Section 3 Home Page for
Math 330 - Number Systems
Spring 2015

Last update: April 27, 2015 - 11:59 PM

Instructor Section Meeting
Michael Fochler, WH 130
      Office hours: Mon 1:15 - 3:00,     Thu 2:30 - 4:00
      mfochler@math.binghamton.edu 		Section 03 Mon, Wed, Fri
Thu 		12:00-1:00
11:40-1:05 		OW 100B
OW 100B

Welcome to Math 330, Number Systems. This is the home page for section 3. Here you find links to your syllabus and other important info for section 3 of Math 330. You will find most of my announcements here rather than on Blackboard which I mostly use for posting your grades.

If you have trouble with any of the links on this site, please e-mail me at mfochler@math.binghamton.edu .

NOTE that this document specifically pertains to section 3 of the course!

Syllabus for section 3:

The syllabus provides information about the objective and the rules and regulations for this course. It also tells you how your grade will be determined.

PREREQUISITES: Math 222 (Calculus 2)

See the syllabus for more information.

The bottom of this document contains a Q & A list (to be extended) of answers to some questions students have asked.

Course Material:
Textbook:
    The Art of Proof: Basic Training For Deeper Mathematics, by M. Beck and R. Geoghegan (Springer, 2010).
The course will follow to a large degree the textbook but some items will be presented in a different order.
    ----------
Additional course material:
    The Beck/Geoghean text provides some exposure to sets and functions but I shall go beyond that. Here are some documents for to give you material in addition to that presented in the textbook. I have taken them from a 330 course that was taught earlier by Prof. Marcin Mazur.
   
  1. Differences in Notation See this document for some remarks, including potential difference in notation between the course, the B/G text and the articles listed above.
  2. Sets part 1: This document is a very basic introduction to sets which many of you should be able to skim through in a hurry, but you should skip nothing and be sure you understand all examples.
  3. Sets part 2: This document covers to a large degree the same material as Sets part 1: Again, many of you should be able to skim through in a hurry. and again, be sure you understand all examples.
    You can skip the following:
    • Ch. 1.11. Set Identities: Everything starting with ``Proof 2'' until the end on p.105
    • Ch. 1.13. Infinite Unions and Intersections: on p. 107: the use of a ``general index set'' J in the union of sets Ai where i is an element of J and exercises 1.14.1., 1.14.2.
    • All of Ch. 1.15. Computer Representation of a Set (i.e., the remainder of the document).
  4. Functions part 1: This document is very brief and it will probably take you more time per page to study it. You can skip chapter 2.4. Floor and Ceiling Functions. Note that I have an important comment on the use of f - 1(y) for both the inverse image (a set!) of y and the image of y under the inverse function f - 1 of f here
  5. Functions part 2: This document focuses on injective, surjective and bijective (invertible) functions. Pick up your copy of Stewart's Calculus and review the chapter on inverse functions. You will see material on injective functions (Stewart calls them one-to-one) and on inverse functions. This will help you understand the document. Skip all proofs as the important ones are given in B/G. but be sure to understand the definitions and examples and draw pictures with functions that you understand well to get a feeling for why the theorems are true.
  7. Lecture Notes: Math 330 - Additional Material ("MF") (MAJOR UPDATE on April 20) This document was previously called "Direct and Indirect Image". I am the author. For that reason it is much more likely to contain errors than the ones listed above as those have probably been vetted by many viewers before having been made accessible on the internet. Caveat emptor! This document will be added to in the future.
    There are reading instructions just after the table of contents. Be sure to look at them first as they tell you what parts of the material are optional (most of it) and which ones you must study. Note that those reading instructions themselves also will be subject to change!
  8. Modular Arithmetic by Miguel A. Lerma. This document contains background material on arithmetic modulo n. I do not plan to teach from it or use anything in there not covered in the book for quizzes and/or exams. This material is strictly for your convenience as it might help you to better understand the material from B/G ch.6.3 and 6.4.

Q & A: Answers to questions of general interest

Q: I want to add this class. What do I have to do?

A: At this point in time all 25 spots in this class are filled up. There was a spot available earlier this week. It was assigned to one of the petitioners by the department.

Q: Is Math 222 an absolute requirement?

A: No, but you must either give proof that you have taken a two semester Calculus sequence at a different college or I'll interview you to see whether you have the talent to catch up on the selected items you need to understand in the second half of the class.

Q: Why is the grading policy in the syllabus so vague?

A: I need to consult with the other instructors of the course. This will not happen until the first week of February.

Best wishes for a successful semester!

Michael Fochler