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程序代写案例-MATH 1090 A
时间：2021-08-01
FACULTY OF SCIENCE
DEPARTMENT OF MATHEMATICS AND STATISTICS
Course: SC/MATH 1090 A 3.0 – INTRODUCTION TO LOGIC FOR COMPUTER SCIENCE
Course Webpage: https://eclass.yorku.ca/eclass/course/view.php?id=36758
Term: Summer 2021
Prerequisite / Co-requisite / Exclusion: SC/MATH 1190 3.00 or SC/MATH 1019 3.00.
No Credit Retained (NCR) Note: This course is not open for credit to any student who has passed
SC/MATH 4290 3.0.
Course Instructor
Natasha May
Email: maynat@yorku.ca
Office Hours: Wednesdays 8:00-9:00 p.m. EST. For confidential matters, please send an email with
MATH1090 in the subject line to book an appointment.
Time and Location
Please note that this is a course that depends on remote teaching and learning. There will be no in-
person interactions or activities on campus.
The first day of class will take place during class time on Wednesday May 12 at 6:00pm via Zoom.
There will be activities to complete between classes in eClass (our course webpage), including reading
notes, watching videos in preparation for the next class, and completing practice problems.
Class Meetings: Wednesdays, 6:00pm – 8:00pm via Zoom, links available in eClass.
You will need to authenticate via Passport York to access eClass and your Zoom class.
You should attend class meetings live, whenever possible, and not just view them later online. Asking
questions is essential to the learning experience, and you should ask questions during class whenever
you are not clear about something. Students who attend live do better than those who do not. The
lectures will be recorded and available on eClass if you wish to go over the more difficult material one
more time.
Technical Requirements
There are technical requirements for students to be able to participate and complete the assessments
of this course. Participation will primarily take place in Zoom and eClass, which will require an internet
connection. Class meetings will require students to have access to a computer with webcam (if
possible) and microphone OR a smart device (smartphone or tablet) with these features. A high-speed
internet connection will be needed to ensure stable interaction during class meetings, which will be 120
minutes at a time.
Here are some useful links for student computing information, resources and help:
• Student Guide to eClass
• Zoom@YorkU Best Practices
• Zoom@YorkU User Reference Guide
• Computing for Students Website
• Student Guide to eLearning at York University
To determine Internet connection and speed, there are online tests, such as Speedtest, that can be run.
Expectations
Email: Use email for administrative or confidential matters, or to book an appointment with me. I will check
email during normal business hours and will respond to every email I receive within three business days.
Forum: Please post all math-related (non-administrative) questions to the Forum on eClass. Students can
answer each other’s questions, and I will periodically monitor the Forum and answer questions too.
Zoom Chat: You will have access to communicate via the chat in Zoom. Given the size of the class it
won’t be possible for the course instructor to keep up with all of the questions and communications in
the chat, so you will be asked to raise your virtual hand in Zoom, or unmute to ask questions not
answered by classmates in the chat. Student volunteers can help facilitate this process, so if you are
willing to ask a question on behalf of your peers, please do!
Communications: Make sure you are subscribed to Course Announcements in eClass! You are
responsible for being actively and regularly on eClass to ensure that you have the latest information
about the course.
Time Management: For a 3-credit course in a traditional classroom, the expected workload is 3 hours
of in-class time each week with an additional 4-6 hours of work per week in preparation, practice
problems, and assignments. For an online course, the expected workload is exactly the same. If you
find you are working less than 5 hours a week, then you are probably not devoting enough time to the
course to reach your peak performance. If you find you are working more than 10 hours a week, then
you are probably devoting too much time to the course. If you find either of these to be true, please
make an appointment to speak with the Course Instructor. Consult these time management resources
for additional support.
Expanded Course Description
This course consists of weekly online activities, and weekly online interactive class meetings with the
instructor. This course involves brief lectures by the course instructor, applying concepts to solve
problems and highlighting important details from the interactive videos. The students are expected to
complete interactive videos posted to eClass in advance of each class, so they are prepared to engage
with the material during the class through solving exercises from the textbook or created in class by the
students or instructor. The majority of class time will be dedicated to investigating concepts and solving
problems. This will be facilitated in a variety of ways, including demonstrations by the course instructor;
large class solutions, where the instructor will pose a problem and then ask students leading questions
to help solve the problem together as a large group; individual or small group solutions, where the
instructor will pose a problem and students will individually or in small groups investigate and solve the
problem before it is taken up.
By taking this course, students will be able to master the syntax and proof techniques of propositional
and predicate logic, as well as their informal semantics. The proper understanding of propositional logic
is fundamental to all levels of computer programming, even the most basic, 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 areas of computer science, including digital design, program
verification, databases, artificial intelligence, computability and complexity, algorithm analysis, and
software specification. Every program implicitly asserts a theorem to the effect that the program will do
what its documentation says it will. Proving that theorem is not merely a matter of luck or patient
debugging. Making a correct program can be greatly aided by a logical analysis of what it is supposed
to do, and, for small pieces of code, a proof that the code works can be produced hand‑in‑hand with the
construction of the code itself.
