Lassonde School of Engineering Course Outline (Fall 2015) |
SC/MATH 1090 3.0 A | Introduction to Logic for Computer Science |
Professor George Tourlakis | Classes: VH D 13:00-14:30, Mondays and Wednesdays. |
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 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 1020 3.0 or EECS1021 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 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 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" 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 30% 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 expectations regarding Academic
Honesty, but also with many other Senate policies, in particular,
with those about Academic
Accommodation for Students with Disabilities, Religious
Accommodation and Repeating
Passed or Failed Courses for Academic Credit. 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 2015
(3-credit) course without receiving a grade is Nov. 9, 2015. There will also be one
mid-term (in-class) test worth 30% Note Date/Time: Wednesday,
October 21,2015. 13:00-14:20. 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).
Finally, there will be a Final Exam during the University's Exam period. It will be worth 40%. Text: G. Tourlakis, Mathematical Logic, John Wiley & Sons, 2008. ISBN 978-0-470-28074-4 Learning Objectives: Students are expected to:
If time permits: We will attempt to make time to cover a
very brief introduction
to computability from
the Appendix of the
text. Last changed: Sep. 10, 2015 |