Mathematical Reasoning

Spring 2022 Course Syllabus

**Course:** Math 109

**Title:** Mathematical Reasoning (Course Catalog)

**Credit Hours:** 4

**Prerequisites:** MATH 18 or MATH 20F or MATH 31AH, and MATH 20C.

**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: numbers, sets, and functions*,
by Peter J. Eccles; published by Cambridge University Press; copyright 2007
(19th printing 2015)

**Subject Material:** We shall cover parts of chapters 1 - 22 (Parts I - V)
of the text. A more complete list of the sections covered can be found on the course
homework page.

**Reading:** *It will be expected that you read the assigned material in advance of
the class period indicated by the* course calendar. The amount
of reading is not large in quantity; however, it is heavy in conceptual
content. You will be expected to write proofs of theorems using the ideas presented in the
assigned reading; therefore, it is absolutely vital that you read the assigned material carefully.
Moreover, since class periods will center on discussion of problems related to the assigned reading,
it is critical that you read the assigned material in advance of the class period it will be
discussed.

**Lecture:** "Lecture" is not really the appropriate term for how the class meetings
will be run: instead of formal lectures, class periods will be used for class discussion based on
problems given the previous class period. These
"problems to think about" will be chosen to illustrate the
important concepts addressed in the assigned reading for that class period. You will be expected to
*actively participate* in class discussions by (1) asking questions and (2) making suggestions
for solving the problems. By *actively participating*, you will gain the deeper
understanding required to analyze mathematical statements and construct your own proofs.

**Homework:** Homework will be assigned on the course
homework page and should be completed by the indicated due date. You
will be asked to turn in (upload to Gradescope) written solutions to a subset of the exercises by the due date
the due date. These homework assignments will be graded *carefully* and will comprise a *substantial* portion of your grade: you will be expected to take them
*seriously* and to write them up *neatly*. A detailed list of homework
guidelines may be found on the homework page. Please make every effort
to complete all the assigned exercises, not just those you turn in: the assigned exercises will be
used as a resource for constructing your exams. Your homework grade will be based on the best four
(4) of six (6) assignments.

**Quizzes:** There will be six (6) 30-minute quizzes given given on the days specified in the course calendar. You will be given exactly 30 minutes to complete your quiz in Canvas and will be provided a 10-hour window (10:00am - 8:00pm) within which to do so. Your cumulative quiz score will be based on the best 4 of 6 possible quiz scores. * There will be no makeup quizzes.* If you miss a quiz for any reason, your cumulative quiz score will be based on your remaining quiz scores.

- You may consult your textbook, notes, and lecture slides during each quiz.
- You may
search the Internet or communicate with another person in any way during a quiz. Doing so would be an academic integrity violation. Please protect your academic integrity: It is of great value to you.**not**

**Midterm Exams:** There will be two midterm exams given during the lecture hour on Wednesday of the fourth and seventh weeks; see the course calendar for the date of the midterm exam. * There will be no makeup exams.* You may bring one 8.5 by 11 inch handwritten sheet of notes with you to the each midterm exam. Yes, you may write on both sides.

**Final Examination:** The final examination will be held at the date and time stated in the course calendar. It is your responsibility to ensure that you do not have a schedule conflict involving the final examination; you should not enroll in
this class if you cannot take the final examination at its scheduled time. You may bring one 8.5 by 11 inch handwritten sheet of notes (written on both sides) with you to the final examination; no other notes (or books) or calculators will be allowed.

**Grading:** Your course grade will be based on the better of the following three (3) weighted averages. Note that the homework grade will be based on your best five (4) of six (6) assignments.

- 30% Homework, 10% Quizzes, 15% Midterm Exam 1, 15% Midterm Exam 2, 30% Final Exam
- 30% Homework, 10% Quizzes, 15% Best Midterm Exam, 45% Final Exam

**Academic Integrity:** Academic integrity is highly valued at UCSD and academic dishonesty is considered a serious offense. Students involved in an academic integrity violation will face an administrative sanction which may include suspension or, in very serious cases, expulsion from the university. Your integrity has great value: Cultivate and protect your academic integrity. For more about academic integrity and its value, visit the UCSD Academic Integrity Website.