The main objective of the course is to enable the student to write and annotate correct formal proofs of
“theorems”, especially in predicate logic. A big secondary goal is to help the student to tell the
difference between a theorem and a nontheorem, and to “DISprove” nontheorems. The student will be
immersed in proof methodologies of propositional, and, much more extensively, of predicate, logic, via
well‑annotated and well‑structured proofs in both the “equational” and the “Hilbert” style of structuring
proofs. Semantics will be introduced (informally, in the predicate case), partly to breathe “meaning” into
the formal syntax of logic, and partly as an indispensable tool for producing the “disproofs” mentioned
above.
By the end of this course, students will be able to
Identify well-formed formulae and evaluate which are tautologies (truth tables,
semantics) in both propositional and predicate logic
Apply axioms, rules of inference and theorems in formulating or constructing different
styles of mathematical proofs (e.g. Hilbert, Equational, Resolution) in both propositional
and predicate logic
Differentiate between truth table techniques and proof techniques and be able to deduce
one from the other (soundness and completeness)
Differentiate between valid and invalid statements
Apply soundness theorem to disprove invalid statements
Differentiate between weak and strong generalization
Course Text / Resources
Course Text: G. Tourlakis, Mathematical Logic, John Wiley & Sons, 2008. ISBN 978-0-470-28074-4
• a link to purchase the ebook through the bookstore is available in eClass
Tentative Schedule
Date Section(s) of the Textbook Exercises from the Textbook
May 12 Introduction and Course Outline
1.1 Boolean Formulae
Review of Induction
1.5 # 1,2,3
May 19 1.2 Induction on the complexity of wff
1.3 Inductive Definitions of Formulae I
1.2.6 Exercise, 1.5 # 4-9
1.5 # 10-13
May 26
Assignment 1.1
due
1.3 Inductive Definitions of Formulae II
1.4 Proofs and Theorems
1.3.14 Exercise, 1.5 #14-20
1.4.11 Exercise
June 2
Assignment 1.2
due
2.1 More Hilbert-Style Proofs
2.2-2.4 Equational Proofs
2.1.3, 2.1.8, 2.1.13, 2.1.18 Exercises,
2.4.22 Exercise, 2.7 #1-20
June 9
Test 1: June 8-9
(covers Ch. 1)
2.5 Using Special Axioms in Equational
Proofs, 2.6 Deduction Theorem and
3.5 Appendix: Resolution
2.5.8 Exercise, 2.7 #1-20
2.6.5 Exercise
3.6 #8-11, 13-22
June 16
Assignment 2.1
due
3.1 Soundness and 3.2 Post’s Theorem
(Completeness)
4.1 The First-Order Language of
Predicate Logic
3.1.2 Exercise, 3.2.3-3.2.7 Exercises,
3.6 #2,3,12
3.6 #1, 4-7
June 22-25 Reading Week
June 30
Assignment 2.2
due
4.1 The First-Order Language of
Predicate Logic
4.1.24, 4.1.26, 4.1.32-34 Exercises
4.3 #1-7
July 7
Test 2: July 6-7
(covers Ch. 2-3)
4.2 Axioms and Rules of First-Order
Logic
4.2.8 Exercise, 4.3 #8,9
July 14
6.1 Inserting and Removing “(∀x)”
6.2 Leibniz Rules that Affect Quantifier
Scopes
6.1.16-6.1.18 Exercises
6.6 #1-6
July 21
Assignment 3.1
due
6.4 Additional Useful Tools
6.5 Inserting and Removing “(∃x)”
6.4.6, 6.4.7 Exercises
6.6 #7-39
July 28
Assignment 3.2
due
8.1 Interpretations
8.2 Soundness in Predicate Logic
8.2.7, 8.2.8, 8.2.9-8.2.12 Exercises
8.3 #1-15
August 4
Test 3: Aug 3-4
(covers Ch. 4&6)
Review
August 12 - 19 Final exam to be scheduled within this exam period.
Evaluation *
The final grade for the course* will be based on the following items weighted as indicated:
Interactive Videos: 20% (weekly)
Reflective Assignments: 15% (3 x 5% each)
Quizzes: 45% (3 x 15% each)
Final Exam: 20%
*Final course grades may be adjusted to conform to Program or Faculty grades distribution profiles.
INTERACTIVE VIDEOS
To succeed in mathematics one needs to do mathematics. This course is designed to encourage
students to succeed by rewarding their participation, studying and doing of mathematics. Providing
more class time for students to do mathematics means students need to spend more time outside of
class studying the course content through watching interactive videos on their own, completing, and
evaluating practice problems. Each video will have an interactive component, a question to answer,
which will be automatically graded. We want to promote learning over grades, so if you don’t earn the 2
points per week, there will also be bonus participation activities to help you receive the full 20% for the
interactive videos. The bonus participation activities will involve you completing a short answer
problem related to the content being studied and evaluating some of your peer’s solutions as well.
