Math 109: Mathematical Reasoning, Lecture E00, Fall 2017

Announcements:

12/04: The final will cover Chapters 1-14.

11/24: See here for a practice final exam and here for practice problems (1 and 2). (Note that these links are provided only to give you more practice problems. Our final may be very different.)

11/19: Midterm 2 sample solutions provided by Haiyu Huang.

11/08: The second midterm (in class, November 16th) will cover Chapters 7-10 and Section 11.1 from Chapter 11. I recommend that you do Homework 7 before Midterm 2. Practice midterms may be found here and here. (Note that these links are provided only to give you more practice problems. Our midterms may be very different.)

10/28: Midterm 1 sample solutions provided by Vincent Yu.

10/16: Midterm 1 will be held in two locations: the usual classroom and an overflow room (YORK HALL 3000A).
• If your last name starts with A-H , then you will be taking the midterm in YORK HALL 3000A .

• If your last name starts with I-Z , then you will be taking the midterm in CENTRAL HALL 222 (the usual classroom).

10/12: The instructor office hours on Tuesday, October 17th, are extended 11:00am-1:00pm. The office hour on Thursday, October 19th, is cancelled.

10/05: The first midterm (in class, October 19) will cover Chapters 1-6. Practice midterms may be found here and here. (You have to scroll down to find the midterms. Note that these links are provided only to give you more practice problems. Our midterms may be very different.)

Your scores will be recorded on TED.

Welcome to Math 109!

Prerequisites: Math 18 or Math 20F or Math 31AH, and Math 20C. Students who have not completed listed prerequisites may enroll with consent of instructor.

Course description: This course uses a variety of topics in mathematics to introduce the students to rigorous mathematical proof, emphasizing quantifiers, induction, negation, proof by contradiction, naive set theory, equivalence relations and epsilon-delta proofs. Required of all departmental majors.

Textbook: An Introduction to Mathematical Reasoning by Peter J. Eccles We will cover most of the book.

Lectures: Attending the lectures is a fundamental part of the course. You are responsible for material presented in the lectures whether or not it is discussed in the textbook.

Reading: Reading the sections of the textbook corresponding to the assigned homework exercises is considered part of the homework assignment. You are responsible for material in the assigned reading whether or not it is discussed in the lecture. It will be expected that you read the assigned material in advance of each lecture.

Homework: Homework will be assigned most weeks. Homework is due every Friday by 5:00pm (and should be placed in the drop-box in the basement of APM) with the exception of Friday, November 10 and Friday, November 24. There will be a total of eight problem sets and you should attempt to complete all of them. No late homework will be accepted. If, for any reason, you cannot turn in a homework assignment, keep in mind that the lowest score will be dropped.

Midterm Exams: There will be two in-class midterms: the first on Thursday, October 19th, and the second on Thursday, November 16th. There will be no make-up exams. If, for any reason, you cannot make it to one of the midterms, you will automatically receive grading option (2).

Final exam: The final exam is scheduled for Thursday, December 14, 8:00am-11:00am. The final exam will be cumulative.

Grading: Your final score will be calculated as the maximum of the following two schemes:
(1) 20% Homework + 20% First Midterm + 20% Second Midterm + 40% Final Exam
(2) 20% Homework + 20% Best Midterm Exam + 60% Final exam

Regrades: Homework and midterm exams will be returned in the discussion sections. If you wish to have your homework or exam regraded, you must return it immediately to your TA. Regrade requests will not be considered once the homework or exam leaves the room. If you do not retrieve your homework or exam during discussion section, you must arrange to pick it up from your TA within one week after it was returned in order for any regrade request to be considered.

Collaboration: You are allowed to discuss homework problems with your classmates. However, the final write-up of solutions should be your own work, and reflect your own understanding of the problems. Copying or paraphrasing part of the solution to a homework problem from a classmate or from the internet is considered academic dishonesty.

Academic dishonesty: Academic dishonesty is considered a serious offense at UCSD. Students caught cheating will face an administrative sanction which may include suspension or expulsion from the university (see here for more information).

List of homework assignments:

• Homework 1, due Friday, October 6th: exercises 1.2, 1.3, 1.5, 2.1 (ii, v, ix, xi), 2.4, 2.5, 2.6.
• Homework 2, due Friday, October 13th: exercises 3.2, 3.3, 3.5, 3.8, 4.1, 4.2, 4.4, 4.7.
• Homework 3, due Friday, October 20th: exercises 5.2, 5.4, 5.6, 6.4, 6.5, 6.6, and problems 16 and 17 from Problems I (page 55).
• Homework 4, due Friday, October 27th: exercises 7.1 (i, iv), 7.2 (iii, v, vi), 7.5, 7.6, 7.7, and problems 11 (i, iii, vi, ix) and 12 from Problems II (page 117).
• Homework 5, due Friday, November 3rd: exercises 8.1, 8.2, 8.3 , 8.5, and problems 14 and 15 from Problems II (page 117).
• Homework 6, due Friday, November 17th: exercises 9.4, 9.5, 9.6, and problems 16 (i, iii, vi), 18, 19 from Problems II (page 118).
• Homework 7, due Friday, December 1st: exercises 10.1, 10.3, 10.4, 11.1, and problems 2 and 10 from Problems III (pages 182-184).
• Homework 8, due Friday, December 8th: exercises 12.2, 12.3, 12.5, 13.1, 14.1, 14.2.

Calendar of topics to be covered by week (approximate and subject to change):

• Week 1: Th (Chap. 1, 2).
• Week 1: Tu (Chap. 2, 3, 4) and Th (Chap. 4, 5).
• Week 2: Tu (Chap. 5) and Th (Chap. 5, 6).
• Week 3: Tu (Chap. 6) and Th (Midterm 1).
• Week 4: Tu (Chap. 7) and Th (Chap. 8).
• Week 5: Th (Chap. 8, 9) and Th (Chap. 9).
• Week 6: Tu and Th (Chap. 10 and 11).
• Week 7: Tu (practice midterms) and Th (Midterm 2).
• Week 8: Tu (Chap. 12).
• Week 9: Th (Chap. 12 and 13) and Th (Chap. 13 and 14).
• Week 10: Tu (Chap. 14) and Th (review).