Time and Location
M W F Period 7, Little Hall 221.
Office hours
M W Period 8, F Period 5, or by appointment in LIT 436.
Announcements
4/24: Bonus problem, practice final, and an announcement about the final have been posted on Canvas.
3/12: We will meet in person tomorrow and move online on Monday. If you can a device tomorrow on which we can test the Zoom streaming available through Canvas, that would be great. Further information with respect to exams and presentations will be posted on Canvas.
3/10: For the time being, the classes will run as usually until it is required to move the course online. The final exam is scheduled for April 30, 3-5pm.
2/24: Solutions to Practice Midterm 2 have been posted on Canvas.
2/20: Here is Practice Midterm 2. Remember that Homework 3 is due on Friday. Since we have not gone over uniqueness of solutions yet, you won’t be evaluated on the last problem of the Homework. However, I encourage you to try completing it for practice. Please fill in midterm evaluations.
2/10: On Wednesday 2/12 I will hold office hours during Period 5. You can also come during the 8th period after 3:15pm.
1/29: I hope you all enjoyed the exam today. You can find Homework 2 below and it is due on Wednesday February 12, 2020 in class.
1/28: Practice Midterm 1 solutions have been uploaded to Canvas. You will have the sheet with equivalences available during the exam. Otherwise it is a closed book exam. Problems in the textbook are an excellent source for practice.
1/23: Division into group presentations has been done on Canvas, where you can connect with your teammates. All your grades will also be recorded through Canvas.
1/22:Practice Midterm 1
1/17: Recommended reading has been updated. We have not covered implication yet, therefore if you do not complete Problem 1.5:3, it will no be held against you. Correction from the class: In the first example on free and bound variables “x is of the form y+1′, it would often be meant that x is free and y is bound, but as it is both x and y are free. A right way to bind y would be “x is of the form y+1 for some y.” I will hold additional office hours on Tuesday 1/21 during the 7th period.
1/8: Homework 1 has been posted below and it is due by Wednesday January 22, 2020, in class.
1/6: Please email me which presentation topic you would like to work on by Monday, January 13. The topics will be distributed at first come first served basis. If I do not receive your choice, I will randomly assign a project to you. Recommended reading will be updated weekly.
Textbook and recommended reading
Daniel J. Velleman, How To Prove It: A Structures Approach, Second Edition, Cambridge University Press, New York, NY 10013.
Recommended book chapters:
Wednesday 4/22: 7.2/7.3
Monday 4/20: 7.1/7.2
Friday 4/17: Presentation on Infinite sets.
Wednesday 4/15: 6.2./6.4./6.5.
Monday 4/13: 6.1./6.3.
Friday 4/10: Presentation on Recursion and induction
Wednesday 4/8: Exam 3
Monday 4/6: 5.4/recap
Friday 4/3: 5.3
Wednesday 4/1: 5.1/5.2
Monday 3/30: 4.6
Friday 3/27: 4.6
Wednesday 3/25: 4.5
Monday 3/23: 4.5
Friday 3/20: 4.4./4.5
Wednesday 3/18: 4.4
Monday 3/16: 4.3
Friday 3/13: 4.2
Wednesday 3/11: 4.1
Monday 3/9: 3.7
Friday 2/28: 3.6/3.7
Friday 2/21: 3.6
Wednesday 2/19: 3.5/3.6
Monday 2/17: 3.4/3.5
Friday 2/14: 3.4
Wednesday 2/12: 3.3
Monday 2/10: 3.2
Friday 2/7: 3.1
Wednesday 2/5: 2.3/3.1
Monday 2/3: 2.2/2.3
Friday 1/31: 2.2
Wednesday 1/29: Midterm 1 on all covered up to now.
Monday 1/27: Preface – 2.1
Friday 1/24: 2.1
Wednesday 1/22: 1.5
Friday 1/17: 1.4
Wednesday 1/15: 1.3
Monday 1/13: Section 1.2
Friday 1/10: Sections 1.1, 1.2
Wednesday 1/8: Preface, Introduction, Sections 1.1. and 1.2.
Description and Goals
This is an introduction to rigorous mathematical proofs. The goal is to learn how to structure a proof that contains no gaps, how to correctly and coherently reason. Some statements may look (intuitively) obvious but one can prove them false, which is why we need to be able to prove what seems to be a triviality. The content we will be working with will likely be quite familiar to you already. You will be responsible to read assigned book chapters before the class and work on problems. You are welcome to discuss together but you have to write up homework solutions independently and you are not allowed to copy any part of your work.