REFLECTIVE ASSIGNMENTS
There will be three reflective assignments in preparation for each of the three quizzes. Each
assignment will have two parts. The first part will be to create and post a unique review question in
preparation for the upcoming quiz. You will post your question to a discussion forum on eClass and
you will be required to review all questions posted before you post to ensure you create a unique
question. The second part will involve you reflecting on the review question you created to explain how
this review question is related to the content for the quiz, what skills and learning outcomes it involves,
and why it is an effective review question. Creating and analyzing a review problem requires that you
have a deep understanding of the course concepts, and allows you to fully demonstrate what you have
learned from the course. This also allows you to get creative and hopefully have fun too! An additional
incentive is that the instructor will choose the best review problems posed for the upcoming quiz.
QUIZZES
Three quizzes, 60 minutes in length each, will be given outside of class, covering specified material
(see the tentative schedule). You will be able to complete each quiz on your own time, over a 48-hour
period, but once you begin the quiz you will have 90 minutes to complete it. The quizzes are meant to
be closed book with no formulae sheets or study aids, and no calculator will be needed. Given that the
quizzes will be online we cannot control the resources you consult while you complete it but be aware
that the quiz length of 60 minutes does not account for any time you take to consult other resources.
So, any time you spend to consult resources may prevent you from completing the quiz. No extra time
will be granted. The additional 30 minutes is provided in case you experience technical difficulties, and
for submitting your quiz on eClass. Please reach out to the instructor immediately if you experience
any technical difficulties.
FINAL EXAM
A final exam will occur during the August examination period, August 12 – 19, and will cover ALL
material covered in the course.
When you submit answers to questions on the quizzes or exam, you should include complete
sentences and explanations and not just a few equations or numbers. Solutions may receive a zero
even for a “correct” answer unless the student explains what the answer represents and where it came
from. You will receive individual feedback and solutions to quizzes and the exam.
You must each complete and write up your own solutions to quizzes and the exam separately. Do your
own work. If you choose to refer to any outside sources, cite appropriately. Please note the complete
academic integrity expectations HERE. Bonus marks will be awarded on the final exam to students
that type up their solutions and submit through Turn-it-in, which is a text matching software. You will
receive a report indicating what percentage of your submission matches other sources, including your
peers’ work, online sources and published material. It is important that you communicate and explain
your own understanding of the solutions to the problems assigned instead of copying someone else’s
understanding and explanation.
Grading, Assignment Submission, Lateness Penalties and Missed Exams
Grading: The grading scheme for the course conforms to the 9-point grading system used in
undergraduate programs at York (e.g., A+ = 9, A = 8, B+ = 7, … , C+ = 5, etc.). Assignments and
tests* will bear either a letter grade designation or a corresponding number grade (e.g. A+ = 90 to 100,
A = 80 to 89, B+ = 75 to 79, etc.) which will be scaled according to their weight for the final grade in the
course. For example, if your final exam grade is given as a mark out of 80 points, then it will be scaled
to a mark out of 20 points since the final exam is worth 20% of your final grade, e.g. if you earn a grade
of 62/80, the grade for your final exam contributing to your final grade in the course will be
(62x20)/80=15.5/20. See the York University Undergraduate Calendar for a full description of York’s
grading system.
Assignment Submission and Lateness Penalty: All students are expected to complete learning
tasks on schedule. It is important to stay on track with your assignments - not only will this help you
feel less stressed, but it is also an important skill you will need in your career. Being able to meet
deadlines and juggle many tasks is an important career and life skill. Thus, it is expected that you will
complete all assignments according to the schedule. Proper academic performance depends on
students doing their work not only well, but on time. Accordingly, assignments for this course must be
received on the due date specified for the assignment. A grace period of 3 days will be granted for
part 2 of each assignment to account for individual needs and technical difficulties. Do not
leave your submission to the last minute. Assignments will not be accepted after this grace
period and will receive a zero.
Missed Quiz: A student who becomes ill, has a personal/family emergency, or a religious observance
may ask for an alternate date for their quiz. The weight of the quiz may be added to the final exam, or a
makeup may be held, at the instructor’s discretion.
Missed Exam: A student who becomes ill, has a personal/family emergency, or a religious observance
may ask for a later date for their final exam or outstanding coursework. To do this, students must
request deferred standing, no later than one week after the missed examination or the last day of
classes, respectively. The student must complete and submit the Final Exam/Assignment Deferred
Standing Agreement form to the Department of Mathematics and Statistics. If the student fails to do
this in the required time frame, the student must petition their home Faculty. If the petition is
successful, the student will have the opportunity to take the exam at a date the instructor chooses
within the window handed down by the petitions committee. Complete details, information and
deadlines for this process can be found via the Registrar’s office Deferred Standing Page. Note:
Petitions for an exam deferral may not be successful, in which case the student will receive a zero for
the exam.
IMPORTANT COURSE INFORMATION FOR STUDENTS
NETIQUETTE
When making use of our online forums, Zoom breakout rooms and chat, students are required to
maintain courteous and respectful communication. Remember that eClass and Zoom are simply an
electronic version of a regular classroom, so the University's Student Code of Conduct continues to
apply. Violation of the Netiquette and/or the Student Code of Conduct will result in immediate loss of
access to eClass and Zoom, and any further applicable consequences in accordance with the
University's Student Code of Conduct and the Code of Rights and Responsibilities.
