# Category Archives: Resources

Getting Started, How-Tos, and so on

## Proof by Contradiction Examples

By request, I’ve done some looking around for  resources related to Proof by Contradiction.  I haven’t found a page with a good “big picture” overview yet, but I have found some decent examples – here goes:

Getting started – some basic examples.  This page has a few examples worked out completely – not too long or involved, and (I hope) not too difficult to follow.

Numberphile: Proof (by contradiction) that there are infinitely many primes.  A really good illustration of proof by contradiction.  The numberphile guys make cool math videos – if you like it, search for numberphile and check out their other stuff.

## Induction Examples

Hi everyone,

I wanted to post some resources on mathematical induction — if you are having trouble with induction, I highly recommend taking a look.

Introductory Examples:  Here is a page with a bunch of examples of proofs by induction, similar to what we have done in class.  This is a good place to start.

Khan Academy: If you find video explanations helpful, here is the Khan Academy on induction:

Even More Videos: This page has a collection of Induction Example videos – I haven’t watched them all, so if you do look at them please tell me what you think:

Advanced/wacky examples: This pdf has some great examples in Section 6(page 4) — they show how induction can be applied to all kinds of different mathematical problems.  Solutions are included.  This is a good resource if you are familiar with induction, and want to take things a little farther.

## Getting Started with WeBWorK

WeBWorK is accessible from on and off campus (anywhere you have access to the internet).  Your first WeBWorK assignment is due on Tuesday, September 10th, at midnight, and will cover the material from the first two weeks of class (primarily from the second week).  Here’s what you have to do:

Assignment.  To get started on your first assignment, you must complete the following three steps.

Step 1.  Log in to WeBWorK here:  http://mathww.citytech.cuny.edu/webwork2/MAT2070/.  I have created Usernames and Passwords for each student registered for my class.

Username.  Your username for WeBWorK consists of your first initial plus your last name, all lowercase (for example, John Smith would have username ‘jsmith’).

Step 2.  Change your password and update your email address.  To do this, select “Password/Email” from the main menu on the left.  Use whatever email address you like (I suggest using one that you check often).

Step 3.  Complete the first assignment, titled Assignment1-Sec1.2-1.3, by clicking on it in the main screen.

If you have any trouble – either with logging in, or with completing the assignment, post a comment here or send me an email and I will get back to you.

WeBWorK Tips:

1. Click on a problem to see the details (the list of problems appears in the menu on the left).  Enter an answer and hit “Submit Answers”.  Don’t worry, if you get it wrong you can try it again.
2. You can work on the problems in any order you wish.  You can do some problems now, and come back and do the rest another day (your work will be saved, as long as you submit your answers).
3. If you want to print out a copy of the assignment, click on the assignment name in the main menu on the left, and then click the link in the main screen area that reads “Download a hardcopy of this homework set.”

## Welcome and Getting Started

This course is MAT 2070, Introduction to Proofs and Logic, taking place in the Fall 2013 semester with Professor Reitz.  We will be using this website in a variety of ways this semester – as a central location for information about the course (assignments, review sheets, policies, and so on), a place to ask and answer questions, to post examples of our work, and to talk about logic, proofs, mathematics, reality and so on.

Getting Started

Anyone on the internet can look around the site and see what we are doing, and even leave a comment on one of the pages.  However, only registered users can create new posts and participate in the discussion boards.

How do I register?

You will need to do two things:

1. If you have not used the openlab before, you must first create an account.  You will need access to your citytech email address (LIVE@CityTech) for this.  Detailed instructions for signing up on the OpenLab can be found here.
2. Once you have created an account on the OpenLab, log in and then join this particular course, 2013 Fall – MAT 2070 Proofs and Logic – Reitz.  To do this, first click the “Course Profile” link at the top left of this page (just under the picture).  Then click the “Join Now” button, which should appear just underneath the circular picture filled with green words.

Problems with the OpenLab or with your CityTech email:

Please let me know if you run into any problems registering or joining our course (send me an email, jreitz@citytech.cuny.edu).  I also wanted to give you two resources to help out in the process:

1.  For problems with your citytech email account, contact the Student Computing Helpdesk, either in person, by phone, or by email:

Student Computing Helpdesk
Location: Namm First Floor – Information Booth
Hours: Monday, Wednesday & Friday: 9:00am – 5:00pm
Tuesday & Thursday: 9:00am – 6:00pm
Phone: 718.260.4900
E-mail: Studenthelpdesk@citytech.cuny.edu

2. For problems registering for the OpenLab, contact the OpenLab admin team, either by email at openlab@citytech.cuny.edu, or by following this link.