RobertTalbert

'''The following code implements a graph coloring in Sage. 
+ The first line loads a package for Sage specifically to deal with graph coloring. 
+ Replace g with any graph. The default below is a randomly generated graph with 10 
nodes and a 0.5 chance of two nodes being adjacent. 
+ vertex_coloring(g) generates a partition of the nodes according to color. 
+ The partition=colors option in the last line will actually color the nodes according to the partition.
'''

from sage.graphs.graph_coloring import *

RobertTalbert

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Nunc ultricies id est at lacinia. Sed lobortis, quam porttitor consequat sodales, ex sem commodo ipsum, ut vehicula mauris tortor quis massa. Mauris vel auctor purus, ac molestie odio. Aenean pretium elementum eros, vitae consectetur augue dignissim dictum. Mauris ac dolor quam. Proin ac pretium orci. Etiam sed mauris nibh. Mauris vulputate massa in lacus dignissim, sed tincidunt lorem maximus.

RobertTalbert

Specifications for Student Work in MTH 201

Specifications for Pass/No Pass work on Guided Practice, Concept Quizzes, and WeBWorK

The rules for determining Pass/No Pass work on these three items are very simple:

• A Pass on Guided Practice is awarded to responses to Guided Practice items in which a good-faith effort to be right is given on all items, and the submission is given before the deadline. A No Pass is awarded if the submission is turned in after the deadline. A No Pass is also awarded if at least one item in the exercise set is blank or does not show evidence of a good-faith effort to be correct, for example if the response is "I don't know". Please note that mathematical correctness is not a factor; you are free to be wrong about an item as long as you show evidence of trying to be right.
• A Pass on a Concept Quiz is awarded if 8 out of 10 questions are answered correctly; otherwise the mark is No Pass.
• WeBWorK problems are the one item in the course that are

RobertTalbert

Title

Overview

Overview

Learning objectives

Basic objectives: Each student is responsible for gaining proficiency with each of these tasks prior to engaging in class discussions, through the use of the learning resources (below) and through the working of exercises (also below).

RobertTalbert

Guided Practice 1.6: The second derivative

Overview

In this section we study the second derivative of a function, which is just the derivative of the first derivative. That is -- "taking a derivative" is something we do to a function, and since the derivative $f'$ is a function, we can take its derivative too. The second derivative is an important ingredient for understanding the subtle behaviors of a function, and in particular the concept of concavity will distinguish between a function that is increasing at an increasing pace and a function that is increasing at a decreasing pace. Our main highlight for this section is to have a clear understanding of the relationships between the sign of $f'$, the sign of $f''$ (the second derivative), the increasing/decreasing behavior of $f$, and the concavity of $f$.

Learning objectives

Basic objectives: Each student is responsible for gaining proficiency with each of these tasks prior to engaging in class discussions, through the use of the

RobertTalbert

Guided Practice for Section 3.1: Direct Proofs

Overview

With this section, we move into the heart of the course by transitioning away from the basic logic and language tools for communicating in mathematics to the actual construction of solutions to mathematical problems. We’ll be looking at direct proofs in this section, which is something we’ve seen and done before. In addition to revisiting this proof technique we’ll be introducing some foundational mathematical content: what it means for one integer to divide another, and the very important notion of integer congruence modulo n. Along the way we will pick up some basic notions of mathematical terminology such as the concept of an axiom and different kinds of results such as propositions and corollaries.

Learning objectives

• State and instantiate the definitions of "divides", "divisor", "factor", and "multiple" and use correct notation to work with these concepts.
• Explain what a "proof" is and what it takes for a proo

RobertTalbert

Fair Warning: This is not a lecture-oriented class or one in which mimicking prefabricated examples will lead you to success. You will be expected to work actively to construct your own understanding of the topics at hand, with the readily available help of the professor and your classmates. Many of the concepts you learn and problems you work will be new to you and ask you to stretch your thinking. You will experience frustration and failure before you experience understanding. This is part of the normal learning process. Your viability as a professional in the modern workforce depends on your ability to embrace this learning process and make it work for you. You are supported on all sides by the professor and your classmates (see "Learning Community"). But no student is exempt from the process and the hard work it entails.

RobertTalbert

MTH 225: Discrete Structures for Computer Science 1 -- Fall 2015 Syllabus

Course Information

• Meetings: Section 01 of the course meets MWF 9:00--9:50am. Section 02 meets MWF 10:00-10:50am. Both sections meet in Mackinac Hall A-2-167.
• Prerequisite: MTH 122 or MTH 123 or MTH 201 or assignment through Grand Valley math placement.
• Textbook: Applied Discrete Structures, March 2013 edtition by Alan Doerr and Kenneth Levasseur. Available free online at http://applied-discrete-structures.wiki.uml.edu/. This will be our primary text for the first half of the course. The second half will use homemade notes and a collection of other free online resources.
• Computer requirements: You will need access to a portable computing device such as a laptop, tablet, or smartphone for occasional in-class computer work. Ideally, you should bring your device with you to class eac

RobertTalbert

MTH 225: Discrete Structures for Computer Science 1 -- Fall 2015 Syllabus

Course Information

• Meetings: Section 01 of the course meets MWF 10:00--10:50am. Section 02 meets MWF 11:00-11:50am. Both sections meet in Mackinac Hall A-2-167.
• Prerequisite: MTH 122 or MTH 123 or MTH 201 or assignment through Grand Valley math placement.
• Textbook: Applied Discrete Structures, March 2013 edtition by Alan Doerr and Kenneth Levasseur. Available free online at http://applied-discrete-structures.wiki.uml.edu/. This will be our primary text for the first half of the course. The second half will use homemade notes and a collection of other free online resources.
• Computer requirements: You will need access to a portable computing device such as a laptop, tablet, or smartphone for occasional in-class computer work. Ideally, you should bring your device with you to class e

RobertTalbert

MTH 225: Discrete Structures for Computer Science 1 -- Fall 2015 Syllabus

Course Information

• Meetings: Section 01 of the course meets MWF 10:00--10:50am. Section 02 meets MWF 11:00-11:50am. Both sections meet in Mackinac Hall A-2-167.
• Prerequisite: MTH 122 or MTH 123 or MTH 201 or assignment through Grand Valley math placement.
• Textbook: Applied Discrete Structures, March 2013 edtition by Alan Doerr and Kenneth Levasseur. Available free online at http://applied-discrete-structures.wiki.uml.edu/. This will be our primary text for the first half of the course. The second half will use homemade notes and a collection of other free online resources.
• Computer requirements: You will need access to a portable computing device such as a laptop, tablet, or smartphone for occasional in-class computer work. Ideally, you should bring your device with you to class e