This course uses a variety of topics in mathematics to introduce students to rigorous mathematical proof. Specific topics include logic (connectives, negation, converse contrapositive, logical equivalence, quantifers, truth tables), naive set theory, basic proof techniques (direct proof, proof by cases, proof by contrapositive, proof by contradiction), mathematical induction, functions (one-to-one, onto, bijective, inverses), relations (equivalence relations, congruence modulo n, partitions of a set), examples from basic number theory (infinitude of primes, the Fundamental Theorem of Arithmetic, the Division Algorithm, the Euclidean Algorithm), and an introduction to epsilon-delta proofs. If time allows, we may cover further examples from combinatorics, group theory, etc.
TEXTBOOK:The official course text is Mathematical Proofs: A Transition to Advanced Mathematics, fourth edition, by Chartrand, Polimeni, and Zhang, published by Pearson. It is optional. The actual text is excellent, and I strongly encourage you to get it if you can find it for a reasonable price.
LECTURES:Lectures will be delivered asynchronously on Canvas. They will be posted by the scheduled lecture time, 11:00-11:50a.m. MWF. Since this course typically includes two midterms taken during lecture, two lectures will be skipped; see the calendar.
Each lecture has a corresponding Canvas assignment where you will submit a brief ~50 word summary of that lecture. The summaries will be graded on completion and will be due one week after the lecture was given. You may summarize the key points in the lecture, you may mention a specific point that caused you confusion, etc., so long as you clearly engage with the ideas presented.
DISCUSSION SECTIONS:Discussion sections will be held in-person according to the Schedule of Classes.
OFFICE HOURS:Office hours will be held remotely over Zoom. See the Zoom LTI Pro tab on Canvas for the schedule and access links.
HOMEWORK:The purpose of this course is to transition you from calculation-focused mathematics to conceptual, proof-based mathematics. Most of this transition will occur as you grapple with the homework, so the homework is the most important component of this course. You will be required to rigorously prove and clearly write solutions rather than simply calculate the correct answer. The homework will provide a place for you to practice the fundamental skills necessary to succeed in the rest of the mathematics major and beyond. Fair warning: it only gets harder from here. Struggling with difficult problem sets is an essential part of learning to do advanced mathematics. Consequently, some questions are much more difficult than others.
Homework will be posted weekly on Canvas. See the calendar for due dates. They will be turned in on GradeScope; see the homework assignments themselves for further directions.
Late homework will not be accepted for any reason. You may miss up to 10% of the overall homework points without penalty to your grade. [Specifically, your homework percentage will be MIN((raw/total)*10/9, 1).] Since this is largely a course on proof writing, you will partly be graded on style. You must use complete English sentences, standard notation, legible writing, etc. Certain parts of homework will be marked "bonus". You should think of these as opportunities to make up for lost points on other homework assignments.
Partial homework solutions will be provided on Piazza. Missing portions will be clearly marked. To give you another opportunity to practice your proof-writing skills and give you another opportunity to get focused feedback on your mathematical writing, you will be required to take responsibility for filling in one missing solution during the quarter. Further directions will be given early in the quarter.
You are encouraged to work together on homework. However, you must write up your solutions separately. You are also strongly encouraged to type up your homework in LaTeX---this is an invaluable skill used daily by every working mathematician, and it's never too early to start learning. To encourage this, .tex source code for each homework will be provided. You are welcome to ask typesetting questions on Piazza, during lecture or discussion sections, and during office hours.
EXAMS:Instead of traditional exams, we will have a series of quizzes. The last quiz will take place during finals week in place of a traditional final and will have the same weight as the other quizzes.
QUIZZES:We will have 6 quizzes during the quarter. Your lowest quiz will be dropped (even if it is 0). Each of your top 5 quizzes will contribute 12% of your final grade. Quizzes will be conducted online through GradeScope during scheduled lecture time, 11:00-11:50am on Wednesdays. Detailed procedures will be announced early in the quarter, including alternate accommodations for students who are unable to take quizzes during the scheduled lecture time.
The components of the course will be weighted as follows:
The course will be curved. The target median will be 3.0 +/- 0.15. This is slightly above the historical median for Math 109 of 2.9, in consideration of disruptions due to the pandemic. The target grade distribution will be roughly 30% A's/30% B's/30% C's/10% D's/F's. These are not quotas, they are merely guidelines for what to expect based on the historical performance of many students in this class. I put a lot of thought into assigning final grades, and exact cutoffs will be determined at the end of the quarter on a student-by-student basis.
I use difficult exams and heavy curves to assign fair grades. This is unusual in UCSD's math department, but I firmly believe it is in students' best interest. Focus on putting your best effort into the course and have faith that grades will work themselves out.
ATTENDANCE:You are paying quite a lot for my time and the TA's time, so take advantage of it! That includes watching lecture, attending discussion section, and attending office hours.
PIAZZA:We will use Piazza for class announcements and discussions.
Post on Piazza whenever you're confused about homework, the lecture, the textbook, course logistics, or anything relevant to the course. Do not let yourself be silenced by the fear of looking stupid. Your classmates, the TA's, and I will answer. You have the option of posting anonymously to classmates, though I encourage you to post as yourself to foster a sense of community with your classmates.
You are very strongly encouraged to post messages on Piazza instead of emailing me or the TA's directly. Private posts can be made if needed.
GRADESCOPE:We will use GradeScope to handle quizzes and for homework submission. Regrade requests are for when the rubric has been marked incorrectly. They are not for arguing with the rubric.
HELP:Help is available from the TA and myself during office hours. The math department (AP&M 7th floor desk) maintains a list of private tutors.
ACCOMMODATIONS:It is important to me personally and the university generally to provide reasonable accommodations to students with disabilities. Students with special needs or disabilities must provide the instructor with an Authorization for Accommodation (AFA) letter issued by the Office for Students with Disabilities (OSD) in the first week of class, or as soon as possible if the situation arises later. Arrangements for UCSD Athletics teams, documented medical emergencies, etc., must be requested with appropriate documentation as soon as possible.
ACADEMIC INTEGRITY:Cheating will not be tolerated. See the UCSD Policy on Integrity of Scholarship.
This class is participating in a pilot project on academic integrity. You will recieve 2% of your overall course grade for accessing two surveys and answering two comprehension questions.