SPRING 2019, SETS AND LOGIC

Time, Location, and Section Number

MWF PERIOD 7, LITTLE  127, Section 8768.

Office Hours During reading days and final exam period (in 478 Little Hall)

  • Friday, April 26, 1:00 -2:30
  • Monday, April 29, 1:30 – 3:00.

Description and Goals

This course is an introduction to formal mathematics. The emphasis in this course is not on learning facts, but rather on learning how to write clear and rigorous proofs. Some of the material covered in this course may be familiar to you. The goal is to understand and write about this material in a formal mathematical way. In addition to attending class, you are expected to carefully read the appropriate sections in the text, and spend time working problems. You are encouraged to get together with other students to discuss problems. Of course, for the problems which you turn in for a grade, you must write up your work individually, and you may not copy from another student.

Text: Daniel J. Velleman, How to prove it, a structured approach, second edition, Cambridge University Press, New York, NY 10013.

Grades

Grades will be based on two exams given in class during the semester, homework problems, and a cumulative final exam. Each of the two exams during the semester will be worth 40 points. There will be seven graded problem sets worth 10 points each. The final exam will be worth 50 points. So there are 200 possible points.  The final exam will be given during the regular final exam period for this section.

Grades will be assigned according to the following:

A: 180-200       A-: 175-179      B+: 170-174       B: 160-169       B-: 155-159
C+: 150-154    C: 140-149       C-: 135-139       D+: 130-134     D: 120-129

Exam Dates

  • The final exam will be given on 4/30/2019 at 3:00 PM – 5:00 PM.

Assignments.

The assignments will be added here, as the course progresses. This will include reading, problem sets to turn in for a grade, and additional problems. I suggest that you do the reading part of each assignment in advance. Some problem assignments  must be turned in for a grade. These will be indicated below. Students are expected to also do the additional problems listed as part of the preparation for the exams.

