## Instructor

Prof. Marco Varisco,
mvarisco@albany.edu
(how to email a professor),
www.albany.edu/~mv312143/

Office: ES-120C,
Office Hours: MWF 10:25–11:20, or by appointment.

## Schedule

MWF 11:30–12:25 in ES-143.

## Description

Introduction to the methods of higher mathematics, with emphasis on how to read, understand, discover, and write proofs. Topics include basic logic, sets, functions, relations, mathematical induction, countable and uncountable sets, elementary number theory, and basic epsilon-delta proofs.

This course will require a significant amount of written and oral presentations. Open only to students majoring in mathematics. (See the University Bulletin.)

## Prerequisites

At least one of AMAT 113 or 119 or 214 or 218 with a grade of **C** or better.
(See the University Bulletin.)

## Grading & Examinations

- 20% — Writing assignments.
- 20% — Oral presentations.
- 20% — Quizzes.
- 20% — Midterm Exam, Friday, October 30, 11:30–12:25 in ES-143.
- 20% — Final Exam, Tuesday, December 15, 3:30–5:30 in ES-143.

There will be daily writing assignments. Most of the early assignments could be completed in less than a page, but initially students are likely to submit much longer solutions. One of the goals is to learn how to write mathematical arguments in an organized and succinct fashion. Toward the second half of the semester some assignments will be longer and more comprehensive, combining a number of techniques and topics. Each assignment will be evaluated for both mathematical correctness and style. It will need to be revised until satisfactory, based on instructor’s written feedback.

One of the three weekly meetings will be devoted to students’ oral presentations, and the students in the audience will also be expected to discuss and evaluate the presentations. The topics of the presentations will be selected and assigned throughout the semester. Each student will present orally at least twice.

Presentations will be 5 to 10 minutes long. Some presentations will explain the solution of a homework assignment, others will provide the proof of a theorem, others will give definitions of mathematical objects, others will present examples and counterexamples. At the end of each presentation the speaker will answer questions from the audience. The criteria used to evaluate these presentations will include organization, validity of argument, pace of speech, and interaction with the audience. Oral feedback will be provided both in class right after the presentation and privately during office hours.

There will be at least eight quizzes, mostly consisting of questions from the homework and statements of definitions/theorems. The lowest score will be dropped, and no make-up quizzes will ever be given.

Class attendance, as well as constructive participation, is required. The maximum number of absences permitted to receive credit for this course is 3 (three). Excessive tardiness may count as absence.

Of course, you are expected to follow the University’s Standards of Academic Integrity and Medical Excuse Policies.