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MATH 4110: Advanced Logic 1 of 7 https://nextbulletin.auburn.edu/courseleaf/courseleaf.cgi?page=/c... In Workflow 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 MATH 4110: Advanced Logic 2 of 7 https://nextbulletin.auburn.edu/courseleaf/courseleaf.cgi?page=/c... 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. 12/18/2014 11:07 AM MATH 4110: Advanced Logic 3 of 7 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. 12/18/2014 11:07 AM MATH 4110: Advanced Logic 4 of 7 https://nextbulletin.auburn.edu/courseleaf/courseleaf.cgi?page=/c... 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 12/18/2014 11:07 AM MATH 4110: Advanced Logic 5 of 7 https://nextbulletin.auburn.edu/courseleaf/courseleaf.cgi?page=/c... 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 12/18/2014 11:07 AM MATH 4110: Advanced Logic 6 of 7 https://nextbulletin.auburn.edu/courseleaf/courseleaf.cgi?page=/c... 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 12/18/2014 11:07 AM MATH 4110: Advanced Logic 7 of 7 https://nextbulletin.auburn.edu/courseleaf/courseleaf.cgi?page=/c... 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. email between Tam and Watkins.pdf Course reviewer comments Preview Bridge Key: 9726 12/18/2014 11:07 AM