ACADEMIC INTEGRITY
All Students are Expected to Engage in Academically Honest Work
Academic integrity benefits everyone in our community. It not only helps you reach the real goal of this
class, learning, but also allows for the university and program to be perceived positively by others.
When students are dishonest, they lose out on valuable learning that will help them perform well in their
career. It can also negatively impact all of the students in the program and at the institution by creating
negative mindsets which may result in fewer outside learning opportunities for students. Academic
dishonesty is any attempt by a student to gain academic advantage through dishonest means or to
assist another student with gaining an unfair advantage. Academic integrity is important regardless of
whether the work is graded or ungraded, group or individual, written or oral. Dishonest acts are major
academic offences and carry serious penalties, ranging from a failing grade on the plagiarized work to
expulsion from the university. For more details, see York’s Academic Honesty Policy and information on
Academic Integrity for Students.
Forms of cheating include:
1. Copying another person's answer to an assignment or test question (for example, via texting or
chat);
2. Consulting or getting help from another person or an online source for an assignment or during
a test (for example, Chegg, Symbolab etc.);
3. Helping others to cheat.
Whenever a student submits work obtained through cheating, the submitting student will be charged
with plagiarism and the sharing or uploading student will be charged with aiding and abetting.
Note also that exams, tests, and other assignments are the copyrighted works of the professor
assigning them, whether copyright is overtly claimed or not (i.e. whether the © is used or not).
Scanning, or taking photos of these documents, constitutes copying, which is a breach of Canadian
copyright law, and the breach is aggravated when scans/photos are shared or uploaded to third party
repository sites.
TECHNOLOGY USE AND PRIVACY
Several platforms will be used in this course (e.g., eClass, Zoom, etc.) through which students will
interact with the course materials, the course director and TAs, as well as with one another. Please
review the syllabus (on eClass) to determine how the class meets (in whole or in part), and how office
hours and presentations will be conducted. Students shall note the following:
• Zoom is hosted on servers in the U.S. This includes recordings done through Zoom.
• If you have privacy concerns about your data, provide only your first name or a nickname when
you join a session.
• The system is configured in a way that all participants are automatically notified when a session
is being recorded. In other words, a session cannot be recorded without you knowing about it.
• Review technology requirements and FAQs for eClass
PROCTORING
This course may require the use of online proctoring for examinations. The instructor may use an online
proctoring service to deliver the exam(s), which would be administered through the Learning
Management System (e.g. eClass, Canvas, etc.). Students are required to have access to minimum
technology requirements to complete examinations. If an online proctoring service is used, students will
need to become familiar with it at least five days before exam(s). For technology requirements,
Frequently Asked Questions (FAQs) and details about the online proctoring service visit Proctortrack
FAQs. Students are required to share any IT accommodation needs with the instructor as soon as they
are able.
York University obtained legal advice on this issue and determined that Proctortrack fully complies with
the privacy laws of Ontario and Canada. Some of the information on the internet about Proctortrack and
privacy is inaccurate. I would prefer not to use this software, but may have to if a high percentage of
cheating is found on assignments and tests.
IMPORTANT DATES
The undergraduate calendar includes the term start and end dates, holidays, exam periods, and
add/drop deadlines. We are in the Summer (SU) term.
All students are expected to familiarize themselves with the following information, available on the
Senate Committee on Academic Standards, Curriculum & Pedagogy webpage (see Reports, Initiatives,
Documents)
• Senate Policy on Academic Honesty and the Academic Integrity Website
• Ethics Review Process for research involving human participants
• Course requirement accommodation for students with disabilities, including physical, medical,
systemic, learning and psychiatric disabilities
• Student Conduct Standards
• Religious Observance Accommodation
RESOURCES
MATHLAB AND TUTORIAL
There will be opportunity for you to get additional help with the course from TAs in MATHLAB, which is
a group tutoring type service, and through a tutorial. You can ask questions pertaining to concepts you
are trying to better understand. You may not ask questions related to assignments, as the TAs are
instructed not to answer assignment questions. You will be polled in the first week of class to
determine the best times to hold these sessions. More information will be available in eClass once
determined.
LEARNING SKILLS SERVICES
Learning skills are about learning how to learn and improving your effectiveness and efficiency as a
learner. Numerous workshops are offered. See Learning Skills Services webpage for details and a
calendar of events. These workshops are for everyone and I highly recommend these workshops.
STUDENT ACCESSIBILITY SERVICES
It is the student's right to request and receive academic accommodations on the basis of a disability.
Student Accessibility Services provides academic accommodation and support to students with
disabilities in accordance with the Ontario Human Rights Commission's Policy on accessible education
for students with disabilities and York University Senate Policy on Academic Accommodation for
Students with Disabilities. Contact Student Accessibility Services for more information. I invite and
encourage you to talk to me about your needs.
COUNSELLING SERVICES
Many students face a variety of personal challenges throughout the term which may have a negative
effect on their academic performance. In such cases, students can make use of York’s Student
Counselling, Health & Wellbeing services. A Personal Counselor can help manage a student’s
coursework under difficult circumstances.
