Course: Math 109
Title: Mathematical Reasoning
Credit Hours: 4
Prerequisite: Math 20F or equivalent
Course Description: This course uses a variety of topics in mathematics to introduce students to rigorous mathematical proof, emphasizing quantifiers, induction, proof by contradiction, and set theory. Students should develop a firm notion of what it means to prove a statement rigorously and be able to write clear proofs using several different strategies by the end of the course. They should learn to move between making full sense of propositions before trying to prove them and considering statements formally so that the symbols can be manipulated even if the overall meaning is unclear. Finally, students should be able to evaluate given proofs, looking at both correctness and elegance.
Textbook: An Introduction to Mathematical Reasoning: numbers, sets, and functions, by Peter J. Eccles; published by Cambridge University Press; copyright 1997 (eighth printing 2006)
Subject Material: We shall cover parts of chapters 1 - 24 (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.
Clickers: In order to facilitate discussion of conceptual ideas, we will be using the iClicker classroom response system. Clicker use will be optional; however, students who miss at most 2 days will have 2 points extra credit added to their cumulative average. Students who miss more than 2 days will earn extra credit based on the percentage of the remaining days they participated.
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 written solutions to a subset of the exercises at the beginning of class on the due date. These homework assignments will be graded carefully by the instructor and TA 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 five (5) of seven (7) assignments. Note that three (3) of the seven (7) assignments are revisions of a previous assignment.
Midterm Exam: There will be one midterm exam given during the lecture period on Thursday of the third week; 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.
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 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 two (2) weighted averages. Note that the homework grade will be based on your best three (3) of four (4) assignments.
Academic Dishonesty: Academic dishonesty is considered a serious offense at UCSD. Students caught violating the UCSD Policy on Integrity of Scholarship will face an administrative sanction which may include suspension or expulsion from the university. You should read the UCSD Policy on Integrity of Scholarship, especially the Students' Responsibility section.