The Mathematics of Language and Linguistics

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1 The Mathematics of Language and Linguistics Instructor: Office: Office hours: Course website: Sunjing Ji TBA TBA, or by appointment & d2l Course description This course introduces students of languages and linguistics to the mathematical foundations of language study, and the application of mathematics to the study of language. The course is divided into 4 major areas: (1) Foundations, which includes Set Theory, Relations, Functions, and some basic algebra; (2) Logic, including both propositional and predicate calculus; (3) Formal Language theory and computation, and (4) Statistics. The class will approach each area from a theoretical angle, and then look at how the tools and skill learned in class can be applied with particular reference to language. Prerequisite: Minimum math placement code of 200. If you do not have this score, you will be administratively dropped from the course. Textbook The textbook will be the following book, available on our course website. Michael Hammond. In preparation. Introduction to the Mathematics of Language. Some students prefer to have additional optional readings. Here are some very nice supplementary texts. Notice that the second one also has software attached for practicing exercises. Barbara Partee, Alice ter Meulen, and Robert E. Wall Mathematical Methods in Linguistics. Kluwer Academic Publishers. Jon Barwise and John Etchemendy Language, Proof, and Logic. CSLI Publications. 1

2 Requirements There will be 12 in-class activities to check your attendance/participation, each of which constitutes 1% of the final grade. The two lowest scores of the in-class activities will be dropped. There will be 6 assignments, each of which constitutes 10% of the final grade. All assignments are due at the beginning of the class on the dates specified in the course schedule. submission is not accepted. No late work is accepted. There will be 2 tests, each of which constitutes 15% of the final grade. The instructor will provide sample questions and take time in class to help prepare for the tests. You should review relevant materials after class as well. Group studies are encouraged to prepare for the tests. Previewing relevant readings from the textbook before class will facilitate understanding the contents discussed in the lectures, completing assignments, and succeeding in the tests. In general, group work is not allowed unless explicitly permitted; plagiarism of any form is not allowed. Grading Grades of A, B, C, D, or E are given for UA courses. The final grade will be calculated by weighting the lecture attendance/participation, assignments and tests according to the following percentages: Honors students Attendance/participation 10% Homework 60% Midterm test 15% Final test 15% In addition to all the requirements listed above, honors students are also required to give an additional 10-minute in-class presentation. The presentation topic has to be relevant to the theme of the class. Contact the instructor to set up an appointment and figure out more details. Excuses If illness or family emergency prevents a student from completing assignments on time or taking an exam on its scheduled date, the student must present verifiable evidence of the reason for absence prior to that date for rescheduling. 2

3 Schedule (Subject to change) Date Topic Jan 13 Syllabus, Intro 1 Jan 15 Set theory 2 Jan 18 Martin Luther King Jr Holiday, no classes 2 Jan 20 Set theory 3 Jan 22 Set theory 3 Jan 25 Set theory 3 Jan 27 Relation 3 Jan 29 Function 3 Feb 1 Review & exercise 3 Readings (chapter) Homework Feb 3 Statement Logic 4 HW1 due Feb 5 Statement Logic 4 Feb 8 Statement Logic 4 Feb 10 Statement Logic 4 Feb 12 Statement Logic 4 Feb 15 Statement Logic 4 HW2 due Feb 17 Predicate Logic 5 Feb 19 Predicate Logic 5 Feb 22 Predicate Logic 5 Feb 24 Predicate Logic 5 Feb 26 Mid-term review 1-4 Mar 1 Mid-term review 1-4 Mar 3 Mid-term test HW3 due Mar 5 Predicate Logic 5 Mar 8 Predicate Logic 5 3

4 Mar 10 Formal Language 6 Mar 12 Formal Language 6 Mar 15 Spring break, no class Mar 17 Spring break, no class Mar 19 Spring break, no class Mar 22 No class Mar 24 Formal Language 6 HW 4 due Mar 26 Formal Language 6 Mar 29 Formal Language 6 Mar 31 Formal Language 6 Apr 2 Formal Language 6 Apr 5 Formal Language 6 Apr 7 Probability 7 Apr 9 Combinatorial 7 HW5 due Apr 12 Conditional Probability 7 Apr 14 Bayes formula 7 Apr 16 Ngram 8 Apr 19 Markov Chain 8 Apr 21 Student presentation Apr 23 Student presentation Apr 26 TBA HW6 due Apr 28 TBA Apr 30 Final review May3 Final test Tips for success 1. Show up in class and turn in all your assignments on time.!!! 2. Do the readings before class and participate in class. 3. Make use of group study and come to my office hours. 4

5 4. Have a good attitude, ask questions, and be determined to succeed. Other UA policies 1. All holidays or special events observed by organized religions will be honored for those students who show affiliation with that particular religion. If this is relevant for you, you must inform the instructor during the first two weeks of class. 2. Absences pre-approved by the UA Dean of Students (or Dean s designee) will be honored. If this is relevant for you, you must inform the instructor during the first two weeks of class. 3. Cell phone policy: cell phones should be off; they are not permitted during class. 4. Plagiarism is not acceptable. See Student Code of Academic Integrity. 5. Threatening behavior is not allowed. 6. It is possible that some course content may be deemed offensive by some students. 7. Students who are registered with the Disability Resource Center must submit appropriate documentation to the instructor if they are requesting reasonable accommodations. If this is relevant for you, you must inform the instructor during the first two weeks of class. 5

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