学霸联盟
DEPARTMENT OF MATHEMATICS AND STATISTICS
Course: SC/MATH 1090 A 3.0 – INTRODUCTION TO LOGIC FOR COMPUTER SCIENCE
Course Webpage: https://eclass.yorku.ca/eclass/course/view.php?id=36758
Term: Summer 2021
Prerequisite / Co-requisite / Exclusion: SC/MATH 1190 3.00 or SC/MATH 1019 3.00.
No Credit Retained (NCR) Note: This course is not open for credit to any student who has passed
SC/MATH 4290 3.0.
Course Instructor
Natasha May
Email: maynat@yorku.ca
Office Hours: Wednesdays 8:00-9:00 p.m. EST. For confidential matters, please send an email with
MATH1090 in the subject line to book an appointment.
Time and Location
Please note that this is a course that depends on remote teaching and learning. There will be no in-
person interactions or activities on campus.
The first day of class will take place during class time on Wednesday May 12 at 6:00pm via Zoom.
There will be activities to complete between classes in eClass (our course webpage), including reading
notes, watching videos in preparation for the next class, and completing practice problems.
Class Meetings: Wednesdays, 6:00pm – 8:00pm via Zoom, links available in eClass.
You will need to authenticate via Passport York to access eClass and your Zoom class.
You should attend class meetings live, whenever possible, and not just view them later online. Asking
questions is essential to the learning experience, and you should ask questions during class whenever
you are not clear about something. Students who attend live do better than those who do not. The
lectures will be recorded and available on eClass if you wish to go over the more difficult material one
more time.
Technical Requirements
There are technical requirements for students to be able to participate and complete the assessments
of this course. Participation will primarily take place in Zoom and eClass, which will require an internet
connection. Class meetings will require students to have access to a computer with webcam (if
possible) and microphone OR a smart device (smartphone or tablet) with these features. A high-speed
internet connection will be needed to ensure stable interaction during class meetings, which will be 120
minutes at a time.
Here are some useful links for student computing information, resources and help:
• Student Guide to eClass
• Zoom@YorkU Best Practices
• Zoom@YorkU User Reference Guide
• Computing for Students Website
• Student Guide to eLearning at York University
To determine Internet connection and speed, there are online tests, such as Speedtest, that can be run.
Expectations
Email: Use email for administrative or confidential matters, or to book an appointment with me. I will check
email during normal business hours and will respond to every email I receive within three business days.
Forum: Please post all math-related (non-administrative) questions to the Forum on eClass. Students can
answer each other’s questions, and I will periodically monitor the Forum and answer questions too.
Zoom Chat: You will have access to communicate via the chat in Zoom. Given the size of the class it
won’t be possible for the course instructor to keep up with all of the questions and communications in
the chat, so you will be asked to raise your virtual hand in Zoom, or unmute to ask questions not
answered by classmates in the chat. Student volunteers can help facilitate this process, so if you are
willing to ask a question on behalf of your peers, please do!
Communications: Make sure you are subscribed to Course Announcements in eClass! You are
responsible for being actively and regularly on eClass to ensure that you have the latest information
about the course.
Time Management: For a 3-credit course in a traditional classroom, the expected workload is 3 hours
of in-class time each week with an additional 4-6 hours of work per week in preparation, practice
problems, and assignments. For an online course, the expected workload is exactly the same. If you
find you are working less than 5 hours a week, then you are probably not devoting enough time to the
course to reach your peak performance. If you find you are working more than 10 hours a week, then
you are probably devoting too much time to the course. If you find either of these to be true, please
make an appointment to speak with the Course Instructor. Consult these time management resources
for additional support.
Expanded Course Description
This course consists of weekly online activities, and weekly online interactive class meetings with the
instructor. This course involves brief lectures by the course instructor, applying concepts to solve
problems and highlighting important details from the interactive videos. The students are expected to
complete interactive videos posted to eClass in advance of each class, so they are prepared to engage
with the material during the class through solving exercises from the textbook or created in class by the
students or instructor. The majority of class time will be dedicated to investigating concepts and solving
problems. This will be facilitated in a variety of ways, including demonstrations by the course instructor;
large class solutions, where the instructor will pose a problem and then ask students leading questions
to help solve the problem together as a large group; individual or small group solutions, where the
instructor will pose a problem and students will individually or in small groups investigate and solve the
problem before it is taken up.
By taking this course, students will be able to master the syntax and proof techniques of propositional
and predicate logic, as well as their informal semantics. The proper understanding of propositional logic
is fundamental to all levels of computer programming, even the most basic, 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 areas of computer science, including digital design, program
verification, databases, artificial intelligence, computability and complexity, algorithm analysis, and
software specification. Every program implicitly asserts a theorem to the effect that the program will do
what its documentation says it will. Proving that theorem is not merely a matter of luck or patient
debugging. Making a correct program can be greatly aided by a logical analysis of what it is supposed
to do, and, for small pieces of code, a proof that the code works can be produced hand‑in‑hand with the
construction of the code itself.
