Department of Mathematical Sciences
Binghamton University

"Where shall I begin?" he asked. "Begin at the beginning," the King said, "and stop when you get to the end."
– Lewis Carroll [mathematician], Alice in Wonderland

Math 330: Number Systems

(a.k.a. Introduction to Higher Math, or simply Proofs)

Section 7, Zaslavsky · Fall 2018

Main class page | Schedule and homework | Announcements | Advice | Term Project | Syllabus


Tom Zaslavsky
    Official web page, personal web page.
    Office: WH-216
    Office Hours:

    E-mail: E-mail is good; use it often.

Class Schedule

    MWF 4:40 - 6:10 in SW-315.

Attendance policy

You are expected to attend all class meetings. The maximum number of absences permitted in this course is 5 (five). Excessive tardiness may count as absence. If you are compelled to be absent, such as by illness, I will expect proof. [University Bulletin]

I will not expel you from the class for absences beyond five, but your grade will be lowered. I expect you to report illnesses or other reasons for absence.


Calculus II (Math 226-227 or equivalent). If you do not satisfy this prerequisite, you may be dropped from the class. [Old University Bulletin, which is smarter than the new one even though out of date.]


Careful discussion of the integers, the rational numbers and the real numbers, including a thorough study of induction and recursion. Countable and uncountable sets. The methodology of mathematics: basic logic, the use of quantifiers, equivalence relations, sets and functions. Methods of proof in mathematics. Training in how to discover and write proofs.

Click on the link for a more detailed syllabus.


The Art of Proof: Basic Training for Deeper Mathematics, by Matthias Beck and Ross Geoghegan, Springer, New York, 2010.

Advice and corrections to the textbook are on the additions page.

All official announcements and assignments are given on the Web site.

I will often mention them in class and by e-mail, but the Web site is the main place to look. Stay up to date.

What You Should Learn From This Course

The subject matter and especially the methods, including how to read, understand, and write proofs.

You accomplish this by attempting all the assignments and not falling behind. (Falling behind in this class is worse than usual. Everything depends on what came before. Believe it.)

This is a writing emphasis course, and therefore there will be a lot of writing. I will be grading your work on the quality of the writing (clarity and grammar) as well as on the content (logic and math). You need all that for writing proofs; if your writing is not clear, your proof cannot be correct.

Grades & Examinations

50% 60% Homework (the main part of the course), and some unannounced quizzes.
15% Midterm Exam, scheduled for Wed., October 17 Wed., October 24, in class. (Note the course withdrawal deadline: Oct. 30.)
15% 0% Term Project Assignment, due on Fri., December 7, at the beginning of class.
20% 25% Final Exam, scheduled for Tue., December 11, 5:40 - 7:40 p.m., in SW 113.

When calculating your course grade there is one more rule: if your homework score is an F then your course grade is an F, regardless of project and exam scores.

Of course, you are expected to obey the Student Academic Honesty Code.

Homework Assignments

See the schedule page for the assignments. Assignments will be announced as the term progresses.

See the Advice page for advice on writing mathematics, especially proofs.

Written work must be handed in on paper. I do not accept electronic submissions. Remove all stubs! Don't hand in messy papers; they must be neatly written (or printed).

Most of your written work will be proofs. Proofs are expected to be complete and correct--but not necessarily the first time! I allow a total of 4 (four) submissions of each proof. That gives you three rewrites; you have 3 (or 4) weeks (from the due date) to complete them. I will return your work to you with the first major error indicated. You will have to figure out what's wrong and fix it. Come to talk with me if you get stuck; I encourage that.

I also expect the proofs to be well written. Writing matters: not only because this is a Writing course, but because correct math must be written clearly and precisely.

How I Grade Homework

Main class page | Schedule and homework | Announcements | Advice | Term Project | Syllabus