Homework
There will be biweekly homework assigned here on every other Wednesday. The lowest grade will be dropped and you can hand in one homework up to 2 days late with no reasoning. Otherwise, late homework will no be accepted unless extreme situation occurs (such as serious illness), for which a proof will be required. Homework will receive two equally weighed grades: one for completeness and one for two randomly selected problems graded in detail. Reach out to me in time with any difficulties when completing homework.
Homework 6
Due on Wednesday April 22, 2020 midnight, online on Canvas. Work out the following problems from the book. Section 6.1.: 17., Section 6.2.: 12., Section 6.3.: 16., Section 7.1.: 19., Section 7.2.: 10., Section 7.3.: 9.
Homework 5
Due on Wednesday April 1, 2020 midnight, online on Canvas. Work out the following problems from the book. Prove item 3. in Theorem 4.3.4; Exercises in Section 4.3.: 19.; Section 4.4.: 6.; Section 4.5.: 17.; Section 4.6.: 4.; Section 5.1.: 15.
Homework 4
Due on Wednesday March 18, 2020 in class. Work out the following problems from the book. Section 3.6.: 10.; Section 3.7.: 3.; Section 4.1.: 2., 5.; Section 4.2.:2.
Homework 3
Due on FRIDAY February 21, 2020 in class. Work out the following problems from the book. Section 3.3.: 19., 23.; Section 3.4.: 13., 24., Section 3.5: 14., Section 3.6.: 8.
Homework 2
Due on Wednesday February 12, 2020, in class. Work out the following problems from the book. Section 2.1.: 3.; Section 2.2.: 2.,; Section 2.3: 2., 9.; Section 3.1: 16.; Section 3.2: 2.
Homework 1
Due on Wednesday January 22, 2020, in class. Work out the following problems from the book. Section 1.1.: 7.; Section 1.2: 3.; Section 1.3: 2., 6.; Section 1.4.: 7.; Section 1.5:3.
Exams
There will be 3 midterms and a final exam. The exams will be closed book, closed notes and no devices will be allowed. Unless you have a serious well-documented reason, there will be no make up exams.
Midterms are tentatively scheduled for the following dates in class
January 29
February 26
April 8
Presentation
Everyone will be required to give a presentation. Presentations will be prepared in teams of 5 and each person will have 5 minutes to present their part.
Presentation topics
1. Why do we need formal proofs. (January)
2. Proof systems and automated proving. (First half of February)
3. Relations and Functions (Second half of February)
4. Recurrence and mathematical induction. (March)
5. Infinite sets. (April)
Grades
Homework will be worth 10 (completeness) + 10 (2 random problems) points each, midterms and a presentation 50 points each and final 100 points = total 400 points.
A above 93%, A- 90-92%, B+ 87-89%, B- 83-86%, C+ 77-79%, C 73-76%, C- 70-72%, D+ 67-69%, D 63-66%, D- 60-62 %, E, I, NG, WF 59% and below.
Honor Code
UF students are bound by The Honor Pledge which states, We, the members of the University of Florida community, pledge to hold ourselves and our peers to the highest standards of honor and integrity by abiding by the Honor Code. On all work submitted for credit by students at the University of Florida, the following pledge is either required or implied: On my honor, I have neither given nor received unauthorized aid in doing this assignment. The Honor Code specifies a number of behaviors that are in violation of this code and the possible sanctions. Furthermore, you are obligated to report any condition that facilitates academic misconduct to appropriate personnel. If you have any questions or concerns, please consult with the instructor or TAs in this class.
Class Attendance
Requirements for class attendance and makeup exams, assignments, and other work in this course are consistent with university policies that can be found at https://catalog.ufl.edu/ugrad/current/regulations/info/attendance.aspx.
Accommodations for Students with Disabilities
Students with disabilities requesting accommodations should first register with the Disability Resource Center (352-392-8565, https://www.dso.ufl.edu/drc) by providing appropriate documentation. Once registered, students will receive an accommodation letter which must be presented to the instructor when requesting accommodation. Students with disabilities should follow this procedure as early as possible in the semester.
Online Evaluations
Students are expected to provide feedback on the quality of instruction in this course by completing online evaluations at https://evaluations.ufl.edu. Evaluations are typically open during the last two or three weeks of the semester, but students will be given specific times when they are open. Summary results of these assessments are available to students at https://evaluations.ufl.edu/results.
Contact information for the Counseling and Wellness Center
https://counseling.ufl.edu, 392-1575; and the University Police Department: 392-1111 or 9-1-1 for emergencies.