The main objective of the course is to enable the student to write and annotate correct formal proofs of
“theorems”, especially in predicate logic. A big secondary goal is to help the student to tell the
difference between a theorem and a nontheorem, and to “DISprove” nontheorems. The student will be
immersed in proof methodologies of propositional, and, much more extensively, of predicate, logic, via
well‑annotated and well‑structured proofs in both the “equational” and the “Hilbert” style of structuring
proofs. Semantics will be introduced (informally, in the predicate case), partly to breathe “meaning” into
the formal syntax of logic, and partly as an indispensable tool for producing the “disproofs” mentioned
above.
By the end of this course, students will be able to
Identify well-formed formulae and evaluate which are tautologies (truth tables,
semantics) in both propositional and predicate logic
Apply axioms, rules of inference and theorems in formulating or constructing different
styles of mathematical proofs (e.g. Hilbert, Equational, Resolution) in both propositional
and predicate logic
Differentiate between truth table techniques and proof techniques and be able to deduce
one from the other (soundness and completeness)
Differentiate between valid and invalid statements
Apply soundness theorem to disprove invalid statements
Differentiate between weak and strong generalization
Course Text / Resources
Course Text: G. Tourlakis, Mathematical Logic, John Wiley & Sons, 2008. ISBN 978-0-470-28074-4
• a link to purchase the ebook through the bookstore is available in eClass
Tentative Schedule
Date Section(s) of the Textbook Exercises from the Textbook
May 12 Introduction and Course Outline
1.1 Boolean Formulae
Review of Induction
1.5 # 1,2,3
May 19 1.2 Induction on the complexity of wff
1.3 Inductive Definitions of Formulae I
1.2.6 Exercise, 1.5 # 4-9
1.5 # 10-13
May 26
Assignment 1.1
due
1.3 Inductive Definitions of Formulae II
1.4 Proofs and Theorems
1.3.14 Exercise, 1.5 #14-20
1.4.11 Exercise
June 2
Assignment 1.2
due
2.1 More Hilbert-Style Proofs
2.2-2.4 Equational Proofs
2.1.3, 2.1.8, 2.1.13, 2.1.18 Exercises,
2.4.22 Exercise, 2.7 #1-20
June 9
Test 1: June 8-9
(covers Ch. 1)
2.5 Using Special Axioms in Equational
Proofs, 2.6 Deduction Theorem and
3.5 Appendix: Resolution
2.5.8 Exercise, 2.7 #1-20
2.6.5 Exercise
3.6 #8-11, 13-22
June 16
Assignment 2.1
due
3.1 Soundness and 3.2 Post’s Theorem
(Completeness)
4.1 The First-Order Language of
Predicate Logic
3.1.2 Exercise, 3.2.3-3.2.7 Exercises,
3.6 #2,3,12
3.6 #1, 4-7
June 22-25 Reading Week
June 30
Assignment 2.2
due
4.1 The First-Order Language of
Predicate Logic
4.1.24, 4.1.26, 4.1.32-34 Exercises
4.3 #1-7
July 7
Test 2: July 6-7
(covers Ch. 2-3)
4.2 Axioms and Rules of First-Order
Logic
4.2.8 Exercise, 4.3 #8,9
July 14
6.1 Inserting and Removing “(∀x)”
6.2 Leibniz Rules that Affect Quantifier
Scopes
6.1.16-6.1.18 Exercises
6.6 #1-6
July 21
Assignment 3.1
due
6.4 Additional Useful Tools
6.5 Inserting and Removing “(∃x)”
6.4.6, 6.4.7 Exercises
6.6 #7-39
July 28
Assignment 3.2
due
8.1 Interpretations
8.2 Soundness in Predicate Logic
8.2.7, 8.2.8, 8.2.9-8.2.12 Exercises
8.3 #1-15
August 4
Test 3: Aug 3-4
(covers Ch. 4&6)
Review
August 12 - 19 Final exam to be scheduled within this exam period.
Evaluation *
The final grade for the course* will be based on the following items weighted as indicated:
Interactive Videos: 20% (weekly)
Reflective Assignments: 15% (3 x 5% each)
Quizzes: 45% (3 x 15% each)
Final Exam: 20%
*Final course grades may be adjusted to conform to Program or Faculty grades distribution profiles.
INTERACTIVE VIDEOS
To succeed in mathematics one needs to do mathematics. This course is designed to encourage
students to succeed by rewarding their participation, studying and doing of mathematics. Providing
more class time for students to do mathematics means students need to spend more time outside of
class studying the course content through watching interactive videos on their own, completing, and
evaluating practice problems. Each video will have an interactive component, a question to answer,
which will be automatically graded. We want to promote learning over grades, so if you don’t earn the 2
points per week, there will also be bonus participation activities to help you receive the full 20% for the
interactive videos. The bonus participation activities will involve you completing a short answer
problem related to the content being studied and evaluating some of your peer’s solutions as well.
