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MATH 4110: Advanced Logic
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Date Submi ed: 11/18/14 10:02 pm
Viewing: Last edit: 11/18/14 10:02 pm
Changes proposed by: TAMTINY
Submi er:
User ID: Phone:
TAMTINY 46572
Proposing
College/School:
Coll of Sciences & Mathema cs
Department:
Mathema cs & Sta s cs
Effec ve Term:
Fall 2015
Subject Code:
Mathema cs (MATH)
Course Number:
4110
Jus fica on for new
course:
Although it is a flourishing field of mathema cs, and members
of the mathema cs department are interested in teaching such
a course, there is currently no advanced undergraduate logic
course in the mathema cs department. The philosophy
department in the College of Liberal Arts has an advanced logic
course on the books which is sufficiently rigorous to count as a
mathema cs course, but it is seldom taught since philosophy is
a rela vely small major. The current course (MATH4110) will be
cross‐listed with the exis ng philosophy course (PHIL4110) and
taught occasionally by philosophy faculty and occasionally by
mathema cs faculty. By cross lis ng the course, it is hoped that
it will become feasible to offer it o en. Mathema cs and
philosophy have always been, and con nue to be, deeply
intertwined. This course will allow Auburn students to see why. Course Title:
Advanced Logic
Abbreviated Title:
Advanced Logic
1. MATH Editor
2. MATH Chair
3. SM Undergraduate
Curriculum Commi ee
Chair
4. SM Editor
5. SM Associate Dean
6. Coordinator Curriculum
Management
7. University Curriculum
Commi ee Chair
8. Coordinator Curriculum
Management
Approval Path
1. 11/19/14 2:22 pm
HOLLIGD: Approved for
MATH Editor
2. 11/19/14 2:31 pm
TAMTINY: Approved for
MATH Chair
3. 12/01/14 4:47 pm
CAMMAVI: Approved for
SM Undergraduate
Curriculum Commi ee
Chair
4. 12/02/14 9:29 am
YARBREL: Approved for
SM Editor
5. 12/02/14 9:33 am
CAMMAVI: Approved for
SM Associate Dean
12/18/2014 11:07 AM
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Weekly
Schedule Contact/Group
Credit An cipated
or Per
Type
Hours
Hours Enrollment
Term?
Course Credit:
Lecture
Can the
course be No
repeated?
3
Weekly
3
25
Total Credit Hours: 3
Grading Type:
Standard Grades
Prerequisites:
P: Math 2630 or Math 2637, MATH 2730 or Consent of
Instructor
Prerequisite Courses:
Corequisites:
Restric ons:
Admin Restric ons:
Course Descrip on:
Advanced topics in logic. For example: soundness,
completeness, incompleteness, set theory, proof theory, model
theory, non‐standard logics.
May Count Either:
MATH 4110 ‐ Advanced Logic
or PHIL 4110 ‐ Advanced Logic
Affected Program(s):
Program Type
Major
Overlapping or
Duplica on of Other
Units' Offerings:
Resources
Program
Title
Requirement or
Elec ve?
BS
Elec ve
Mathema cs
No
N/A
(1). Students will be able to state and understand the
fundamental results in the metatheory of first‐order logic.
Course
Objec ves/Outcomes
(2) Students will be able to apply techniques (such as proof by
induc on and construc ng models) to give rigorous proofs of
basic facts in the metatheory of first‐order logic.
(3) Students will clearly understand the intricacies of a
non‐trivial mathema cal proof: the completeness of first‐order
logic with iden ty.
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Is this course
considered University
Core?
https://nextbulletin.auburn.edu/courseleaf/courseleaf.cgi?page=/c...
No
Week 1 Review of syntax and seman cs of proposi onal logic
Week 2 Review of syntax and seman cs of predicate logic with
iden ty
Week 3 Natural deduc on for predicate logic with iden ty
Middle of week 3. First problem set due.
Beginning of week 4. Graded first problem set returned, last
day to drop.
Week 4. Set theory: sets, rela ons, func ons.
Week 5. Set theory: cardinality, finite and infinite, countability.
End of week 5: Second problem set due.
Week 6. Elementary metatheory of proposi onal logic.
Week 7. Using induc on to establish metalogical results.
Middle of week 7: Midterm exam.
Week 8. Senten al connec ves and completeness.
Course Content
Outline
Beginning of week 8: Midterms returned.
Middle of week 8: W deadline.
Week 9. Compactness for predicate logic.
Middle of week 9: Problem set 3 due.
Week 10. Elementary metatheory for the syntax of first‐order
logic.
Week 11. Introducing the formal study of truth, models, and
implica on.
Middle of week 11: problem set 4 due.
Week 12. A new formal proof system.
Week 13. Establishing soundness for first‐order logic.
Middle of week 13: problem set 5 due.
Week 14. Establishing completeness for first‐order logic.
End of week 14: Mock final exam.
Week 15. Further results stated: e.g. Lowenheim‐Skolem,
incompleteness.
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Final exam period: Final exam.
1. Four best scores from five problem sets, each of four is worth
10% of grade.
Students work through problems on their own and
thereby come to understand the material. Problem set 1 will
have ques ons assessing learning outcome 1. Problem sets 2
and 3 will have ques ons assessing learning outcomes 1 and 2.
Problem sets 4 and 5 will have ques ons assessing learning
outcomes 2 and 3.
2. Midterm exam. 17.5%.
Students are examined on their understanding of the
material covered in the first half of the course. Several
ques ons on the midterm will assess learning outcomes 1 and
2.
Assignments /
Projects
3. Mock final exam. 10%.
Students are assessed on material from the first 14
weeks of the semester. They have a chance to prac ce the kinds
of ques on which will appear on the final exam. There will be
at least one ques on on the final exam exclusively assessing
each learning outcome.
