|
Lassonde School of Engineering Course Outline (Fall 2021) |
| SC/MATH 1090 3.0 B | Introduction to Logic for Computer Science |
| Professor George Tourlakis | Classes:
11:30-13:00,
Tuesdays and Thursdays (by ZOOM via eClass). First Class: September 9, 2021 |
|
DON'T PANIC :-) (This course is very similar to a
serious programming course; but easier)
Course Description: Note: This course is a
degree
program requirement for Computer Science, Computer
Security, and Computer and Software Engineering
majors. It is expected and recommended
to be taken in the second year
of your studies as it is a prerequisite for a
number of core (= required) 3rd year EECS courses. Learning to use Logic,
which is what this course is about, is like learning
to use a programming language. In the latter case,
familiar to you from courses such as EECS 1021 3.0
or EECS1022 3.0, one learns the correct syntax
of programs, and also learns what the various
syntactic constructs do and mean, that is, their semantics.
After that, one spends the rest of the course on
increasingly challenging programming exercises, so
that the student becomes proficient in programming
in said language. We will do the exact
same thing in MATH1090: We will learn the syntax of
the logical language, that is, what
syntactically correct proofs look
like. We will learn what various
syntactic constructs "say" (semantics). We will be
pleased to learn that correctly written proofs are
concise and "checkable" means toward certifying and even discovering
mathematical "truths". We will also learn via a lot of practice
how to write a large variety of proofs that certify
all sorts of
useful "truths" of mathematics. While the above is
our main aim, to equip you with a Toolbox that
you can use to certify or discover truths, we will
also look at the Toolbox as an object of study
and study some of its properties (this is similar to
someone explaining to you what a hammer is good for
before you take up carpentry). This study belongs to
the "metatheory"
of Logic. The content of the
course will thus be: The syntax and semantics of propositional and predicate logic and how to build "counterexamples" to expose fallacies. Some basic and important "metatheorems" that employ induction on numbers, but also on the complexity of terms, formulas, and proofs will be also considered. A judicious choice of a few topics in the "metatheory" -- such as proving the validity of the technique known as "the deduction theorem" -- will be instrumental toward your understanding of "what's going on here". The mastery of these metatheoretical topics will make you better "users of Logic" and will separate the "scientists" from the mere "technicians". There are a number of methodologies for writing proofs, and we will aim to gain proficiency in two of them: The Equational methodology and the Hilbert methodology.In both methodologies an important required component is the systematic annotation of the proof steps. Such annotation explains why we do what we do and has a function similar to comments in a program. OK, one can readily agree that a computer science student needs to learn programming. But Logic? Well, the proper understanding of propositional logic is fundamental to the most basic levels of computer programming, while the ability to correctly use variables, scope and quantifiers is crucial in the use of loops, subroutines, and modules, and in software design. Logic is used in many diverse areas of computer science including digital design, program verification, databases, artificial intelligence, algorithm analysis, computability, complexity, and software engineering. Besides, any science that requires you to reason correctly to reach conclusions uses logic. Prerequisite:
MATH 1190 3.00 or EECS/MATH 1019 3.00. Course work and evaluation: There will be several (>= 4) homework assignments worth 24% of the total final grade. The
homework must be each individual's
own
work. While consultations with the instructor, tutor, and among students, are part of the learning process and
are encouraged, nevertheless, at the end of all this
consultation each
student will have to produce an individual
report rather than a copy (full or
partial) of somebody else's report. Follow these links to
familiarise yourselves with Senate's and Lassonde
School's expectations regarding Academic
Honesty, and Academic
Integrity. Please also familiarise yourself
with many other Senate policies, in particular,
with those about Academic
Accommodation
for
Students
with Disabilities, Religious
Accommodation, Repeating
Passed
or
Failed
Courses for Academic Credit. Please also check these two links!
Student
Rights
and Responsibilities and Counseling and
Disabiliy Services.
The
concept of "late assignments" does not
exist in this course (because full
solutions are posted on the due
date). Last date
to drop a Fall 2021 (3-credit) course without
receiving a grade is Nov. 12, 2021.
Note: Missed tests
with good
reason (normally medical, and well documented) will have their weight transferred
to the final exam. There are no "make up" tests.
Tests missed for no acceptable reason
are deemed to have been written and failed
and are graded "0" (F). There are no "make up"
assignments nor transfer of weight of missed ones.
The only time the
weight of an assessed
component
is transfered to the final is when the component
is missed
with due cause (illness). This does not apply to assignments since the
student has typically 3 weeks to do any given
assignment.
There will be a Final Exam during the University's Exam period (by eCLASS/Moodle). It will be worth 40% of the total final grade. Text: G. Tourlakis, Mathematical Logic, John Wiley & Sons, 2008. ISBN 978-0-470-28074-4 Learning Objectives: Students are expected to:
Last changed: Jul 24,
2021 |