REFLECTIVE ASSIGNMENTS
There will be three reflective assignments in preparation for each of the three quizzes. Each
assignment will have two parts. The first part will be to create and post a unique review question in
preparation for the upcoming quiz. You will post your question to a discussion forum on eClass and
you will be required to review all questions posted before you post to ensure you create a unique
question. The second part will involve you reflecting on the review question you created to explain how
this review question is related to the content for the quiz, what skills and learning outcomes it involves,
and why it is an effective review question. Creating and analyzing a review problem requires that you
have a deep understanding of the course concepts, and allows you to fully demonstrate what you have
learned from the course. This also allows you to get creative and hopefully have fun too! An additional
incentive is that the instructor will choose the best review problems posed for the upcoming quiz.
QUIZZES
Three quizzes, 60 minutes in length each, will be given outside of class, covering specified material
(see the tentative schedule). You will be able to complete each quiz on your own time, over a 48-hour
period, but once you begin the quiz you will have 90 minutes to complete it. The quizzes are meant to
be closed book with no formulae sheets or study aids, and no calculator will be needed. Given that the
quizzes will be online we cannot control the resources you consult while you complete it but be aware
that the quiz length of 60 minutes does not account for any time you take to consult other resources.
So, any time you spend to consult resources may prevent you from completing the quiz. No extra time
will be granted. The additional 30 minutes is provided in case you experience technical difficulties, and
for submitting your quiz on eClass. Please reach out to the instructor immediately if you experience
any technical difficulties.
FINAL EXAM
A final exam will occur during the August examination period, August 12 – 19, and will cover ALL
material covered in the course.
When you submit answers to questions on the quizzes or exam, you should include complete
sentences and explanations and not just a few equations or numbers. Solutions may receive a zero
even for a “correct” answer unless the student explains what the answer represents and where it came
from. You will receive individual feedback and solutions to quizzes and the exam.
You must each complete and write up your own solutions to quizzes and the exam separately. Do your
own work. If you choose to refer to any outside sources, cite appropriately. Please note the complete
academic integrity expectations HERE. Bonus marks will be awarded on the final exam to students
that type up their solutions and submit through Turn-it-in, which is a text matching software. You will
receive a report indicating what percentage of your submission matches other sources, including your
peers’ work, online sources and published material. It is important that you communicate and explain
your own understanding of the solutions to the problems assigned instead of copying someone else’s
understanding and explanation.
Grading, Assignment Submission, Lateness Penalties and Missed Exams
Grading: The grading scheme for the course conforms to the 9-point grading system used in
undergraduate programs at York (e.g., A+ = 9, A = 8, B+ = 7, … , C+ = 5, etc.). Assignments and
tests* will bear either a letter grade designation or a corresponding number grade (e.g. A+ = 90 to 100,
A = 80 to 89, B+ = 75 to 79, etc.) which will be scaled according to their weight for the final grade in the
course. For example, if your final exam grade is given as a mark out of 80 points, then it will be scaled
to a mark out of 20 points since the final exam is worth 20% of your final grade, e.g. if you earn a grade
of 62/80, the grade for your final exam contributing to your final grade in the course will be
(62x20)/80=15.5/20. See the York University Undergraduate Calendar for a full description of York’s
grading system.
Assignment Submission and Lateness Penalty: All students are expected to complete learning
tasks on schedule. It is important to stay on track with your assignments - not only will this help you
feel less stressed, but it is also an important skill you will need in your career. Being able to meet
deadlines and juggle many tasks is an important career and life skill. Thus, it is expected that you will
complete all assignments according to the schedule. Proper academic performance depends on
students doing their work not only well, but on time. Accordingly, assignments for this course must be
received on the due date specified for the assignment. A grace period of 3 days will be granted for
part 2 of each assignment to account for individual needs and technical difficulties. Do not
leave your submission to the last minute. Assignments will not be accepted after this grace
period and will receive a zero.
Missed Quiz: A student who becomes ill, has a personal/family emergency, or a religious observance
may ask for an alternate date for their quiz. The weight of the quiz may be added to the final exam, or a
makeup may be held, at the instructor’s discretion.
Missed Exam: A student who becomes ill, has a personal/family emergency, or a religious observance
may ask for a later date for their final exam or outstanding coursework. To do this, students must
request deferred standing, no later than one week after the missed examination or the last day of
classes, respectively. The student must complete and submit the Final Exam/Assignment Deferred
Standing Agreement form to the Department of Mathematics and Statistics. If the student fails to do
this in the required time frame, the student must petition their home Faculty. If the petition is
successful, the student will have the opportunity to take the exam at a date the instructor chooses
within the window handed down by the petitions committee. Complete details, information and
deadlines for this process can be found via the Registrar’s office Deferred Standing Page. Note:
Petitions for an exam deferral may not be successful, in which case the student will receive a zero for
the exam.
IMPORTANT COURSE INFORMATION FOR STUDENTS
NETIQUETTE
When making use of our online forums, Zoom breakout rooms and chat, students are required to
maintain courteous and respectful communication. Remember that eClass and Zoom are simply an
electronic version of a regular classroom, so the University's Student Code of Conduct continues to
apply. Violation of the Netiquette and/or the Student Code of Conduct will result in immediate loss of
access to eClass and Zoom, and any further applicable consequences in accordance with the
University's Student Code of Conduct and the Code of Rights and Responsibilities.
