Syllabus
| Fall 2015 | MWF | 10:50 | - | 11:50 | a.m. | WH-100B |
| R | 8:30 | - | 9:55 | a.m. | WH-100B | |
| Instructor: | Fernando Guzmán | WH-116 | x-72876 | |||
| e-mail: | fer@math.binghamton.edu | |||||
| Office Hours: | M: | 1:00 | - | 2:00 | p.m. | |
| (subject to change) | R: | 10:00 | - | 11:00 | a.m. | |
| F: | 3:00 | - | 4:00 | p.m. | ||
| or by appointment | ||||||
| Add/Drop deadline: | Friday | Sep. | 11 | |||
This course is a 4-credit course, which means that in addition to the scheduled lectures/discussions, students are expected to do at least 9.5 hours of course-related work each week during the semester. This includes things like: completing assigned readings and homeworks, studying for tests and examinations, preparing written assignments, and other tasks that must be completed to earn credit in the course.
The purpose of this course is twofold. On one hand, it explores the properties of different number systems, including the natural numbers ℕ, the integers ℤ, the rational numbers ℚ, and the real numbers ℝ. On the other hand, it presents those properties in a logical fashion, so that it will be clear what properties are consequences of others properties. There is a heavy emphasis on proofs, exploring a number of proof methods.
Writing is an essential part of the communication among mathematicians. For that reason, clear and neat writing is emphasized. This course is a Harpur College W course; hence, it may be used to satisfy the all-college writing requirement.
By the end of the semester students are expected to be familiar with the basic properties of the number systems, and be able to prove most of those properties from initial principles (axioms). Those proofs will come sometimes from class notes, sometimes from the textbook, but most of the time, from the student's own work. In any case, the student is expected to present clear and logically sound arguments in the proofs.
| Textbook: | The Art of Proof | M. Beck and R. Geoghegan | |||
| Springer, 2010 | |||||
We plan to cover most of the material in parts I and II, following closely the order and logic framework of the textbook. If time allows, we will go into some of the topics in part III. Even though the book includes proofs for some propositions, most of the proofs are left as exercises for the student. We plan to present in class some of these proofs, with the remaining left as homework. Some of those homework proofs will be collected every week, and some will be presented on the board by students.
One of the goals of this course is that you learn to distinguish correct from incorrect proofs. You will be given plenty of examples of correct proofs in class.
The course grade will be based on:
| Grading: | |||||||
| Homework | Mondays | 20% | |||||
| Test 1 | Monday | Sep. | 28 | 10% | |||
| Midterm | Thursday | Oct. | 22 | 20% | Cumulative, Part I | ||
| Test 3 | Monday | Nov. | 16 | 10% | |||
| Final Exam | Friday | Dec | 18 | 30% | Cumulative, Part II | ||
| Class participation | Daily | 10% | |||||
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