Math 109: Mathematical Reasoning, Spring 2017

Time and Place: M-W-F 4:00p-5:00p in Mande B-210

Course description: This course uses a variety of topics in mathematics to introduce 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

Material covered: Probably most of the book.

Instructor: Rayan Saab
E-mail: rsaab (at) ucsd (dot) edu
Office: APM 5157
Office Hours : Monday 5:00pm-6:00pm or by appointment.

Discussion sessions:
- (C01) Wednesday 5:00p-5:50p, APM 5402
- (C02) Wednesday 6:00p-6:50p, APM 5402
- (C03) Wednesday 7:00p-7:50p, APM 5402
Teaching Assistants:
- Daniel Kroes, section (C01)
  - E-mail: dkroes (at) ucsd (dot) edu
  - Office Hours: ~~Tuesday 12:00 - 1:00 pm and Thursday 1:00 - 2:00 pm~~ Monday 11:00 am - 1:00 pm, Tuesday 12:00 pm - 1:00 pm and Thursday 1:00 pm - 2:00 pm. in APM 6414
- Michelle Bodnar, sections (C02) and (C03)
  - E-mail: mbodnar (at) math (dot) ucsd (dot) edu
  - Office Hours: ~~Monday 11:00 am - 1:00 pm and Wednesday 2:00 - 4:00 pm in APM 6434~~

Announcements:

June 12, 2017 My lecture notes: Lecture notes 6 (updated). (May contain errors or typos, use at your own risk)
June 2, 2017 Midterm 2 and its solution.
May 31, 2017 My lecture notes: Lecture notes 6. (May contain errors or typos, use at your own risk)
May 18, 2017 A Reminder that Midterm 2 (May 22, in class) will cover everything (Chapters 1-11) up till (and including) the portion of Chapter 11 that we cover on Friday May 19. In particular, the focus will be on material from Chapters 7-11, but you may need the concepts discussed earlier.

May 12, 2017 -- updated May 18, 2017 My lecture notes: Lecture notes 5. (May contain errors or typos, use at your own risk)

May 8, 2017 My lecture notes: Lecture notes 4. (May contain errors or typos, use at your own risk)

May 2, 2017 My lecture notes: Lecture notes 3 -- updated to include my notes on Chapter 7. (May contain errors or typos, use at your own risk)

April 27, 2017 Midterm 1 and its solution.

April 21, 2017 Practice midterms may be found here and here. (You have to scroll down a little to find the midterms. Note that these links are provided only to give you more practice problems. Our midterms may be very different.)

April 21, 2017 My lecture notes: Lecture notes 3. (May contain errors or typos, use at your own risk)

April 18, 2017 Midterm 1 (April 24, in class) will cover Chapters 1-6.

April 15, 2017 My lecture notes: Lecture notes 2. (May contain errors or typos, use at your own risk)

April 8, 2017 My lecture notes: Lecture notes 1. (May contain errors or typos, use at your own risk)

March 27, 2017 Welcome to Math 109!

Homework: Due at 5:00 p.m., on the dates indicated -- (please remember that copying solutions from each other or from the internet is an academic integrity violation!)
List of homework assignments: (Solutions provided after the submission deadline, by your TA's Michelle Bodnar and Daniel Kroes)

Homework 1, due Thursday, April 13: Problems 1.2, 1.4, 1.5, 2.1 (i,ii, ix, xi), 2.4, 2.5, 2.6 --- solutions
Homework 2, due Thursday, April 20: Problems 3.2, 3.3, 3.5, 3.8, 4.1, 4.3, 4.4, 4.7 --- solutions
Homework 3, due Thursday, April 27 (I strongly advise you do this HW before Midterm 1): 5.1, 5.2, 5.4, 5.6, 5.7, 6.4, 6.5, 6.6, 6.7 --- solutions
Homework 4, due Thursday, May 4: Problems 7.1 (iii,iv), 7.2 (iii, iv, v), 7.4 (vi ,vii), 7.5, 7.7, and Problems 10, 12 from the Problems II questions on pages 116/117. --- solutions
Homework 5, due Thursday, May 11: Problems 8.1, 8.2, 8.3 (iii), 8.5, and Problem 15 from the Problems II questions on pages 117/118. --- solutions
Homework 6, due Thursday, May 18: Problems 9.4, 9.5 and Problems 16 (ii,iii, vi), 18, 19, 20 from the Problems II questions on page 118. --- solutions
For chapter 9, I also recommend that you do Problems 9.6, 9.7 (though you are not required to submit solutions to these two problems).
Homework 7, due Thursday, May 25: Problems 10.1, 11.1, 11.5, and Problems 1, 4, 14 from the Problems III questions. Additionally, solve the following problem:
Let n be a positive integer and let A be a subset of {1,2,...,2n} with n+1 elements. Use the pigeonhole principle to show that A contains two consecutive integers. --- solutions
Homework 8 , due Thursday, June 1: Problems . --- solutions
Homework 9 , This HW will not be collected but it is important that you do it to prepare for the final. Problems 13.1, 13.4, 14.1, 14.2, 14.4, 15.1 (i, iv, viii), 15.2, 15.3, 15.5 and 21, 23, 26 from the Problems III questions.

Lecture: Attending the lecture is a fundamental part of the course; you are responsible for material presented in the lecture whether or not it is discussed in the textbook. You should expect questions on the exams that will test your understanding of concepts discussed in the lecture.

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:

In genreal, homework will be assigned every one or two weeks.
Homework is due at the dates posted on this webpage (in the Homework section) by 5:00 pm.
No late homework will be accepted but the lowest HW score *may* be dropped.
As a main focus of this course is proof writing, your solutions must be written in complete English sentences, including punctuation.
If you choose to handwrite your homework, your handwriting must be clearly legible. That said, you are encouraged to type up your assignments using LaTex.
You may discuss your assignments with your classmates but you *must* write your own solutions.

Midterm Exams: There will be two in-class midterms: the first on Monday, April 24th (in class) and the second on Monday, May 22nd (in class). Note: Since there are no makeup exams, if you miss an exam for any reason then your course grade will be computed with the final exam counting 60% of your weighted average (see below).
Final exam: The final exam is scheduled for June 15th, 3:00pm-6:00pm.
You must pass the final examination in order to pass the course.

Grading: Your final score will be calculated as the maximum of the following two formulas:
(1) 20% Homework + 20% First Midterm + 20% Second Midterm + 40% Final Exam
(2) 20% Homework + 20% Best Midterm Exam + 60% Final exam
Note that 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.
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. Click here for more information.