  • January 7. Read the Introduction Pages 1 – 6, and Section 1.1, Pages 8 – 13. No problems to turn in.  Additional  problems: # 1, 5, 6, 7 (all parts of each) on pages 13 – 14.
  • January 9. Read Section 1.2. Problems to turn in # 4, 6, 8, 12, 17 (all parts of each) on pages 24 – 26.  Due January 16. This is problem set 1.  Additional problems # 1, 5, 7, 9, 11, 14, 16, 18 (all parts of each).
  • January 11. Read sections 1.3 and 1.4. No problems to turn in. Additional problems: #6 (all parts) on page 34 and # 4, 5, 9 (all parts of each) on page 42.
  • January 14. Read Section 1.5. Problems to turn in # 9, 10 (all parts of each) on page 54.  Due January 23.  This is problem set 2. Additional problems # 1, 6, 8 (all parts of each).
  • January 16. Read section  2.1. No problems to turn in. Additional problems # 3, 5, 7, 8, 9 (all parts of each).
  • January 18. Read Section 2.2. No problems to turn in. Additional problems # 1 (parts c and d), 2 (parts c and d) 3 (all parts) on page 72. Also, begin reading the notes Properties-of-real-numbers.
  • January 23. No problems to turn in. Continue reading the notes: Properties-of-real-numbers. Try to prove all parts of Theorem 1.4.
  • January 25. Read sections 1.1, 1.2, and 1.3, in the Book of Proof (see link above). Also, try to prove the remaining parts of Theorem 1.4 and Theorem 1.5 in the Properties of Real numbers (see link above).
  • January 28. Read sections 1.5 and 1.7, in the Book of Proof (see link above). Also, try to prove the remaining parts of Theorem 1.5 and Theorem 1.7 in the Properties of Real numbers (see link above).
  • January 30. Read section 3.1 of the How to Prove it text. Problems to turn in: Prove Theorem 1.7 part (h) and Theorem 1.15 part (d) of the notes on Properties of Real numbers. Due February 6. This is problem set 3. Additional problems # 11, 12 on page 94 of the text.
  • February 1 and February 4. Read section 3.2 of the How to Prove it text. No problems to turn in. Additional problems # 3, 4, 7, 8, 9, 11, 12 on pages 106 – 107 of the text.
  • February 6 and February 8. Read the part of section 3.3 of the How to Prove it text from the beginning, up to Example 3.3.4. No problems to turn in. Additional problems # 2, 3, 6, 7, 19 (all parts of each) on page 122 of the text.
  • February 11 and February 13. Read section 3.4 of the How to Prove it text. No problems to turn in. Additional problems # 2, 3, 4, 5, 6, 12, 13  on pages 133 – 134 of the text.
  • February 22 and February 25. Read section 2.3 of the How to Prove it text. Read again sections 3.3 and 3.4 of the text. Problems to turn in: # 18 and 19 on page 134 in section 3.4 of the text. Due March 1. This is problem set 4. Additional problems # 12 and 17 on page 122 in section 3.3 of the text and # 7, 8, 14, 15, 16, 17  on pages 133 – 134 in section 3.4 of the text.
  • February 27. Read Section 3.5. No problems to turn in. Additional problems # 4, 5, 6, 7, 8, 9, 15, 30,  (all parts of each) on pages 143 – 146 of the text.
  • March 1. Read section 3.6 No problems to turn in. Additional problems # 1, 2, 3, 4, 6, 7, (all parts of each) on pages 153 – 154 of the text.
  • March 11. Read section 4.1 Problem to turn in: # 9 on page 171 in section 4.1 of the text. This is part of problem set 5. Due March 20. Additional problems # 4, 5, 6, 7, 8, 10, 11, 12 (all parts of each) on pages 170 – 171 of the text.
  • March 13 and March 15. Read section 4.2. Problem to turn in: # 11 part (a) on page 179 in section 4.2 of the text. This is the final part of problem set 5. Due March 20. Additional problems # 8, 9, 10 (all parts of each) on page 179 of the text.
  • March 18. Read section 4.3. No problems to turn in. Additional problems # 3, 4, 5, 12, 13, 14, 15, 16, 17, 18 (all parts of each) on pages 186 – 188 of the text.
  • March 20, March 22, and  March 25. Read section 4.4. Problem to turn in: # 10 and # 22 on pages 199 – 202 in section 4.4 of the text. This problem set 6. Due March 27. Additional problems # 5, 6, 7, 16, 17, 18, 20 (all parts of each) on pages 199 – 202 of the text.
  • March 27 and March 29. Read Section 4.6. Problem to turn in: # 13 (both parts) on page 223 in section 4.6 of the text. This is problem set 7. Due April 3. Additional problems # 1, 2, 3, 10, 11, 12 (all parts of each) on pages 222 – 225.
  • April 12. Read Section 5.1. No problems to turn in. Additional problems # 3, 6, 7, 11, 15, 17 (all parts of each) on pages 233 – 236.
  • April 15. Read Section 5.2. No problems to turn in. Additional problems #  3, 5, 7, 8, 9, 18 (all parts of each) on pages 243 – 245.
  • April 17. Read Section 5.3. No problems to turn in. Additional problems # 3, 6, 7, 16, 18 (all parts of each) on pages 252 – 255.
  • April 19. Read Section 6.1. No problems to turn in. Additional problems # 1, 2, 3, 9, 10, 11, 12 (all parts of each) on pages 265 – 267.

Course Policies.

  • Closed-book policy: No use of calculators, or books will be allowed during any in-class exams.
  • Policy related to make-up exams: Written medical documentation is required for make-up exams.
  • Policy on class attendance: Daily attendance is required as consistent with university policies that can be found in the online catalog at: https://catalog.ufl.edu/ugrad/current/regulations/info/attendance.aspx.

  • Additional Information and Links:

    Grades: Grading will be in accord with the UF policy stated at https://catalog.ufl.edu/ugrad/current/regulations/info/grades.aspx.

    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 in this class.”

    Class Attendance: “Requirements for class attendance and make-up 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.