Introduction to advanced mathematics MATH – 215 Filippo Calderoni University of Illinois at Chicago August 26, 2019 1/20
Introducing myself The instructor § Research Assistant Professor in the department of Mathematics Statistics and Computer Science § PhD in 2018 at University of Turin (Torino, Italy) § Specialize in Mathematical Logic 2/20
General Info Room : AH 303 Schedule : Mon–Wed–Fri at 09:00 – 09:50 Office hours : Friday 10–12 and by appointment. Email : fcaldero@uic.edu Course webpage : click here! 3/20
General Info: textbook Main textbook : Eccles, P. An Introduction to Mathematical Reasoning: Numbers, Sets and Functions . Cambridge: Cambridge University Press. (1997) Another textbook : Sundstrom, T. Mathematical reasoning: writing and proof (Available online!) 4/20
Important dates Date Event August 26, M First class. September 2, M Labor Day holiday. No classes. October 4, F Midterm I. November 4, M Midterm II. November 29, F Thanksgiving holiday. No classes. December 6, F Instruction ends. December 10, Tu Final exam. (10:30–12:30) 5/20
Participation Attendance § Attendance is not required, but it is strongly recommended . § Students are responsible for all of the material covered in the lectures. § Find a concise summary of each lecture in course webpage. § If you miss a lecture, you should ask your classmates for notes. 6/20
Participation Attendance § Attendance is not required, but it is strongly recommended . § Students are responsible for all of the material covered in the lectures. § Find a concise summary of each lecture in course webpage. § If you miss a lecture, you should ask your classmates for notes. Instructor’s tip Problems on the exams will be similar to problems discussed in class. 6/20
Participation Attendance § Attendance is not required, but it is strongly recommended . § Students are responsible for all of the material covered in the lectures. § Find a concise summary of each lecture in course webpage. § If you miss a lecture, you should ask your classmates for notes. Instructor’s tip Problems on the exams will be similar to problems discussed in class. You are encouraged to participate actively: Ask questions, make comments, stop me. 6/20
Active participation Actively participation consists of various activity: § coming to office hours, 7/20
Active participation Actively participation consists of various activity: § coming to office hours, § exchanging email communication with the instructor, 7/20
Active participation Actively participation consists of various activity: § coming to office hours, § exchanging email communication with the instructor, § participating to in-class discussion, 7/20
Active participation Actively participation consists of various activity: § coming to office hours, § exchanging email communication with the instructor, § participating to in-class discussion, § . . . 7/20
Active participation Actively participation consists of various activity: § coming to office hours, § exchanging email communication with the instructor, § participating to in-class discussion, § . . . Ask questions, make comments, stop me. 7/20
Grades The final grade for the course will be based on the grade of the following components: homework assignments, two in-class midterm exams, and a final exam. The final grade Each component will be weighted as follows: § 20% Homework (lowest score will be dropped) § 20% Midterm I (Friday October 4, in class) § 20% Midterm II (Monday November 4, in class) § 40% Final Exam 8/20
Homework § The usual schedule will be one problem set per week. § Problem sets will be posted on the course webpage, typically on Friday. § Usually the due date will be on a class day, in which case the set is due at the beginning of class. 9/20
Homework § The usual schedule will be one problem set per week. § Problem sets will be posted on the course webpage, typically on Friday. § Usually the due date will be on a class day, in which case the set is due at the beginning of class. First week grace No homework on first week!!! 9/20
Homework submission Paper submission is required. Submission guideline § Use full-sized paper (A4, notebook paper, etc) 10/20
Homework submission Paper submission is required. Submission guideline § Use full-sized paper (A4, notebook paper, etc) § Write your full name near the top of the front page. 10/20
Homework submission Paper submission is required. Submission guideline § Use full-sized paper (A4, notebook paper, etc) § Write your full name near the top of the front page. § Please, staple multiple pages. 10/20
Homework submission Paper submission is required. Submission guideline § Use full-sized paper (A4, notebook paper, etc) § Write your full name near the top of the front page. § Please, staple multiple pages. § Typesetting solutions is not required, but... 10/20
Homework submission Paper submission is required. Submission guideline § Use full-sized paper (A4, notebook paper, etc) § Write your full name near the top of the front page. § Please, staple multiple pages. § Typesetting solutions is not required, but... § ...writing should be legible! 10/20
Homework submission Paper submission is required. Submission guideline § Use full-sized paper (A4, notebook paper, etc) § Write your full name near the top of the front page. § Please, staple multiple pages. § Typesetting solutions is not required, but... § ...writing should be legible! Late submission Late homework will not be accepted without prior permission from the instructor. 10/20
Homework submission § Homework is individual § Solutions must be written in your own words! 11/20
Homework submission § Homework is individual § Solutions must be written in your own words! Instructor’s tip This course addresses an essential aspect of math: writing down proofs. Don’t overlook exposition! 11/20
Homework submission § Homework is individual § Solutions must be written in your own words! Instructor’s tip This course addresses an essential aspect of math: writing down proofs. Don’t overlook exposition! Ask questions, make comments, stop me. 11/20
Exams General policy § Notes or books will not be allowed. § Collaboration of any kind on the exam is prohibited. § Makeup exams will only be given in case of a verifiable emergency or a formal request by the UIC athletic department. § Do not schedule travel on an exam date. 12/20
“The faculty of the University of Illinois at Chicago shall make every effort to avoid scheduling examinations or requiring that student projects be turned in or completed on religious holidays. Students who wish to observe their religious holidays shall notify the faculty member by the tenth day of the semester of the date when they will be absent unless the religious holiday is observed on or before the tenth day of the semester . In such cases, the students shall notify the faculty member at least five days in advance of the date when he/she will be absent. The faculty member shall make every reasonable effort to honor the request, not penalize the student for missing the class, and if an examination or project is due during the absence, give the student an exam or assignment equivalent to the one completed by those students in attendance. If the student feels aggrieved, he/she may request remedy through the campus grievance procedure.” Please, visit https://oae.uic.edu/religious-calendar/ 13/20
The course Content Introduction to methods of proofs used in different fields in mathematics. Prerequisite(s): Grade of C or better in MATH 181 and approval of the department. 14/20
Proof: “The process or an instance of establishing the validity of a statement especially by derivation from other statements in accordance with principles of reasoning.” 1 In particular, a proof must be ... . (Fill in the gap) § complicated § confusing § consistent § convincing § chalkboard written § incomplete § correct § lengthy § readable 1 From Webster dictionary. 15/20
Proof: “The process or an instance of establishing the validity of a statement especially by derivation from other statements in accordance with principles of reasoning.” 1 In particular, a proof must be ... . (Fill in the gap) § complicated § confusing § consistent § convincing § chalkboard written § incomplete § correct § lengthy § readable 1 From Webster dictionary. 15/20
The skill of writing proofs § Comparable to write an essay, coding, give precise instructions. § Can also be viewed as a pedagogical act. 16/20
The skill of writing proofs § Comparable to write an essay, coding, give precise instructions. § Can also be viewed as a pedagogical act. Consist of various aspects: § Understanding the underlying mathematical ideas. § Using the appropriate vocabulary/specific terms. § Motivating each of your assertions. § Avoiding wrong and misleading conclusions. 16/20
The skill of writing proofs § Comparable to write an essay, coding, give precise instructions. § Can also be viewed as a pedagogical act. Consist of various aspects: § Understanding the underlying mathematical ideas. § Using the appropriate vocabulary/specific terms. § Motivating each of your assertions. § Avoiding wrong and misleading conclusions. Hasn’t much to do with: § Performing difficult computations. 16/20
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