ACADEMIC INTEGRITY
All Students are Expected to Engage in Academically Honest Work
Academic integrity benefits everyone in our community. It not only helps you reach the real goal of this
class, learning, but also allows for the university and program to be perceived positively by others.
When students are dishonest, they lose out on valuable learning that will help them perform well in their
career. It can also negatively impact all of the students in the program and at the institution by creating
negative mindsets which may result in fewer outside learning opportunities for students. Academic
dishonesty is any attempt by a student to gain academic advantage through dishonest means or to
assist another student with gaining an unfair advantage. Academic integrity is important regardless of
whether the work is graded or ungraded, group or individual, written or oral. Dishonest acts are major
academic offences and carry serious penalties, ranging from a failing grade on the plagiarized work to
expulsion from the university. For more details, see York’s Academic Honesty Policy and information on
Academic Integrity for Students.
Forms of cheating include:
1. Copying another person's answer to an assignment or test question (for example, via texting or
chat);
2. Consulting or getting help from another person or an online source for an assignment or during
a test (for example, Chegg, Symbolab etc.);
3. Helping others to cheat.
Whenever a student submits work obtained through cheating, the submitting student will be charged
with plagiarism and the sharing or uploading student will be charged with aiding and abetting.
Note also that exams, tests, and other assignments are the copyrighted works of the professor
assigning them, whether copyright is overtly claimed or not (i.e. whether the © is used or not).
Scanning, or taking photos of these documents, constitutes copying, which is a breach of Canadian
copyright law, and the breach is aggravated when scans/photos are shared or uploaded to third party
repository sites.
TECHNOLOGY USE AND PRIVACY
Several platforms will be used in this course (e.g., eClass, Zoom, etc.) through which students will
interact with the course materials, the course director and TAs, as well as with one another. Please
review the syllabus (on eClass) to determine how the class meets (in whole or in part), and how office
hours and presentations will be conducted. Students shall note the following:
• Zoom is hosted on servers in the U.S. This includes recordings done through Zoom.
• If you have privacy concerns about your data, provide only your first name or a nickname when
you join a session.
• The system is configured in a way that all participants are automatically notified when a session
is being recorded. In other words, a session cannot be recorded without you knowing about it.
• Review technology requirements and FAQs for eClass
PROCTORING
This course may require the use of online proctoring for examinations. The instructor may use an online
proctoring service to deliver the exam(s), which would be administered through the Learning
Management System (e.g. eClass, Canvas, etc.). Students are required to have access to minimum
technology requirements to complete examinations. If an online proctoring service is used, students will
need to become familiar with it at least five days before exam(s). For technology requirements,
Frequently Asked Questions (FAQs) and details about the online proctoring service visit Proctortrack
FAQs. Students are required to share any IT accommodation needs with the instructor as soon as they
are able.
York University obtained legal advice on this issue and determined that Proctortrack fully complies with
the privacy laws of Ontario and Canada. Some of the information on the internet about Proctortrack and
privacy is inaccurate. I would prefer not to use this software, but may have to if a high percentage of
cheating is found on assignments and tests.
IMPORTANT DATES
The undergraduate calendar includes the term start and end dates, holidays, exam periods, and
add/drop deadlines. We are in the Summer (SU) term.
All students are expected to familiarize themselves with the following information, available on the
Senate Committee on Academic Standards, Curriculum & Pedagogy webpage (see Reports, Initiatives,
Documents)
• Senate Policy on Academic Honesty and the Academic Integrity Website
• Ethics Review Process for research involving human participants
• Course requirement accommodation for students with disabilities, including physical, medical,
systemic, learning and psychiatric disabilities
• Student Conduct Standards
• Religious Observance Accommodation
RESOURCES
MATHLAB AND TUTORIAL
There will be opportunity for you to get additional help with the course from TAs in MATHLAB, which is
a group tutoring type service, and through a tutorial. You can ask questions pertaining to concepts you
are trying to better understand. You may not ask questions related to assignments, as the TAs are
instructed not to answer assignment questions. You will be polled in the first week of class to
determine the best times to hold these sessions. More information will be available in eClass once
determined.
LEARNING SKILLS SERVICES
Learning skills are about learning how to learn and improving your effectiveness and efficiency as a
learner. Numerous workshops are offered. See Learning Skills Services webpage for details and a
calendar of events. These workshops are for everyone and I highly recommend these workshops.
STUDENT ACCESSIBILITY SERVICES
It is the student's right to request and receive academic accommodations on the basis of a disability.
Student Accessibility Services provides academic accommodation and support to students with
disabilities in accordance with the Ontario Human Rights Commission's Policy on accessible education
for students with disabilities and York University Senate Policy on Academic Accommodation for
Students with Disabilities. Contact Student Accessibility Services for more information. I invite and
encourage you to talk to me about your needs.
COUNSELLING SERVICES
Many students face a variety of personal challenges throughout the term which may have a negative
effect on their academic performance. In such cases, students can make use of York’s Student
Counselling, Health & Wellbeing services. A Personal Counselor can help manage a student’s
coursework under difficult circumstances.
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