Felleisen
ISBN-13: 978-0262560993
ISBN-10: 0262560992
Available at: Amazon

If you want to learn more about recursive proofs.
The Little Prover - 1st Edition
Daniel P. Friedman and Carl Eastlund
ISBN-13: 978-0262527958
ISBN-10: 0262527952
Available at: Amazon

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.

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,

Course Material

Programming Language






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:

Appropriate Use of Course Materials

It is important to recognize that some or all of the course materials provided to you are the intellectual property of Drexel University, the course instructor, or others. Use of this intellectual property is governed by Drexel University policies, including the IT-1 policy found at: https://drexel.edu/it/about/policies/policies/01-Acceptable-Use/
Briefly, this policy states that all course materials including recordings provided by the given prior written approval by the University. Doing so may be considered a breach of this policy and will be investigated and addressed as possible academic dishonesty, among other potential violations. Improper use of such materials may also constitute a violation of the University's Code of Conduct found at: https://drexel.edu/cpo/policies/cpo-1/ and will be investigated as such.

Recording of Class Activities:

In general, students and others should not record course interactions and course activities in lecture, lab, studio or recitation.
Students who have an approved accommodation from the Office of Disability Resources to record online lectures and discussions for note taking purposes should inform their course instructor(s) of their approved accommodation in advance. The recording of lectures and discussions may only be carried out by the students enrolled in the class who have an approved accommodation from Disability Resources with their instructors’ prior knowledge and consent. Students with approved accommodations may be asked to turn off their recorder if confidential or personal information is presented.
If a student has any comments, concerns, or questions about provided class materials and/ or recording, talk to your course instructor first. If this does not resolve the issue, you can also reach out to the Department Head, and use the process described for a grade appeal to move your concern forward. The process described for grade appeals can be found at: https://drexel.edu/provost/policies/grade-appeals/

Tentative Course Schedule

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

Week Topic Reading Homework
(1) September 21, 2020 Lecture 1: Introduction to Racket
Lecture 2: Lists in Racket
Quick: An Introduction to Racket with Pictures
So You Want to be a Functional Programmer (Part 1)
List, Iteration, and Recursion
Lab 1 and Lab 2
Homework 1
(2) September 28, 2020 Lecture 3: Equational Reasoning
Lecture 4: High Order Functions
How to Write Proofs: a quick guide
High-order list operations (Ignore Haskell Part)
Anonymous Function Tutorial
Lab 3 and Lab 4
Homework 2
(3) October 5, 2020 Lecture 5: Peano Arithemtic
Lecture 6: Binary Arithemtic
Peano Axioms
Binary Arithmetic
Lab 5 and Lab 6
Homework 3
(4) October 12, 2020
(Columbus Day)
Lecture 7: Boolean Logic
Lecture 8: Normal Forms
Chapter 2.1-2.6 from Book fo Proof Lab 7 and Lab 8
Homework 4
Quiz 1 Tuesday
(5) October 19, 2020 Lecture 9: Predicate Logic
Lecture 10: SAT Solvers
MiniSat in Browser
Boolean Satisfiability Problems
Lab 9 and Lab 10
Quiz 2 Tuesday
(6) October 26, 2020 Midterm Exam
Lecture 11: Natural Deduction (P1)
Deduction Proof Checker
Chapter 4 from Book of Proof
Midterm Tuesday
Lab 11 Thursday
(7) November 2, 2020 Lecture 12: Natural Deduction (P2)
Lecture 13: Natural Deduction (P3)
Chapter 6 from Book of Proof
Pages 142 to 183 of Symbolic Logic: A First Course
Lab 12 Thursday
Homework 5
(8) November 9, 2020 Lecture 14: Natural Deduction (P4)
Lecture 15: Induction (Part 1)
Chapter 2.6-2.12 from Book fo Proof (predicates)
Predicate Logic Slides from CMU
Lab 13 and Lab 14
Homework 6
(9) November 16, 2020 Lecture 16: Induction (Part 2)
Lecture 17: Induction (Part 3)
Chapter 10 from Book of Proof
Lab 15 and Lab 16
Homework 7
Quiz 3 Tuesday
(10) November 24, 2020 - Thanksgiving - No Classes
(11) November 1, 2020 Lecture 18: Induction (Part 4)
Lecture 19: Grey Codes
  Lab 17 and Lab 18
Homework 8
Quiz 4 Tuesday
(12) December 7, 2020 Final Exam - Online