University at Albany, College of Arts and Sciences

Department of Mathematics and Statistics

AMAT 299: Introduction to Proofs, Spring 2015


Prof. Marco Varisco, (how to email a professor),
Office: ES-120C, Office Hours: MWF 10:25–11:20, or by appointment.


MWF 9:20–10:15 in ES-143.


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, and elementary number theory.

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


Ron Taylor, Introduction to Proof, Journal of Inquiry-Based Learning in Mathematics, No. 4, 2007.
Available free of charge here.

Additional reading material will be distributed in class.


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

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 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.

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.

This syllabus is subject to change. All official announcements and assignments are given in class, and this web page may not be up to date.
Marco Varisco.