|
Lassonde School of Engineering Course Outline (Fall 2024) |
| SC/MATH 1090 3.0 A | Introduction to Logic for Computer Science |
| Professor George
Tourlakis email: gt@cse.yorku.ca |
Classes:
13:00-14:30,
Mondays and
Wednesdays (CB 121) First Class: September 4, 2024 |
|
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
often 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 or EECS/MATH 1028 3.00. Course work and evaluation: There will be several (>= 4) homework assignments worth 28% 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 https://www.yorku.ca/secretariat/policies/policies/academic-accommodation-for-students-with-disabilities-guidelines-procedures-and-definitions/,
Religious
Accommodation. Please also check these two links!
Student
Rights
and Responsibilities and Student Accessibility
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 2024 (3-credit) course without
receiving a grade is Nov. 8, 2024.
Students may drop a course from Nov. 9-Dec. 3 but in
this case they receive a "W" on their
transcript.
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. No grade transfer is possible if the component has been assessed (graded) already.
There will be a Final Exam during the University's Exam period. 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: Aug. 14,
2024 |