# Math 109: Mathematical Reasoning, Lecture E00, Winter 2018

### Time and Place: TuTh 9:30am-10:50am, APM B412

 Instructor: Adrian Ioana E-mail: aioana@ucsd.edu Office: APM 5210 Office Hours: Tu 12:00pm-1:00pm and Th 11:00am-12:00pm Section E01: F 4:00pm-4:50pm APM B412 Teaching Assistant: Haiyu Huang E-mail: hah019@ucsd.edu Office Hours: MW 1:00pm-2:00pm in APM 5218.

Announcements:

02/22: The final will cover Chapters 1-15.
02/22: See here and here for practice final exams 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.)
02/15: The second midterm (in class, February 27th) will cover Chapters 8-12. I recommend that you do Homework 7 before Midterm 2. Practice midterms may be found here, here and here. (Note that these links are provided only to give you more practice problems. Our midterms may be very different.)
01/17: The lecture on Thursday, February 1st, is cancelled. We will be having a make-up lecture next Wednesday, January 24th, from 5:00-6:20pm in WLH (Warren Lecture Hall) 2114.
01/15: The first midterm (in class, January 30th) will cover Chapters 1-7. Practice exams may be found here, 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

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 Wednesday by 4:00pm and should be placed in the drop-box at the frontdesk on the 7th floor of APM. There will be a total of nine 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 Tuesday, January 30th, and the second on Tuesday, February 27th. 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 Tuesday, March 20, 8:00a-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

In addition you must earn a passing grade on the final examination in order to pass the course.

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 Wednesday, January 17th: exercises 1.2, 1.3, 1.5, 2.1 (ii, v, ix, xi),2.3, 2.4, 2.5, 2.6.
• Homework 2, due Wednesday, January 24th: exercises 3.2, 3.3, 3.5, 3.8, 4.1, 4.2, 4.4, 4.7.
• Homework 3, due Wednesday, January 31st: exercises 5.2, 5.4, 5.6, 6.4, 6.5, 6.6, and problems 14 and 17 from Problems I (page 55).
• Homework 4, due Wednesday, February 7th: exercises 7.1 (ii, iv), 7.2 (ii, iv, vi), 7.5, 7.6, 7.7, and problems 11 (i, ii, iv, vi, ix) and 12 from Problems II (page 117).
• Homework 5, due Wednesday, February 14th: exercises 8.1, 8.2, 8.3, 8.4, 8.5, and problems 14 and 15 from Problems II (page 117).
• Homework 6, due Wednesday, February 21st: exercises 9.4, 9.5, 9.6, and problems 16 (i, iii, vi), 18, 19 from Problems II (page 118).
• Homework 7, due Wednesday, February 28th: exercises 10.1, 10.3, 10.4, 11.1, 12.3, 12.5 and problems 2 and 10 from Problems III (pages 182-184).
• Homework 8, due Wednesday, March 14th: exercises 13.1, 13.5, 14.1, 14.2, 15.3, 15.5, problem 12 from problems III, and problem 1 from Problems IV.

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

• Week 1: Tu (Chap. 1, 2) and Th (Chap 2, 3).
• Week 2: Tu (Chap. 4, 5) and Th (Chap. 5, 6).
• Week 3: Tu (Chap. 6) and Th (Chap. 7).
• Week 4: Tu (midterm 1) and Th (no lecture).
• Week 5: Tu (Chap. 8) and Th (Chap 9).
• Week 6: Tu and Th (Chap. 10 and 11).
• Week 7: Tu (Chap. 12) and Th (Chap. 12 and review for midterm).
• Week 8: Tu (midterm 2) and Th (Chap. 13).
• Week 9: Chap. 14.
• Week 10: Tu (Chap. 15) and Th (review for final).