4. Final exam. 27.5%.
Students are assessed on their understanding of the
material from the whole course. There will be at least one
ques on on the final exam exclusively assessing each learning
outcome.
5. A endance. 5%.
Regular a endance deepens student understanding, and
is worth 5% of the overall grade.
Learning outcome 1 Rubric.
Assignments throughout the course (on the problem sets and
various exams, see Assignments/Projects) will assess learning
outcome 1.
Rubric and Grading
Scale
bAn excellent student recognizes the names of, and can state,
with complete accuracy, a broad selec on of the fundamental
results in the metatheory of first‐order logic with iden ty. They
demonstrate, through explana on and applica on, a
comprehensive understanding of these results.
A good student recognizes the names of, and can state, with
some degree of accuracy, a limited selec on of the
fundamental results in the metatheory of first‐order logic with
iden ty. They can demonstrate, through explana on and
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applica on, a good understanding of these results.
A reasonable student recognizes the names of, and can state,
perhaps with a limited degree of accuracy, at least some of the
fundamental results in the metatheory of first‐order logic with
iden ty. They demonstrate, at least to some extent, through
explana on and/or applica on, a par al understanding of these
results.
A weak student recognizes the names of, and can, to a limited
extend, state at least some of the fundamental results in the
metatheory of first‐order logic with iden ty. They have a poor
understanding of these results.
A poor student shows li le to no knowledge of the
fundamental results in the metatheory of first‐order logic with
iden ty.
Learning Outcome 2 Rubric.
Assignments throughout the course (on the problem sets and
various exams, see Assignments/Projects) will assess learning
outcome 2.
An excellent student can apply, with some crea vity and in
contexts when they are needed but not obviously so,
mathema cal techniques such as proof by induc on and model
construc on to give careful and successful mathema cal proofs
of a number of basic facts in the metatheory of first‐order
logic. A good student can apply, in contexts when they are obviously
called for, mathema cal techniques such as proof by induc on
and model construc on to give almost wholly rigorous
mathema cal proofs of a number of basic facts in the
metatheory of first‐order logic. A reasonable student can apply, when instructed to do so,
mathema cal techniques such as proof by induc on and/or
model construc on in an a empt to give a mathema cal proof
of at least some basic facts in the metatheory of first‐order
logic. A weak student shows a very limited capacity to apply, when
instructed to do so, mathema cal techniques such as proof by
induc on and/or model construc on in a emp ng to prove at
least some basic facts in the metatheory of first‐order logic.
A poor student shows li le to no knowledge of how to use
techniques such as proof by induc on or model construc on,
and has li le to no knowledge of when such techniques are
called for.
Learning Outcome 3 Rubric.
Assignments throughout the course (on the problem sets and
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various exams, see Assignments/Projects) will assess learning
outcome 3.
An excellent student has a clear comprehension of the details
of an intricate, non‐trivial mathema cal result: the
completeness of first‐order logic with iden ty. They can give a
clear and comprehensive outline of the major steps in the proof
using their own words and without notes. They have a clear
understanding of how the steps relate to one another. They can
supply the details for many of the individual steps in the proof
when asked to do so.
A good student has some comprehension of the details of an
intricate, non‐trivial mathema cal result: the completeness of
first‐order logic with iden ty. They can give a clear but perhaps
only par ally complete outline of the major steps in the proof
using their own words and without notes. They have a strong
but not excellent understanding of how the steps relate to one
another. They can supply at least some of the details for some
of the individual steps in the proof when asked to do so.
An acceptable student has a limited comprehension of the
details of an intricate, non‐trivial mathema cal result: the
completeness of first‐order logic with iden ty. They give a
confused but recognizable outline of the major steps in the
proof using their own words and without notes. They
demonstrate at least some understanding of how the steps
relate to one another. They are able to make some limited
headway towards explaining the details of at least some of the
individual steps in the proof when asked to do so.
A weak student has a very par al comprehension of the details
of an intricate, non‐trivial mathema cal result: the
completeness of first‐order logic with iden ty. They can state
the theorem, and can give a par al explana on of the main
steps in the proof, but only when given access to notes. They
recognize some of the major steps of the proof, but cannot
clearly see how they relate to one another. They struggle when
asked to supply details for any of the individual steps in the
proof.
A poor student shows li le to no understanding of the
completeness of first‐order logic with iden ty. They might be
able to state the result, but show li le comprehension of how
to prove the result, even when allowed to use notes. They have
li le to no understanding of the steps required for the proof.
Grade is determined as follows. Each of the grade components
(except a endance) assesses (although not exclusively so) at
least one of the learning outcomes (see Assignments/Projects
for more details).
1. Four best scores from five problem sets. (40%, so 10%
for each counted problem set). Each problem set is
worth 100 points. 90 and above is an A, 80‐90 a B, 70‐80
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2.
3.
4.
5.
A achments
a C, 60‐70 a D, 60 and below an F.
Midterm exam. 17.5%. 100 points. 90 and above is an A,
80‐90 a B, 70‐80 a C, 60‐70 a D, 60 and below an F.
Mock final exam. 10%. 100 points. 90 and above is an A,
80‐90 a B, 70‐80 a C, 60‐70 a D, 60 and below an F.
Final exam. 27.5%. 100 points. 90 and above is an A,
80‐90 a B, 70‐80 a C, 60‐70 a D, 60 and below an F.
A endance. 5%. Each class mee ng carries one
a endance point. A endance for the whole class earns
one a endance point. 85% of total a endance points
earns full a endance credit. If the student has n% of the
total a endance points available and n is less than 85,
then the student earns (n/85)*100 of the total
a endance grade.
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